PAPERS PUBLISHED · 3.2.3 Falling film absorbers VI 3.2.3.1 Tube side heat transfer coefficient 71...

OPTIMISATION OF OPERATING PARAMETERS FOR VARIOUS ABSORPTION SYSTEMS USING RENEWABLE ENERGIES

PAPERS PUBLISHED

(SIX PAPERS)

TA-Z^]

BY

MOHAMMAD ALTAMUSH SIDDIQUI

DEPARTMENT OF MECHANICAL ENGINEERING Z. H. COLLEGE OF ENGINEERING & TECHNOLOGY

ALIGARH MUSLIM UNIVERSITY ALIGARH (INDIA)

1991

OPTIMISATION OF OPERATING PARAMETERS FOR VARIOUS ABSORPTION SYSTEMS USING RENEWABLE ENERGIES

Thesis Submitted for the Degree of

©ottor of ^I)ilos(opIjj> IN

MECHANICAL ENGINEERING

BY

MOHAMMAD ALTAMUSH SIDDIQUI

DEPARTMENT OF MECHANICAL ENGINEERING Z. H. COLLEGE OF ENGINEERING & TECHNOLOGY

ALIGARH MUSLIM UNIVERSITY ALIGARH (INDIA)

1991

CERTIFICATE

I certify that the thesis entitled 'Optimisation of

Operating Parameter"? for Various Absorption Systems Using

Renewable Energies' supplicated by me without supervisor for

the award of the degree of Doctor of Philosophy in

Mechanical Engineering, is a record of my own work carried

out at the Department of Mechanical Engineering, Zakir

Husain College of Engineering and Technology, Aligarh Muslim

University, Aligarh. The matter embodied in this thesis has

not been submitted for the award of any degree.

> » Dated: 2 4.5.1991 ( Mohammad Altamush Siddigui )

Reader, Department of Mech. Engcj. Z.H. College of Engg. & Tech Aligarh Muslim University, Aligarh - 202 002 (INDIA)'.

ACKNOWLEDGEMENT

In the praise of Almighty Allah, the most Benificient and Merciful who showed the path of righteousness and blessed me to get the strength of doing this work inspite of the teaching, de'"^lopment and research loads of the department.

I wish to thank Dr. Noor Afzal, Professor and Chairman and Dr.-Ing S.H. Mohsin, Professor and Ex-Chairman, Department of Mechanical Engineering, Aligarh Muslim University for extending their co-operation and providing facilities for doing this work.

I am indebted to my senior colleagues at AMU particularly to Professor S.R. Khan, Department of Mechanical Engineering, Professor M. Salman Beg, Department of Electrical Engineering and Professor Tariq Aziz, Department of Applied Mathematics for providing valuable suggestions, encc"''r.~ ~cments, criticism and help during the course of this work.

Special thanks are due to Mr. Naiem Akhtar and Mr. Munawwar Shees, who had been my students, for their help and co-operation during the compilation of the thesis. Thanks to Mr. Mohd. Rashid, Badre Alam and Masood Alam for their patience in typing the work and Mr. Mohd. Nairn for tracing the figures.

Lastly, I would like to thank my wife for the tolerance she had in bearing the hardships, and mention the negligence that I had towards my son Khubaib and my younger brothers, Badre Alam, Mehboob Alam and Mehfooz Alam. Finally, I would like to thank my parents who showed me their love and affection.

M-y^ Dated: 24.5.1991 ( Mohammad Altamush Siddiqui )

TABLE OF CONTENTS

LIST OF PUBLICATIONS RELATED TO THE Ph.D. WORK i

LIST OF TABLES m

LIST OF FIGURES iv

ABSTRACT vii::

NOMENCLATURE xi

Chapter

1. INTRODUCTION

1.1 Need of the day I 1.2 Practical refrigerant-absorbent systems 2 1.3 Literature review 7 1.4 Present work 12

1.4.1 Model I 13 1.4.2 Model II 13 1.4.3 Model III 15

2. MATHEMATICAL FORMULATION 19

2.1 System description 19 2.2 System modelling 2 2 2.3 Thermodynamic property equations 25

2.3.1 Enthalpy 2 5 2.3.2 Equilibrium pressure 29 2.3.3 Solution refrigerant temperatures 30 2.3.4 Density 31 2.3.5 Viscosity 35 2.3.6 Thermal conductivity 37 2.3.7 Specific heat 40 2.3.8 Surface tension 42 2.3.9 Thermal coefficient of expansion 43 2.3.10 C r y s t a l l i z a t i o n line 43

2.4 Equations of state for computer simulation 4 4

3. SYSTEM DESIGN 5j

3.1 Thermal design for single-phase heat transfer b'6 3.1.1 Baffled shell and tube exchangers 58

Chapter Page

3.1.1.1 Shell side geometric parameters 58 3.1.1.2 irhell side heat transfer

coefficient 61 3.1.1.3 Shell side pressure drop 61 3.1.1.4 \ahe side heat transfer

Coefficient 63 3.1.1.5 Tube side pressure drop 6 5

3.2 Thermal design for two phase heat transfer 65 3.2.1 Boiling heat transfer coefficient 6 5 3.2.2 Condensation heat transfer coefficient 68 3.2.3 Falling film absorbers VI

3.2.3.1 Tube side heat transfer coefficient 71

3.2.3.2 Flooding in wetted-wall columns 73 3.2.4 Pressure drop in two phase heat transfer 74

3.2.4.1 Boiling inside tube 74 3.2.4.2 Horizontal in-shell condensation 79

3.3 Design of distillation column 81 3.3.1 Tray numbers 82 3.3.2 Tower diameter 86 3.3.3 Liquid depth 89 3.3.4 Pressure drop for the gas 91

3.4 Heat transfer from the gases 95 3.5 Specific design procedure 98

4. COST EVALUATION AND FUNCTIONAL RELATIONSHIPS 103

4.1 Sources of energy and coolants 103 4.1.1 Biogas energy 105 4.1.2 Liquified petroleum gas 110 4.1.3 Solar energy 113 4.1.4 Cooling water 121

4.2 Vapour absorption system 126

5. RESULTS AND DISCUSSION 138

5.1 Economic analyses of the energy sources [Model I] 138

5.2 Economic analyses of energy-sources plus cooling water [Model II] 161

5.3 Economic analyses of absorption systems and their operating costs [Model III] 2 03

6. CONCLUSIONS AND RECOMMENDATIONS 235

6.1 Conclusions 23 5 6.2 Recommendations 240

Page

REFERENCES 2 41

APPENDICES 2 56

Al Properties of pure ammonia and water, LiBr-H^O, LiNO--NH- and NaSCN-NH^ solutions 256

A2 Equations for J, friction and R-factors in

Baffled exchangers 263

A3 Dimensions for tray towers 2 70

A4 Equations for emissivities of carbon

dioxide and water vapour 2 71

AS Solar flux calculations 273

A6 Tube count entry allowance 2 76

A7.1 Flow chart for main program 277

A7.2 Flow chart for design of absorber 2 78

A7.3 Flow chart for design of condenser 279

A7.4 Flow chart for design of evaporator 280

A7.5 Flow chart for design of generator 2 81

A7.6 Flow chart for design of preheater 282

LIST OF PUBLICATIONS RELATED TO THE Ph.D. WORK

1. M. Altamush Siddiqui, 'Economic analysis of biogas for

optimum generator temperature of four vapour absorption

systems', Energy Conversion and Management, 27 2,

pp 163-169 (1987) .

2. M. Altamush Siddiqui, 'Optimal cooling and heating

performance coefficients of four biogas powered

absorption systems', Energy Conversion and Management,

31 1, pp 39-49 (1991).

3. M. Altamush Siddiqui, 'Economic biogas and cooling-water

rates in a lithium bormide-water absorption system',

International Journal of Refrigeration, 14 1, pp 32-38

(1991).

4. M. Altamush Siddiqui, 'Economic analysis of biogas/solar

operated lithium bromiue water absorption systems',

Proceedings of the 25th Jntersociety Energy Conversion

Engg. Conference, American Institute of Chemical

Engineers, N. York, 2 pp 211-216, Aug. 12-17 (1990).

5. M. Altamush Siddiqui, 'Optimisation/operating variables

in four absorption cycles using renewable energies',

Proceedings of the 25th Intersociety Energy Conversion

Engg. Conference, Am^rxcan Institute of Chemical

Engineers, N. York, 2 pp 277-282, Aug. 12-17 (1990).

11

6. M. Altamush Siddiqui, 'Economic biogas and cooling water

rates in four vapour absorption systems', IJR (revised

paper in review).

7. M. Altamush Siddiqui, 'Economic analysis of

ammonia-solar absorption cycle', presented in the

National Seminar on Economic Utilisation of Renewable

Energy Resources, A.M.U., Aligarh, May 11-12 (1990).

Note: Manuscripts of the papers that have already been

published are enclosed.

LIST OF TABLES

Table Page

2.1 Constants for the saturated enthalpy equation 2 7

2.2 Constants of equation (2.42) 28

3.1 Value of C for various flow regimes 78

4.1 Break up for the costs of biogas plants 109

5.1 Percentage deviation in the minimum operating 150 costs of the various cycles [Model I]

5.2 Percentage deviation in C, and COP at V, = W 167 from C. ^. (MR = 8.0) " '^

bw,min

5.3 Percentage deviation in the costs of various 18 8 cycles [Model II]

5.4 Values of the constant M in equation (5.4) 202

5.5 Percentage deviation in the costs of various 229 cycles [Model III]

5.6 Optimum operating parameters in LiBr-H„0 systems 231

5.7 Optimum operating parameters in H_0-NH-, systems 232

5.8 Optimum operating parameters in LiNO-,-NHo systems 23 3

5.9 Optimum operating parameters in NaSCN-NH^ systems 2 34

Al.l Constants for the saturated enthalpy equations 257 and equilibrium pressures

A3.1 Recommended dimensions for tray towers 2 70

A5.1 Sunshine hours and solar flux at Aligarh 275

A6.1 Tube count entry allowance 2 76

LIST OF FIGURES

Page Figure

2.1 Vapour absorption refrigeration system 2 0

3.1 Schematic diagram of a single-pass heat-exchanger 56

3.2 (a) Distillation column 83

(b) McCabe-Thiele stepwise construction 83

(c) Weir height and crest over weir 83

(d) Weir and tray size 83

5.1 Variation in components performance with t 14 0

5.2 A , V. , V, with t at t = 5°C 142 s b 1 g e

5.3 A , V, , V, with t at t = -15°C 143 s D i g e

5.4 C, , C, , C with t at t = 5°C 146 b i s g e

5.5 C, , C, , C with t at t = -10°C 147 b i s g e

5.6 Optimum values of t with t^ for cycles 152 using biogas "

5.7 Optimum values of t with t_ for cycles 15 3 using LPG ^

5.8 Optimum values of t with t^ for cycles using solar energy ^

154

5.9 Optimum values of COP and HCP with t ... (biogas) 158

5.10 Optimum values of COP and IICP with t ... (LPG) 159

5.11 Optimum values of COP and HCP with t ... (Solar) 160

5.12 variation in C , C^^^, C^, C^^, C^ with t^ 163

V

Figure

5.13

5.14

5.15

5.16

5.17

5.18

5.19

5.20

5.21

5.22

5.23

5.24

5.25

5.26

5.27

5.28

5.29

5.30

C^ , COP, V, and W with t^ bw b £

Minimum values of C^^ with MR

Values of C^^ at Vj =W with MR

Minimum values of C^^ with MR

Minimum values of C„ , with MR sw

Minimum values of C, with MR

Values of C. at V, =W with MR bw b

Minimum values of C, with MR Iw

Minimum values of C with MR sw

Minimum values of C, with MR bw

Values of C, at V, =W with MR bw b



Minimum values of C. with MR bw

Values of C^ at V^=W with MR bw b



LiBr-H20)

LiBr-H20)

LiBr-H20)

LiBr-H20)

H2O-NH2)

H2O-NH3)

H2O-NH3)

H2O-NH2)

LiN0--NH2

LiNO^-NH^

LiNO^-NH^

LiNO^-NH^

NaSCN-NH,

NaSCN-NH.

NaSCN-NH.

NaSCN-NH.

Values of COP with MR

5.31 t at C, . and MR with t . go bw,min o wi

5.32 t at C, when V,=W and MR with t . go bw b o wi

Page

166

169

170

171

17 2

173

174

175

176

177

178

179

180

181

182

183

184

189

191

192

VI

Figure ^^^e

5 33 t at C, . and MR with t . 193 ^••^^ ^go lw,min o wi

5.34 t at C . and MR^ with t . 194 go sw,min o wi

5.35 COP and HCP at t with t (bicxgas) 197 o o go e

5.36 COP and HCP^ at t wi-ch t^ (Vj^=W) 198

5.37 COP and HCP at t with t^ (LPG) 19 9 o o go e

5.38 COP and HCP at t with t^ (solar) 200 o o go e

5.39 t with t for different values of x^ 204 a e a

5.40 C^, C^, C^^, C^, C , C^, C^y, C^y^ with 209

t for LiBr-H„0 at t , = 15°C e 2 el

5.41 C , C , C , C , C, , C, , C , C . with 210 a e ae s b 1 sy syt

t for H„0-NH-, at t , = 15°C e 2 3 el

5-^2 C^, C^, C^^, C^, C^, C^, C^^, C^y^ With t^ 211

for LiN0,-NH-, at t , = 15°C 3 3 el

5.43 C , C , C , C , C, , C, , C , C . with t 212 a e ae s b 1 sy syt e

for NaSCN-NH, at t , = 15°C 3 el

5.44 C , C , C , C , C, , CT , C , C ^ with t 213 a e ae' s b 1 sy syt e

for H^O-NH, at t , =-10°C z 3 el

5.45 C , C , C , C , C, , C, , C , C ^ with t 214 a e ae' s b 1 sy syt e

for LiNO^-NH, at t , =-10°C 3 3 el

5.46 C , C , C , C , C, , C, , C , C ^ with t 215 a e ae s b 1 sy syt e

for NaSCN-NH^ at t , =-10°C 3 el

^•^^ ^c' ^g' ^cg' S ' S ' ^1' sy' ^syt ^^^^ c ^19 for LiBr-H„0 at t , = 15°C

2 el

5.48 C , C , C , C , C, , C, , C , C ^ with t 220 c g eg s b 1 sy syt c

for H„0-NH^ at t , = 15°C 2 3 el

Vll

Figure Page

5.49 C , C , C , C , C, , C, , C , C ^ with t 221 c g eg s b 1 sy syt c for LiNO-,-NH^ at t T = 15°C

3 3 el

5.50 C , C , C^ , C , C, , C,, C , C ^ with t 222 c g eg s b 1 sy syt c

for NaSCN-NH^ at t , = 15°C 3 el

5.51 Cg with t^ 226

5.52 C ^ with t 228 syt e

ABSTRACT

Economic analyses of LiBr-H20, H2O-NH2, LiNO^-NH^ and

NaSCN-NH^ vapour absorption refrigeration systems using

different sources of energy, have been carried out to

optimize the operating variables. The sources of energy

understudy, are flat plate solar collector, biogas and

liquified petroleum gas. The costs of the system

components : evaporator plus absorber, condenser plus

generator and the total system cost including the costs of

the precooler and preheater in the system, costs of energy

and cooling water, are exhibited graphically for a \\?ide

range of operating conditions. The analyses have been

repeated for the given absorption systems using various

sources of energy, separately. The costs of the absorption

systems have been obtained after designing their individual

components through a computerized design procedure for given

operating conditions. The costs of the absorption systems,

sources of energy and cooling water include the material,

fabrication and installation costs at a standard market

rates.

A computerized-design-procedure for the four vapour

absorption systems have been presented in detail. Empirical

equations for the thermodynamic and thermophysical

properties of H2O-NH2 solution, LiBr-H^O solution, pure

IX

ammonia and pure water have been developed. Relations for

finding the capital and running costs of the sources of

energy and cooling-v;ater have been developed after

estimation. Relations for finding the heating values of

solar collector, biogas and LPG in terms of temperature have

also been obtained.

The analyses were done using three different models :

Model I Economic analyses of the energy sources for

optimizing generator temperatures

Model II Economic analyses of the sources of energy plus

cooling water for optimizing generator and

condensing temperatures along with solution flow

ratios.

Model III Economic analyses of the absorption systems

including their operating costs for optimizing

absorber, condenser, evaporator and generator

temperatures along with the solution flow-ratios.

A comparative study between the four absorption systems

with different sources of energy has been done. The

percentage increase in the costs of the three ammonia

systems from that of LiBr-H20 system has been estimated.

Also, the percentage decrease in the costs of LiNO^-NH-, and

NaSCN-NH^ systems from that of the H2O-NH2 system, operating

in the refrigeration mode, has been calculated. Graphs

depicting the optimum system-variables and the corresponding

performance coefficients of the systems operating in the

refrigeration and air-conditioning modes, have been

prepared.

liOMENCLATURE

2 A Active area, area of perforated tray, m a

ACP Absorber coefficient of performance, diraensionless

A, Down spout cross-sectional area, m

2 A Net cross flow area, m n

2 A Area of perforations, m o ^

2 A Free area between the downspout apron and tray, m /area P 2

of the absorber plate, m 2

A Area of solar collector, m s

2 A Tower cross sectional area, m

2 A , Area occupied by tubes on one baffle, m

A Fractions of A , dimensionless

2 A Flow area, m X

B, Percentage deviation in the costs of the biogas powered

three ammonia cycles from those of the LiBr-H„0 cycle/

LiNO^-NH^ and NaSCN-NH^ cycles from those of the

H2O-NH2 cycle

C Specific heat, kJ/kgK/Cost, rupees

C, Clearance between two tubes in the tube .Jxindle

CCP Condenser coefficient of performance, dimensionless

COP Cooling coefficient of performance, dimensionless

C„ Flooding constant, empirical r

C Orific coefficient, dimensionless o

d Diameter of tube, m/Diameter of hole to be drilled,

d Equivalent inside diameter of tube bundles, m

m

d- Inside diameter, m

d Outside diameter of tube, m/Diameter of perforated hole o

or orifice, m

D , Diameter of channel cover, m ch

D Equivalent diameter of shell due to layout of tubes in es ^

a heat exchanger, m

D. Inside diameter of tube/shell, m

D , -, Outside diameter of tube bundle, m otl

D Inside diameter of shell, m s

D , Diametral shell-baffle clearance, m sb

D Heat exchanger-nozzle diameter, m z ^

f Friction factor, dimensionles s

F, Tilt factor for beam radiation b

F Fraction of total tubes in cross-flow c

F, Tilt factor for diffuse radiation d

F, Fraction of cross-flow area available for bypass flow

F,, Cost of boring one hole in a pipe of thickness (th),

rupees; F refers to fabrication

dx Cutting price for pipes having diameter(d), using

hacksaw, rupees

F Cutting price of plates per meter length using hacksaw,

rupees

F A Cost of drilling a hole in a plate of thickness (th),

rupees

F^ Collector heat-removal factor, dimensionless

Xlll

F , Cost of arc welding per metre length(wd), rupees wl F-, Collector efficiency, dimensionless

FB Tilt factor for reflected radiation

/ 2 g Acceleration of gravity, m/s

2 g Conversion factor, equal to 1.0 kg.m/Ns in S.I. units

2 G Mass velocity, kg/hm

2 Gs Gas mass rate, kg/sm

G -, Vapour flow from the (n-!-l)th plate of the rectifying

section, kg-mol/h

G Vapour flow into the reflux condenser, kg-mole/h

G.I. Symbol for galvanised iron

2 h Heat transfer coefficient, W/m K

h^ Dry-plate gas-pressure drop as head of clear liquid, m

h„ Gas-pressure drop as head of clear liquid, m

hj Gas-pressure drop due to liquid hold-up on tray, m

hp. Residual gas-pressure drop, m

h Weir height, m

h. Weir crest, m

ho Back-up of liquid in downspout, m

H Specific enthalpy, kJ/kg/Correlating parameter in

two-phase flow, dimensionless

H^ Monthly average of the daily beam radiation on a

horizontal surface at the same location on a clear day, 2

kJ/m -day

H Monthly average of the daily diffuse radiation on a

horizontal surface, kJ/m -day

XIV

H Monthly average of daily global radiation on a

horizontal surface at the same location on a clear 2

day, kJ/m -day

H Monthly average of the daily extra-terrestrial

radiation which would fall on a horizontal surface, 2

kJ/m -day

H„ Monthly average of daily radiation falling on a 2 tilted surface, kJ/m -day

HCP Heating coefficient of performance, dimensionless

/ H Enthalpy of combustion, kJ/kg of fuel

2 I Solar constant (1353x3.6 kJ/hm ) sc

J, Colburn j factor for ideal tube bank related to k

heat transfer, dimensionless

J, ,J ,J-,,J Correction factors for baffle bypassing, baffle b c 1 r J c V

configuration, baffle leakage and adverse temperature

gradient, respectively

K Thermal conductivity, W/m K

1 , Baffle cut, m

1 Baffle spacing, m

1 Length of sealing strip, m

L Length of heat transfer surface, m

L^ Length of heat exchanger including the inlet and

outlet-heads, m

^m+1'^n'^r'^w liquid flow from the (m+l)th plate, nth plate, reflux

condenser, stripping section, kg-mole/h

2 Lq Liquid mass rate, kg/sm

L Length of nozzle for the inlet and outlet-head, m

XV

(L/G) (L/G)^ L iqu id-gas flow r a t i o s a t r e c t i f y i n g and s t r i p p i n g R' S

sections, respectively

L-, Percentage increase in the costs of LPG powered,

ammonia cycles from those of LiBr-H20 cycle, and

LiNO^-NH^ and NaSCN-NH^ cycles from those of H20-NH^

cycle

L,-, Percentage increase in the costs of LPG powered

LiBr-H„0 or H„0-NH^ cycles from those of the same

cycles when operated using biogas

m Mass flow-rate/TR (kg/h)

MR Mass flow ratios of the solution from the absorber to

the refrigerant entering the condenser (m-,/m.), kg of

solution/kg of refrigerant

n Number of days

n^,n ,n Rate of flow of the fuel, products and reactants, f p r '^ respectively, moles/h

N, Number of baffles b

N Number of tubes in one cross flow section c

N Number of cross flow rows in each window cw

N, Number of holes to be drilled on each baffle

N Total number of sealing strips in a heat exchanger

N , Number of sealing strips on the top and bottom arcs

of the baffle

N^2 Number of sealing strips on the side arcs of the

baffle

N Total number of tubes in a heat exchanger

p^ Centre-to-centre spacing of tubes in tube bundle

(tube pitch), p for tube pitch normal to flow, p n '- P

for tube pitch parallel to flow, m

XVI

P Absolute pressure; P^, P^, P^, P„, P^ are pressures o, o " y •*-

in the absorber, condenser,evaporator, generator and

rectifier, respectively, bar PW Capacity of water pump, W

P ,P Partial pressures of carbon dioxide and water vapour, c w

bar

P Total pressure of the gas mixture, bar

A P Pressure drop, bar

q Rate of heat transfer per tube of 1 m length, W

2 q/A Net radiant heat exchange, W/m

q Average quality of vapour

q ,q. Quality of vapour at the exit and inlet, respectively ex ^in -^ 2 r

Q ,Q ,Q Heat released by the absorber, condenser and 3 C JT

rectifier, respectively, kJ/h

Q Cooling effect produced by the evaporator, kJ/h Q Heat required in the generator, kJ/h

3 Q, Heating value of biogas, kJ/m

3 Q, Heating value of liquified petroleum gas, kJ/m

Q Useful heat available at the exit of solar collector,

kJ/hm^

R, ,R-, Correction factors for the effect of bundle bypass

and baffle leakage on pressure, respectively

2 S Solar flux, kJ/hm /suppression factor defined by

Eqns. (3.34) to (3.36)

S Monthly average of the sunshine hours per day at the

location, h

S^ Minimum cross sectional-area between rows of tubes, 2

flow normal to tubes, m

XVI 1

S Monthly averaqe of the maximum possible sunshine max

hours per day at the location, i.e. the day length on

a horizontal surface, h

2 S , Shell-to-baffle area for one baffle, m sb

2 S Tube-to-baffle leakage area for one baffle, m

2 S Area for flow through window, m w

S Gross window area, m

2 S , Window area occupied by tubes, m wg

wt

S, Percentage increase in the costs of solar powered,

ammonia cycles from those of LiBr-H^O cycle, and

LiNO^-NH^ and NaSCN-NH^ cycles from those of H2O-NH2

cycle

S,I Percentage increase in the costs of solar powered

LiBr-H O or H„0-NHn cycles from those of the same

cycles when operated using biogas

t Temperature, °C

th Thickness of plate, m

T Temperature, Kelvin/Tray diameter, m

T ,T Refrigerant and solution temperatures, respectively,

Kelvin

? ,T ^, Tray spacing in the distillation column, m rsp rspl -I L n /

TR Tonnage of refrigeration (12600 kJ/h)

TV1,TV2 Throttle valves

A t Temperature drops from inlet to outlet of the heat

exchanger, At^, At^, A t , ^t , ^t are for the

absorber, condenser, evaporator, generator (solar

operated) and rectifier, respectively, °C

t Condensing temperature, °C (t,=t =t =t ) I f a c r

XVlll

A t Log mean temperature difference, °C m

AT Approach temperatures (3 K for water as a coolant),

/^T , AT , AT are for the absorber, condenser and 3i C 2^

rectifier, respectively, Kelvin

U Loss coefficient from bottom, top and sides of a 2

solar collector, Wm K

U Overall heat transfer coefficient based on shell side ^ 2

tube area, W/m K V Gas velocity based on A , m/s a a

3 V Volume flow rate of biogas, m /h

V Remaining vapour leaving the reflux condenser and

entering the main condenser, kg-mol/h

V,V„ Superficial velocity at flooding, m/s r

3 V, Volume flow rate of LPG, m /h

V Velocity through an orifice, m/s

V Minimum gas velocity through perforations below which

excessive weeping occurs, m/s

V _ Average velocity of two phase fluid, m/h

V -, Velocity of solar-hot water flowing in the generator,

m/s

of V-j Percentage increase in the costs/three ammonia cycles

from LiBr-H20 cycle or LiNO^-NH, and NaSCN-NH, cycles

from H^O-NH, cycle

^11 Percentage increase in the cost of LiBr-H„0 or

H2O-NH2 cycles at V, =W from those of the same cycles

at minimum operating cost of biogas

w Hour angle, radians

XIX

W Volume flow rate of water, W^, W^, W^, W , V ^ are

respectively for the absorber, condenser, evaporator, 3

generator and rectifier, respectively, m /h

W Weir length, m

W Weights of stainless steel, Vl^, W^^, W^^, W^, W^^,

W , W^, W- , W are respectively for baffles, ss t f z z '^ -^ channel covers, flanges, shell, tube sheet, sealing

strips, tube, flanges for nozzles, nozzle, kg

W r r: Effective length of the weir, m err -^

W. Weight of insulating materials, kg

X Concentration of liquid ammonia per kg of solution in

H^O-NH^, LiNO^-NH^ or NaSCN-NH^/concentration of

lithium bromide salt (%) in LiBr-H„0 solution

X c Concentration of liquid ammonia in LiNO^-NH^ or

NaSCN-NH /concentration of lithium bromide salt (%)

in LiBr-H^O solution that would lead to

crystallization at the preheater-exit

d.(M),Xd_(M) Standard size inside and outside diameters of 1 O

stainless steel tubes (for M=5 sizes), m

y Concentration of ammonia in the vapour phase, weight

per kilogram of the gas mixture

z Average flow width for liquid on a tray, m

Z Actual air-fuel ratio

Z^ Theoretical a i r - fue l r a t i o

XX

Subscripts

a Absorber side

la Refers to capital cost of absorber

ae Absorber-evaporator

am Ambient

av Average

A Ammonia

b Biogas

lb, 2b Refers to capital and running costs of biogas,

respectively

bn Burner

bk Ideal cross flow section

bw Biogas plus water

c Condenser side

Ic Refers to capital cost of condenser

eg Condenser-generator

en Convective

e Evaporator

le Refers to capital cost of evaporator

eb Elbow

el leaving evaporator

ex Exit

f Frictional

g Generator side/gravity

gb Burned gases from biogas

XXI

gc Solar-hot water in the generator

gi Inside surface of generator tube

gk Gasket

gl Burned gases from LPG

gs Average temperature of burned gases

gl,g2 Refers to flow-rate of solar heated water for t <81°C

and for t >81°C,respectively g

Ig Refers to capital cost of generator

i,il Inside/inner

in Insulation

1 L i q u i f i e d p e t r o l e u m g a s (LPG) /L iqu id

Iw LPG p l u s w a t e r

1 1 , 2 1 R e f e r s t o c a p i t a l and r u n n i n g c o s t s of LPG

m M i x t u r e

m,m+l mth and (m+l ) th p l a t e i n d i s t i l l a t i o n column

m Momentum

ms Mild steel

min Minimum

n,n+l nth and (n+l)th plate in the distillation column

N Number of tubes

o/Ol Outside/outer/orifice

l,os, 2/Os Capital and running costs of ordinary flat plate solar

collector, respectively

p Pure component

pc Precooler

ph Preheater

XXll

pr Tray plate

r Rectifier/radiant

R Rectifier

s Solar energy/shell side

sat Saturated

sn Solution and Isn capital cost of solution

s,o Ordinary solar collector

sp Space temperature

lsp,sp Screw pump

ss Sealing strip

St stainless steel

s,t Tubular solar collector

sw Solar plus cooling water

sy System cost

syt System plus operating cost

S Stripping section

t Tubular/tube

tt turbulent-turbulent/tube thickness

tv turbulent-viscous

ts thickness of shell

tz thickness of nozzle

TP Two phase

vt Viscous-turbulent

vv Viscous-Viscous

w,W Water

XXlll

wk Ideal window section

wa,wc Average temperatures of fluids in the absorber and

condenser respectively

we,wr Average temperatures of fluids in the evaporator and

rectifier, respectively

wi Inlet temperature of water

wo Outlet temperature of water

WW Properties of water at wall temperatures

z Horizontal surface

Superscripts

1 Liquid

Iv Liquid-vapour

V Vapour

Non-dimensional parameters

Gr Grashoff number, p^pgd"^ AT/;a^

Gz Graetz number, Re.Pr. d/L

Nu Nusselt number, hd/K

Pr Prandtl number, p-c/K

Re Reynold number, Vd/;a, Gd/;a, Am/j\dyL

XXIV

Greek letters

cC Void fraction

p Slope, inclination of solar collector, radians

e Angle of incident ray, radians

4) Latitude, radians

(|)-| Lockhart-Martinelli multiplier

2

d) Martinelli-Nelson multiplier

TT Equal to 3.141592653

P Density, Kg/m

p Dynamic viscosity, Kg/m-s

o" Surface tension, N/m | Stefan-Boltzmann constant

(=5.669x10"^ W/m^K^)

r) Pump efficiency

S Thickness of tube or plate, m/Declination, radians

A Difference

G Emissivity

G Heat exchanger effectiveness

(9 At the rate of

1. INTRODUCTION

1.1 Need of the day

Refrigeration is characterized by the transfer of

thermal energy from a region of low temperature to a region

of higher temperature. Cold storage of food products is an

important application of refrigeration. Many food stuffs

like fruits, vegetables, meat, fish and milk products can be

maintained in a fresh state for a significantly longer

period if they are kept at low temperature. An increase in

the number and capacity of cold storage systems will make a

significant contribution to the alleviation of food storage,

by arresting the spoilage. In addition to this, air

conditioning of buildings have become very important in the

present day life. This has led to the improvement in human

comfort, increase in industrial production and feasibility

of establishing high technology industries, which require

controlled environment.

The absorption process is one of the earliest methods

for producing refrigeration. The scientific basis for the

absorption refrigeration process was proposed by Faraday in

1823. However, Ferdinand Carre produced the first patent of

an intermittent absorption system in 1850. The continuous

absorption system using water ammonia solution was developed

by Mignon and Rouart and shown at the London Exhibition of

1862. Around 1870 vapour compression and air refrigeration

system were developed to a stage that they competed well

with the absorption machines. The thermodynamic assessment

of these refrigeration processes was made by Linde and

Gewerbsblatt in 1871. It was concluded that the mechanical

refrigeration process should be more efficient than the

absorption process since the energy supplied to the

compressor is of much higher thermodynamic quality than the

heat supplied for driving the absorption machines. On the

other hand, the fact that the absorption process operates

well with low grade heat, is advantageous when this form of

energy in abundantly available [1].

Due to the increasing cost of conventional energy

sources the vapour absorption systems are gaining more and

more importance. It has, therefore, attracted the

researchers, especially in the fields of solar energy,

biomass energy, wind energy, waste heat recovery etc., to

re-examine the potentiality of vapour absorption cycles,

which utilise low grade thermal energy.

1.2 Practical refrigerant absorbent systems

Absorption refrigeration cycles are heat operated

cycles in which a secondary fluid, the absorbent, is

employed to absorb the primary fluid, gaseous refrigerant,

which has been vapourised in the evaporator. In the basic

absorption cycle, low pressure refrigerant vapour is

converted to a liquid phase (solution) while still at low

pressure. Conversion is being made possible by the vapour

being absorbed by a secondary fluid, the absorbent.

Absorption proceeds because of mixing tendancy of miscible

substances, and generally, because of an affinity between

absorbent and refrigerant molecules. Thermal energy

released during the absorption process must be dissipated to

a sink. This energy arises from the heat of condensation,

sensible heats and heat of dilution [2]. The refrigerant

absorbent solution is pressurized in the solution pump and

then conveyed via a heat exchanger to the generator, where a

portion of the refrigerant gets separated from the solution,

that is, regenerated by a distillation process.

The success of the absorption process depends on the

choice of the appropriate pair of refrigerant and absorbent.

This aspect has been considered in reasonable detail by

Buffington [3] and Macriss [4]. In general, selection of

the working fluids for the absorption cycles are based on

(a) Chemical and physical properties of the fluids, and

(b) Acceptability range for certain thermophysical and

thermodynamic properties of the fluids.

Some of the desirable characteristics of a refrigerant

absorbent mixture are :

(i) low viscosity of the solution under the desired

operating conditions; this reduces the pump work,

(ii) freezing points of the liquids should be lower than

the lowest temperature in the cycle.

(iii) good chemical thermal stability,

(iv) non-corrosive, non-toxic and non-flammable,

(v) high equilibrium soli±)ility of the refrigerant in the

absorbent, and

(vi) a large difference in boiling points of the absorbent

and the refrigerant.

Based on the above requirements for the choice of the

working fluid, following refrigerant absorbent pairs have

been recommended by different authors [3-25] for practical

applications.

Absorbents

LiBr, Lil, LiSCN, CsF, RbF LiCl or

their multiple salt solution

H2O, NaSCN, LiNO^, CaCl2 °^ others

ethers, esters, asmides, amines

and others

Refrigerants

Water

Ammonia

Halogenated

organic compounds

(R12 or R22)

In spite of a large number of refrigerant-absorbent

combinations available, only a few pairs are widely used.

Lithium bromide-water mixture is popular for space air

conditioning [5,6,26] and has following attractive features:

(i) the refrigerant, that is, water has a very high

latent heat of vapourisation,

(ii) the absorbent is non-volatile,

(iii) the system operates at low pressure and hence, the

pumping work is low, and

(iv) the solution is non-toxic and non-flammable.

However, the main disadvantages of using lithium

bromide water are :

(i) temperatures corresponding to refrigeration cannot be

reached because water freezes at zero degree

centigrade,

(ii) water cooled absorber is required because lithium

bromide is not sufficiently soluble in water to

permit the absorber to be air cooled,

(iii) lithium bromide salt is highly corrosive to the

materials of construction except to high quality

stainless steel, and

(iv) the LiBr-H O solution crystallizes at certain

conditions of temperature and concentration, which

may block the passage.

Water-ammonia is one of the oldest combinations

successfully employed for industrial air conditioning and

refrigeration [9, 2 4, 2 7]. Water-ammonia mixture has

certain favourable thermodynamic characteristics. Some of

them are :

(i) large negative deviation from Raoult's law,

(ii) low molecular weight of ammonia and hence, large heat

of vapourization,

(iii) temperatures corresponding to refrigeration (that is,

35°C at one atmosphere) can be reached,

(iv) water is a proper absorbent due to its low cost,

availability and non-toxicity, and

(v) both the refrigerant and absorbent molecules meet the

requirements for hydrogen bonding extremely well, and

are highly stable; and in general, quite compatible

with ordinary materials of construction.

However, because of the high affinity between ammonia

and water, although their boiling points are spread apart by

about 133°C, some water is always vapourised from the

generator with the ammonia vapour and a complex rectifying

system is needed. Ammonia being corrosive to copper and

brass, generally steel vessels are used for its

construction.

Sodium thiocyanate-ammonia solution also possesses many

desirable features [1] such as :

(i) in expensiveness,

(ii) non-explosive character,

(iii) chemical stability,

(iv) safety and non-corrosiveness in steel vessels, and

(v) solubility of sodium thiocyanate in ammonia is very

large.

But, the viscosity of NaSCN-NH^ solution is so high

that this system is commonly used in intermittent absorption

refrigeration systems [17]. Lithium nitrate-ammonia mixture

is also a good combination and has been experimentally

tested by Chinnappa [28] as an intermittent absorption

refrigeration system. Also, the viscosity of LiNO_-NH-. is

found to be high because of which it has not gained much

attention for continuous operation.

1.3 Literature review

The utilisation of solar energy as heat input to the

generator of absorption cooling units has been reported by

numerous researchers. These include efforts by Maoriss [4],

Duffie et al. [5, 26], Nielsen et al. [18], Lof [29], Trombe

et al. [30], Williams [31], Eisenstadt et al. [9, 32],

Chinnappa [19], Swartman et al. [33, 34] and Farber [35].

The basic conclusion of these papers is the demonstrated

ability of solar energy flat collectors to achieve the

required temperatures necessary to provide heat input to

operate the refrigeration units. In recent years, the

experimental incorporation of an absorption chiller into a

solar heating and cooling system has also been accomplished.

Noteworthy experiments have been conducted by Ward et al.

[36-40], Namkoong [41], San Martin et al. [42, 43], Jacobsen

[44], Johnston [45], Bong et al. [46], Kouremenos et al.

[47], Anand et al. [48] and Clerx et al. [49],

Lot production of lithium bromide absorption machines

has been organised by a private organisation Penzkhimmash

[50]. The refrigeration units of capacity 1 MW produced by

Penzkhimmash, are intended to produce cold water upto 7°C by

using hot water with a temperature of 90-120°C or steam

under a pressure of upto 0.17 MPa [50]. The most typical

sources of heat for these units are secondary heat resources

and bleed-offs of turbines in low-pressure thermal power

stations. The VNII kholodomash (All Union Scientific-

Research Institute of Refrigerating Machinery) [51] has

developed number of air-conditioning systems, based on

lithium bromide-water absorption machines, for

air-conditioning mines at about 24-26°C. Since temperature

of the air, compressed by the mine compressors, range from

145-160°C, a portion of the conpressed air is utilised in

the generator of the lithium bromide absorption machine for

air conditioning mines.

A critical factor in the utilization of solar

absorption cooling systems is the economic feasibility. A

number of solar assisted and biogas powered absorption

systems have been proposed by several researchers cited

above, and many others in refs [52-54], for use in the urban

and rural populations of the world. Most of these are

readily available, but are still unable to compete with

conventional refrigeration systems due to high operating

costs. This may be, probably because there is insufficient

experience for evaluation of their cost effectiveness

[5,55,56]. Solar driven absorption chillers have been shown

to be technically feasible, but are not cost effective even

to date [57-60]. The feasibility of an absorption cycle as

heat pump, has also been assessed for space heating but the

study is as yet in a preliminary stage [57,61,62]. Although

a number of reviews on the absorption technology are

available in literature, but these are restricted to either

elementary concepts, cost analysis or commercialisation.

The choice of the refrigeration system depends upon the

requirements and the operating conditions. The main

parameters affecting the performance of the absorption

systems are the absorber, condenser, evaporator and

generator temperatures and the refrigerant absorbent

solution pumping rates. The amount of energy required to

operate absorption machines will depend upon the

10

temperature, pressure and solution concentration in the

generator, and heating capacity of the energy-source. The

slection of the absorber and the condenser temperatures are

restricted due to the availability of the temperature and

flow rate of the cooling media. The evaporator temperature

will depend upon the temperature of the space to be

conditioned; while the solution pumping rates can be

controlled by adjusting the refrigerant-absorbent

concentrations.

Because of large number of variables involved in the

design of absorption cycles, extensive study is highly

desirable in order to find the optimum operating conditions

for a better system performance and economy. Optimization

of the operating parameters in absorption cycles,

corresponding to better yield in performance or minimum

energy requirement, have been carried out by several

investigators. Optimization of the generator temperature in

solar powered H„0-NH^ and LiBr-H„0 systems have been

reported by Prasad [53], Prasad et al. [63] and Alizadeh et

al. [64]. Optimization reported by Prasad and Gupta [63]

and Prasad [53] are based upon ideal performances of the

absorption systems. Alizadeh et al. [64] did not discuss

the operating cost of the system. Economic evaluation of

solar operated H^O-NH^ system has been presented by Shiran

et al. [65]. But they [65] did not discuss at all the

11

operating temperatures and the solution pumping rates.

Economic evaluation of biogas for optimizing the generator

temperature in LiBr-HÔ system has been presented by

Siddiqui et al. [54]. Optimization of NaSCN-NH^ and

LiNO-,-NH-, systems have not been reported so far. Similarly,

a comparative study between the absorption cycles using

either one or other sources of energy has also not been

presented in the available literature. The effect of the

cooling media on the absorber and condenser temperatures and

the subsequent operating costs of the absorption systems

have also gone unnoticed. Use of preheater in the

absorption cycles, using solid absorbents create problem of

crystallization for some conditions of operation. This has

not been discussed anywhere. Optimization of the various

temperatures in lot produced LiBr-H20 absorption

refrigerating machines, corresponding to the minimum sizes

of the evaporator/absorber and condenser/generator

combinations, have been carried out by Shmuilov et al. [50]

for a limited operating conditions. This study [50] has

been carried out for different models of LiBr-HÔ system,

but not for the different operating conditions.

Optimization of the operating temperatures, based on the

costs of the absorption systems, has not been reported till

date for the other absorption cycles such as HÔ-NH^ and

LiNO^-NH^ combinations.

12

1.4 Present work

In view of the discussion in the preceding sections,

this work has been taken up to examine the potentiality of

the various absorption cycles, using different sources of

energy, and produce a wide range of economic operating

conditions. Economic analyses of HjO-NH^, LiNO^-NH-,

NaSCN-NH^ and LiBr-H-O absorption systems using renewable

energies have been carried out to optimize the generator,

absorber, condenser and evaporator temperatures, and the

refrigerant-absorbent mass flow ratios. The sources of

energy selected for optimization are flat plate/evacuated

solar collector, biogas and liquified petroleum gas (LPG).

The given absorption systems have been simulated and the

dimensions and sizes of each components are obtained using a

computerized-design-procedure and correspondingly their

costs estimated.

For optimizing the various operating parameters in the

absorption cycles, using different sources of renewable

energies, three different models have been developed. In

Model I, the generator temperature is optimized

corresponding to the minimum amount and hence, the minimum

cost of energy source. In Model II, the generator and the

condensing temperatures and the solution mass flow ratios

are optimized corresponding to the minimum costs of the

energy plus cooling water. In Model III, the evaporator,

absorber, generator and condenser temperatures as well as

13

the solution mass flow ratios are optimized corresponding to

the costs of absorption system components, total cost of the

system and the cost of the system plus the sources of energy

and cooling water.

1.4.1 Model I

Optimization of the generator temperatures for the

fixed values of the absorber, condenser, rectifier and

evaporator temperatures have been carried out corresponding

to the minimum cost of the sources of energy to operate the

absorption system. The analysis is repeated for the four

absorption cycles with biogas [66], solar collectors and LPG

as the sources of energy, being used separately. The same

study was further extended for the three ammonia systems

operating in the refrigeration mode using biogas [67], solar

collectors and LPG. A comparative study between the sources

of energy, used in the absorption systems, has also been

done. Graphs depicting the optimum generator temperatures

and the corresponding cooling and heating performance

coefficients for a wide range of operating conditions, have

been prepared [66,67].

1.4.2 Model II

Economic analysis of overall-operating costs in the

four absorption cycles, for optimizing the generator and the

14

condensing temperatures have been carried out keeping the

inlet cooling water temperature, evaporator temperature and

the solution pumping ratios fixed. The analysis has been

further repeated, with the different sources of energy and,

to obtain the optimum pumping ratios. The condensing

temperatures is a common name given to the absorber,

condenser and the rectifier temperatures, when they are

assumed to be equal. Effect of using the preheater, on the

system performance, heat input and crystallization of the

solution entering the absorber has also been studied [68,69]

In this study, the approach temperatures at the exit of the

absorber, condenser and the rectifier are kept constant,

while the exit temperature of the cooling water is varied

along with the condensing temperature.

The performance of the absorber and the condenser

generally depend on the temperature of the cooling medium.

Hence, for a system to be economical, the optimum absorber

and condenser temperatures must also be known. The heat

input to the generator through hot water from solar

collectors, combustion products of biogas or LPG and the

disposal of waste heat from the absorber, condenser and

rectifier using cooling water, both account in the operating

costs of the absorption systems. In the optimization of a

single variable, where only the generator temperature is

varied, keeping the remaining parameters fixed [66,67], the

15

optimum conditions are not affected by the cost of the energy

source. For example, minimum volume of biogas [66] will

turn to a minimum operating cost. But, optimization with

respect to more than one variable need formulation of a

certain criteria. Optimization on the basis of the total

costs of the energy source and cooling water will differ

from place to place and depend upon their method of

estimation, availability and market standards. Therefore,

in order to have a better choice for the selection of the

optimum parameters that may be applicable at different

places, analysis at equal volume of biogas and cooling water

has also been carried out along with the economic analyses.

This basis of selecting the optimum parameters, which depend

upon the thermodynamic properties, are found to be very

close to the optimum values obtained corresponding to the

minimum operating costs.

1.4.3 Model III

Economic analysis of the absorber plus evaporator and

the condenser plus generator are carried out to optimize the

operating pressures [70] and temperatures [71] in LiBr-H^O

and H2O-NH2 systems. Optimization of the evaporator and

absorber temperatures are done corresponding to the minimum

cost of the absorber and evaporator, and those of the

condenser and generator are carried out corresponding to the

minimum cost of the condenser plus generator. The same

analysis has been repeated for the total cost of the system

16

plus the costs of the energy source and cooling water; the

total cost of the system include the costs of the preheater

and precooler. This study, has also been repeated for the

different pumping ratios. The entire analysis is then

carried out for the four absorption systems [72] operating

in the air-conditioning mode and the three ammonia systems

operating in the refrigeration mode, using the various

sources of energy, separately. The inlet temperatures of

the hot water or gas in the generator, cooling water in the

absorber, condenser and rectifier, and the chilled water or

brine in the evaporator, are fixed with a certain specified

drop or rise in their temperatures while flowing through the

respective components.

For a comparative study between the various absorption

cycles, their manufacturing, installation and overhead costs

must be available from a single source. But, unfortunately

there is not a single firm in the world which is

manufacturing all the four absorption systems under study.

Also, a wide range of analysis is possible only through a

computer programme. Therefore, the capital costs of lithium

bromide-water, water-ammonia, sodium thiocyanate-ammonia and

lithium nitrate-ammonia absorption systems have been

obtained after designing the system components, for a set of

operating conditions, using a computer program developed for

the purpose. The absorber, condenser, evaporator.

17

generator, precooler and preheater are designed using

standard methods given in the literature. The costs of the

absorption system include the cost of material needed to

construct a heat exchanger - shell, tubes, baffles,

nozzles, etc., for each component in the system, and the

costs of fabricating, installing and charging the system.

In the present study, the precooler and preheater

effectivenesses are fixed and taken equal to (6 =€ =0.75).

It is observed by Siddiqui et al. [54] that there is minor

effect on the optimum generator temperatures with the heat

exchanger effectiveness. The heat exchangers having high

effectivenesses lead to low operating costs because of

improved performance due to subcooling and reduction in heat

input to the generator.

A general procedure for designing various components in

the vapour absorption cycles has been presented. Empirical

relations for the different factors needed in the heat

transfer and fluid flow equations for the design of

baffled-shell and tube type heat exchangers have been

developed. Empirical equations for the properties of

H^O-NH^ liquid-solution and gas-mixture, LiBr-H«0 solution,

pure ammonia, pure water, and CaCl„-H„0 (used as a brine)

have been developed. Relations for finding the capital and

running costs of the sources of energy and cooling water

have been developed after estimation. Relations for finding

the heating values of biogas and LPG have been obtained.

Average values of solar flux on an inclined collector

surface have been estimated for Aligarh. The ordinary flat

plate collector, with two glass covers and selective coating

have been chosen for low temperature applications in the

generators of the absorption system, while evacuated

tubular-flat collector has been selected for high

temperature applications, each employing storage systems.

The working fluid for the ordinary collector is assumed to

be water and for the tubular collector is air. For the

tubular collectors organic solutions may be used in the

storage tank,while water in the ordinary collector.

Equations for shell diameter with number and sizes of

the commercially available pipes are developed. Relations

for the emissivities of carbon dioxide and water vapour,

their correction factors and the other constants needed in

the calculation of radiative heat transfer, have been also

obtained with respect to their operating temperatures and

pressures. Graphs showing the optimum system variables and

the corresponding performance coefficients of the systems

operating in the refrigeration and air conditioning modes

have been drawn.

2. MATHEMATICAL FORMULATION

2.1 System description

The vapour absorption refrigeration system, having

different components and state points, is shown in Fig. 2.1.

The absorbent-refrigerant solution is pumped to the

generator. The affinity of the absorbent refrigerant pair

is reduced at an elevated temperature and a part of the

refrigerant vapourizes and condenses in the condenser. The

condensate, after getting subcooled in the precooler, is

throttled through TVl to the evaporator. The refrigerant

vapourizes in the evaporator and thus, cooling is produced.

The subcooling in the precooler improves the performance of

the system. The remaining solution mixture (weak in

refrigerant) from the generator is separated and brought to

the absorber through the preheater and throttle valve TV2.

The solution in the absorber, maintained at a low

temperature and pressure, absorbs the refrigerant vapour

from the evaporator, and thus, the cycle is complete.

The volatility differential between water and ammonia

is not sufficient, and hence, H_0-NH^ system needs a

rectifier and an analyser to ensure high concentration of

the refrigerant ammonia entering the condenser. The

LiNO^-NH^, NaSCN-NH^ and LiBr-H20 systems using solid

absorbents, do not require any such rectification as in the

20

Qc

is

C ondenser

5 $ Precooler

V\AA\V\y^

Evaporator

3 loy PPP heater ^/VVVV\A/V

¥9 2k

Absorber

\

^

Oe

AN - Analyser G - Generator Q - Rate of heat transfer

Q a

R - Rectifier TV-Throttle valve

Fig.2-1 Vapour absorption refrigeration system

21

HÔ-NH-, system. Thus, pure ammonia vapour enter the

condensers of the NaSCN-NH^ and LiNO^-NH^ systems. For

simplicity, it is assumed that pure ammonia vapour enter the

H„0-NH^ system, as well.

Also, in the condenser of LiBr-HÔ system, pure water

enters. Hence the concentration of LiBr salt in the

condenser evaporator circuit is taken zero (i.e. x = 0.0)

and the concentration of ammonia vapour in the condenser

evaporator circuit is taken unity (x = 1.0).

The heat input to the generator in the absorption

system is obtained by burning biogas or LPG, or by passing

hot water from solar collectors, as the case may be. The

cooling effect produced in the evaporator can be used for

space cooling and the heats of condensation and absorption

evolved in the condenser and the absorber can be used for

space heating. In ammonia absorption cycles, toxic ammonia

vapour flows in the evaporator, hence, indirect cooling

using brine is preferred for the space cooling. But, with

LiBr-HÔ system, its evaporator can be directly connected to

the space, because water is non-toxic. For efficient

cooling and compact system design, water cooled condensers

and absorbers are preferred. Thus, the heated water after

taking heat from the absorber and condenser, is sprayed in

the spray pond for cooling down to about 5 K above the wet

bulb temperatures of the atmospheric air, and then pumped

22

back to the absorber and condenser to complete the cycle.

Similarly, chilled water or brine from the evaporator is

sprayed in the duct for cooling and dehumidifying the

space-air to be cooled.

2.2 System modelling

The mass, concentration and enthalpy equalities for the

refrigerant absorbent combinations in the vapour absorption

cycles, at different state points are as follows :

Mass equalities

m^ = m2 = m3 (2.1)

m. = m^ = m^ = m^ = mo = mn (2.2) 4 5 6 7 8 9

m^Q = m^^ = m^2 ^2.3)

Concentration equalities

Xj = X2 = x^ (2.4)

^4 ^5 ^g ^7 ^8 ~ ^9 (2.5)

^10 ^11 ^12 (2.6)

Enthalpy equalities

^1 ~ ^2 (negligible pumping) (2.7)

23

Hp. = H^ ( isenthalpic expansion) (2.8)

H,, = H,„(isenthalpic expansion) (2.9)

Pressure equalities

The mass transfer equilibrium implies :

P = P and P = P = P (2.10) a e c g r

These pressures relate the refrigerant temperature to

the solution temperature and concentration.

The mass and energy balance to each component as a

control volume, lead to the following relations :

m, = m. + m-jQ (2.11)

" 1 1 " " 4 4 ^ "^10^10 (2.12)

m^/m^ = (y^ - X^Q)/{X^ - X^Q) = MR (2.13)

" 10 "" ' 4 4 ~ ^i)/(^i " ^10^ (2.14)

Q^ = mgHg + m^^H^^ - m H (2.15)

Qc = ^^(H^ - H^) (2.16)

Q^ = mg(Hg - Hg) (2.17)

Qg - m^H^ + m^QH^Q - m3H3 + Q^ (2.18)

• r " ''l3"l3 " "'4"4 " '"14 14 (2.19)

mg = TR x 3600 x 3.5/(Hg - Hg) (2.20)

24

ACP = Q^/Q„ (2.21) a g

CCP = Q^/Q„ (2.2 2)

COP = Q^/Q (2.23)

HCP = (Q^ + Q^ + Qr- /Qrr (2.24)

For the absorption cycles using fluids other than

H^O-NH-,, Q is zero. The mass and energy balance to the 2 3 r

precooler and preheater lead to :

Hq = Ho + C (t - t ) (2.25) y 8 pv c e

Hg = H5 - e^ (Hg - Hg) (2.26)

H3 = H^ + (m^Q/m^) ^ (Hj Q - H^^) (2.27)

%c = "'4Sv^^9 - e^ (2.28)

V = lSl^^3 - a) (2.29)

^9 = ^C^^c - ^e^ "• e (2.30)

^6 = c - C (^p8/^p5)-(^c - e) (2.31)

^3 = a S(^10/"^l)-(Sl0/Sl^'^S ~ a^ (2-32)

4l = tg - S(^g - ta) (2.33)

Similarly, mass and concentration balance on the

rectifier, lead to the following equations :

m^3 = m^ + mj_^ (2.34)

25

"^13^13 = % ^ 4 ^ ^14^14 ^^-^^^

1 14 = " 4 y4 - ^13^/^yi3 - ^14^ ^^'^^^

^13 = ni4(y4 - ^l4)/(yi3 " ^14^ (2.37)

2.3 Thermodynamic property equations

2.3.1 Enthalpy

The equation for enthalpy in terms of temperature and

concentration for LiBr-H^O are taken from ASHRAE [73], for

NaSCN-NH^ and LiNO^-NH^ from Ferreira [74] as given in

Appendix Al. The enthalpy equations for pure ammonia, pure

water and H^O-NH-, mixture have been obtained using the

procedure given in Ziegler and Trepp [75], and presented

[66] as follows :

Saturated enthalpy

The reference states of zero enthalpy are taken as 0°C

for saturated ammonia as v/ell as for saturated water.

Pure components

H^ = a^ + a^T + a2T^ + a3T^ + (a^ + a^T^)?

+ agP^ (2.38)

Hp = b^ + b^T + b^T'^ + b^T^ + (b^ + h^/T^

+ bg/T- - )? + b p- /T- - (2.39)

26

Water-ammonia mixture

H"*- = (1-x) H-'- + X H]^ + [(C^ + C,/T + C^/T^) m w A o X ^

+ (C3 + C^P + Cj/T + Cg/T^).(2x-l) + (C^

+ CgP + Cg/T + CJ^Q/T^).(2X-1)^].X(1-X) (2.40)

where a . , b. and C. are cons tants , given in Table 2 . 1 . I l l

«m= (^-y) « > ^ «I '- '

The data for the concentration of ammonia in the vapour

phase is taken from Marcel Bogart [76] and correlated in

terms of pressure and concentration of ammonia in the liquid

phase, as follows :

J i y = Z d. x + (d^ + djjx) .x P (2.42) i=0 ^ ^ ^

where d., d_, and d^ are constants given in Table 2.2. 1 7 8 ^

The saturated enthalpy equations of ammonia and water

in the liquid and gas phases cover the following ranges of

temperature and pressure as reported in [75]:

230 K < T < 500 K and 0.2 < P < 50 bar

The enthalpy equations for H^O-NH^ mixture developed as

above, are found to be in good agreement with the tabulated

values in refs [73] upto the pressure of 20 bar. On the

other hand, the polynomial form of equations developed by

Jain and Gable [77] can be used only for two pressure

27

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29

ranges : [3.45 to 5.52 bar] and [17,23 to 24.13 bar]

Latent heat of vapourization

Using the saturated enthalpy equations (2.38) and

(2.39) for the pure ammonia and water, the latent heat of

vapourization for ammonia and water can be obtained from :

H- ^ = H^ - H^ (2.43) P P P

and that of the H„0-NH^ mixture.

H-'- = H^ - H-*- (2.44) m m m

Superheated enthalpy

The superheated enthalpy for pure water vapour is taken

from Siddiqui et al. [54], as given in the Appendix Al. The

superheated enthalpy data for pure ammonia-vapour, from

Arora [78], have been correlated as :

H^^P = 2.3678756 t - 0.72779902 t + 1379.8894 (2.45) A g C

2.3.2 Equilibrium pressure

The equilibrium pressure equations for LiBr-H^O

solution and pure water have been taken from ASHRAE [73].

The equilibrium pressure equation for NaSCN-NH,sol uti on.

LiNO^-NH^ solution and pure ammonia are taken fr om

30

Ferreira [74]. These equilibrium pressure equations taken

from the different references are given in Appendix Al.

Experimental equilibrium pressure data for the H2O-NH2

solution from Perry and Chilton [79] have been related as :

P = exp [11.289381 + 0.58506864 x - {2864.7202

+ 1576.0613 (l-x)^}/T]

Range: 0.2 < x < 1.0 and 273.16 < T < 393.16 K (2.46)

2.3.3 Solution refrigerant temperatures

Equating the equilibrium pressure equations for the

refrigerant-absorbent solutions with the equilibrium

pressure equations for the refrigerants, the solution

temperatures can be represented in terms of the refrigerant

temperatures as follows :

Lithium nitrate-ammonia

Tg = [S3 + S4(l-x)^]/[A - s^ - S2(l-x)-^] (2.47)

Sodium thiocyanate-ammonia

Tg = [s^ + Sg(l-x)-^]/[A - s^ - SgX] (2.48)

VJater-ammonia

Tg = [s^^ + s^^{l-x)^]/[A - Sg - S-^QX] (2.49)

31

where,

A = s^3 + s^,/T^ + S^3/T2 (2.50)

Lithium bromide-water

T = B(T - 255.382) + C s r

where,

3 . 3 . B = "£ u. x^ and C = J w. x (2.51

i = 0 ^ i=0 "-

Range: 273.16 < T < 383.16 K, 278.15 £ T < 449.16 K

and 45 <_ X <_ 70% (2.52)

where,

T = solution temperature (Kelvins)

T = refrigerant temperature (Kelvins)

where s., u. and w. are constants given in Table Al.1 of the 1 1 1 ^

Appendix Al

2.3.4 Density

The equations for density in terras of temperature and

concentration for NaSCN-NH^ and LiNO^-NH-, solutions are

taken from Ferreira [74], as given in Appendix Al. The

experimental density data for LiBr-H^O solution taken from

ASHRAE [2], for H2O-NH2 solution from Bogart [76], for pure

32

water and pure ammonia from refs [78], and for aqueous

solution of CaCl2 from Ch. 12-45 of Perry Handbook [80],

have been correlated as follows :

Lithium bormide-water

1 P = [ 1 . 4 5 9 0 2 9 + 0 . 2 7 6 8 7 5 9 8 E - 2 x I m

+ ( - 0 . 2 2 6 6 6 0 7 4 E - 1 + 0 . 4 2 9 0 7 6 2 6 E - 3 x ) .

( T - 2 7 3 . 1 6 ) ] . l . O E + 3 ( 2 . 5 3 ]

Water-ammonia

p-"- = 1075.7596 + 0.32246832 E-1 T. (-10.049441 I m

- 13.265566 x) + 0. 909 289 49. E-1 T^.

(0.52290183 E-3 - 0.24832278 E-1 x)

Range: [0.0 <_ x <_ 0.5], (with error upto 0.2 to 2%) (2.54)

P-*- = 1000.5831 - 482.84528 x + 1.8901175 T i m

- 0.54252692 E-2 T^

Range: 0.5 < x < 1.0, (with error upto 2%) (2.5 5)

Saturated water

/5p = 9 2 4 . 9 3 8 8 4 - 0 . 2 6 1 0 3 8 0 8 E+2 P + 0 . 4 6 6 3 7 3 T

- 0 . 7 7 1 8 5 8 7 3 E - 3 T^

Range: 273.16 £ T <_ 400 K, (with error upto 0.77%) (2.56)

33

P' ' = 0 . 2 1 2 4 5 2 1 4 E+3 P /T + 0 . 9 7 7 3 5 7 9 9 E-4

+ 6 3 1 . 0 7 2 9 4 / T ^ + 0 . 2 7 7 3 5 7 5 4 E+23/T-'--'-

+ 0 . 3 7 6 9 1 1 5 1 E+27 P^/T'^'^

R a n q e : 2 7 3 . 1 6 < T < 400 K, ( w i t h e r r o r u p t o 0.6%) ( 2 . 5 7 )

Saturated ammonia

F = 700.94647 - 6.260643 P - 0.22460699 T P

+ 0.44655363 E-3 T^,(with error upto 2%) (2.58)

p"^ = 0.21388012 + 287.55188 P/T - 1906151.5/T^ P

+ 0.27928234 E+26/T-'-"'- - 0.255 E+26 P/T"''"'-,

(with error upto 1.5%) (2.59)

Liquid water (at one atmosphere)

P-'- = 1000.1885 - 0.52829016 E-1. (T-273 .16 ) P

- 0.34998786 E-2.(T-273.16)^

Range: 273.16 < T < 413,16 K, (with error upto 0.7%) (2.60;

Aqueous solution of CaClp

P-"- = 905.0 + 386.63 x.(0.4 E-1 + 0.2135 E-4 T) / m

- 116.25 E-1 x^.(0.388 E-2 + 0.366 E-4 T) (2.61)

34

2.3.5 Viscosity

The equations for the viscosities of NaSCN-NH^ and

LiNO^-NH^ solution are taken from [74] and given in

Appendix Al. The viscosity data for the other solutions and

pure components, are correlated and presented below :


The viscosity data of ASHRAE [2] are related in terms

of concentration and temperature as follows :

u-'- = [(1.7650152 + 0.32196343 E-2 x ' m

- 0.33326805 E-3 x^ + 0.12705402 E-4 x^).

exp(-0.027(T-273.16)} + 0.0178 x].1.0E-3

Range: 10 <_ x <_ 30% and 273.16 £ T <_ 350.16 K,

(with error upto 7%) (2,62)

u^ = [(2.3587019 - 0.23850093 E-1 x ' m

- 0.43801876 E-3 x^ + 0.41959618 E-4 x"^).

exp{-0.03(T-273.16)} + 0.0132 x].1.0E-3

Range: 30 £ x _< 50% and 2 73.16 £ T £ 350.16 K,

(with error upto 6%) (2.63)

u""" = [ ( 1 . 9 7 0 9 5 2 7 + 0 . 1 0 9 9 6 4 5 5 E - 1 x

- 0 . 5 9 0 8 8 0 8 5 E-4 x"^ + 0 . 3 1 1 1 9 0 2 2 E-7 x ^ ) .

e x p { - 0 . 0 2 9 ( T - 2 7 3 . 1 6 ) } + 0 . 0 2 1 x ] . 1 . 0 E -3

35

Range: 50 <_ x £ 60% and 273.16 £ T £ 350.16 K,

(with error upto 8%) (2.64)

Water-ammonia

For a binary mixture of two liquids the equation given

in Ch. 3-282 of Perry Handbook [80] is used, which is

written in terms of the viscosities of liquid ammonia and

water as:

In p-'- = X In p^ + (1-x) In p^ + 2x (1-x) G^^ (2.65)

where G^„ is an adjustable parameter normally obtained from

experimental data. The above equation can correlate for

both polar and non-polar liquid mixture viscosities upto

about 15% error.

The viscosities of aqueous ammonia given in terms of

temperature at 26% concentration, are taken from Ch. 3-2 52

of Perry Handbook [80] and using the viscosity equations of

pure water and ammonia, values of G, „ are calculated and

correlated as :

G^2 = 1.8424034 - 0.99686859 E-2 (T-273.15) (2.66)

Using the above relation for G, „, the values of u were 12 'm

compared with the experimental data given in International

Critical Table V.5:20 [81] at 25°C for the different

36

concentrations; and were found in good agreement.

Saturated water

The viscosity data for saturated water taken from

refs [78] are related as :

n-"- = 1.4679906 E-3 .exp{-0 . 0 261 (T-273.16)} P

-0.15948702 E-3

Range: 273.16 £ T £ 423.16 K, (with error upto 3%) (2.67)

p^ = 15.8361 E-6.exp(2.9178 P/T)

+ 66.816 E-6 P/T - 0.597/T^

Range: 273.16 <. T _< 450 K, (with error upto 2%) (2.68)

Saturated liquid ammonia

The viscosity data taken from refs [82] are related as:

p^ = 0.98 E-3.exp(-0.67065 E-2 T) + 0.78536 E-4 IT

Range: 223.16 <. T £ 323.16 K, (with error upto 2.5%) (2.69)

Ammonia vapour

The viscosity data of ammonia gas at atmospheric

pressure are taken from Ch. 3-248 of Perry Handbook [80] and

correlated as :

37

u^ = 5.2342 E-6.exp(0.2398 E-2 T)

+ 449.381 E-6/T - 1.76581 E-l/T^

Range: 253 < T < 500 K, (with error upto 1%) (2.70)

Aqueous solution of CaCl2

The viscosity data taken from Ch. 12-44 of Perry

Handbook [80] have been related as :

u^ = ( 0 . 4 1 4 2 6 6 - 0 . 4 4 4 E -3 x - 0 . 1 3 7 E-4 T^ ' m m

+ 0 . 3 1 2 E-7 T^) . e x p ( - 0 , 1 2 9 8 E - 1 T

+ 0 . 8 6 E - 1 x ) ( 2 . 7 i ;

2.3.6 Thermal conductivity

The equations for thermal conductivity of NaSCN-NH-, and

LiNO^-NH^ solutions taken from Ferreira [74] are given in

Appendix Al. The equations for thermal conductivity of the

other solutions and pure components, used in the present

study, are given below :


The thermal conductivity data taken from the refs [83]

are related as follows :

K^ = [(11.945 - 0.94 E-1 T + 0.15987 E-3 T^) x

+ 573.22833].1.0 E-3

39

Ranqe: 273.16 < T < 398 K, (with error upto 2%) (2.74)

,v K" = [25.78.exp{-7.25 P/(T-273.16)}

- 720.03418 P/(T-273.16)

+ 607388 P/(T-273.16)^ - 0.161 E+9/

(T-273.16)-^] .1.0 E-3

Range: 273.16 <. T <_ 398 K, (with error upto 2%) (2.75)

Saturated liquid ammonia

The thermal conductivity data from refs [82] are related

as :

K^ = 0.4354446.exp(-0.27864 E-3 T) + 24.39/T

+ 2310.8552/T^

Range: 223.16 < T < 323.16 K, (with error upto 3%) (2.76)

Ammonia gas

The data taken from Ch. 3-314 of Perry Handbook [80]

for the ammonia gas at one atmosphere, are correlated as

follows :

K^ = 88.5605 E-3.exp (-1.6464483 E+5/T^)

+ 0.643407/T + 553.64/T^ + 3.9735 E+4/T-^

Range: 253 <. T •< 513 K, (with error upto 2%) (2.77)

40

Aqueous solution of CaCl^

The data taken from Ch. 12-45 of Perry Handbook [80

are related as :

K-"- = 0.635-0.157648 E-2 T-0.14071 E-2 x m

+ 0.4919 E-5 T^ (2.78

2.3.7 Specific heat

The equations for specific heat of NH^-NaSCN and

NH^-LiNO^ solutions are taken from Ferreira [74] as given in

Appendix Al. The equations for the various solutions and

pure components are given below :


The specific heat data for LiBr-H-O solution taken from

ASHRAE [2] are related in terms of LiBr salt concentration

as :

Cn = 4.259 - 0.053843 x + 2.307 E-4 x^ (2.79)

VJater-ammonia

The specific heat data taken from International

Critical Table V.5:115 [81] and Perry Handbook [80] are

correlated as follov/s :

41

C^ = 4 . 1 5 1 9 - 0 . 4 3 1 6 5 6 8 8 E-2 x + ( 0 . 3 0 3 4 5 E - 3 x m

+ 0 . 2 3 8 9 6 E - 4 ) . ( T - 2 7 3 . 1 5 ) - 0 . 3 4 9 E -6 x

. ( T - 2 7 3 . 1 5 ) ^

R a n g e : 0 . 0 _< x <_ 0 . 4 and 2 7 5 . 5 5 <_ T _< 3 3 4 . 1 5 ( 2 . 8 0 )

Saturated water

The specific heat data of saturated liquid water and

v/ater vapour are taken from refs [78] and related as :

C-"- = 4.2686 - 0.3538 E-2 (T-273.16) P

+ 0.255 E-4.(T-273.16)^

Range: 273.16 £ T £ 573.16 K, (with error upto 2%) (2.81)

C^ - 7.636 - 0.3715 E-1 T + 0.5965 E-4 T^ P

- 0.27293817 E-6 P.T^

Range: 273.16 <. T <_ 450 K, (with error upto 2%) (2,82)

Saturated liquid ammonia [82]

C""- = 4.444544 - 0.5064 E-2 T + 0.21567 E-4 T^ P

Range: 223.16 £ T <_ 323.16 K, (with error upto 1.6%) (2.83)

Ammonia gas at one atmosphere [80]

C^ = 1.9556 + 0.789 E-4 T + 0.4032684 E-4 T"*"'

42

Range: 253 £ T <_ 513 K, ( w i t h e r r o r u p t o 1%) (2 .84

Aqueous s o l u t i o n of CaCl- [80]

C-*- = 36 .824 - 0 ,697 x - ( 0 . 1 2 3 6 6 m

+ 0 .1248 E-2 x) T + 0 .1398 E-4 T^ x ( 2 . 8 5 )

2 . 3 . 8 S u r f a c e t e n s i o n

S a t u r a t e d w a t e r

The d a t a f o r s u r f a c e t e n s i o n of s a t u r a t e d w a t e r a t the

l i q u i d vapour i n t e r f a c e , a r e t a k e n from r e f s [84] and

r e l a t e d i n t e r m s of p r e s s u r e and t e m p e r a t u r e a s g iven

below :

a- = [6 .64332 - (235 .80637 P - 1 3 . 7 3 5 P ^ ) / T

+ 0 .3661916 E - 09 T ^ / P ] . 1 . 0 E-2

Range: 273 .16 £ T _< 450 K, ( w i t h e r r o r u p t o 3%) ( 2 . 8 6 )

Saturated ammonia

The surface tension data for ammonia at the liquid

vapour interface, taken from V.4:442, 447 of refs [81], are

related as :

Op = 15.5863/T - 0.54614477 E-4 T - 16.310587 E-3

43

Range: 233 £ T <_ 398 K, (with error upto 5%) (2.87)

2.3.9 Thermal coefficient of expansion

Pure water

The coefficient of expansion data for water have been

taken from refs [85] and related in the following

mathematical form :

p = 0.23174 E-02 - 0.297332/T - 87.617157/T^ (2.88)

Pure ammonia

The value of p for ammonia is found to be constant in

the temperature range of -50 to 50''C [85] and is,

p - 2.45 E-03 (2.89)

The average value of p for a mixture of H„0-NH^ solution is

roughly estimated to be

^m = Pw^l-^^ -" A^ ^2.90)

2.3.10 Cyrstallization line

The equations for concentration of LiNO^ and NaSCN salt

in the absorbent circuit (absorber, preheater and generator

side), which may lead to crystallization because of

temperature changes in each component, have been taken from

Ferreira [74] and presented in Appendix Al. The

44

concentrations leading to crystallization for LiBr salt are

taken from Bogart [76] and related as :

X = 9.8459 E-2 {T-273.15) + 59.7995 (2.91) c

in the range 300 <. T _< 375 K. The upper limit for the

concentration of LiBr salt is 70%.

2.4 Equations of state for computer simulation

The properties of the refrigerant-absorbent solutions,

the pure refrigerants and the other fluids used in the

various components of the absorption cycles, have been

calculated by using the property equations in the form of

SUBROUTINES. These properties, at different state points in

the cycles, depend upon the temperature, pressure and

concentration of the working fluids. For computer

simulation, the equations of state around the different

components have been presented below in a general form. For

a specific fluid, the property equations are modified

according to those given in section 2.3. For example, the

viscosity equation of water vapour is related in terms of

temperature and pressure, whereas, the viscosity equation of

ammonia vapour is in terms of temperature only. In such

cases, the dependents in the equations, will have to be

changed.

Absorber

45

Tube Shell

P = P = P(T ) a e e T = [T . + T + At /2]/2 wa '• wi a " a' •"

X = x ( T ,p : a a a

^^m= ^V^^t^Vî^/

^1 = â (T -T .-At ) ] a wi a

H-, = H (T ,P ,x ) 1 m a' a a ' ' p wa

pV ^pV(T p ) ' ' p a a ' ' p wa

pi = Pl^^.r^,) P = u^T ) ^w ^p ao'

" = P>.'^.^ c'' = ci(T ) p wa'

V V , u = u T ,P ^ p a' a

K'' = Ki(T ) p wa

^ 1 m \ in a a

C'" = CÎT ,x ) a a

C -, = C m

m a' a'

cr = cr (T ,p ) p a a

46

Condenser

Shell Tube

A t P^ = P(T^); T^ is assigned T^^ = [T^^ + ^^ + l^^^^

p"^ = P"^{T ,P ) P^ = P^iT ) ' ' p e c ' p wc

P^ = P^(T ,P ) p^ = u^(T ) ' ' p e c ^ ' p wc

p^ = u' CT ,P ) u^ = u^(T .) ^ ^p c c • w ^p CI

u^ = u^(T ) C" = C- (T ) ^ ^p c p wc

C^ = C^(T ) K " = K- (T ) p c p wc

: r- = c" B^ = B (T ' p5 r rp^-'wc

K^ = K-'-(T ) p c

H^^ - H^^ + 0.68 C^{t -t ) C C CO

Evaporator

47

T u b e S h e l l

P = P ( T ) e e

T = [T T + T + £ , t / 2 ] / 2 we •• e l e " e '

H„ = H (T , P ) 8 p e e ^t^= Vln[(T^l-VAt^)/

« f l = ^ ^ ^ e ' ^ e ^ ( T ^ l - T ^ ) ]

H^^ = H"'-^(T ,P ) p e e

W a t e r , i f t >5°C e

^V P'' = P (T , P )

p e e p - = p l ( T ) p we

P^ = P ; ( T ^ ' P ^ ) P = H K T ) we

V ,

'^p e e H ^ ( ^ e o )

U^(T ) " p e C" = c l ( T )

p we

V V , C = C T ,P

p e e C a C l „ - H „ 0 , i f t <5°C

2 2 e

C^ = C-'-(T ) P e

b ^ „1 p- = P (T )

m we

%S = ^ V

)i- = U (T ) ^m we

K"*" = K"'"(T ) P e

o- = a- (T , P ) p e e

b 1 U"(T ) ' m eo

C^(T ) m we

R e c t i f i e r

S h e l l Tube

P = p T = ( T . + T + A t / 2 ) / 2 r e wr wi r " r

X. = 0 .0 ( f o r L iBr-H„0) ^ t ^ = A t / l n [ ( T -T . ) / *i c. lU JT IT W X

= 1 .0 ( f o r ammonia c y c l e s )

r 4 * wi ^

y = y P ^ = p l ( T ) - r - 4 p wr

X = y u = u (T ) r - r '^ ^ p wr

T = T(T , x ) u " = u"'-(T . ) r 5 c r '^w '^p r i

^ 1 4 = > ^ ( T ^ ' P r ) C' ' = C p ^ V ^

H, = H ^ " P ( t ^ , t ^ ) K^ = K^(T ) 4 p g c p wr

«4 - " m ^ ^ r ' ^ r ' - r ^ ' ^ ^ K ^ \ . ^

( f o r NH^-H^O)

" l 4 = " ^ ^ ' ^ 1 4 ^

HJ;^ = H^^(T ,P , x , y ) r m r r r '- '^r

P" = P ^ ( T ^ . P , )

p wr

49

P" = P'j^r'-r^

„v = u^(T ,P ) ^ ^p r r

u = u (T ,x )

C"- = C1(T^,X^)

K"- = K1(T^,X^)

H^^ = H^^ + 0.68 C'"(t^-t^^)

Generator

Shell Tube

P = P Solar g c

X = * t = 10 MR-1.0 ^ ^ t ,-t

ln[-'sol q

t , -t -At sol g " gc

X = X,„ The properties of hot fluid

from the storage tank of the

y, = y(P ,x ) solar collectors are • 13 -^ q q g g

T = T (T ,x ) S c l ' ^^^^"^^ ^y equa t ion g s ' c' g

evaluated a t the temperature t , , I g e l ( 3 .118 )

»10 = «m^\'V,xg^ Bioqas and LPG

"l3 = "m^^g'^g'^lS^ «V=^gl^

p g g At^=ATg^/l"[(Tg^-Tg)/

P^ = ^^(Tg'Pg) (T , -T -AT )] gb g gs

' ' m g g € = € (T ,P L) c c gs' c

^ ^P g g

e = e (T ,p L) w w gs w

u = u (T ,x ) '^ ^m g g

a = a (T ,6 ) c c gs c

C^ = C^(T ,x ) m g g

a = a (T ,6 ) w w gs w

plO m b = b (T ,6 ) c c gs' c

K" = K-'-(T ,x ) m g g b = b (T ,e ) w w gs w

O" = cr (T ,P ) p g g

C = C (P^,P L) c c T c

C = C ([P +P ]/2)

50

The temperature T is '^ gs

defined by equation (3.116)

and (3.117).

Preheater

51

Shell Tube

T = (T + T )/2 T = (T + T^)/2 • Vrt- a J ht

A t ^ - (V^3^-^^ll-â)/

ln[(T^-T3)/(T^^-T^)]

^wh = ( ht - hs)/2

' t m nt a

Hll = "^â'â'â^

' s ro ns g

Ps = 'î<"hs'>'g'

s m ns g

C" = C^(T, , ,x ) t m nt a

K? = K^^ht'-a^

K^ = ^^^hs'-g) B" = p (T, , ) rt 'm ht

Precooler

52

Shell Tube

T = (T,+T )/2 ps 6 c V ^ 9+ e /2

A t ^ = [(VT5)-{Tg-T^)]/ T = (T ^+T )/2 wp pt ps

ln[(T^-Tg)/(Tg-T^)] Hg is defined by Eq. (2.25)

H, is defined by Eq. (2.26) t = p( V ' e )

p-^ = p-^iT ,P ) s p ps c

V V / '^t ' p pt e

p""" = p^(T ) ' s ^p ps V V /

u = u^ T ,P ^w rp wp e

C^ = C^(T ) s p ps C^ = C (T ,,P )

t p pt e

K^ = Ki(T ) s p ps KY = K (T ,,P )

t p pt' e

Pt = Pp^V^

3. SYSTEM DESIGN

The proper use of the basic concepts of heat transfer

in the design of practical equipments is an art. The

designers of the heat transfer equipments should keep in

mind the differences between the ideal conditions for and

under which the basic concepts were developed and the real

conditions of the mechanical expression of their design and

its environment. The result must satisfy process and

operational requirements such as availability, flexibility

and maintainability and so economically. An important part

of any design process is to consider and offset the

consequences of error in the basic knowledge/ and its

subsequent incorporation into a design method, in the

translation of design into equipment, or in the operation of

the equipment and the process. Heat exchanger design is not

a highly accurate art under the best of conditions.

The procedure for the design cf process heat exchangers

given in Ch. 10-24 of Perry Handbook [80], is listed below :

(i) Process conditions such as streeim compositions, flow

rates, temperatures, pressure, etc. must be

specified.

(ii) Required physical properties over the temperature and

pressure ranges of interest must be obtained.

54

(iii) The type of heat exchanger to be employed is chosen.

(iv) A preliminary estimate of the size of the heat

exchanger is made using a heat transfer coefficient

appropriate to the fluids, the process, and the

equipment.

(v) A first design is chosen, complete in all details

necessary to carry out the design calculations.

(vi) The design chosen in step (v) is evaluated, or

rated, as to test its ability to meet the process

specifications with respect to both heat transfer

and pressure drop.

(vii) On the basis of the result of step (vi), a new

configuration is chosen if necessary and step (vi)

repeated. If the first design was inadequate to

meet the required heat load, it is usually necessary

to increase the size of the exchanger while still

remaining within specified or feasible limits of

pressure drop, tube length, shell diameter, etc.

This will sometimes mean going to multiple exchanger

configurations.

viii) The fine design should meet process requirements,

within reasonable expectations of error, at lowest

cost. The lowest cost should include operation and

maintainance cost and credit for ability to meet

55

long term process changes as well as installation

cost.

For our present study, the vapour absorption systan

components in Fig. 2.1, have been generally considered to be

shell and tube heat exchangers of the type shown in

Fig. 3.1. However, slight modifications have been

incorporated in the design and cost estimations of the

different components depending upon their applications. In

the condenser, refrigerant vapour from the generator is

assumed to enter the baffled-shell and condense over the

bundle of tubes; while, the cooling vater is allowed to flow

through the tubes to remove the heat of condensation. The

evaporator is considered to cperate dry expansion, which are

generally recommended [86] for cooling capacities upto

1000 KW, with the refrigerant boiling inside the tubes after

taking heat from the coolant (brine/water), that is supposed

to pass through the baffled shell. The absorber is a

vertical shell and tube heat exchanger where the refrigerant

absorbent solution coming from the generator is arranged to

fall in the form of film v/etting the inside surface of the

tubes; while, the refrigerant vapour from the evaporator is

allowed to enter at the bottom of the tubes and pass through

the annular space formed by the falling film. The heat

evolved due to the absorption, inside the tubes, is rejected

by forcing the cooling water through the baffled-shell.

56

^•|v\\\\uvv^mi\\\\\sb

I—

0; > O

.. , CJ

c c n

j =

u

"O o a> i =

o c o

• ^

o LO

C

o JZ u

a x:

m o CL I

cn C

o

E O v _ cn a

u

o E x: u

00

57

The generator is also a shell-and-tube heat exchanger

which is placed vertically. The fluid which is supplying

heat to the generator, that may be either biogas, LPG or hot

water from solar collectors, is arranged to flow through the

tubes, while the absorbent refrigerant solution from the

absorber is allowed to boil in the shell and generate

desired quantity of refrigerant vapour for the condenser.

In the absorption systems using solid absorbents, separators

in the form of circular plates are considered to be mounted,

two on each tube of the generator. These separators are so

spaced, that the refrigerant vapour escapes up into the

condenser, while the denser fluid subsequently fall down.

In the H„0-NH^ system, ammonia vapour generating out,

which is generally accompanied by traces of water vapour, is

drawn through the stripping and rectifying sections of the

distillation column for increasing the ammonia concentration

A secondary condenser is to be placed at the top of the

rectifying section for supplying condensed H„0-NH-, mixture.

This enhances the distillation process. The design of this

condenser is similar to that of the main condenser in the

absorption cycle. The precooler and preheater are

baffled-shell and tube heat exchangers in which the working

fluids, unlike the other components discussed above, do not

change their phase during the process. Hence, the precooler

and preheater are designed using the heat transfer and flow

equations for single phase fluids.

The equations for film coefficients and pressure drops

that will be used for the design of various components in

the absorption cycles, which have been either taken from

standard references or correlated from the results available

in literature are presented below according to their

applications.

3.1 Thermal design for single phase heat transfer

3.1.1 Baffled shell and tube exchangers

The method given here is based on the research

summarized in final report, Co-operative Research Program on

Shell and Tube Heat Exchangers [87]. The method assumes

that the shell side heat transfer and pressure drop

characteristics are equal to those of the ideal tube bank

corresponding to the cross flow sections of the exchanger,

modified for the distortion of flow pattern introduced by

the baffles and the presence of leakage and by pass flow

through the various clearances required by mechanical

construction.

3-1.1.1 Shell side geometric parameters [80,87]

Number of tube rows crossed in one cross flow section

59

D [1-2 (1 /D^)] N = -s 2 _ ^ _ (3.1)

Fraction of total tubes in cross flow F ,

1 D -21 , D -21 ^c = b ^ ^ 2-| ^ Sin (Cos-1 -| £) ^ ^ °otl otl

T D -21 - 2 Cos"^ -i ^] (3.2)

^otl

Number of effective cross flow rows in each window N , cw

0.8 1.

cw p N = (3.3)

Baffle spacing 1 ,

Ig = L/(Nj^ + 1) (3.4)

Cross flow area at or near centre line for one cross flow

section S , m

^m - ^st^s - °otl ^ - ^ ^ (Pt - ^o^^ ^3-^^

where p = p for rotated in-line square layout and p = p,

for triangular layouts

Fraction of cross flow area available for bypass flow

60

F ^ = ( D - D ^ , ) 1 / S (3.6 bp s otl s' m

Tube-to-baffle leakage area for one baffle S^^,

S ^ = 6.223 X 10"^ d N^ (1 + F ) (3.7) tb o t c

Shell-to-baffle leakage area for one baffle S , ,

S ^ = D D [7T - Cos'-'-d - 21 /D ) ]/2 (3.8) sb s sb c' s

where the value of the term Cos (1 - 21 /D ) is in radians c s

and is in between 0 and7r/2.

Area for flow through v;indow S , ^ w

S = S - S ^ (3.9 w wg wt

S = D [Cos"-'-{l- 21 /D ) - (1- 21 /D ) wg s"- c' s c s

/l-(l- 21^/Dg)^]/4 (3,10)

V = (V )' ^ - c)^4 ^3.11)

Equivalent diameter of window D (required only if laminar

flow, defined as Re < 100, exists) s —

\ = 4sy[(V2)N^(l-F^) d^ + D e ] (3.12

e^ = 2 Cos'^d- 21^/D^) (3.13

61

3.1.1.2 Shell side heat transfer coefficient

Shell side Reynolds number Re ,

Re = d m/(3600 p, .S„) (3.14) s o ' b m

Shell side heat transfer coefficient for an ideal tube bank

K = tJv< ^^/^ ).(K/ lOOOpC )^/^/3600] jC K. m

A^^/>.y-'* (3.15)

Heat transfer coefficient for baffled-shell and tube

exchangers is given by

h = h, J J-, J^J (3.16) s k c 1 b r

that accounts for the various factors involved due to the

baffle and tube configurations in the heat exchanger shell.

The factors J, , J , J,, J,, J are obtained from the k c' 1' b r

respective curves plotted in Ch. 10 of Perry Handbook [80].

These are correlated and given in Appendix A2.

3.1.1.3 Shell side pressure drop

The procedure for calculating pressure drops in the

shell are taken from Ch. 10-30 of Perry Handbook [80] as

follows :

62

P r e s s u r e d r o p f o r an i d e a l c r o s s f low s e c t i o n ^ Pj^]^'

A P ^ ^ = 1.5432 X 10"^° f^m^ N^/Cps^ ) . (pJJ/pj^) ° ' ^^ ( 3 . 1 7 )

P r e s s u r e d r o p f o r an i d e a l window s e c t i o n hP , ,

I f Re > 100 s —

A P , = 3 .858 X 10"''"^ m^{2+0.6 N ) / S S p ( 3 . 1 8 ) wk cw m w

I f Re < 100 s

A P , = 4 .669 X 10 ^ ( u , m / S S P ) . [ N / ( p ^ - d ) wk '^b ^ m w cw '^t o

+ (1 /D^) ] + 7 . 7 1 X 10 "'" m^/S S P s ' w ^ ' m w (3.19

P r e s s u r e drop ac ro s s the s h e l l s ide (excluding nozzles)

s

AP^ = [(N^ - l ) (^Pbk) % ^ \ ^Pwk^ ^

^ 2 A P b k \ ( l + N ^ w / \ ) ( 3 . 2 0)

The factors f^, Rj and R are obtained from the curves

plotted in standard references and correlated in the form

given in Appendix A2.

63

The values of h and A P calculated using the above s s

procedure are for clean exchangers and are intended to be as

accurate as possible, not conservative (i.e. low) [80],

3.1.1.4 Tube side heat transfer coefficient

For laminar flow in horizontal tubes several

relationships are applicable, depending upon the value of

the Graetz number. For Gz < 10 0, Hausen's [82] equation is

recommended by Perry in Ch. 10-15 [80].

Nu = 3.66 + [0.085 Gz/(1 + 0.047 Gz^'^^)]

, / w> 0.14 /oil

^^b^^w^ (3.21

For Gz > 100, the Sieder-Tate relationship [89] is

satisfactory for small diameters and AT's

Nu = 1.86 Gz^/^ {p,/p^)^'^^ (3.22) b w

A more general expression covering all diameters and AT's

[80] is obtained by including an additional factor 0.87

(1 + 0.015 Gr-^/-^), that is :

Nu = 1.6182 Gz-"-/ (1 + 0.015 Gr"'"/ )

, / w>0.14 •(V^'w^ (3.23

64

Turbulent flow equations for predicting heat transfer

coefficients are usually valid only at Reynolds number

greater than 10,000, while the transition region lies in the

range 2000 < Re < 10,000. Although, no simple equation

exists for accomplishing a smooth mathematical transition

from laminar flow to turbulent flow, Hausen's equation [88]

fits both the laminar and the fully turbulent extremes quite

well between 2100 and 10,000 [80].

Nu = 0.116 (Re^/^ - 125) Pr- /- [l + (d^/D^^^]

.(VP^)"-" (3.24)

Numerous relationships have been proposed for

predicting turbulent flow in tubes. For high Prandtl number

fluids, relationships derived from the equations of motion

and energy through the momentum heat transfer analogy are

more complicated and no more accurate than many of the

empirical relationships that have been developed [76].

For Re > 10,000, 0.7 < Pr < 700, L/D > 60 and

properties based on bulk temperature, the Sieder - Tate

equation is recommended in Ch, 10-16 of Perry Handbook [86].

Nu = 0.023 Re°-^ Pr^/^ (p /p ) 0-1^ (3^25)

65

3.1.1.5 Tube side pressure drop

For steady flow in uniform circular pipes running full

of liquid under isothermal conditions, pressure drop is

obtained using Fanning or Darcy equation given in

Ch. 5-24 of Perry Handbook [80] which is expressed as :

AP^ = 4 f^L GI X 7.716 x 10"-^^/(2P d. ) (3.26) t t t 1

2 where G =4m/(7T N d.) and the values of f are obtained

from the correlations, developed using the data from

standard references, given in Appendix A2, The pressure

drop computed by equation (3.26) does not include the

pressure drop encountered when the fluid enters or leaves

exchangers.

3.2 Thermal design for two phase heat transfer

3.2.1 Boiling heat transfer coefficient

Boiling of liquids has been of considerable interest to

nuclear, chemical and mechanical engineers and consequently

a lot of work has been done to obtain general correlations

for predicting heat transfer coefficients and pressure drops

for flows with boiling.

In commercial equipment, the boiling process occurs in

two types of situations one, of pool boiling as in flooded

66

evaporators, and the other, of flow or forced convection

boiling as in direct expansion evaporators.

Heat transfer rates in forced convection boiling are

substantially higher than those of pool boiling. In forced

convection boiling, heat is transferred by conduction or

convection through the liquid film/vapour core interface.

Experimental data on heat transfer rates in the two phase

forced convective region are correlated by an expression of

the form :

h^p/h^^(or h^p/h^) = f(l/H^^) (3.27)

The above correlation covers both the saturated nucleate

boiling region and the two phase forced convective

region [91]. It is assumed that both nucleation and the

convective mechanisms occur to some degree over the entire

range of the correlation and that the contributions made by

the two mechanisms are additive :

S P = ^b + ' cn ( -28)

The convec t ive c o n t r i b u t i o n given by Chen [9 2] i s expressed

as :

h^^= 0.023 [ G ( l - q ^ ^ ) d ^ / p ^ ] ° - ^ P r ° ' ^ K ^ / d ^ ) . F (3.29)

The equation of Forster et al. [93] can be used as the basis

67

for the evaluation of the nucleate boiling component, h .

Their [85] pool boiling analysis was modified to account for

the thinner boundary layer in forced convective boiling and

the lower effective superheat that the growing vapour bubble

sees. The modified equation [91] is :

h, = 0.0012 i u h ' - ' ' (CÔ-^5 (P^)°-'%°-'V

{a°-5 (^1)0.29 (H1^)0.24 (^V)0.24^^

(AT ^)°'^'* (AP J^-'^^.S (3.30) sat sat

where F is a function of the Martinelli parameter H^^ and S tt

is the suppression factor defined as the ratio of the mean

superheat seen by the growing bubble to the wall superheat

^"^sat' S is a function of the local two phase Reynolds

number Re.,-. The functional relations for obtaining the

values of F and S, taken from Kreith [94], are given below :

F = 1.0, l/H^t < 0-1 (3.31)

F - 2.35 [1/H^^ + 0.213]°-^^^ 1/H^^ > O.l (3.32)

where,

^/«tt = (âv/l-âv)"'' (^V/0^)°-' (>aVp')°-' (3.33)

S - [1 + 0.12 Re^pl^]-^ ; Re^p < 32.5 (3.34

68

S = [1 + 0.42 Re°-''^]"^; 32.5 < Re_,p < 70 (3.35) rjrp — if —

S = 0.1 ; Re^p > 70 (3.36)

and

Re^p = Re^ F^'^^ x lO""^ (3.37)

Re, = (1 - q _) Gd-Zu-*- (3.38) = 1 = <1 - ^av^ ^di/>^'

q = (q + q. )/2 (3.39)

3.2.2 Condensation heat transfer coefficient

Condensation occurs when vapour is cooled sufficiently

below the saturation temperature to induce the nucleation of

droplets. Nucleation may occur homogeneously within the

vapour or heterogeneously on the entrained particulate

matter. Heterogeneous nucleation may also occur on the

walls of the system, particularly if these are cooled (an

example is that of a surface condenser) . The forms of

heterogeneous condensation are dropwise and filmwise.

Filmwise condensation occurs on a cooled surface that is

easily wetted. On non-wetted surfaces, the vapour condenses

as drops that grow by further condensation and coalescence

and then roll over the surface. New droplets then form to

take their place.

69

There are two basic models that describe dropwise

condensation. The first postulates that condensation

initially occurs in a filmwise manner on a thin unstable

liquid film covering the surface. On reaching a critical

thickness, the film ruptures and the liquid is drawn into

droplets by surface tension forces. This process

continually repeats itself. The second model assumes that

the droplet formation is a heterogeneous nucleation process.

In general, the state of the design art for dropwise

condensation is poor, with considerable contradictions in

the literature. The droplet nucleation model appears more

likely at low condensation rates (i.e., temperature

difference upto 5°C). At higher condensation rates, there

may be a film disruption mechanism as an intermediate stage

before establishing fully developed filmwise condensation.

The condensate wets the surface and forms a continuous

liquid film when filmwise condensation is taking place. The

hydrodynamics of film flow are well known, gravity, vapour

shear, and surface tension forces, either singly or together

serve to promote removal of the condensate film. Two major

condensation mechanism are the gravity-controlled (vapour

space) condensation and vapour shear controlled (forced

convective) condensation.

For a pure, saturated vapour, the resistance at the

vapour/liquid interface is small and, to a first

70

approximation, may be neglected. For a superheated vapour

containing a non-condensible gas or a multicomponent vapour

mixture, significant resistance to both heat and mass

transfer at the vapour/liquid interface exists. Mass and

heat transfer processes occur in parallel within the gas

phase and must be considered together to establish the

respective driving forces. Heat transfer also takes place

through the condensate liquid film to the wall and then to

the coolant. With a pure saturated vapour, the temperature

drop across the liquid film represents the major resistance

to heat transfer. For laminar film condensation over a

single horizontal tube, the following relation given by

Nusselt for calculating heat transfer coefficient [95] is

used :

h = 0.725 [p-^ip-^ - /0 )gH-'- (K^)^/

{p^d^(t-t^)}]°-" (3.40:

When condensation occurs on a horizontal tube bank with

N tubes placed directly over one another in the vertical

direction, the heat transfer coefficient may be calculated

by replacing the diameter d in equation (3.4 0) with N d .

Thus ,

^N = h N~^/^ (3.41)

71

For undisturbed laminar flow over all the tubes,

equation (3.41) is, for realistic condenser sizes, overly

conservative because of rippling, splashing and turbulent

flow [90]. Kern proposed an exponent of -1/6 on the basis

of experience, while Freon-11 data of Short and Brown [96]

indicate independence of the number of tube rows. It seems

reasonable to use, no correction for inviscid liquids, and

Kern's correction for viscous condensates. Thus, Kern's

equation for the condensation of viscous vapours over N

tubes can be written as :

h„ = h N"^/^ (3.4 2) N t

3.2.3 Falling film absorbers

3.2.3.1 Tube side heat transfer coefficient

These devices are important in commercial applications

in which the heat released during absorption is high,

dictating the use of a heat transfer surface adjacent to the

liquid. The usual arrangement is to flow the liquid

absorbent downward in film flow inside the tubes of a

vertically oriented heat exchanger bundle, with coolant flow

on the shell side. The feed gas may be introduced either at

the top (cocurrent) or the bottom (counter current) of the

exchanger. A difficult design problem is the one of

72

distributing the liquid feed uniformly to the top perimeters

of a multiplicity of tubes at the top of the exchanger,

since by-passing the gas is a serious matter if high solute

removals are required. Falling film shell and tube heat

exchangers have been developed for a v/ide variety of

serivces and are described by Sack [97], The fluid enters

at the top of the vertical tubes. Distributors or slotted

tubes put the liquid in film flow in the inside surface of

the tubes, and the film adheres to the tube surface v/hile

falling to the bottom of the tubes. The film can be cooled,

heated, evaporated, or frozen by means of the proper heat

transfer medium outside the tubes. These falling film

exchangers are used in various services as liquid coolers

and condensers, evaporators, absorbers, freezers, etc.

Principal advantages of falling film exchangers are

high rate of heat transfer, no internal pressure drop, short

time of contant (very important for heat sensitive

materials) easy accessibility to tubes for cleaning, and, in

some cases, prevention of leakage from side to another.

For streamline flow of the falling liquid, where the

Reynolds number (4G/3600 p) is less than 2000, Bays and

McAdams [98] have given the follov/ing expression for

calculating film coefficients :

7 3

h = 0.67 [(K^p^g/;a^){10 00 C p"^^/

(K L P^/^g^/^)}]^/? (4G/3600 ;a)^/^ (3.43)

where G = m/(Ad.N ) and p is evaluated at the average film

temperature.

For turbulent flow of the falling liquid in the

absorber tubes, McAdams cites a dimensionless empirical

equation attributed to T.B. Drew, which is presented by

Kern [90] as :

h = 0.01 [(K^^g/P^) .(10 00 C >a/K)

.(4G/3600 /a)]-"-/ (3.44;

3.2.3.2 Flooding in wetted wall columns

When gas and liquid are in counter flow inside the

wetted wall columns, flooding can occur at high gas rates.

Diehl and Koppany [99] correlated flooding data from a

number of sources, including their own work, and developed

the following expression :

V = Y^^^{a- /p')^''' (3.45)

F = 1.22, when 3.2 d /c > 1.0 (3.46)

F^= 1.22 (3.2 d/o- )°*^, when 3.2d /cr <1.0 (3.47

74

F^= (Gs/Lq) 0-25 (3.48)

The flooding data covered column sizes upto 50 mm

diameters; the above correlations should be used with

caution for larger columns as pointed out in Ch. 18-45 of

Perry Handbook [80]. Here cr is in m-N/m.

3.2.4 Pressure drop in two phase heat transfer

3.2.4.1 Boiling inside tube

Two phase pressure drop in the tube of a heat exchanger

consists of friction, momentum change, and gravity which can

be expressed as :

A p = A P ^ + A P + A P (3.49) f m g

The entrance and exit pressure losses, usually

considered in a compact heat exchanger application, are

neglected because of

(i) the lack of two phase data for these pressure losses,

and

(ii) their small contribution to the total pressure drop

for tubular exchangers.

The evaluation of A P due to momentum and gravity

effects, is generally based on a homogeneous model [91].

75

This is the simplest two-phase flow model. The basic

premise is that a real two-phase flow can be replaced by a

single-phase flow with the density of the homogeneous

mixture defined by

1/^m = (1-^av)/^' + %v^P^ ^2-'°

The pressure drop/rise due to an elevation change is

AP = + P g L sin e (3.51) g — ' m ^

Gravity pressure drop predictions from this theory are good

for high quality and high pressure applications. For low

velocities and low pressure applications, the following

equation, which takes into account the velocity slip between

two phases via the void fraction oC:

^ P = + [p'^il-d) + p'^cQ g L sin 0 (3.52) y

The momentum pressure drop/rise from the homogeneous

model is :

^Pm=G'f(l/^m,ex) " ^^/Pm,in^^ ^3.53)

The densities in equation (3.53) are calculated using

equation (3.50) at inlet and outlet conditions, respectively

for the liquid and vapour.

76

The frictional pressure drop, AP^r is calculated on the

basis of separated flow Model. The best known separated

flow model is the Lockhart and Martinelli [100] correlation.

In the Lockhart-Martinelli method, the two fluid streams are

considered segregated. The conventional pressure-drop

friction-factor relationship is applicable to individual

streams. The liquid-and gas-phase pressure drops are

considered equal irrespective of the flow patterns.

The Lockhart and Martinelli functions for liquid and

vapour are defined as follows :

^1 " ^Pf/A^i and (3.54)

<^l = -^Pf/APv (3.55)

The Lockhart-Martinelli method was developed for

two-component adiabatic flows at a preasure close to one

atmosphere. Martinelli and Nelson [101] extended this

method for forced convection boiling for all pressures upto

the critical point. A new parameter ^ called Martinelli-

Nelson frictional multiplier was then defined as :

^\o == V ^ ^ O (3.56)

Martinelli and Nelson have presented curves for d)? as lo

77

function of quality and pressure for water in refs [91].

Although similar curves could be prepared for a specific

refrigerant, this would involve a great deal of

calculational work. Alternate procedure is to use the

Lockhart-Martinelli correlation which is independent of any

particular fluid and is pressure dependent only through the

fluid properties used. The relation between (j) and (f) given

in Ch. 4 of ASHRAE [2] is rewritten as follows :

(})f = (l)?(l-q ) ^ - ^ ^lo ^1 ^av 3.57

where (p is a function of the type of (dissipative) flow

pattern and a parameter H. The parameter H is also a

function of the type of flow pattern, the quality q , and 3. V

the fluid properties (which makes H slightly pressure

dependent). The parameter H is defined in refs [2] for four

possible dissipative flow patterns as follows :

"tt = (PVP^)av-(^/^'^)°-' (Vq^v- 1)' (3.58)

.V ,^1, 1 , V, H^^ = (P VP )av-(^ /> )-(l/q... - 1)

av

.[348/(Re^)°-^] (3.59)

H tv ^^''/^^)av(HVp^).(i/qa^ - 1)

(0.00286). (Re-'-)°- 3.60)

78

«vv = (P''/P')av(>^V)-(l/q3^ - 1) (3.61)

where,

Re^ = p^V^^ dg/p^ (3.62:

Re^ = ph^^ dg/p^ (3.6 3;

V . = m/(P^ + PV2).A^ (3.64) rf ' X

Equation (3.58) has also been represented by equation (3.3 3)

in a different form.

The Lockhart and Martinelli correlations are

represented in the equation form [91] as :

(})J = 1 + C/H + 1/H^ (3.6 5)

or

6^ = 1 + CH + H^ (3.66) ^ V

where the value of C is dependent upon the four possible

single-phase flow regimes and are tabulated below [91] :

Table 3.1 Value of C for various flow regimes

Liquid Vapour Symbol C

Turbulent Turbulent tt 20

Viscous Turbulent vt 12

Turbulent Viscous tv 10

Viscous Viscous vv 5

79

AP, is the frictional pressure drop for the liquid flow lo

alone, in the same tube, with a mass flow rate equal to the

total mass flow rate of the two-phase flow. AP^^ is the

frictional pressure drop for the vapour flow alone, in the

same tube, with a mass flow rate equal to the total mass

flow rate of the two-phase flow. The frictional pressure

drops, AP-, or A P can be calculated from the ^ lo vo

equation (3.26) .

3.2.4.2 Horizontal in shell condenser

In the condensation of a pure saturated vapour the

vapour enters the condenser at its saturation temperature

and leaves as a liquid. The pressure drop is obviously less

than that which would be calculated for a gas at the inlet

density of the vapour and greater than that computed using

the outlet density of the condensate [90]. The mass

velocity of inlet vapour and outlet are, however, same. In

the absence of extensive correlations reasonably good

results are obtained when the pressure drop is calculated

for a mass velocity using the total mass flow and the

average density between inlet and outlet [90]. Thus, for

condensation taking place inside the shell, pressure drop is

calculated from :

AP^ = [30.864 f^(N^ + 1)03^3^/2 D^^ P^^ (3.67)

The equivalent diameter, D for a triangular layout of the

tubes in the shell, is given by

D = (1.095 PI - d^)/do (3.68) es ^t o

G = m p,/{D^l C, ) (3.69) s s' t s s b

where f is calculated using the equations given in

Appendix A2. The average density of the fluid in the

condenser, at its saturation temperature, is given by the

following expression :

P^„ = {P^ + P" )/2 (3.70: a v

Assuming the pitch, p equal to 1.25 times the outer

diameter of the tubes (d ) in a baffled-shell and tube heat o

exchanger, the shell diameters are taken from Table 9 of

Kern [90] and correlated in terms of the tube number for a

triangular layout as follows :

D^ = [1.332(N, - 3.634)°*^ + 2.695]d ,

N^ >. 4.0 (3.71

If the number of tubes in the shell are N < 4.0, the

following equation is used :

D^ = (3.9531 N^)°-^ d^ (3.72)

3.3 Design of distillation column

In the water-ammonia refrigeration system, a little

amount of water escapes from the generator along with the

ammonia vapour. In order to increase the ammonia

concentration, rectification of the vapour is generally done

in a direct contact heat exchanger known as Analyser. The

analyser consists of a series of trays where distillation of

the refrigerant vapour takes place. For supplying liquid to

the top plates of the distillation column, a reflux

condenser known as rectifier or Dephlegmator is used.

The distillation column is provided with an

intermediate feed entry point and a suitable liquid vapour

contacting means such as tower packing, sieve-, valve-,

grid- or bubble cap trays, or plates above and below the

feed entry point.

In the present study, Sieve trays have been selected

for the rectification column of the H„0-NH-, system, because

of their low construction costs [102]. The tray is a

horizontal sheet of perforated metal, across which the

liquid flows, with the vapour passing upward through the

perforations. The vapour, after getting dispersed by the

performations, expands the down coming liquid. Thus,

turbulent froth is created, rendering a sufficient

interficial surface for mass transfer. The trays are

subjected to flooding because of the liquid being pushed

82

back by the upward flowing vapour. The liquid is led from

one tray to the next by means of down spouts, or downcomers.

The depth of liquid on the tray required for gas contacting

is maintained by an overflow outlet known as weir.

3.3.1 Tray numbers

The theoretical number of trays required in the

rectifying and stripping sections of the column are

calculated using McCabe-Thiele Stepwise construction.

McCabe-Thiele method of designing distillation columns lead

to the constant molar overflow concept. That is, the molar

rates of flow of liquid and vapour in a particular zone of

the column remain constant [76].

Mass and concentration balance over the control volume

R, in Fig. 3.2(a), lead to :

^n+1 = ^n ^ ^ (3-73

^n-fl^n+l = V n " ^r (3.74)

And balances on the rectifier show that

G^ = L^ + V (3.75)

and

^r^r " ^r^r + ^ ^r ^3.76

l-l.'^l-'t-TrdVn .

L r i j ' t n '

'm-

l X ^m I * rr.

G ll2X T"

Traym.1

Trgym

13" Troy 1

S^ ,y2

^ ^ n > l , Yn + i

• i . .

I ^

83

5.56Ai bar

^ 0 0 01 0-2 0-3 OM 0-5 0-6 0-7 0-8 0 9 10

Concentration of NH3 ( x ) in NH3-H20(liquid phase)

Fig.3-2(a) Distillation cdumn Fig-3-2(b) McCabe-Thiele stepwise constructicn for number of trays in the rectify-ing(R)and stripping(5)sections

cicvvn spout

-column

, Perforated tray

Fig.3-2(c) Schematic showing weir height (hy^/and crest os/er weir (h^)

Fig-3-2(d) Schematic showing weir and tray size

84

Equations (3.73) and (3.74) can be solved to give

^n+1 " ^^/^^R^'n ^ [1-(L/G)j^]x^ (3.77)

The reflux ratio (L/G)„ can be obtained from equation

(3.75), with the assumption that constant molar overflow

exists, in following form :

(L/G)j^ = (L^/V)/[(L^/V) + 1] (3.78)

Thus using equations (3.77) and (3.78), the concentration

y , can be expressed as : ^ n + 1 ^

n+l = (L^A^/^^V^^ ^ 1 n

+ x^/(l + L^/V) (3.79)

Since x = y at the top most plate (tray) of the rectifying

section, the above equation can also be written as :

y ^ - , = m x + ( y - m x ) (3.80)

or

^n+1 = i Xn ^ ^ (3.81)

where, equations (3.79) to (3.81) are straight lines passing

through the point (x , y ).

85

A similar analysis, making mass and energy balance on

the control volume S, will lead to the following equations :

G + L = L ^, (3.82) m w m+1

G y + L x = L , , x ^ T (3.83) m- m w X m+1 m+1

With theconstant molar overflow, the concentration of

ammonia vapour at the mth tray may be expressed as :

^m = ( / S m+1 - f^^/^^S - ^ ^ \ ^''^'^

Equation (3.84) is another straight line that passes through

the point (x , y ), where, x = y . ^ w -'w w - w

Another assumption in the method of McCabe-Thiele is

that the composition of the liquid and vapour streams

leaving any tray are in equilibrium with each other [76],

Thus, on a theoretical tray, y is in equilibrium with x ,

y with x , etc. But in actual practice, this equilibrium m m IT ' n

is seldom attained, hence tray efficiency is used for

finding the actual number of trays from the theoretical tray

counts. The tray efficiency, which depends not only on the

fluid properties but on the hydraulic and mechanical tray

design methods as well, is roughly chosen to be 0.50 in the

present study.

For the known operating pressure and mass flow rates of

86

the liquid and vapour in the column, the concentrations

X { = X.), x.( = x,„) and x,( = x, ) are obtained using r 4 f iU w 1

equations (2.1) to 2.14). The concentrations x^ = y^ and

X = y are located at B and C respectively on a 45° line as w " w

shown in Fig. 3.2(b). Knowing the value of L /V in the

rectifying section, the values of ra and C are calculated

from equations (3.79) to (3.81). Thus, y_ .T( ~ Yf^ ^^ then obtained using equation (3.81) with x ( = x^). The - n r

equilibrium concentration of ammonia in the vapour phase at

point A, is computed from the equation (2.42) corresponding

to x^. Taking the value of y at A, equal to that at A^, the

value of X at A„ is then calculated from equation (3.81).

This is repeated until the point (x , y ) is reached, and

the number of steps counted which will be the theoretical

tray count in the rectifying section.

Similar steps are followed between the points (x , y ) ' w -'w

and (x^, y^) to calculate the tray counts in the stripping

section.

3.3.2 Tower diameter

The distillation tower should be designed to accomodate

the flow rates and the allowable gas pressure drop.

Approach to flooding and assurance to avoid excessive

weeping and entrainment, must be established.

87

For a given type of tray, at flooding the superficial

velocity of the gas V , which is the ratio of volumetric

rate of gas flow and the net area of cross flow, is

expressed in refs [102] as follows :

Vp = Cp[P^ - P'')/P^]^'^ (3.85)

The correlation for the flooding constant Cp has been

presented in refs [102] in the following form :

C„ = [< ln(Gs/Lq) .(p^/p'')°-^ + p] (cr/0.02)^'^ (3.86)

where, the parameters oC and p have been defined for

(A /A ) > 0.1 as : o a

cC= 0.0744 T + 0.01173 (3.87; rsp

B = 0.0304 T + 0.015 (3.88) " rsp

For (A /A ) < 0.1, the values of oC and B from the equations O 3, •

(3.87) and (3.88) are multiplied by (5A /A + 0 . 5 ) . Where, O 9.

the ratios of the perforated hole area to the active area

(A /A ) are defined as : O 3.

A^/A^ = 0.907(d^/p^)^ (3.89)

Equation (3.89) is applicable for such arrangements where

the holes are placed in the corners of equilateral triangles

at distances between centres of from 2.5 to 5 hole

diameters. For actual design, the superficial velocity of

gas may be little less than V , nearly 80 to 85 percent for

non-foaming and 75 percent or less for foaming liquids.

Thus, with a factor of 80 percent, the velocity will

become

V = 0.8 V^ (3.90) r

The net cross flow area is then given by

A = Gs/p^V (3.91) n

and the total cross sectional area of tower.

\ = V ^ - \t^ (3.92;

Thus, the tray diameter which is same as that of the column,

is calculated from

T = /4A^/7t (3.93)

The tray areas occupied by one downspout (A,) are given

in refs [102] as a percentage of A for different sizes of

weir length W. The weir lengths are expressed as some

fractional value of T. The fractions of T and A , taken

from refs [102] are given in Appendix A3.

89

A well designed single pass cross flow tray can

3 ordinarily be expected to handle upto 0.015 m /s of liquid

per meter of the tower diameter T. The tower diameter must

be selected so that it satisfies the following condition for

the liquid flow

Lq/p^T < 0.015 (3.94)

The downspout area can be written in terms of the fraction

A^ = A^ A^^ (3.95)

The area available for active perforations (A ) is given by a

A = a A - 2A^ - area taken by (tray support

+ disengaging and distribution zone) (3.96)

If the area covered by the tray support is assumed to

be 15% of A and those occupied by the disengaging and

distributing zone be 5% of A ., then,

A^ = 0.8 A^ - 2A^ (3.97)

3.3.3 Liquid depth

In choosing the tray spacing T adequate insurance

90

against flooding and excessive entrainment should be

present. For special cases where tower height is of

considerable importance, spacings of 0.15 m have been

used [102]. From cleaning point of view, tray spacing of

0.5 m would be more workable [102] except for the smallest

tower diameters.

Liquid depth will be the sum of the weir height h and

the crest over the weir h, , as shown in Fig. 3.2(c);

although in the perforated area the equivalent clear liquid

depth will be smaller. To ensure good froth formation,

liquid depths of 0.15 m have been used [105]. Depth of

0.1 m is more common [102], which is maximum, while the

minimum limit for the liquid depth is 0.05 m.

Thus, for the present study, the liquid depth has been

chosen to be 0.1 m and hence,

h-L + h^ = 0.1 (3.98)

The liquid crest over the weir is given [102] by the

following equation :

h^ = 0.666(Lq//O^W) .(W/Wg^^)^/-^ (3.99)

Using the geometry of Fig. 3.2(d), Treybal [102] has

obtained an equation of the form :

91

(W^^^/W)^ = (T/W)^ - {[(T/W)^- 1]°-^+ 2h^/W}2 (3.100)

Equations (3.99) and (3.100) have been solved for W^^^/W

iteratively, with different values of h^, within an error of

+2%. Thus, knowing the value of h,, which satisfies the

equations (3.99) and (3.100), the weir height h is

calculated from the equation (3.98).

3.3.4 Pressure drop for the gas

Pressure drop calculations for the gas flowing in the

tower, will consider the effects for flow of gas through the

dry plate and those caused by the presence of liquid. The

pressure drop is expressed as head of clear liquid [102] in

the following form :

^G = ^D ^ ^L ^ \ ^3.101)

Dry plate pressure drop, h may be due to the losses in

pressure at entrance to the perforations, friction within

the perforation owing to the plate thickness, and at the

exit [106],

^D = ^^0^0^""/ 2gpl).[0.4 (1.25 - A^/A^)

"" ^ pr/^o + ^ " V \ ^ ^ ^ (3.102:

The orifice coefficient C is expressed, over a range of

92

5 /d = 0.2 to 2.0, in the following form [107] :

Co = 1-09 ( V V ^ 0-25 (3.103)

The Fanning friction factor f, is calculated from the

equations given for tube flow in Appendix A2, with Reynold

number Re . The Reynolds number for the perforations in the

tray, is given by

Re = d V /u^ (3.104) o o o "

where V is the velocity of gas through the perforations and

is defined as :

V = Gs/P^A (3.105)

The hydraulic head, h,. is the equivalent depth of clear

liquid and is an estimate of that which would be obtained if

the froth formed due to the liquid, in the perforated region

of the tray, collapsed. This head is usually less than the

height of the outlet weir, which decreases with the increase

in the gas flow rate. The equation recommended by Foss and

Gerster [108] for obtaining the value of h is : Li

\ = 6.10 X 10~^+ 0.725 h - 0.238 h V (p^)°'^ L w w a

+ 1.225 Lq/ p^z (3.106)

93

where,

V = Gs/(P^A ) and z = (W+T)/2 (3.107) a a

Residual gas pressure drop, h may be as a result of

overcoming surface tension as the gas issues from a

perforation. The equation recommended for h [102] is :

h„ = 60- / P^d g (3.108) R ' o^

The flow of liquid under the down spout apron results in a

pressure loss as it enters the tray. The equation suggested

for calculating the pressure drop [10 4, 109], which is taken

equivalent to three times the velocity heads, is :

h^ = (3/2g).(Lq/ P^A^^)^ (3.109)

where. A, is smaller of the two areas, the downspout cross

section. A, or the free area between the downspout apron and

the tray, A . The area for liquid flow under the apron is

obtained by assuming that the downspout apron is set at a

distance equivalent to 1/2 h above the tray, so that W

A„ = 1/2 h W (3.110)

Thus, the difference in liquid level inside and immediately

outside the downspout, h^ will be the total pressure loss

94

resulting from the liquid and gas flow for the tray, that

is ,

h^ = hj + h^ (3.111)

For safe design of rectifying columns, it is desirable

that the equivalent liquid level in the downspout be more

than half the tray spacing.

h + h, + h, < T /2 (3.112) w 1 3 rsp'

In the present study, check on the flooding is done for the

tray spacing 10 percent greater than twice the liquid level

as above.

^rspl = 2.2 (h^+h3^+h3) (3.113

The minimum gas velocity through the tray holes below

which weeping may occur is calculated from refs [102] :

V = (0.0229cr/^^) [p^(p'')2/ (p"") d^cT ] ° ' " ^

.(& /d )0-293(2A d //3 p3)2.8/(z/d^)0.724 pjT O 3 O u

( 3 . 1 1 4 :

Thus, if the velocity of gas through the holes, V is kept

much higher than the minimum velocity, V the tray will not ow

95

weep excessively.

3.4 Heat transfer from gases

When hot products of some combustible gas is used as a

heating source, the heat transfer may take place due to

convection as well as radiation, depending upon the

temperature, emissivities and mean-beam length of the

radiating gas components.

The convective heat transfer coefficient of gases were

calculated using the simplied equations given by Holman [95]

for turbulent flow of air, in the form given below :

h = 0.95 (T - T . ) ^ / ^ (3.115) en gs gi

The temperatures of the burned gases of biogas and LPG,

although the adiabatic flame temperature of the latter is

higher than the former, are assumed to be entering the

generator tubes at T . = T , = 523.15 K and hence, with a ^ gb gl

drop in temperature of the gases A T = 100 K at the

generator exit, the average temperature are expressed as :

'"gs = ^ V •*• ""g -^ V ^ ^ ^ / ^ ^^'^^^^

and

gs = 'gl - Tg "^V^^^/^ ^ " ^ ^

96

Similarly, the average temperature of the hot water/

organic solution from the solar collectors, flowing through

the generator tubes will be given by

t T = (t , + t - A t J2)/2 (3.118) gel sol g gc'

Of the gases encountered in heat transfer equipments,

carbon monoxide, hydrocarbons, water vapour, carbon dioxide,

sulphur dioxide, ammonia, hydrogen chloride and the alcohols

are among those with emission bands of sufficient magnitude.

Gases like hydrogen, oxygen, nitrogen, etc. do not show

absorption bands in the wavelength regions of radiation heat

transmission at the temperature ranges of industrial

applications.

In the present study, carbon dioxide and water vapour

are of considerable importance, especially for biogas and

LPG which are selected to be used in the absorption cycles.

The net radiant heat exchange between a gas containing

carbon dioxide and water vapour and the surface enclosing

the gas is calculated from the following equation^ which has

been presented by McAdams in [110],

q/A - (S € [(4+a+b-c)/4] (T^ - T ^ ) (3.119) y / civ gs gi

the radiant heat t rans fe r coeff ic ient i s then obtained fr om

97

\ = ^ ^g,av [4-^a+b-c)/4] (T^3-Tg\)/(Tg3-Tg. ) (3.120)

where,

e = C € + C € (3.121) g, av c c W W

The average values of a,b and c in equation (3.120) will

depend upon the proportional values of the emissivities of

the various gas components.

The proportion of the emissivities for carbon dioxide

and water vapour are calculated as follows :

e = € / ( e + c ) (3.12 2) c ,p c' c w

G = 1 - e (3.123 w,p c,p

Thus, the average values of a, b and c may be calculated as

a = a € + a e (3.124) c c,p w w,p

b - b e + b e (3.125; c c,p w w,p

c = 0.65 e^ ^ + 0.45 e (3.126) c,p w,p

The constants 0.65 and 0.45 in the equation (3.126) are

change in emissivities for carbon dioxide and water vapour,

respectively and have been taken from refs [110], The

mathematical relations for the values of e , e , C , C , a , c' w c w c

98

a , b and b obtained from the results exhibited w c w

graphically in refs [110], have been developed and presented

in Appendix A4.

3.5 Specific design procedure

The various components of the absorption cycles are

designed by initially assigning certain values of

temperatures (t. and t respectively, for the inside and

outside surfaces of the tubes with respect to the

temperatures of the working fluids), tube numbers (N. ), heat

exchanger lengths (L) and minimum tube sizes (d. and d ).

Subsequently, the inside and outside surface areas, flow

areas, tube centre to centre distance, average temperatures

of the working fluids and the shell and the tube, are

calculated. Thereafter, the properties of the working

fluids are computed at the given temperatures, pressures and

concentrations in the shell and tube, and the various

dimensionless parameters evaluated for calculating the

tube-side and shell-side film coefficients. The overall

heat transfer coefficient for a given heat exchanger may

then be calculated from,

^/"s = V ^^i"^ ^^o ^" V ^ i ^ / 27rL Kg^+ 1/hg (3.127)

and the rate of heat transfer per tube in a shell.

99

q = U A A t ^ s o m (3.128)

Thus, knowing the value of q, the inside and outside

tube surface temperatures, which were initially assigned

certain random value, may be re-calculated from :

t , , (3.129) ^ol = t - q/ A h

^' O S

t., = t^, - q ln(d^/d. )/(27\L K^.) (3.130) IX ox o x oX-

And, the number of tubes required in a shell of the given

heat exchanger for holding^ heat Q,is obtained from

N^ = Q/(qx3.6) (3.131)

The calculations for the values of q are repeated until the

surface temperatures t. and t converge to a minimum

assigned value. The above calculations are then again

continued until the difference in the assigned and

calculated values of N converge to a given limit.

Pressure drops in the tubes and shells are calculated

and the tube diameters and baffle numbers, respectively are

varied for adjusting the pressure drops upto a maximum limit

of 10%. The pressure drop in the falling-film-absorber

tubes is assumed to be negligible. But, the diameter of the

tubes are varied and adjusted so as to prevent overflow due

100

to high gas velocities. Similarly, pressure drops in the

tube and shell of the generator are assumed to be

negligible, because the refrigerant-absorbent solution

flowing through the shell having no baffles, may have

negligible resistance due to friction; whereas, the pressure

drop in the fluids flowing through the tubes are of less

importance.

The flow charts for the computerized design of the

various components is given in Appendix A7. The equations

and the procedure for designing the precoolers and

preheaters are quite similar, hence, flow chart, only for

the preheater, has been exhibited.

The absorber shell-side film coefficients are obtained

using equations (3.1) to (3.16), and those on the tube side

from the equations (3.43) and (3.44). The condenser film

coefficients on the tube side are given by equations (3.21)

to (3.25) and those on the shell-side, by equations (3.40)

and (3.42) .

Similarly, the film coefficients for the shell and tube

sides in the evaporators are obtained from the equations

(3.1) to (3.16) and the equations (3.28) to (3.39),

respectively.

The heat transfer coefficients for the refrigerant-

absorbent solutions boiling in the generator-shell are

101

calculated using the boiling equations (3.28) to (3.39),

whereas the tube side coefficients for hot products of the

biogas and LPG are obtained from the equations (3.115) to

(3.126).

The heat transfer coefficients for hot water from the

storage tanks of the flat-solar collectors, for low

temperature applications, are calculated from the following

equation taken from Ch. 10-17 of Perry Handbook [80].

h = 1057 (1.352 + 0.02 t).(V°^^/d^*^) (3.132

For high temperature requirements in the generators

where tubular collectors are proposed to be used (that is,

for t > 81°C), organic fluids in place of water may be

circulated through the storage tanks and the generator

tubes. The film coefficient for organic fluids, given in

Ch. 10-17 of Perry Handbook [80], is presented below :

h = 423 (V°-^/d°'^) (3.133) sol 1

The film coefficients for the single-phase fluids in the

precooler and preheater-shells and tubes, respectively are

evaluated from the equations (3.1) to (3.16) and equations

(3.21) to (3.25) .

The shell-side pressure drops in the fluids flowing

through the absorber, evaporator, precooler and preheater

102

are obtained using the equations (3.17) to (3.20), and for

the fluids condensing in the condenser shell, are calculated

from the equation (3.67). The tube-side pressure drops in

the precooler and preheater are computed using the equation

(3.26); whereas, those in the evaporator tube, for the

boiling refrigerants, is obtained from the equations (3.49)

to (3.66) .

4. COST EVALUATION AND FUNCTIONAL RELATIONSHIPS

4.1 Sources of energy and coolants

A major part of our energy requirements today, is met

by burning fuels. Industrial boilers are heated by using

coal or fuel oil. Road, sea and air transport are also

powered by fuels. Even the versajbile electrical energy is

produced mainly by burning fuels like coal or natural gas.

Ever since the invention of the engine, we have been

increasingly dependent on concentrated sources of energy

like coal, petroleum and natural gas. Lately, we have also

begun to use uranium as a fuel in our nuclear reactors.

These fuels are mined from a small number of mineralised

zones in the outer layers of the earth. Accumulation of

these enriched pockets, has occured over millions of years

by a rare combination of very slow physical and chemical

processes. It is for this reason that these fuels are rare

and virtually non-renewable.

The local reserves of coal in India are known to be

about 80 billion tonnes, out of which nearly 200 million

tonnes of coal are mined annually. This is expected to rise

to 400 million tonnes by the turn of the century. With this

rate of consuming coal, the reserves in India may not last

long. The oil resources in India are even more limited

104

about 500 million tonnes. Nearly 30 million tonnes are

tapped from this stock every year, and is expected to

increase upto 50 millions by the end of this century. Such

is the predicament that is faced while satisfying the energy

requirement of an increasing population in a country like

India. The danger of running out of energy resources like

coal, oil and natural gas can be averted in many ways.

The use of solar energy is an important trend in

engineering and economic considerations. Most parts of the

world live in regions which are favourable for the use of

solar energy. Solar power plants are particularly efficient

in middle Asian countries where the mean solar radiation

2

intensity is 1500 - 2000 kW.h/m . It is in these regions

that the demand for cooling is great. Short term storages

of fruits and vegetables or milk and developing a normal

microclimate for animal locations, is highly needed in such

countries. The maximum demand for cooling coincides in time

v;ith the maximum in solar radiation, which creates

favourable conditions for the operation of solar cooling

systems.

This increasing demand of energy, can also be met

through the waste organic materials, which produce useful

gases like methane, ethane, carbondioxide, etc. These

gases,generated out of the biomass and commonly known as

biogas, have very high potential of producing heat energy.

105

Biogas energy is a good source, especially for agrobased

rural areas and places where electricity failure is

frequent, for running heat operated systems. Also, natural

and Liquified petroleum gases (LPG) v^ich are available,

especially in urban areas for cooking and to some extent for

running engines, have high calorific values and may be used

in the heat operated systems. Thus, the useful heat

available from solar flat-plate collectors, biogas and LPG

have been estimated and their economic analyses carried out

for use in the vapour absorption cycles, which are heat

operated systems.

4.1.1 Biogas energy

Biogas is generally a mixture of methane, carbon

dioxide and water vapour. Its composition depends upon the

type of biomass used. A typical animal dung yielded biogas

ha ing a composition [111, 112] of :

Methane (CH^) = 55% and Carbon dioxide (CO ) = 45^

where, the water vapour which would have been generated in

the biogas plant, is supposed to be condensed before

entering the supply line. The heating value of biogas is

calculated on the basis of the standard reference

temperature as 25°C using the procedure given by Kadambi and

Prasad [113].

106

The generalized combustion equation from [113] is as

follows :

C H + (x + y/4) O^ + 3.76 (x + y/4) N_ -X y - ' 2 -"' 2

X CO2 + y/2 H2O + 3.76 (x + y/4)N2 ^ " •

Thus, combustion equation for the given composition of

biogas, will be

[0.55 CH^+ 0.45 CO2] + 1.55(02+ 3.76 N2) ——

CO2+ 1.1 H2O + 1.55 (O2 + 3.76 N2) (4.2

The theoretical equation for air fuel ratio taken from [113]

is given by,

Z^ = 137.85 (x + y/4)/(12 x + y) (4.3)

Since the actual value of air fuel ratio, Z will be always

greater than the theoretical value Z , to ensure complete

combustion the generalised equation will modify as :

^x"y " (Z/Z^) .(x+y/4) .(O2+ 3.76 N2) —^

x CO2 + y/2 H2O + (Z/Z^ -l).(x + y/4)02

+ 3.76(Z/Z^).(x + y/4)N2 (4.4)

107

The theoretical air fuel ratio for the above equations is

calculated to be, Z = 15.047; for 10% excess air supply in

the combustion chamber, the actual ratio will turn out to

be, Z = 16.55. Substituting the respective values of x, y,

Z and Z , the modified combustion equation (4.4) can thus,

be written in a simpler form as :

0.55 CH^ + 0.45 CO^ + 1.705 {O2 + 3.76 N^)

CO + 1.1 H2O + 0.155 O2 + 6.41 N2 (4.5)

For the reactants and the products of combustion,

assuming steady flow and no shaft work, the first law of

thermodynamic implies

T n [h (T ) - h (T )] - 5 n [h (T ) ^ p p p p s ^ r"- r r

- h^(Tg)] + n^AHg = Q (4.6)

If the reactants are assumed to enter the combustion chamber

at a temperature of 40°C and one atmospheric pressure, the

specific volume using perfect gas equation, comes out to be, 3

V = 25.7 m /Kg-mole. Assuming that the number of moles of

the reactants, products and fuel are equal (n = n = n^), ^ r p f

using the respective values of specific enthalpies for the

reactants and the products taken from [113] at T = 25°C and

108

T = 40°C, the heating values of biogas are correlated as r

follows :

Q^ = 17963.9 - 12.645(T - 273.15) b p

- 1.75 X 10"-^ (T - 273.15)^ (4.7 XT

A combustion equation, similar to the equation (4.7)

for obtaining the heating value of biogas has also been

obtained by Siddiqui et al. [54].

The equation for obtaining volume of biogas required in

a cooling system, can be expressed as :

Vj = Q^.TR/(COP,Qj^) (4.8)

A cost-volume relationship for different sizes of

biogas plant was presented, on the basis of the Economic

analysis conducted by the Khadi and Village Industries in

India (1978) [114], by Siddiqui et al. [54]. In order to

account for the existing cost of biogas plants, with little

modifications for those in the refs [54], the economic

analysis has been done on the basis of Aligarh 1988 - market

rates. The break-up for the capital and yearly running

costs are given in Table 4.1.

109

m 0

m 0) N

• H

(n

•p

c dJ i- 0)

M-l 4-1 •ri T!

S-l 0

4-<

in CJ CU a 3 u

c • H

4-)

w 0 u

m •p c ro a en CO

cr 0

• H Xi

> 1

\ ro

E ivD

>, 03

TD \

ro

e •^

>, rd

TD ^

ro E

ro

> i rtJ

ro

e CN

o •H +J a

•H

u <D Q

o o

• o ^ C4 CN

O O

• i n (N r-i i H

o o

• i n r-i r-^ IT)

o o

• o o i n 0 0

o o

• o VD r-i H

o o

t

o i n O-i

o o

• o a\ r-ro

o o

• o o i n

>x>

o o

• i n 00

^ r H

O O

• i n r~ vo

o o

• o "* ro ro

o o

• o o i n i n

o o

• i n

•^ o r-{

O O

•

o o yo

o o

• i n i n ro CN

o o

• o o o ^

-p m 0 U

rH (T3 -P • H

a fd

u

0) E CO M

4-1

'O C to

M QJ

X! f H 0 x; U) n j

en i-{ G QJ +J W

0) > 0 4-> in

Ti c to

en C

• H

a, • H CL,

c ^ 0 +J

•H 0) +J H O 4-1

U 0 -P in T^ c c 0 to u

4J

• <u cn.H en c C -iH w

>. iH ^ •H C > (0

•H +J

u ^

r H to 4J O tH

o o U3 CN CN

i n •^ ro i n r - l

i n CN

vo i n

o i n

r~-nH CN ro

O O

i n CN CN

o rsi

00 t ^ 00 ro

o "^ r ro CN CN

o 00

o • ^

^ i H

o o

<D r i H

o r ro r-i r H

o i n

r^ • ^

o o

i n ' J '

CN

o i n

r^ 0 0 r-t

o r -

cri l o

CM

^£> i H

CM

cn

r H

>* i n

[ ^

r H M

O i n

0 0 •^ rH

o CNJ

o o iH

in r ro ro

in t^

0 0

o 1X>

rH

o in

o in r-^

o CVJ

rH tl* O

(U

Q) U 0 +J •H XS c Q) Q. X <u

i H to d c c <:

dP O nH

M 0)

rH 0

x; in to t j i

TS c to

<D B n3 S-l m c 0

c o • H -p to

•H U Q) U a CD Q

dP ro ^^

Q) J-l 0 -P 0 :3 M -p in

C 0

c o • H • p to

• H

u 0) M

a 0) Q

i n

> 0 -P in

Xi C to

t j i C

• H 04

•H

a c 0

c o •H • p to

• H

u tu (-1

a (U Q

c 0 -p

IT) l o

•

C2J

—

> i

n M 3

H cn

m 0

-P in 0 u

u -p •H rH

i n

•

M to 0) > i

to

CU u c 0

cn C

•H 4-> C

• H lO

a IW 0

-P in o u

i H to

• p 0 H

0 • p

cgj

CN

rM CTi

o i n

•^t

o r H

i n IX>

o r

o o

o ro

o i n

CN r-o

o i n

oq H r H

i n rH

o CTi ro

O CO

i n •^ r-

i n

ro

•=}•

•^ ^O

(U E o u c

• H

rH to 3 c c <:

(U u

•H H Q j

cn C

•H t H r H OJ in

0) IH Hi C to S

4-1 in 0 u CJi

c • H

c c 3 M

> rH S-l to 0) ><

X3

X! n

±10

The capital and the yearly running costs from Table 4.1,

assuming 16 hours operation per day, are correlated as

follows :

C,^ - 16967 7°-"^°^ (4.9) lb b

and

C^^ = 3770 V°-^^ (4.10) 2b b

Using present worth method, assuming life of the biogas

plant as 15 years and interest rate on the investment as

10% [54], the total yearly running cost of biogas will be

given by.

C^ = 6 . 6 6 7 X 1 0 " ^ C, , + 0 . 5 5 7 7 8 C„, ( 4 . 1 1 ) b l b ZD

4.1.2 Liquified petroleum gas (LPG)

The liquified petroleum gas which is generally a

mixture of a number of gases such as propane, butane and

ethane can be obtained from Gas Service Agencies through

registered connections. For a typical LPG, that is

available at Aligarh(India), its composition is :

Propane (C^Hg) = 6.88%, Iso-butane (C.H „) = 16.54%,

n-butane (C.H-,Q) = 76.58%.

Ill

Average molecular weight for the given composition of the

various gases in LPG, comes out to be 57.2 kg/kg-mol.

The LPG available in the standard size cylinders, is

supplied with the following specifications :

Maximum working pressure = 16.57 bar

Test pressure = 24.85 bar

Total \ ?eight of LPG = 14.20 kg

Using perfect gas equation, volume occupied by LPG in the

cylinder, at a pressure of 16.57 bar and temperature 40°C,

3 comes out to be 0.39 m , which at one atmospheric pressure

3 will be equivalent to 6.4 m .

The combustion equation for the LPG is :

[0.7658 C^H^Q + 0.1654 C^H^Q + 0.0688 C^Hg] +

6.3968 0^ + 24.052 N2 -* 3.9312 CO^ +

4.9312 H^O + 6.3968 O2 + 24.052 H^ (4.12)

and the theoretical air fuel ratio is calculated to be

Z^ = 15.46. With 10% excess air, the actual air fuel ratio

will become Z = 17.0. Making use of the combustion

equations,the modified form for LPG will be,

112

0.7658 C H-j Q + 0.1654 C^H^Q + 0.0688 C^Hg +

7.036 O2 + 26.457 N2 -^ 3.9312 CO2 + 4.9312 H2O +

0.63968 O2 + 26.457 N^ (4.13

Thus, the heating values of LPG obtained using the same

procedures given for biogas, are correlated in the following

form :

Q, = 102649.64 - 39.455 (T -273.15) 1 p

- 9.0155 X 10"- (T -273.15)^ (4.14)

The volume of L P S , needed to operate a cooling

system, will then be expressed as :

V^ = Q^.TR/(COP.Q^) (4.15)

The cost of LPG is calculated on the basis of the standard

rates fixed by the government of India for the different

items as follows :

Cost of cylinder = Rs. 450.00

Cost of burner = Rs. 125.00

Cost of gas regulator with connecting tube = Rs. 75.00

Total = Rs. 6 50.0 0

113

Thus, the capital cost for obtaining the LPG connections,

C^^ = 650.00 (4.16)

The running cost on LPG will be the cost of gas purchased

from the local agencies which is Rs. 57.00 per cylinder or

Rs. 8.90 per cubic metre of gas. Assuming the time of

operation, for the cooling system as 16 hours daily and 325

effective days in a year, the yearly running cost of LPG can

be v/ritten in terms of volume [72] as follows :

C^^ = 46280.0 V^ (4.17)

The total yearly cost of LPG, using present worth method and

return in 15 years with 10% interest rate will be given by,

C^ = 6.667 X 10 ^ C-j_ + 0.55778 C^^ (4.IS

4.1.3 Solar energy

The refrigerant-absorbent solution in the generator of

the absorption cycles, can be heated by passing hot fluid

from the solar collectors. The collectors may be flat-plate

or concentrated type, where the fluid such as water or air

get heated either by forced or free convection. The heat is

then stored in storage tanks, where from it is supplied to

the generator by using secondary fluids. The available

114

temperatures in ordinary flat plate collectors are low and

range from 80-115°C, but are generally below 90°C. Recently

evacuated-tubular-flat collectors have been developed where

the temperature is expected to rise as high as 150°C or even

more, depending upon the flow conditions and the properties

of the working fluids.

The useful heat available from the solar collectors is

obtained from the efficiency equations given by Ward and

Ward [115]. For U = 3.86 W/m^°C, F^ = 0.95, A = 1.0 m^,

ToC = 0.85 and m C =10.0 W/°C, the heat removal factor is

calculated from the following equation :

F^ = (mC/UA )[1 - e-(^l"V"^^ h (4.19) K p

which comes out to be, F^ = 0.795. And the useful heat per

unit collector-area is calculated from :

Q^ = F^liTd) S - U (t^-t,^n/[l - F^UA^/ mC ] (4.20) b K O ctm i\ p

VJith air as the working fluid in the tubular

collectors, the useful heat available at the collector exit

can be written in a simplified form [72] as :

Q^ = 0.975 S - 4.427 (t - t ) (4.21 s o am

For ordinary flat plate collector, with two glass

115

covers and water as the working fluid in it, the useful

heat [72] is given by

Q = 0.8156 S - 13.665 (t^ - t^^) (4.22; ^s o am

Equation (4.22) has been derived by assuming the value of

mC equal to 90 W/°C.

The solar flux, S falling on an inclined surface,

located at Aligarh (27°5' N-lat. and 78°4' E-long.) is

calculated using the procedure given by Sukhatme [116], the

average value of which comes out to be,

S = 2436.577 kJ/hm^ (4.23

for the months of April to October which is generally a hot

period in the northern parts of India. The calculations for

the solar flux at Aligarh are presented in Appendix A5.

The cost of solar collectors will depend upon the

material and labour required in fabricating it. An ordinary

flat plate collector, for operation at temperatures below

90°C, and an evacuated tubular collector for higher

temperature operations are designed and their costs

estimated as follows :

116

2 Ordinary flat-plate collector of 2 m collection area, with

two glass covers and selective coating [71]

2

M.S. sheet (2m x 1 mm)

G.I. pipe {<^ = 0.0158 m and 20 m length)

G.I. pipe {(p = 0.03176 m and 2 m length)

G.I. elbow ip = 0.0158 m, 5 Nos. ), @ Rs. 9 each

G.I. Tee (0 = 0.03176 m, 2 Nos.), @ Rs. 35 each

Glass wool (15.5 Kg)

Plywood (2.6 m^) , @ Rs. 161.5/m^

Glass sheets (2 m^, 2 Nos.), @ Rs. 286/m^

Selective coating

Water pumps

Supports for the collector Total cost of material

Tax on the material @ 7%

2 Fabrication of 2 m collector (taken as 15% of material cost)

Assembly, fitting and piping Rs. 300.00

Rs.

Rs.

Rs.

Rs.

Rs.

Rs.

Rs.

Rs.

Rs.

Rs.

Rs.

Rs.

Rs.

Rs.

1 8 8 ,

605 ,

146

45 ,

70 ,

6 2 0 .

420 ,

572 ,

200

1 5 0 ,

3 0 0 ,

3 , 3 1 6 ,

2 3 4 ,

5 0 1 .

. 00

.00

.00

. 00

.00

00

,00

. 00

.00

.00

.00

.00

00

00

2 Total cost of 2 m collector Rs. 4,380.00

Reflector :

2

Aluminium sheet (2 m x 1 mm) Bs. 110.00

Plywood (2.3 m^) RS. 370.00

Side frame and supports RS^ 200.00 Total cost of material R5, 680.00

117

Tax on the material g 7% Rs. 47.60 2

Fabrication of 2 m reflector Rs. 200.00 2

Total cost of 2 m size reflector Rs. 928.00

Storage tank :

Tank size (({) = 0.5 m, H = 0.92 m) = 0.18 m'

Insulation (0.15 m thick, 25 Kg) Rs. 1,000.00

M.S. sheet (55 Kg) Rs. 825.00

Total cost of material Rs. 1,825.00

Tax on the material (7%) Rs. 128.00

Fabrication, piping and fitting Rs. 365.00 (taken as 20% of the material cost)

3 Total cost of 0.18 m storage tank Rs. 2,318.00

From the above cost-analysis, the total cost of a 2 m

area ordinary-collector having two glass covers, a reflector

and a storage tank comes out to be Rs. 7,626.0 0.

Adding 20% of the above cost for overhead charges and

10% for installation of the system, the capital cost of flat

plate collector can be expressed in terms of collector area

as :

^l,os = 455^ \ (4-24)

11!

2 Running cost of a 2 m flat plate collector :

Depreciation on the equipment (5%) Rs. 4 96.0 0

Painting and cleaning Rs. 300.00

Repair and maintenance (2.5%) R s . 250.00

Power consumption by pumps Rs. 27.00

Total cost Rs. 1,073.00

2 Thus, running cost per m area is expressed as :

C^ = 536.5 A (4.25) 2 , OS s

Evacuated tubular collectors (Owens-Illenois model) [40]

Copper tube dimensions

Inner tube : 0 = 6.35 mm, S. - 0.76 mm

Outer tube : (|) = 12.7 mm, S = 0.813 mm

Length : 0.95 m

Number of tubes in one module : 8 -t- 8 = 16

Glass tube (corning) : 0 = 65 mm, S = 3 mm

Insulating block (Polyeurathane foam) : (J) = 55 mm, length

60 mm

Copper for one tube-set (0.9975 kg)

Silicon rubber (37 gm) , @ Rs. 75 per kg.

Polyeurathane (130 gm) , g Rs. 50 per kg

Corning glass tube (1.43 kg), Q Rs. 200 per kg

Rs.

Rs.

Rs.

Rs.

1 5 9 ,

2,

6,

2 8 5 ,

.60

.80

.50

,20

119

Steel end plate (0.046 kg), @ Rs. 50 per kg Rs. 2,30

Total cost of material for one tube-set Rs. 456.40

Assuming the costs of fabrication and evacuation of

each tube equal to the cost of material for one tube-set, 2

the total cost of 16 tubes, in one module of 2 m area,

comes out to be Rs. 14608.00

2 Aluminium sheet of size (2.1 m x 1 mm) Rs. 115.00

Support for collector Rs. 550.00

Storage tank (0.36 ra"^ size) Rs. 4636.00

Sub-total Rs. 19909.00

Assuming 20% overhead charges and 10%

installation cost, the additional

cost on the sub-total will be Rs. 5960.00

Solution pump for pumping hot organic-solution

in the generator Rs. 200.00

Blower (for air as the working fluid) Rs. 2800.00

Total cost for a 2 m module Rs. 28882.00

Cl,ts = ^'''^ \ (4-26

The volume of the storage tank for tubular collectors

is taken double the size of the tank used for the ordinary

flat-plate collectors, because, for temperatures higher

than 100°C, air is used as the working fluid due to some

desirable advantages [115].

120

The running costs on the tubular collector per unit

area are estimated below :

Depreciation on the equipment (10%) Rs. 1444.00

Repair and maintenance (1% [117]) Rs. 145.00

2 Power consumption by blower (for the 1 m Rs. 30 0.0 0 area collector and the generator)

Total running cost Rs. 1889.00

Thus, the running cost on the tubular collector, in

terms of the collector areas is expressed as :

C^ ^ = 1889.0 A (4.27 2 , ts s

The area of solar collector required to operate an

absorption system are expressed in the following form :

A^ = 1.2 Q .TR/(COP.Qg) (4.28

The numerical value (1.2) in equation (4.28), represents 20%

increase in the collector area for the storage tank during

off sunshine durations.

Using present worth method and assuming life of the

solar collectors as 15 years, with interest rate on the

investment as 10%, the total running cost for the two types

of collectors wil be given by.

^s,o = '•'"' - 10'' ^l,os ^ 0-^5778 C^^^^ (4.29)

121

a n d

C = 6 . 6 6 7 X 10 ^ C, ^ + 0 . 5 5 7 7 8 C„ , ^ ( 4 . 3 0 ) s , t ± , t s z , i : b

4.1.4 Cooling water

Since the condenser and absorber of the vapour

absorption cycles release tremendous amount of heat, nearly

twice as high as their refrigerating capacity, for compact

design and efficient operation of the system components,

water-cooled heat exchangers should be preferred. The

volume flow rates of water required for cooling the

absorber, condenser and rectifier, respectively are

expressed in the following forms :

W = Q TR/[pc(t - t )] (4.31 a a wo,a wi

W^ = Qc-™/[P^(^wo,c - ^wi^] ( -32)

W„ = Q .TR/[pC(t ^ - t )] (4.33: r r v/o, r wi

The total amount of cooling water required will then become,

W = W + W + W (4.34 3 C IT

The outlet temperatures of the cooling water are assumed to

be expressed as :

t = t - A T (41S) wo, a a a v i . j _>;

122

t = t - AT (4.36) wo,c c c

t = t - A T (4.37) wo,r r r

Equations (4,31) to (4.33) will modify accordingly if the

analysis, based on approach temperature is to be considered.

If the temperatures A T^ = Zi T^ = A T^ = A T^ and t^ = t^

= t = t^, then the total amount of water needed to cool the r f

absorber, condenser and rectifier, written in terms of the

system capacity and its performance, will be given by

W = Q^.TR/[PC(t^-AT^-t^^)].(HCP/COP) (4.38

The cost of cooling water will depend upon its availability

and installation of the cooling devices. The warm water

from the absorber, condenser and rectifier can be cooled

dov/n to about 4 - 5.5 K above the wet bulb temperature of

atmospheric air by using evaporative cooling devices such as

cooling tov/ers or spray ponds [86]. Cooling towers require

high pumping heads and have a very short life, especially

the wooden deck type, unless better and more expensive

materials which do not absorb water, such as plastic, are

used. Spray ponds are made of concerete with steel pipe and

nozzle arrangements and have a comparatively longer

life [68].

123

The initial cost of constructing spray ponds of

different sizes with pipe and nozzle arrangements, using

conventional methods of design, was estimated on the basis

of local standard rates. The sizes of ponds selected were

based on the volume of water required per hour, with 10%

oversize construction to avoid overflow.

The cost of a pump with capacities of 0.093, 0.373 and

0.746 KW were collected from the local market and calculated

in terms of volume flow rate of water (W).

The capacity of water pump needed to deliver the

required amount of water is calculated from

PW = p g H W X lO""^/ 3600 r] (4.39

Assuming the total pumping head due to the absorber and

condenser/rectifier heights, the pond depth and losses in

the pipes as H = 10 m and efficiency of the pump, n = 65%,

the volume flow rate of water in terms of pump-capacity is

written as:

W = 23.85 32 PW (4.4 0)

The capital cost of water, which includes the cost of

spray pond with nozzles and pipes, cost of the pump and cost

of fitting and installation, were estimated and functionally

related as [68] :

124

C, = 1887.2748 W^'^^^^^^ (4.41) Iw

Make-up water to replace the loss due to evaporation, drift

and bleed off is supplied at the bottom of the pond through

a float valve which tends to maintain a constant water level

in the pond. In actual practice, make-up water may go upto

15% of the actual volume of water required. Thus, the

yearly running cost in terms of W is given by,

C, = 595.7455 w°-^^2887 (4_42) 2w

The yearly running cost given by equation (4.4 2) includes

the cost of make-up water, electrical expenses for pumping

(at Re. 0.85 per kVJh), 10% of C, for maintenance and 5% of

C, against depreciation, with the assumption that the

system operates for 16h per day and 325 days in a year.

With the life of the spray pond and pump equal to 15

years and interest rate on the investment as 10%, using

present worth method, the total running cost of water per

year

C,, = 6.667 X 10 ^ C, + 0.55778 C„ (4.43 w Iw 2w

The flow rates of chiJ.led water or brine circulating

through the evaporator shell is obtained from the following

equation which is similar to the equations (4.31) to (4.33):

125

W^ = Qe-TR/[PC(t^^^^ - t^,^^)] (4.44)

For evaporation temperatures below 5°C, aqueous solution of

CaCl2 may be used as brine. In the present study,

properties of the aqueous CaCl„ solution have been evaluated

for 30% salt-concentration. The averaged values of pC in 3

equation (4.44) have been taken to be 4187, KJ/m °C for

3 water and 3627.6 kJ/m °C for CaCl- brine.

Similarly, the flow rate of hot water from the solar

collectors, which is entering the generator tubes for

supplying heat, may be calculated from :

W = Q .TR/[|OC(At ) ] (4.45 g g gc

For generator temperatures below 81°C, water is circulated

in the storage tank (which is getting heated from the

ordinary flat plate collector at about 90°C), and the value 3

of P C v/ill then be 4187 kJ/m °C. Whereas, for generator

temperatures above 81°C, organic fluids are suggested to be

used (which are assumed to be heated by circulating air,

coming from tubular collectors at about 110°C for A/C mode

and 145°C for refrigeration mode) for which Pc = 2092

kJ/m^°C [80].

Thus, the velocity of hot water or organic fluid,

whichever may be the working substance, is calculated from

126

the following expression :

V , = W / A (4.46) sol g X

where, A is the flow area through the generator tubes. The

equation (4.46) is required in the equations (3.132) and

(3.133) for calculating the tube side film coefficients.

4.2 Vapour absorption system

The entire absorption system is designed, for the

various refrigerant-absorbent combinations using different

sources of energy, using a computer program which consists

of a Main and several Subroutines. Subsequently, the costs

of material needed for the shell, tubes, baffles, nozzles,

sealing-strips, flanges, etc. of each component, their costs

of fabrication, installation and overhead charges were

estimated. The costs of the various parts of a heat

exchanger will depend upon the density and volume of the

material required.

Weight of stainless steel for constructing the heat

exchanger shell will be given by.

W = 71- 8_ (D + S^ ) L P ^ (4.47 s ts s ts s st V -1. -i '

where L is the length of the shell plus the heads at the

inlet and outlet and is calculated as :

127

L = L - 2d +2(2 D^) (4.48 s o z

In equation (4.48), the length of the exchanger-head is

taken equal to twice the nozzle diameter. The tubes are

supported, at the two ends of the shell, on the tube-sheets,

the thickness of which are assumed equal to the outside

diameter of the tube.

Weight of the flanges which are to be welded at both

ends of the shell, the inlet-head and the outlet-head for

fastening each other with the nut and bolt arrangements, is

obtained as :

W. = 67rs. [(D + 28^ ) + S. ] S^ .P ^ (4.49) fs fs "• s ts fs ts St

The thickness of one flange (S^ ) on which holes for • r s

inserting bolts are to be drilled, is taken thrice as S ts

The weight of two channel covers will be given by,

^ch =^/2-(Dch ^ s ^ s t ) ^^-50^

and the thickness of these covers are taken equal to the

thickness of the shell (S, ). The cover diameter, ts '

°ch = ^s + 2 6^^ + &^^ (4.51)

Weight of four shell nozzles on each heat exchanger,

12!

\ = ^^ \ z ("z + \-z) ^st ^^-^2^

The diameter of the nozzle (D ) depends upon the shell z

diameter (D ), the sizes of which are taken from Kern [90]

and listed in Appendix A6.

The length of each nozzle is taken equal to the outside

diameter of the nozzle and is expressed as :

L = D + 2 &^ (4.53) z z tz

Weight of flanges on the four nozzles may be calculated

from :

W^^ = 4 7T S^ (D +28^ + S^ ) S^ P fz fz z tz fz tz ' st 4.54

where, 5 is assumed to be equal to three times S ^2 t;

Weight of the two stationary tube sheets.

W.u =/r/2.fD^, S P ^1 (4.55 sh ch sh st' V t . j-j

where, S is considered to be equal to the tube diameter

(d^).

Weight of the tubes, having wall thickness & , will be

\ ^ Vtt^^i + \t^ "^-Pst ( -5

Equation for the weight of 25% cut baffles,

129

where 1 = 0.25 D and the thickness 8, = 3 6 , come out to C S D T-T-

be

W = N D2/8 A27T- e^ + sin e^)?>^ p^^ (4.57

V ;eight of sealing strips, the diameter of which are taken

equal to those of the tube, is obtained from.

"ss= "^^t^^i ^ \ t ) ^ss^ss^st ^^-'^^

and the length of each strip is calculated as

1 = (1 + S, ).{N, - 1) (4.59) ss s b b

The sealing strips are often installed to reduce bypassing

of the tube bundles (Ch. 11-11 of Perry Handbook [80]). It

means that, the sealing strips will have to be mounted near

the periphery of the baffles, just outside the diameter

D , . Since the baffles are assumed to be arranged such

that the 25% cuts appear at the top and bottom of the heat

exchanger, number of the strips on the top and bottom will

be different from those on the remaining two sides of the

baffle. If the strips are assumed to be mounted each after

four tubes, the total number of sealing strips will be given

by

N^^ = 2 [Integer (N^^ + N^^) " 1 V 4 (4.60)

130

where, N which are for the top and bottom arcs of the

baffle, is obtained as :

N^, = [7 - 2 cos-l((D^ - 21^)/D^^;L^].D^^^/ 2p^ (4.61

and N ^ which are for the side arcs of the baffle, is given si

by

Ns2 = ^ ° ^ " ' [(^s- 2 Ic^/^otl^-^otl/ 2Pt (4.62)

The thicknesses, S^ , &^ and S.. for various tube diameters ts tz tt

are obtained from the following relation which has been

correlated for the standard sizes given in refs [90]

S^ = 0 . 1 7 2 X 10 ^ + 0 . 5 6 5 x 10 •"" D. - 0 . 1 1 2 D^ ( 4 . 6 3 ) t 1 1

for 0.0068 < D. < 0.307 m, for D. > 0.307 m, 8^ is taken to — 1 — 1 t

be 9.53 X 10~-^ m.

Area o c c u p i e d by t h e t u b e s on one b a f f l e i s c a l c u l a t e d

from :

\ b = D 2 . a / 8 . [ 2 7 r - 2 c o s - 1 {(D^- 2 1^ ) / D^^^ }

+ s i n [2 cos"-*- {(D^- 2 1 ^ ) / D^^^} ] ( 4 . 6 4 )

Thus number of d r i l l s on one b a f f l e w i l l be equa l t o

^d r = \ b / \ ^ ^ s s - Ns2 ^^-65

131

o

In equation (4.76), number of the strips N^2 has been

subtracted because they do not pass through the baffles but

pass from the area left out due to 25% cut.

The costs of stainless steel pipe, stainless steel

plate, glass wool, rubber gasket and asbestos rope with

plaster of Paris, according to 1988 Aligarh rates, are

rupees 60.0, 50.0, 40.0, 5.0 and 40.0 respectively, per

kilogram weight.

Insulations are provided only on the outside surfaces

f the generator, precooler, preheater and the evaporator.

The glass wooll insulations are to be covered by asbestos

ropes and then by the plaster of Paris. The rubber gaskets

will be used to provide cushion and seal to the various

joints. The cost of 15 mm size bolt-with-nut is Rs. 1.50

each and that of 8 mm size is Re. 0.75 each. The 15 mm size

bolts are meant for the shell flanges, each being placed at

50 mm pitch, and the 8 mm size bolts are for the nozzle

flanges, to be placed at 30 mm pitch.

The costs of the various size stainless steel elbows

are related in terms of their diameters as :

^eb = 305 d + 4.17 (4.66)

The costs of different sized LPG burners are related as :

132

C^ , = 68.828 + 1015.38 D (4.67) bn, 1 s

and those of biogas burners are correlated as :

C^ ^ = 68.27 + 998 D (4.68) bn,b s

The costs of the working fluids (C^^^) perkg-. weight, in the

absorption cycles, at Aligarh rate, are as given below :

Lithium bromide salt - Rs. 960.00

Lithium nitrate salt - Rs. 1100.00

Sodium thiocyanate - Rs. 180.00

Liquid ammonia - Rs. 100.0 0

Distilled water - Rs. 50.00

The costs of stainless steel needle valves of two different

sizes are :

(i) 19.0 mm diameter Q Rs. 130.00 each

(ii) 12.5 mm diameter @ Rs. 75.00 each

The needle vales are to be used as expansion valves, the

largev one on the solution side and the smaller one on the

refrigerant side.

The costs of fabricating any component of the

absorption system, include drilling, boring, cutting,

grinding, shaping, welding and other manufacturing process

133

costs [70]. These costs are correlated functionally

depending upon the amount and nature of work [72]. For

stainless steel jobs, as per local (Aligarh) 1988 marketing

Workshop rates, the costs of various processes are presented

below :

Cutting price for pipes using hacksaw

F. = 26.88 d°"^^ + 0.666 (4.69) dx

Cutting price of flat plates using hacksaw, per metre

length

F = 21.53 + 4.4E+3.th - 5.56E+4.th^ (4.70! px

Cost of drilling holes in flat plates

p(|)

Cost of boring holes in pipes

^db " 798.64.th - 0.07 + (1.6 + 19.4E+3.th) d (4.72

F^. = 22.77.th°-^'* + 27.2 d (4.71

Cost of arc welding per metre length

F^^ = 31.0 wd^-^"^ + 0.25 (4.73

134

For circular cuts using drills, 50% of the cutting

costs is increased for grinding and shaping. The costs of

various size screw type pumps, used for pumping solution

from the absorber to the generator are correlated as :

C, - 504.59 PW°*^ (4.74 Isp

Since there is only one moving part in the absorption

cycle, that is, the solution pump, very little maintenance

cost will be incurred [70]. Thus, assuming 10% of the

initial cost of the system-components against depreciation,

repair and incidental charges, using present worth method

and spreading over a life of 15 years with 10% interest

rate, the total cost of each component in terms of their

capital costs may be expressed as :

C = 0.1224 C, (4.75) d JLa

C^ = 0 . 1 2 2 4 C^^ ( 4 . 7 6 )

C^ = 0 . 1 2 2 4 C^^ ( 4 . 7 7 )

Cg = 0 . 1 2 2 4 C^g ( 4 . 7 8 )

%h = 0 - 1 2 2 4 C^p^ ( 4 . 7 9 )

%c = ° - 1 2 2 4 C^p^ ( 4 . 8 0 )

A s s u m i n g 20% of t h e i n i t i a l c o s t o f s c r e w pump a s t h e

135

running cost per year, the total cost of the pump, spread

over a life of 15 years, using present worth method is given

by

C = 0.178226 C, (4.81) sp Isp

It is to be noted that the cost of the burner is included in

the cost of generator for the LPG and biogas powered

systems, respectively.

Assuming that the cost of fresh solution, for

re-charing the absorption systems during accidental

leakages, will be nearly 20% of its initial cost at the time

of installing the system; using present worth method the

total cost of solution per annum will be expressed as :

C = 0.178226 C, (4.82) sn Isn

The cost of the solution C, includes the cost of the Isn

absorbent as well as the refrigerant depending upon their

masses according to the concentrations in the absorber.

Assuming that, about 10% of the initial cost of the

system is required in installing, fitting and charging, with

20% overhead charges on the absorber, condenser, evaporator,

generator, precooler and preheater for the manufacturers

profit and taxes, etc., the total cost of the absorption

system will be given as :

136

Csy = 1-1 tl-2 ( W ^ e ^ W ' S c ^ •*• • ' S n ^ ' ' ^

The total costs of the system including their operating cost

will be

C ^ = C + C + C syt sy w energy (4.84)

The cost of energy may be either C , C, or C, depending upon

the source of energy used.

The low pressure-side-component costs of evaporator

plus absorber,

C = C + C ae a e (4.85)

and the high pressure side costs of the condenser plus

evaporator,

C = C + C eg c g

4.86

Similarly, the costs of energy plus cooling water may be

expressed as :

bw b w

C-, = C, + C Iw 1 w

(4.87)

(4.88)

and

C = C + C sw s w 4.89

137

In the above discussion for the cost of absorption

systems, only general methods and equations have been

presented. For specific applications, slight modifications

have been done depending upon the requirement.

5. RESULTS AND DISCUSSION

5.1 Economic analyses of the energy sources (Model I)

The generator temperature was varied for a set of

condensing and the evaporator temperatures and the

corresponding values of COP, Q, ,Q-,, and Q were computed.

In this model, the values of Q, , Q,, and Q^ are assumed to

vary with the generator temperature t . The average y

temperatures of the products of combustion for biogas and

LPG is assumed to be T = (373.15 + t ) and the temperature p g

of the hot fluid from the solar collectors is t = (t + 5 ) . o g

The ambient temperature is taken to be 10°C lower than the

temperature of the condensing fluids (t^). Hence, the volume

of biogas, volume of LPG and the areas of solar collectors

per TR were obtained for each value of the generator

temperature and correspondingly, the costs of biogas, LPG

and solar collectors were calculated. The analyses has been

carried out for the condensing temperatures, t = t = t 3. C V

t^ = 25, 30, 35, 40 and 45°C, and repeated for the

evaporator temperatures from -25 to 15°C, in case of the

three ammonia absorption cycles, and from 2.5 to 15°C, in

case of the LiBr-H 0 cycle.

139

Variation in the components coefficient of performance

The variation in performance of the absorber (ACP),

condenser (CCP), evaporator (COP) and absober plus condenser

(HCP) with t for t = 5°C, t^ = 30°C and t^^ = 20°C are

shown graphically in Fig. 5.1 for the four absorption

cycles. It has been observed from the figure that at lower

generator temperatures, the coefficient of performance

increase rapidly with a little increase in t and then ^ ^ g

become almost constant, especially for the fluids using

solid absorbents. But, the values of COP at very high

generator temperatures,start decreasing. On the other hand^

for the H_0-NH^mixture, the performance curves increase to a

maximum value and then steaply decrease to very low value

even with a little increase in t . g

The performance curves for H 0-NH- system, presented by

the same author in refs [ 67] , are some-what different from

those plotted in the Fig. 5.1. This is because, the study in

refs [67] was based on the assumption that pure-ammonia left

the generator; and hence, analysis on the

distillation column was neglected for simplicity.

The respective plots of ACP, CCP, COP, and HCP, for

are seen LiNO^-NH^ and NaSCN-NH^ solutions/ to be very close and

140

(b 0-9 u c o i 0-8 o

CL

07

0-6

ABSORBER ,ACP

• — • LI Br -H2O L)N03-NHj

^ ^-NaSCN-NhT-j H9O - NH-

CONDENSER,CCP

2 ^ - - - J . • •— • -»

/

0;

o u

Qj 0-8 c o CL

o 07

0-6

0-5

EVAPORATOR COP (Cooling)

17

]-5

1-3

M

ABSORBER * CONDENSER (Heating) ^with Q^

,_•- .—-•2 without Op /

50 60 70 80 90 tg ; c 50 60 70 80 90

h g . 5.1 Variation in components COP with generator temperature (tg) for different absorption system5(te = 5 t . t a m - 2 0 T , tar:tc-tr = tf =30°C

141

similar to each other, except that the NaSCN-NH^ cycle

operates v\rell at higher generator temperatures.

The performance of the absorption system-components are

found to be highest for the LiBr-H20 solution and lowest for

the H„0-NH^ solution. The deviation in the values of ACP for

the LiBr system from those for the LiNO^ and NaSCN systems

are seen to be more as compared to the deviations in the

values of CCP. This may be because large amount of heat is

being released in the absorber of the LiBr-H„0 cycle as

compared to those released by its own condenser or by the

absorber and condenser in the LiNO-, and NaSCN ammonia

cycles.

Variation in the area of solar collectors and volume flow

rates of biogas and LPG.

The Variation in A , V, , and V, with the generator

temperature, at fixed values of the ambient, absorber,

condenser and rectifier temperatures, are shown in Figs.

(5.2) and (5.3). The plots of A^, V , V for the four

absorption cycles operating in the air-conditioning mode are

shown in the Fig. (5.2) while those for the three ammonia

cycles, applicable in the refrigeration mode, are shown in

Fig. (5.3). It can be seen that these plots show minima in

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142

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144

the areas of the solar collectors and the volume flow rates

of biogas [66] and LPG at certain values of t , which will y

be chosen to be the optimum generator temperatures (t ) in

the Model I. The solar collectors,for operations of the

absorption cycles at t = -15 °C, are evacuated-tubular type

the areas of which come out to be less than those of the

ordinary flat plate collectors; this is because of very high

collection efficiencies in them, although the former is

costlier than the latter. Because of sharp variations in

the COP of the H_0-NH-, cycles, as shown in Fig. 5.1, large

variations in A , V, and V, are experienced with a little

change in the value of t . And hence, the optimum values of t in the H„0-NH- cycle,will be almost same while g 2 2 ) ^

operating by using any one of the three sources of energy.

The plots of A in Fig. (5.2), show that the minimum size

of the flat-solar collectors, required for supplying heat to

the absorption cycles,will be smallest in case of LiBr-H„0

cycle and largest in the H^O-NH-, cycle. The minimum

collector area for NaSCN-NH- cycle is found to be more than

the area required in the LiNO^-NH^ cycle. In the

refrigeration mode, the area required by H„0-NH-, cycle is

very high as compared to those required in the NaSCN and

LiNO^ systems. These variations can be clearly seen in the

Fig. (5,3). The volume flow rates of biogas, exhibited in

the Fig. (5.2), show that the LiBr-H„0 cycle require lowest

145

volume of biogas, as compared to the H2O-NH2 cycle where

largest amount of biogas [66] is needed. The minimum

volume of biogas required in the NaSCN system is found to be

slightly more than that is needed to operate the LiNO^

system. Also it has been seen that the H^O-NH^ cycle would

require nearly double the amount of biogas as in the NaSCN

and LiNO^ systems. The volume flow rates of LPG plotted for

the different absorption cycles, are seen to be almost

similar in nature to those plotted for the biogas systems,

as is evident from the Figs. (5.2) and (5.3).

Variation in the costs of the energy sources

The variation in the costs of solar collectors, biogas

and LPG with the generator temperature are shown in Figs

(5.4) and (5.5) for operations at t = 5°C and -10°C,

respectively. Also, these plots, same as those seen for A ,

V, , and V, , show minima, corresponding to which the optimum

generator temperatures will be selected. The plots for the

different evaporation conditions of the absorption cycles,

show that the minimum costs of the solar collectors, for the

purpose of air-conditioning spaces, would be nearly twice

the costs of the LPG required to operate the absorption

systems at the same operating conditions; the costs of LPG

being about 32% more than the costs of biogas. In the

10 -5 -

9-5

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J 1 1 L

1/1

Q-^ 10.5h

AO A5 50 55 60 65

L i N O o - NH.

cn ^5 \_ dj c

UJ

o

'3

s

o A

3

\ »>- • — • - •

J 1 I L

9.0

8.0L

LiBr- H2O — Solar - - - LPG •—•Blogas

146

3-0

3-0

2-0

• \

1 1 1 . 1 1 .

30 AO 50 60 70 75

NaSCN - NH

11

10 i

A -

-X-

\ .

J L

• • K - « — • — '

AO A5 50 55 60 65 A5 50 55 60 65 70 tg,C

Fig.5-4Variation in C|.,,C| , C^^with generator

temperature (t g ) at tam-l 5 "c , te = 5 'c,

c = ^ a - V = 25C for different absorption cycles

147

0 0

a

^ ex 9 ' ^ CD

ro

Ln ^

\ \ \

\ \ \

/ y

^

1 1 1

• \

• \ •

• /

•

1

-

_

-

m

O

O O

LT) CD

O CD

-I in CO

CT) r-o CO

ro en -v^

\ \ 1 1

J. 1 ; /

/ /

/

• — • * "

1

• \ -• 1 1 -• ; • -\ •

/ •

• _ . / -

1 QO tD

1

O

o

o

o

o en oo •*->

o

o ro

o CNl

/ -

/ y^

(T) (Tl CN

L GO (J3 <r

o

o o

o CD

J C

a.

ID c a m a g

I/)

o

u

ID

O D O O > 0;

o

O u

c

spuDsnoLji ui S9adn^ ' A 6 J 9 U 3 | 0 \SOJ

c o

a > LO

ui

o

u >>

E .-a --

JZ

o

II

° T3 c

(b a

^ o a ' E "

o - o o

0; LO

cn "

0; JZ

E a

148

refrigeration mode where the tubular collectors have been

generally employed, the minimum costs of the solar

collectors will be about 2 to 5 times the costs of the LPG.

A comparative study between the minimum costs of the

different energy sources in the various absorption

cycles, through the plots exhibited in Fig. (5.4), show

that the operating costs of LiBr-H 0 cycle are the lowest,

while those of the NaSCN-NH^ cycle are the highest. On the

other hand, at t = -10°C and tj = 35°C, as shown in Fig. ' e f ^

(5.5), the operating costs of the H^O-NH^ cycle appear to be

the highest as compared to LiNO^ and NaSCN ammonia cycles;

the costs for LiNO-NH-, and NaSCN-NH^ cycles being almost the

same.

The percentage increase in the minimum operating costs

of the three ammonia cycles from those of the LiBr-H„0

cycle, and the LiNO^ and NaSCN ammonia cycles from those of

the H20-NH^ cycles, have been obtained and presented in

Table 5.1 for the different condensing temperatures at t =

5"C and t^ = -10°C, respectively. The tabulated values show

that the rate of increase in the operating costs of the

H20-NH^ cycle at t^ = 5°C is becoming more towards the

higher condensing temperatures as compared to those in the

LiNO^ and NaSCN ammonia cycles. At t = -10°C, the

deviations in the operating costs of the LiNO^ and NaSCN

ammonia cycles from those of the H„0-NH^ cycle are found to

149

be negative, except at t^ = 25°C, where the cost of solar

collectors for the NaSCN-NH-. cycle is 22.7% higher than the

cost for the H-O-NH, cycle. This is because of the high

generator temperature required in the NaSCN-NHn cycles,

which will utilize the evacuated tubular collectors, for the

given conditions.

The costs of biogas (C, ) for the LiBr-H^O cycle at t =

5°C, and for the H20-NH^ cycle at t - -10°C have been also

tabulated. The values of L, , and S-,-, in the Table 5.1, are

the percentage increase in the costs of LPG and solar

collectors from those of biogas for the LiBr-H„0 cycle at

5°C and H^O-NH^ cycle at -10°C, respectively.

The costs of biogas, LPG and solar collectors may also

be obtained for other cycles in the table, using the

following relations :

Cost of biogas = (1 + B,/100)C, (5.1)

Cost of LPG = (1 + L-^/100).(l + L-| j /100)Cj (5.2)

Cost of solar collector = (1 + S,/100).(l + S-,-,/100)C,

(5.3)

The variation in the optimum generator temperatures,

v>7ith the absorption cycles, v/ill be the same as have been

obtained corresponding to the minimum collector-area and

volumes of biogas and LPG, because minimum cost of the

energies will correspond to the minimum amount of the

energy.

150

u

8

^

H l

PQ

o\° r3 Z 1

00 Q

• H hJ

• —

0^^ -^

§ (

o\o

O S ' - "

S-l CQ • H J

O ( N - ^

tC o\° 1 ^

• i n ^D r H

• i n CO rH

• CT\ o (N

• r^ IX) 'S"

w ftJ 2

m ^ ^

3 ^ 1

r-•

'^ OJ

in

^ (N

(Ti

• 00 fNJ

on

f N n

•H 2 C#lO

00

U 4-1 o

-P ^

^ ro

fN]

CM

00 00

IT) CM

00

CNl i n OM

<T\ o^

IX) 00

o 00

00 r^ r o

00

- ^ 00

00 00

IX) O i n

00 <Ti IX)

00 oo

O X ^ ON 3 o\o

31 1 •—

pa OM---•H K o\o H I 1 —

00

00

oo

o

rsi 00

i n

• CN 00

00

U oo--~ CO g o'P

2 i

00

O oo-->

J 1 ^

ro

E 1 •—

•H m cr:

CTi r-i

rH

CO rH

O 00

CM

r H

O CM

O 00

LD r H 00

O 00

H •

OO CN

i n •

00 OM

>X5

IX)

i n

00

00

i n 00

<X)

i n

00

IX)

CM

CM

00 00

o

u o O

uT

C/3

r H

r H

X3

u

U 00 ^

oo ro -~

o (N

tn

0 0 T! ^-^ Z o\o 1 ^

1

^ r CM

• 0 0

<x> in

• r~ o VD

1

0 0 0 0 VD

o'P

00 00

00

00 oV

•H Z

r - IX) CO ' ^

CM CNl

in 00 1

<D

1

H in 1

in

CN I

<X) 00 I

o in

in in

r \ i I

i n fNl

o oo

I

CM

I

i n oo

Osl in I

in 00 r^

oo t^ 00 "X) o oo 1

r^ 00

1

CO

1

oo i n 1

cTi CN i n i n

•H ^A

s g 1

o\o • — ^

O^ CN] 1

r--00 1

00 • ^

i

00 i n 1

00 fNj i n 00

1X5 IX)

0 0 CN CNl VD

^ CN 1

r H 00 1

rH

1

i n

1

r~- H CN CO

in

I

oo ^-

o s CNl g a X 1 —

in "* in in

o CTl 0 0 IX)

C7 0 0 0 0 [ ^

^ o o CTl

o

151

Variation in the optimum generator temperatures

The optimum generator temperatures, obtained

corresponding to the minimum costs of the energies, have

been plotted with t^ for the different evaporator

temperatures and the absorption cycles as shown in Figs

(5.6) to (5.8).

The Variation in the values of t_ with t^ are almost go f

linear and increase with the increase in the condensing

temperatures [67]. The t plots for the H2O-NH2 and

LiBr-H~0 cycles are found to be continuous straight lines,

irrespective of the type of energy used. The plots for the

NaSCN-NH^ cycle are also continuous, except when operated

using the solar energy. On the other hand, the t plots for

the LiNO-,-NH^ cycle are discrete lines, especially when

operated by LPG and solar energy. The discrete lines, for

the values of t show that the optimum values represent

straight lines only for small ranges of the condensing

temperatures.

The optimum generator temperatures have been plotted

for a range of evaporator temperatures from t = 2.5 to 15°C

in case of LiBr-H^O cycle and from -25 to 15°C in case of

the three ammonia cycles. It has been observed that the

values of t increase with the decrease in the evaporator

temperatures. With the change in evaporator temperatures,

the t lines represent constant slopes. For the evaporation

130

^ 70 O ^ 50-E 0 30

o a 170

fc 150h cn

E 130

CL O

10

90

70

50

30

H2O - NH3

=-25/ ?* -! 5 130

J I L

L1NO3- NH3

152

50-

30

te = - 2 5 X ^ 7 0

J L J L

50-

30

L i B r - H 2 O

Crys ta l l i za t i on ranqe

J I I 1 — : , — L e =- V -20 C

NaSCN-NH-^ / /

20 25 30 35 AO A5 20 25 30 35 AO A5

Fig.5-5 Variation in the optimum generator temperatures (tgo ) with condensing temperature(t j) for different values of te in the various absorption cycles operated using biogas energy

.u

o

in

"a

CL

E

H 2O - NH3 L i B r - H9O 153

Crys ta l l i za t i on range

5 /7.5*C

-J 1 1 1 l _

.1NO3- NH3 1> =-25 C

,^-20 170

N G S C N - N H T <e / - 2 5 C

' -20 ^ / /

'' ^ '' -in / / / /

'' '' ' / -5 / / ' y /

/ ' / . / / / / / / ^

20 25 30 35 ^0 50 t ^ . c 20 25 30 35 AO A5

Fig. 5.7 Variation in the optimum generator temperatures ( tgo) with condensing temperatures (t | ) for different values of tein thevarious absorption cycles operated using LPG

154

CL

E

O B \_

C <b

E

O

130

no

90

70

50

30

150

130

no

90

70

50

30

H 2O - NH3

te =-25c/3l5 130

1 I I 1 L 30

L1NO3-NH3 W - 2 5C

10

L i 3 r - H 2 0

C r y s t a l l i z a t i o n range

te^ZSC

te =-25-C / ' / - 2 0

N Q S C N -NH3 / / ,,i5

J L 20 25 30 35 AO A5 20 25 30 35 40 45

t f C Fig.5-8 Variation in the optimum generator temp-

eratures(tgo) with condensing temperature(t|) for different values of t^ in the various absorption cycles operated by solar energy

155

conditions of about 10°C which correspond to the

air-conditioning mode, the optimum generator temperatures

are found to be around 90-110°C for hot climatic conditions;

which may go down even upto 70 to 80°C for moderate climates

of around 25 to 30°C. However, for applications,

corresponding to the refrigeration modes, generator

temperatures around 120-130°C are required. For low

evaporator and high condensing temperatures, the solutions

using solid absorbents, crystallize very often at the exit

of the preheater where the temperature of the solution is

expected to reach the temperature in the absorber; the

concentration of the absorbents remaining equal to those in

the generator. The crystallization ranges are shown in the

Figs(5.6) to (5.8) by dashed lines. The figures show that

the problem of crystallization arise mostly in case of the

NaSCN-NH, solution and hence its operation below t = -10"C

is very difficult. Also the LiBr-H-0 solution crystallizes

at lov; evaporation and high condensing temperatures, hence

precautions should be taken to avoid such problems.

At high evaporator temperatures, that is above 0°C, the

values of t in the LiBr, LiNO^ and H„0-NH-, cycles ar? go 3 2 3 - '

found to be close to each other, for low condensinc

temperatures (t^); but for high values of t^ the t s ii t - r go

the H„0-NH^ cycle are lower than those in the LiBr-H„0 am

LiNO^-NH^ cycles. On the other hand, at low evaporator

156

temperatures for refrigeration purpose, the values of t in

the H^O-NH-, cycle are found to be the lowest. The lowest

values of t in case of the H-o-NH-, cycle is contradicting go 2. i -^

the results plotted by the same author in refs [67]. This is

because, the optimum values of COP for the H„0-NH^ cycle

appear at lower values of t (refer Fig. 5.1) as a result of

the extra load Q^ on the generator, which had been in

neglected/refs [67] for simplicity. The optimum generator

temperatures in the NaSCN-NH^ cycles are found to be the

highest for the entire range of the evaporator temperature.

The rate of change in the slope of the t lines with ^ ' go

t^ appear to be the highest in case of NaSCN-NH^ solution

and lowest in the H„0-NH-, cycles; for the cycles using

biogas and LPG,the slope of the t lines in the LiNOo-NH-, ^ ' ^ go 3 3

are little higher than those of the LiBr-H„0 cycle. The

slopes of the solar operated LiNO^, LiBr and H«0-NH-, cycles,

are almost equal.

The optimum generator temperatures , plotted for the

different sources of energies in Figs (5.6) to (5.8), are

found to be smallest in case of the solar operated systems

and highest for the LPG systems.

Variation in the optimum values of COP and HCP

The optimum values of COP and HCP, obtained

157

corresponding to t for the four absorption cycles ' = go

operating at different condensing temperatures and using the

various sources of energies have been exhibited graphically

with t , as shown in Figs (5.9) to (5.11). It is seen that e

, the optimum values of COP and HCP increase with the

evaporator temperature. The plots have been also represented

by Siddiqui [67], but as straight lines. Because there [67],

the optimum values had been split in two parts and were

plotted separately for the air-conditioning and

refrigeration modes. The COP and HCP plots are seen to have

generally continuous variations, except in case of the solar

operated-LiNO^, NaSCN and LiBr systems, the plots for HCP

appear as discrete lines for some values of the

condensing temperatures, refer Fig.(5.11).

It is obvious from the above figures that the optimum

performances, COP and HCP, are highest for the LiBr-H~0

solution and lowest for the H-O-NH-,, except at t- = 25 and

30°C, where the COP goes beyond those of the LiNO^ and NaSCN

ammonia cycles. The COP s of LiNO^-NH^ and NaSCN-NH^ are

1 ^ ,- • • . . • w i t h almost same having minor variations/t , as is evident from

the Figs (5.9) to (5.11).

It has been also observed that the performance of the

absorption cycles decrease with the increase in the

condensing temperatures. The optimum values of COP and HCP,

158

Q_ U X

• o c o a. o

e I O

2.0[-

18

1-6

1-A

1-2

1-0

as 06

04

0-2

0-0

t, r 25 C

_1 1 I 1 L

1-8

16

1-A

1-2

10

0-8

0-6

OA

0-2

o-n

1, r 3 5 C

^ ^ ^ . 2

•-4=:*==*'*^"''^'^ ''^

^ . 1

1 1 1 1 1

1) = 30C . _ . LiBr - H2O — LiN03-NH3 .2 o-o- NaSCN-NH^.^ ' ' ' ,2 -- - H2O-NH3*

I ' I 1 L.

\t ; A O C

J \ I L

Fig

-30-20 -10 0 10 20 . -30-20-10 0 10 20

5-9 Variation in the optimum values of ZOP and HCP with t^for different condensing temperatures(tf ) in various absorption cycles operated using biogas energy

169

a. X •o c o a. O

E D E "5. o

1-8

15

lA

12

10

0-8

ae

0-2

00

-.•'

J I I I L

1-8

1-6

VA

1-2

1-0

0-8

0-6

a4 0-2

00

-

-

- 2^

2

-

-

-

<1

•

^ "

1 ^

1

y y

r _ _ , - ' " ' '

' 1

• r35 C

^ ^ ^ / ' ^ •

/ /

•

1

• - - •

•

-1 . i .1

. - . LiBr - H2O — LiN03-NH3

o-o^4aSCN-NH3 - -..H2O-NH3 .--•''

^ j s ^ a c r /

^^J**^^ / _ - ^ C ^ ^ ^ /

•^^^^^ / - O " ^ ^

/ / •

/ • •

- ^ •

^.^ . - • ^

~ ^ ^ y " * ' ' ^ * ^ ^ ^ .^-—-0-'^*'^ /

-0—-o-^ ^ 1 • '

_ •

^ ^ y

1 - . 1 — J J

M --

.^•^ 2,

^ 2 ^

( .--• '

^ ^ 1

1

30 C

-30-20 -10 0 10 20

t, = 60 C

-30 -io -10 6 10 20 te,C

Fig. 5-10 Variation in the optimum values of COP and HCP with te for different condensing temperatures(tf) in various absorption cycle operated using LPG

^ • ^ ' 1-COP

l . & i - 2 - H C P

t , c 2 5 C

.•2 . .^ /2

tf = 30 C , _ . LiBr - HoO

LiN03-NH3 yl o-<> N Q S C N - N H : ^ / ' 2

H20-NH3*^ y ?

160

-30-20-10 0 10 20 O-30-20-10 0 10 20 te,C

Fig. 5-11 Variation in the optimum values of COP and HCP with te tor different condensing temperatures (t |) in various absorption cycles operated using solar energy

161

obtained for the biogas and LPG-powered systems, are almost

same. But, the COPs and the HCPs for the solar operated

systems are comparatively lower than those with the other

sources of energies. This is because, at low generator

temperatures, which is obviously in case of the solar

operated systems, the optimum COPs and HCPs fall on the

increasing slopes of the performance curves shown in the

Fig. (5.1), instead of the flat regions.

The rate of increase in the optimum values of COP and

HCP is highest in case of the H„0-NH-, cycle, and show very

poor performance at subfreezing conditions.

5.2 Economic analyses of energy source plus cooling water

(Model II)

The generator and condensing temperatures were varied

keeping the mass flow ratio (MR) and the evaporator

temperature (t ) fixed, for different temperatures of the

cooling water. The study has been done for t . = 2 0 , 25 and ^ ^ wi

30°C and repeated for the evaporator temperatures from -15

to 15°C, in case of the three ammonia absorption cycles, and

from 2.5 to 15°C, in case of the LiBr-HpO cycle. The

analysis was extended for the various absorption cycles

using different sources of energies and repeated for MR = 2

to 24 kg of solution per kg of refrigerant for obtaining the

optimum mass t\o\^ ratios (MR). In this model, the values

162

of Q , Q, , and Q-, were calculated, as had been done in the s b 1

Model I, by assuming them to be temperature dependent with

t , and correspondingly the solar collector-areas and volume

flow rates of biogas and LPG were obtained. Similarly, the

volume flow rates of cooling water in the absorber,

condenser and rectifier were calculated using the equation

(4.38) with Z T = 3K, the inlet water temperature being w

t . in each component. wi '^

Variation in the costs of the energy-sources and cooling

water

of water The costs/(C ), biogas (C. ), LPG (C,), biogas plus

water water (C, ) and LPG plus/ (C, ) have been plotted with the

bw '^ ' Iw

condensing temperature (t^) for the various absorption

cycles at t = 10°C, t . = 25°C and MR = 8.0, and shown in - e ' wi

the Fig. (5.12).

The increase in the values of C, and C, and the b 1

subsequent decrease in C with t^, show minima when the two

costs are added. Thus, it can be seen that the values of

C, and C, decrease with t^ upto to certain temperature and

reach to a minimum cost corresponding to which the optimum

condensing temperatures were selected; the costs, then

increase gradually with the further increase in t^.

The cost of the solar collectors and hence, C have sw

not been plotted in the Fig.(5.12), because the slopes of

163

\f) o

>. U~)

z. u 0

E 0;

>-1/)

m X 2

O 2 _ j

E 1 /

'i/i

>-

I 2

O

X

E 1/1

>-in

o X

m

1 cn ID

s N

J

OO uS

1 CO i n

i y

1

O <x>

•

1

r;-LT)

" • - - .

1 cn iT)

5 u

\ \

1

O

<r

1^

•*>

1 ^ 1 r - CM i n ^

u

1 > 1

I?) i n

u

1 A 1 ' -V^ '

°9 1 i n ^

N

/ f

1 » 1 .

CD fT> <r <»•

* " • " - .

1 .— i n

t

o i n

-

1

Q i n

. p ^ i n

•

•

5 J3 u V

•N >

k. 1

i n

- j -

_)

• ^ **

1 , ^ cn <

\ y /

cn^ -J-

1 CM

- j

1.

v j

.—•

<r

I <r v j

• •

^^

1 r~> <t

1 KD v j

1 op 00

1

i n

^

J

u

J " - .

' ^ > ^ ' . CO op <r rS

" • ^ 1

f^ cn

^ o

• ^ • - . .

i /< 1 (NJ CO

•^ cn

J3

I" '

v j <^

• f • •

1

>-oi

/ —k/ —'—

CO ro

1 r cn

• - . .

1

o ro

\ \

1 csi rb

• 1 -^

t o CO

^.

1 J

<X) CO

~~»

1 -up cn

• 1 . V

rn

1

t > O

1 t ^ O

1

c~-

6

1

i n o

1 <X» O

1 i n CD

1 tX)

o

O - J

U3 cn

CM cn CO (~o

i n O

-J _

i n

CO m

cn

o

ci

^ o _

• CO . « -cn -^

cn

O cn

CSJ

i n O

U /

1

v:r o

CM

00 cn

cn

o rn CD

-J a

1 _ i •D C a \_

1/1

Q.

a cn o

O

\I\ O cn o .5__ I—

o

\S\

o

o-sz .•—' c c o g

'-r^ CL

Q

o c

. *—• "D

^Q II CO

| i

S''^ LD

<L) CSI

D II

o •> ^ -^ <Li

E.^ ^ o cn "

c 0; ^ •D O C

8 ^ dj '^

JZ O - > - ' l _

dJ

jz Q-t : o

! ^ 03 B o ^ ^ ^

spuDsnoq] ui Sdd6n}~{'(^\j^j\^'^;)'^j)s\so-j LP cn

164

C are found to be very high even at very low condensing s temperatures, due to which the minima for C^^ generally

appear at t^ = t . + 5°C.

'-'- r wi

The plots for the different absorption cycles, in the

Fig. (5.12), show that the minimum operating costs Cj^^ and C, are highest for the H„0-NH^ solution and lowest for the Iw ^ 2. 6

LiBr-H20; the costs for the NaSCN-NH^ being higher than

those for the LiNO^-NH,.

It is to be remembered that in this model the generator

temperature also varies along with the condensing

temperatures, but the various costs have been plotted only

with respect to t^. The corresponding values of the optimum

generator temperatures have been plotted for a wide range of

operating conditions and shall be discussed later on.

Optimization on the basis of economic analysis,

especially where two variables and hence, costs of two

different sources are involved, will lead to the optimum

points which may differ from place to place depending upon

the methods of cost estimation, availability and market

standards. Therefore, in order to have the maximum choice

for the selection of the optimum parameters at different

places, a cost and performance study was carried out at a

condition of equal flow rates of biogas and cooling water in

the generator and the absorber-condenser-and-rectifier unit,

respectively.

165

Figure 5.13 shows variation in C^^, COP, V ^ and W with

the condensing temperature (t^) at t^ = 5°C and 15°C for the

LiBr-H„0 cycle and, t-,= 5°C and -15°C for the three ammonia

cycles. It can be seen from the Fig. (5.13), that the values

of C, and COP corresponding to the points where Vj and W

curves intersect (refer to equal V, and W) and at the

minimum values of C, , are very close to each other. This bw' -^

suggest that the equal values of V, and W may also be one of

criteria for selecting the operating parameters in the

absorption cycles. The percentage deviation of C, and COP

at equal y, and W from those at the minimum values of C,

are given in Table 5.2.

From Table 5.2, it can be seen that the performance of

the systems and their operating costs are nearly same with

minor deviations, especially in the LiBr^ LiNO-, and NaSCN

systems. In case of H-O-NH^ cycle, the deviations are more

and hence, the operating conditions corresponding to

C, . will be more suitable at places where costs similar bw,min ^

to those estimatedin the present study, exist.

Variations in the operating costs with MR

The minimum operating costs of the four absorption

systems, obtained at the optimum values of t^, and the

operating costs corresponding to the equal V, and W, have

been plotted with the mass flow ratio (MR) for biogas, LPG

and solar operated systems, and presented in Figs (5.14) to

(H2O- NH3 Cycle) /^ bw

166

32 34 36 38 AO

5 6 3 -

(LiN03 - NH3 Cycle)

l o z 5 C

A.70 Z Z H U O A 36 38 AO 42 44

3-86-

3-82-

3-65-

3-60-

38 40 42 44 46

(NaSCN -NH3Cycle) 1 - te : B'C

2 - l e r - 1 5 'C

5-65

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t f , C 34 36 38 40 42

Fig-5.13 Variation in C^ , .COP,Vb and W with the condensing temperature t^ for different absorption cycles and evaporator temperatures indicaung the deviations at equal V^and W(«) fro. Ti the optimum(x)conditions (MR^8.0 , tw i : :30r )

167

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168

(5.29). All the curves, drawn for the different values of

t and t ., show a minima thus, giving optimum values of the e v/i

mass flow ratios (MR ).

The optimum values of MR in case of biogas and LPG

powered LiBr-H^O cycles, shown through the Figs (5,14) to

(5.16) are very prominent at high evaporator and low cooling

water temperatures. At lower values of t and high values of

t . , the crystallization puts a limit on the efficiency and

hence, instead of taking MR , the flow ratios are chosen ^ o

just near the crystallization line in the working range

[68]. However, in the solar operated LiBr-H20 system (Fig.

5.17) the values of MR are found to be higher than those in

o

the LPG and LiBr-H„0 cycle. The crystallization limit is

•r

shown by a staight line which is obtained using the equation (2.91).

The values of MR for the HpO-NH^ cycles, as can be

seen in the Figs (5.18) to (5.21) are found to increase with

the decrease in the evaporator temperatures. Having no any

problem of freezing in the selected ranges of study, the

H^O-NH^ cycles should be operated at MR for a better

economy. At low evaporator temperatures where the generator

temperatures required are high and hence, evacuated-solar

collectors are to be used, the optimum values of MR in such

cases, are lower than those operated by using flat plate

ordinary collectors. For instance, in Fig. (5.21) at t . = ^ wi

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30°C, the value of MR at t = -5°C is lower than that at o e

t = 0°C; which is only because at 0°C the value of t is e ^ g

low and hence, flate plate collectors are required.

In the LiNO-,-NH^ cycle, the values of MR obtained from

the Figs (5,22) to (5.24),- for the biogas and LPG powered

systems are comparatively lower than those for the LiBr-H„0

and H^O-NHT cycles. These optimum values (MR ) are found to 2 3 o

be almost same for all the evaporator temperatures shown m

the figures. The crytallization lines drawn using the y

respective equations given in Appendix Al appear at v^y low

values of MR, which are much below the optimum values (MR ).

In solar operated LiNO-, cycle, the values of MR shown in

Fig.(5.25), follow the same trend as in the case of H„0-NHo

cycle, that is, they increase with the decrease in t . And at t . = 25°C, the MR for t = -10 to 15°C, are higher than wi o e / y

that for t = -15°C. Similarly, at t . = 30°C, the MR for e - wi o

t = 0 to 15"C are higher than those for t = -5 to -15"C. e ^ e

This is only because low cost ordinary collectors are

employed for the lov/ generator temperatures, In case of

NaSCN-NH-, cycles using biogas and LPG , the trend for the

values of MR and the problem of crystallization are similar

to those of the biogas and LPG operated LiBr-H^O systems as

can be seen by comparing the plots in the Figs (5.26) to

(5,28) by those in the Figs (5,14) to (5.16). The

crystallization lines shown in the Figs (5.26) to (5.28) are

186

drawn using the concentration equations given for the

NaSCN-NH^ solution in Appendix Al, The optimum values of MR

for the solar powered-NaSCN shown in Fig. f5.29), are

similar to those obtained for the solar assisted LiNO^ and

H^O-NH, cycles. The crystallization ranges for the curves

plotted in the Fig. '5.29), are shown by dashed lines so as

to make the presentation clear.

In the above analyses for the values of MR, shown in

Figs (5.15) to (5.29), a comparative study between the

various sources of energy show that the solar powered

I systems are costier than the biogas and LPG operated

systems, the biogas systems being the cheapest.

A comparative study between the costs of the absorption

systems show that for the air conditioning mode LiBr-H„0

system would be most economical and for the refrigeration

mode, among the three ammonia cycles, LiNO-, and NaSCN

systems would be cheaper than the HpO-NH^ cycle; with the

limit that NaSCN-NH^ solution creates severe problems of

crystallization. The comparison has been also done by

studying the deviation in the costs from one another. The

percentage increase in the minimum operating costs of the

three ammonia cycles, working in the air-conditioning mode

from those of the LiBr-H„0 cycle, and the decrease in the

costs of LiNO^ and NaSCN cycles from those of the H^O-NH-,

cycle have been obtained for t = 5°C and -10°C. The same

187

has been presented in Table 5.3 for the three types of

enerqies. At t = 5°C the rate of increase in the operating ^ e

costs of the H2O-NH cycle with the cooling water

temperatures (t . ) is higher than those of the LiNO^ and

NaSCN systems. However, the deviation in the costs of LiNO^

and NaSCN ammonia cycles from the LiBr-H20 cycle are nearly

same. Further, at t = -10°C, the decrease in the operating

costs of the LiNO^ and NaSCN ammonia cycles from those of

the H^O-NH^ cycle, are almost same for the biogas and LPG

systems; with some variations for the solar powered systems.

The results obtained in the Model I (Table 5.1) were almost

similar to the results given in the Table 5.3 are given in

in the form of C , B, , Vi T , VT , L, , , L, , S, , , and S, so that b - i - l-L J- J-J- -L -L-L J-

equations (5.1) to (5.3) may be used for calculating the

operating costs of the other cycles, under study, because

they are presented as a percentage of either LiBr-H^O or

H20-NH^ cycle.

Variation in the optimum values of COP with MR

The optimum values of COP, obtained corresponding to

the minimum costs: C, , C, , and C and at equal volumes of bw Iw sw ^

V and W, for fixed evaporator and cooling-water

temperatures and mass flow ratios, have been presented in

Fig. (5.30) with MR for t = 5°C and -15°C at t . = 20°C. it e Wl

u o U-) II

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189

OP

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0-8

0-6

O.A

0-2

0-0

, _ . L iBr -H2O L1NO3-NH3

•o—oNaSCN - NH3 H2O - NH3

J I 1 1 1 L

0-8

0-6

0-A

0-2

0 0

Solar/System

• • • - . 1

/ ^ ^ ^ ' ^ ^

- 2

Bioyus/ System

at equal V^ and W

- at te - 5 ' C

at U

0-6

ae

OA

0-2 - /

-15 c

• ' - — - . |

0-0 I , ,1 I 1 I L.

0-8

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0-A

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J L J i L... 0-0

LPG /System

J 1 1 1 1 L.

0 A 8 12 16 20 2A 0 A 8 12 16 202A

MR,kg of solution/kg of refrigerant Fig.5'30 Variation in the optimum performance of tour

absorption cycles with mass flow ratio(MR) forte = 5'Cond te==15°Cat t ^ i = 20°C

190

is seen that the COP curves rise towards higher values with

the increase in MR, reach to a maxima and then gradually

decrease with the further increase in MR. Also, it is found

that the COP of the LiBr-H20 cycle is the highest while for

the H2O-NH2 cycle is the lowest. The COPs of LiNO^ and NaSCN

ammonia cycles are almost the same. In the cycles using

solid absorbents, the maximum values of COP fall around MR =

6 to 10, while those for the H„0-NH-. solution, are around MR

= 10 to 16. For the H^O-NH^ cycle, it has been already seen

through the Figs (5.18) to (5.21), that the optimum values

of MR corresponding to the minimum operating costs and equal

V, and W/ are around 10 to 16 ' kg of solution/kg of

refrigerant. For the solutions using solid absorbents, the

optimum values of MR are in the range of 6 to 10 kg of

solution/kg of refrigerant, except for the solar operated

systems where the optimum flow ratios (MR) are comparatively

higher.

Variation in the generator temperatures (t _)_

The optimum values of t obtained for the minimum go

operating costs and at equal V, and W corresponding to the

optimum mass ratios (MR), have been exhibited in Figs (5.31)

to (5.34) for the different values of t and t .. The t s e wi go

show straight lines with t . and have constant slopes with

changes in the evaporator temperature.

(b i _

O \_

CL E

o o \—

c

no

90

70

50

30

E I 130 Q.

O 110

90

70

50

30

H2O - NH3

no

90

70

50

30

LiBr - HoO 191

15 20 25 30 15 20 25 30

NaSCN - NH3

15 20 25 30 30

tp ^-15 C

15 20 25 30

^wi' ^ Fig. 5-31 Variation in the optimum generator temperatures

with t^ j tor diffeient values of te in the various absorption cycles operated using biogas(oorre ponding to the minimum operating costs C^yy and MRo)

192

Y 110

^ 90

H20 - NH3

o D cr

70h

50

SC 3 0 15

O

CL

E

O

C

130

110

90

70

50

30

110

90

70

50

30

LiBr - H2O

20 25 30

LiN03- NH3

5 20 25 30

NaSCN- NH3

90h

70h

50

30 15 20 25 30

Wi,C 15 20 25 30

Fig. 5-32 Variation in the optimum generator temperatures with twj for different values of te in the various absorption cycles operated using biogas (corresponding to V5 =\N and MRo )

o

11 0

90

00 7 0

O 50

30 E ^

i _

o 0 \^ t <b CJi

E

E - ^ - j

Q. o

130

no

90

70

50-

30

H2O - NH3

10

90

70

50

30

LiBr - H2O 193

LiNO^- NH3 NaSCN - NH3

30 15 20 25 30 15 2 0 25 30

ig. 5-3 3 Variation in the optimum generator temperatures for different values of t^^jin the various absorptic cycles operated using LPG( corresponding to th-

minimum operating costs C|,^and MRo)

L iB r - H2O

tp = 2-5 C

194

'^ 20 25 30 . ,5 20 25 30

Pin CO/ \/ • ^Wi X

Varjatjon in the optimum generator temperatures with tw, for different values of t.in t h r . . . ; . .Z tein the various

(corresponding to Th^Z^r.-""^""^ solar energy u:ng to the minimum operating

absorption cycles operated .corresponding to the costs Cswand MR„)

195

It can be seen in the Figs (5.31) to (5.33) that for

high values of t in the LiNO_, and H^O ammonia cycles

and low values of t in the LiBr-H„0 and NaSCN-NH^ cycles,

operated by using biogas and LPG, the t lines are

discrete. They are not continuous lines for the entire range

of t . . For the solar operated systems, the t lines are wi ' -' go

stly discrete in the LiNO^ and NaSCN ammonia cycles, at mo

low values of t . e

The optimum generator temperatures are found to be the

highest in the LiNO^-NH-, and lowest in the LiBr-H„0 cycle.

The t s in the biogas and LPG powered-NaSCN systems are

higher than the H^O-NH-, using same energy sources. For the

solar operated cycles, the values of t in the NaSCN and

H„0 ammonia cycles are nearly same.

Fiqs (5.31) and (5.32) show that the t s at equal V, ^ go ^ b

and W are lower than those obtained at C, . , except for bw,min '^

the HpO-NH3 sytem where the values of t at equal V, and W

are higher. A comparison between the curves in the Figs

(5.32) and (5.33), show that the values of t at C, go lw,min

are lower than those at equal V, and W, except in case of the LiBr-H„0 cycle where the t s in the LPG system are Z go -

lower at low values of t . but become higher for high values

of t . . For the solar operated systems, shown in Fig.

(5.34), the t s are found to be lov/er than those for the

LPG systems. Further _ more, slope of the t lines in the -' " go

196

solar- systems are lower than those for the biogas, LPG at

equal V, and W, except in case of the H^O-NH^ system where

the slopes are almost similar irrespective of the source of

energy used.

Variation in the optimum values of COP and HCP

The values of COP and HCP obtained corresponding to the

optimum generator temperature (t ) for the minimum

operating costs of the biogas, LPG and solar powered systems

and at equal V, and W, have been shown in Figs (5.35) to

(5.38).

Similar to the result obtained in the Model I for the

various absorption systems, the COP of the LiBr-H„0 cycles

are the highest and very poor for the H„0-NH-, cycles, except

at some high values of t where the COP and HCP for the ^ e

H„0-NHT cycle become better than those of the LiNO-, and

NaSCN-systems; the performances of the LiNO-. and NaSCN

ammonia cycles remaining almost same.

The COP and HCP plots in the Figs (5.35) to (5.38) are

again smooth curves in place of straight lines as had been

presented by the same author [68,69], for the reasons

already discussed in the Model I. But, for certain operating

conditions, the COP and HCP plots do not appear as single

curves, as in cases of the LiNO^ and NaSCN-ammonia cycles

shown in the Figs (5.37) and (5.38).

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The systems performances at C, . and equal V, and W, - '^ bw,mxn ^ b

shown in Figs (5.35) and (5.36) are almost same, except for

the H„0-NH^ cycle which shows better values at C, .

A Comparison betv/een the COPs and HCPs at C, • and ^ lw,min

equal V and W, through the Figs (5,36} and (5.37) show that

the performance of the H„0-NH-. cycle are better v;ith LPG as

a source of heat; the performances of the other systems

being almost same for the two conditions.

Figs (5,37) and (5.38) show that the HCPs for the LPG

powered absorption systems are higher as compared to those

for the solar operated cycles . Hov/ever the COPs for the

solar operated-LiBr, LiNO^ and NaSCN systems are better than

the LPG powered systems especially at lov/ values of t . ; the

performance curves for the H„0-NH-. cycle remaining same for

the tv;o sources of energies.

Optimum condensing temperatures

The optimum condensing temperatures (t_) that were

obtained corresponding to the minimum operating costs,

C, ,c, and C ,min foi the different values of t and t .

in the various absorption cycles are found to have very

little effect due to the change in the evaporator

temperatures; their values obviously increase with t ..

The averaged-optimum values of t^, for the various

202

conditions under study, turns to have the following form of

equation:

t^ = t . + M (5.4)

f ,o wi

Where, the values of the constant M in the equation (5.4)

are tabulated in Table 5.4 for the four absorption cycles using different sources of energy.

Table 5.4 Values of constant M in equation (5.4)

Energy LiBr-HÔ HÔ-NH^ LiNO^-NH^ NaSCN-NH^

Solar 5.0 5.0 5.0 5.0

LPG 9.55 5.5* 7.38 7.7

Biogas 11.6 6.5* 8.7 9.25

Vj = W 9.7 (7.6+ 8.55 (8.5 + 0.083t ) 0.047t )

*At t . = 20°C the values of t_ for t = 10, 12.5 and 15°C wi f e ,

in LPG powered HÔ-NHo cycle are 26.25, 28,75 and 30°C,

respectively; and for the biogas powered H„0-NH^ cycle,

t^ - 28.0, 29.0 and 31.5°C, respectively.

The optimum condensing temperatures at equal V, and W

can also be obtained by substituting equation (4.8) in

(4.38). With PC = 4187KJ/m'^°C and T = 3K, the aquation for w

the optimum values of t^ will become,

t^ ^ = (HCP. Q,/4187) + t . + 3.0 (5.5) f,o b o wi \-^ • I

Thus, knowing the values of HCP and Q, at t one can find o b go

the t^ ^ for the given values of t r , o wi

203

5 - 3 Economic analyses of the absorption systems and their

operating costs (Model III)

Before starting the design of the vapour absorption

system components the concentration of the refrigerant

absorbent solution (X ) with which the absorber is to be a

charged are chosen. This concentration (X ) will depend upon

the temperature of the solution in the absorber (t^) and a

that of the vapour coming from the evaporator (t^). Figure 5.39 shows the variation in the absorber temperatures with

t at different values of X for the four absorption cycles. e a r- -!

These plots are straight lines which are found to shift with

t towards high concentrations of liquid ammonia in the

ammonia cycles, and low concentrations of lithium bromide

salt in the LiBr-H„0 cycle, for a fixed value of t . For a ^ a

fixed evaporator temperature, high values of t lead to low a

values of X in the ammonia cycles, and to high values in

the LiBr-H^O cycle. Such conditions of t and the subsequent ^ Si

value of X , due to X and MR, may lead to the problems of

crystallization, especially at the preheater-exit.

For high coefficient of performance, it is desirable to

have low absorber temperature and high evaporator

temperature. Also, to avoid crystallization at the exit of

the preheater-shell, the concentration (X ) in the LiBr-H„0

system were calculated at (t = t . + 8.0), keeping the a wi

H20-NH3 LiBr - H-7O 204

u

D

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XQ=0-30 0-35 aA 0A5 J 1 ^

57.5

-15-10 -5 0 5 10 15 20

LiN03- NH3 NaSCN- NH3

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\j=0-A aA25a45OA75O-500

0525 ) =0.A 0.- 25 OAS 0- 75 0-500

' " " " " -0 525

5-10-5 0 5 10 15 20

,c Fig.5-39 Variation in the absorber temperature(IQ ) with

the evaporator temperature(te) for different concentrations(Xa)of ammonia in H2 0-NH3,LiN03-NH3 NaSCN-NH3/lithium bromide in LiBr-H2O solutions

20!

value of t in the range 7.5 to 8.5°C. The evaporator

temperatures were chosen to be t = 7.5°C for t ^ = 20°C, and

t = 8.0°C for t . = 25"C and 30"C. In order to have a e wi

similarity in the analysis the values of t and t , chosen

above for the LiBr-H„0 cycle, were assumed to be same also

For the three ammonia cycles operating in the refrigeration

mode, the values of X were calculated at t = t . + 8.0 and

t = -15°C. e

The temperature of the hot water, from the storage tank

connected to the ordinary flat plate collector with one

reflector and two glass covers, entering the generator is

assumed to be not more than 90°C, while the temperature of

some organic fluid, from the storage tank connected to the

tubular collectors, is assumed to be 110°C for the

generators operating in the air-conditioning mode and 145°C

for those operating in the refrigeration mode. The inlet

temperatures of the hot products of biogas and LPG were

chosen to be 250°C, with a temperature drop of 100°C upto

the generator exit. The drops in the hot water temperature,

flowing through the solar powered generators, were fixed to

be 7°C, while the rise in the temperature of the cooling

water through the condenser is taken as 10°C and that in the

absorber equal to 7°C, with a view to keep lower

temperatures in the absorber for better COP. The space to be

air conditioned is assumed to be maintained at 25"C, where

206

the chilled water after taking heat from the space, enters

the evaporator at 22°C and leaves it at 15°C. Similarly, the

temperature of the refrigerated space is assumed to be 0°C..

where the CaCl^ brine enters the evaporator at -3°C and

leaves it at -10°C.

With the above conditions of the fluids flowing in the

various components, the absorber, condenser, evaporator,

generator precooler and preheater were designed for

different values of t and t keeping in mind the heat e c ^ ^

transfer and fluid flow characteristics. The analysis was

repeated for t . = 2 0 , 25 and 30°C with the solution mass ^ wi

flow ratios MR = 4 to 20 kg of solution/kg of refrigerant.

In designing the system components^ the length of each

heat exchanger were taken as 1.0 m and number of tubes and

hence, the diameter of the shell were calculated. The

arrangement of the tubes in the shell were considered to

have triangular pitch, equal to 25% greater than the

diameter of the tube (d ). The number of the 25% cut baffles o

in the shell were calculated iteratively with an allowable

pressure drop of 10%. The tube inside diameters were

selected after iterative checking to allow pressure drop in

the tubes not more than 10%. The pressure drop for the

falling film in the absorber will be negligible hence,

conditions to avoid flooding in the absorber tubes were

considered. The generator height was assumed to be 20% more

207

than that which have been calculated for the given operating

cinditions. This additional height was meant for employing

flat plates to act as separators for the pure refrigerants

and the remaining absorbent-refrigerant solution. Such

separators were used only for the systems using solid

absorbents. For H^O-NH^ systems, where water is the

absorbent a portion of it may also escape along with the

refrigerant ammonia, hence, a complex rectifying and

stripping sections have been designed to ensure pure

refrigerant in the condenser^evaporator circuit. The reflux

condenser, used for supplying liquid mixture in the

distillation column, were designed using the general methods

of designing the condensers for the given conditions of

concentrations, pressure and temperatures in the rectifiers.

The costs of the absorber, condenser, evaporator,

generator, precooler and preheater were calculated after

estimating the amount of material and labour required. The

cost of installing and charging the absorption systems,

costs of the fluids used, insulation and overhead charges

were also estimated along with the costs of the biogas, LPG,

or solar collectors (whichever is used as the heating

source) and the cooling water.

The above costs were estimated by fixing the values of

t ., t , MR, X , X and t . along with the inlet

temperatures of the heating and cold-fluids as have been

208

already discussed. The values of t and t were varied, and - e c

correspondingly the temperatures t and t and the

performances COP and HCP were calculated. In this Model III,

the parameters Q , Q, , Q, have been calculated at fixed

temperatures of the source of energy, taking average of the

inlet and outlet conditions of the heat source and the

refrigerant-absorbent solution, with specified drops in

their temperatures, respectively. Similarly, the volume flow

rates of the cooling water in the absorber, condenser and

rectifiers, hot water in the generator and coolant in the

evaporator were calculated at fixed inlet and outllet

temperatures.

Variation in the costs of the low pressure operating

components

Variations in the costs - C C and C with the a e ae

evaporator temperature (t ) are shown in Figs (5.40) to

(5.43) for the four absorption cycles, using solar heat,

biogas and LPG, operating in the air-conditioning mode; and

in Figs (5.44) to (5.46) for the three ammonia cycles

operating in the refrigeration modes. The values of t . , wi

t^^ and MR are same for all the plots shown in Figs (5.40)

to (5.46); whereas, the values of X and X depend upon the

type of the solution used and their operating temperatures.

The values of t and t in the Figs (5.40) to (5.46), c g

209

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correspond to the optimum condenser temperatures (t ) that

will be discussed later on. The cost of the absorber

decreases with the increase in the evaporator temperature

while the cost of the evaporator subsequently increases, as

can be seen from the Figs (5.40) to (5.46). It is evident

from the temperature-concentration relationships, between

those of the solution and the refrigerant, that for a fixed

value of X , t will increase with t . This has been already a a e ^

shown in the Fig. (5.39).

With the increase in the absorber temperature, the

loq-mean-temperature difference (At ) in the absorber shell •^ m

and tube assembly, will increase so that the rate of heat

transfer (q) per tube in the shell will also increase

subsequently. This leads to lesser number of tubes in the

shell and hence, the size and cost of the absorber will

decrease with the increase in t (or t ).

a e

Similarly, the cost of the evaporator, with the

increase in the values of tg, will increase because the values of A t in the evaporator shell and tube will m decrease with t and hence, the rate of heat transfer oer

e tube in the shell will decrease leading to increase in the

size of evaporator. On summing the costs, C and C which a e

have opposing effects with t , the costs of the absorber

plus evaporator (C ) show minima at certain values of t . ae e

The plots for C have been drawn for the various absorption ae

217

cycles using different sources of energy and shown in the

same figures where C^ and C^ are presented. a. S

The values of C , C and C shown in the Figs (5.44) a e ae

to (5.46) for the three ammonia cycles operating in the

refrigeration mode at t = -10°C show almost similar ^ e

variations when compared v/ith the absorption systems as

have been already discussed, through the Figs (5.41) to

(5.43), for operations in the air-conditioning mode.

The curves exhibited in the Figs (5.40) to (5.43), for

the different absorption cycles operating at t , = 15°C,

show that very high costs are involved in the H„0-NH^

cycles. However, the cost of the evaporators, in the cycles

using ammonia as refrigerant, are nearly same for the

H^O-NH^ and the LiNO^-NH^ solutions but are slightly low for

the NaSCN-NH, solution. This may be because the values of

optimum evaporator and absorber temperatures corresponding

to the minimum values of C are lower for the NaSCN-NH^.

ae 3

A comparison between the LiNO-, and NaSCN systems show

that the costs C , C and C are higher in case of the a e ae ^

LiNO-NH system.

Variation in the costs of the high pressure operating

components

The values of C^, C and C are plotted with t in c g eg ' c

218

Figs (5.47) to (5.50) for the four absorption cycles

operating in the air conditioning mode at t_. = t = 25°C,

MR = 8.0 and t , = 15°C.

el

It can be seen from the figures that the cost of the

condenser decreases with t because of increase in the c

values of A t and q for the condenser, and subsequently there will be decrease in its size and costs. On the other hand, the generator cost increases with t . This is because, ^ c

at fixed value of X , the solution temperature t increases

with t and hence, the values of A t and q in the generator c m ^ ^

will decrease, leading to the increase in the size and cost

of the generator. It can also be seen that the costs of the

condenser plus generator (C ) for the various absorption ' ^ eg

minima cycles using different sources of energy, show/at certain

values of t , as does C with t . c ae e

A comparative study between the various absorption

cycles for the components operating at the high pressure

(P^ = P )/ that are C^, C and C^ , show that the M2O-NH2

system is very expensive as compared to the other systems.

One of the reasons for the high costs in H-O-NH, system is

that C^ includes the cost of the reflux-condenser and C C g

includes the cost of the distillation column which are

additional equipments in this cycle. The cost of the solar

powered LiNO^ and LiBr systems are found to be almost equal,

but are less than those of the NaSCN-NH^ system. It is

119

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interesting to note that the values of C and C for the

gas operated LiNO^ systems are higher than those for the

LiBr-H„0 system; although the values of C for these systems

are nearly equal.

Variation in the cost of the energy sources

The cost of the energy sources have also been plotted

in Figs (5.40) to (5.46) with t and the Figs (5.47) to

(5.50) with t . c

Th e cost of the sources of energy C , C, and C, are

seen to be decreasing with t . Although, while studying the

variation in the costs of the system components and energy

sources with t or t , the values of t and X remain fixed, e a g g

but the load on the generator slightly decreases with the

increase in the absorber temperature. This is because the

enthalpy of the solutions (H^) entering the generator shell,

which depend upon the enthalpy of the solution coming out

from the absorber-tubes, will increase with the temperature

t_; this reduces the load on the generator (Q ). a ^ ^g

The plots drawn for the costs of the energy sources, in

the Figs (5.47) to (5-50), show that C , C, and C, increase

considerably with the increse in t ; this is only due to

increase in the load Q with t . The nature of C , C, and g g s b

C, with t is just reverse of those plotted with t . 1 c -' " G

224

The values of C are greater than the values of C, and s

C, ; C, being the lowest for the given absorption systems.

Similar results were also obtained in the model I and II.

In the air conditioning mode, the values of C are found to

be highest for the NaSCN system and lowest for the LiNO^

system. And those for the LiBr-H„0 are costlier than the

H^O-NH-, system. The Values of C, and C, are lowest for the 2 3 - ' b 1

LiBr-H„0 and highest for the H„0-NH,, whereas, for the

LiNO^ and NaSCN systems they are almost equal. All these

variations depend upon the generator temperatures. High

values of C ,C, and C, indicate that high generator

temperatures are required in the absorption cycles. In the

refrigeration mode, the values of C are highest for the

H„0-NH^ system due to the high heating loads required in its

generator, v/hile C is the lowest in the LiBr-H„0 system^The

values of C in the NaSCN system are lower than those in the s ^

LiNO-, system. On the other hand, the effect . on the costs of

the biogas and LPG for the various absorption systems are

almost similar to those in the air conditioning mode.

Variation in the costs of the absorption systems

The cost of the absorption systems (C ), using various

sources of energy, which include the cost of the precooler

and preheater along with the costs of the lov/ pressure side

and high pressure side components and their installation

225

charges, have also been plotted v/ith t^ in the Figs (5.40)

to (5.46) and with t in the Figs(5.47) to (5.50). Similar

graphs for the C have been presented separately in Fig.

(5.51) for a different value of t, .. All the curves for C

shov/ minima, both with t^ and t as do C and C e c as eg,

respectively.

It can be seen from the figures, that the values of

C for the biogas pov/ered systems are highest v;hile those

for the solar assisted systems are the lov/est. These

variations in C , although the costs of the energy sources sy -

have not been included in it, are only due to the change in

size of the generator which will obviously depend upon the

heating capacities of the sources of energy. Water having

very high heating capacity will lead to a lov/ sized

generator in the solar operated systems.

A comparative study for the values of C between the

absorption cycles shov; that the liBr-H„0 system will be the

cheapest while the H^O-NH^ system will be very expensive

and may be about 50% more than the costs of the LiNO- and

NaSCN systems.

Variation in the total costs of the system including their

operating costs (C ^) '^ ^ syt

The values of C have also been plotted along v ith

C^^ and C in the Figs (5.40) to (5.46) and v/ith C and 3.G S^ CQ

c o D O

JZ

I/)

<V CL D

cr

O

A5

AA

A3

A2

Al

AO

29

28

27

26

V

30

29

281-

27

19

18

17H

16

H2O NH-

// • / > , ^ ' '

7 8 9 10 11

LiNOo - NH.

I •i

/ / • /

/ / • /

7 8 9 10

27

26

25

2A

18[-

17

16

30

29

28

27

19

18

17

16

\

X. ^ ^

L i B r - H 2 O

Solar

- - - L P G

•—• Biogas

226

h V

/ /

NaSCN - NH3

t

/.'

6 7 8 9 10

Fig. 5.51 Variation in the costs of various absorption systems, designed to operate using different sources of energy , with te at t^ o(twi = t MR .8-0 , tel r l s ' C )

am-

227

and C in the Figs (5.47) to (5.50). A separate plot for sy ^

the values of C have also been shown in Fig. (5.52)

for different conditions. Since, effect on C is only due ttieir

to the inclusion of the energy costs/variation will depend

upon the amount of the energy required in each of the

absorption cycles. From the Fig.(5.52) it is clearly observed

that, the H„0-NH-. systems are the costlier and the LiBr-H^O

are the cheapest, while the costs of LiNO-, and NaSCN systems

are almost equal. Depending upon the costs of C , C, and C-,

as explained earlier/ the solar operated systems will be

more expensive; while the biogas-powered systems will be the

cheapest.

A comparative study betv/een the various absorption

systems has been also done by obtaining the percentage

deviation of the three ammonja systems from the LiBr-H„0

systems operating in the air conditioning mode, and the

deviation in the costs of LiNO^ and NaSCN systems from those

of the H^O-NH^ system for the refrigeration mode. These

deviations have been presented in Table 5.5.

Because the source of energy play a vital role in the

performance and economy of absorption systems, the optimum

operating temperatures in the various components have been

chosen to be those corresponding to the minimum values of

C . The optimum temperatures and the subsequent values of

228

6Ah

63

62

%

C O

D O

61

52

51

50h

49 c I/)

CL D

Q:

to

O

^ Z.6

35

35

3A

33

32

H 2 O - NH3

/ \ /

_ N /

I I I I

7 8 9 10 11

L 1 N O 3 - N H 3

^

~

—

-

/ /

/ , /

/ * / • ^ ^y 1 N*- •

• / \ • •\ /

• > •

1 1 1 1

7 8 9 10 n

A1

AO

39

38

37,

30

29 28

L i B r -H2O

\

A8

Ul

A6

35

3A

33

321-

31

te,C

Solar LPG

• — • Biogas

s ' • \ / \ ^ '' • \ / •

\

^.-K-* /

7 8 9 10 11

NaSCN - NH3

J I I I

6 7 8 9 10

Fig. 5-52 Variation in the costs of absorption systems^ including their operating costs ^with teot

^c,o(^wi=^am=30'^,^^R = S.0,tei' = 15"C)

229

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COP and HCP have been tabulated belov/ for the various

absorption systems using different sources of energy. The

optimum values are given for the optimum values of MR

obtained correspondingly to the minimum cost C syt

The optimum temperatures and the performance

coefficients of the LiBr-H„0, H-O-NH-, LiNO -NH^ and

NaSCN-NH^ systems, corresponding to the minimum values of C ^, are given in the Tables 5.6, 5.7, 5.8 and 5.9, syt' =

respectively.

From the Tables, it is observed that the effect of t . on the

and the type of energy used,/evaporator temperatures is

very little. However, the values of t , t , t and MR are • a c g

found to increase with t . . It can also be estimated that wi

the optimum values of t come out to be nearly 10, 8, 8. Sand a

8.5°C above the inlet-water temperatures (t . ) in case of '^ wi

LiBr-H20, H^O-NH^, LiNO^-NH^ and NaSCN-NH^ systems,

respectively; while the optimum temperatures t are found C f O

to be about 15 to 18°C higher than t . for the systems operating in the air conditioning mode. It is also

interesting to note that the values of t , in the ^ c,o

absorption systems operating for the refrigeration purpose,

are slightly lower than those found in the air conditioning

mode.

231

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6. CONCLUSIOUS AND RECOMMENDATIONS

6.1 Conclusions

In the present study economic analyses of four vapour

absorption systems, sources of energy and cooling water were

done with an aim to optimize the various operating

parameters.

The analyses were followed by using three different

models, the first of it optimized only the generator

temperature, the second optimized the generator and

condensing temperatures along with the solution mass flow

ratios and the third optimized the generator, condenser,

absorber and the evaporator temperatures along with the

solution-flow-ratios. The following conclusions have been

drawn :

1. Economic analyses of the sources of energy in the various

absorption cycles show that for the purpose of air

conditioning, the costs of the solar collectors would be

nearly twice the costs of LPG; and for refrigeration, the

solar collectors would be about 2 to 5 times costlier

than the LPG; the costs of LPG being about 32% higher

than those of the biogas.

2. The cost of the energies are found to be lowest for the

LiBr-H^O cycle, operating in the air-conditioning mode

and for the LiNG^ and MaSCN ammonia cycles in the

236

refrigeration modes. But crytallization puts a limit in

the efficiency of the NaSCN-NH,, solution, due to which

LiNO^-NH^ system prove to be better.

3. Optimization of t , show that for evaporator temperatures

of about 10°C in a LiBr-H^o cycle, optimum generator

temperatures, for hot climates, may go as highas

90-100°C, while for moderate climates, they may go down

about 60 to 80°C. But, for the refrigeration conditions

(say, t = -15°C), the generator temperatures in the

LiNO^-NH^ rise to around 120-130°C.

4. The optimum values of COP corresponding to t for the

minimum cost of energies, are found to be highest for the

LiBr-H-0 solution and lowest for the H^O-NH-, solution;

they being almost equal for the LiNOo-NH-> and NaSCN-NH

solutions.

5. Optimization of the solution mass-flow ratio (MR),

corresponding to the minimum cost of energy plus cooling

water, show that the values of MR for the LiNO^ and o 3

NaSCN ammonia cycles are lower than those for the

LiBr-H20 and H2O-NH2 cycles; the MR s fall near the

maximum values of COP.

6. Economic analyses of the sources of energy plus cooling

water show that solar-powered systems are costlier than

the biogas and LPG powered systems; the biogas operated

systems being the cheapest.

237

7. For the air-conditioning mode, LiBr-H„0 system and for

the refrigeration mode LiNO-,-NH-. and NaSCN-NH-, systems

would be most economical. But, NaSCN-NH^ solution creates

a problem of crytallization, hence, LiNOo-NH-, system

should be prefered.

8. The values of t , through the Model II, for the LiBr-H„0 go ^ I

cycle, at t = 10°C, will range from 46-70°C, when solar

operated; 60-90°C while using biogas and 61-86°C when

LPG-powered. And those in the LiNO-,-NHT cycle, at t =

-15°C, ranges from 78-114°C (for solar), 104-132°C (for

biogas) and 106-133°C (for LPG).

9. Analysis at equal V, and W suggests that, this can also

be one of the criteria for selecting the operating

parameters, because the operating conditions at equal

V, and W are close to those at the minimum operating

costs.

10. The optimum condensing temperatures for the solar

pov/ered cycles fall at 5°C above the inlet water

temperature (t . ) . For the absorption cycles using LPG

and biogas, other than the NHo-HpO, the optimum

temperatures will be around 7.5 to 11°C above the value

of t .. While for the H^O-NH^ cycle, the optimum values wi z J

are about 5.5 to 8°C above t .. wi

11. Economic analysis of the low-pressure operating

components show that the cost of the absorber plus

evaporator are highest in the H„0-NtU system and lowest

238

in the LiBr-H20 system. In the refrigeration mode, the

cost of the NaSCN-NH^ system is higher than the cost of

LiNOo-NH-j system.

12. Economic analysis of the high-pressure operating

components show that H„0-NH^ system is very costly

because it includes the costs of the additional

equipments, the reflux-condenser and the distillation

column. The costs of the LiNO^-NH^ and LiBr-HÔ

system-components are almost equal, but less than the

NaSCN-NHo sytem.

13. The LiBr-H20 system iu the Model III will be the

cheapest for the air-conditioning-applications; while

the costs of the HÔ-NH-, systems will go as high as

about 50% more than the costs of LiNO, and NaCSN

systems.

14. Including the costs of the energy-sources in the cost of

the systems, show that LiBr-HpO system is cheapest,

while the HÔ-NH^ is the costlieit. The solar operated

systems are more expensive, while the biogas systems are

the cheapest.

15. The optimum generator temperatures in the Model III, for

LiBr-H„0 system operating in the air-conditioning mode,

are around 75 to 92°C, while for the LiNO-.-NH-, system,

that has been found more suitable in the refrigeration

mode, it ranges from: 95-117°C (with Biogas and LPG) and

239

115-128°C (with solar energy).

16. The optimum values of the evaporator tempcjratures for

the ammonia cycles range from 8-9°C, while for the

LiBr-HpO cycles it will be 9.5°C, operating in the

airconditioning mode; while in the refrigeration mode;

for the three ammonia cycles, the values of t range - ' eo ^

within -14.0 to -14.5°C.

17. The optimum values of the absorber temperature for the

LiBr-H„0 system comes out to be about 10°C, while for

the ammonia cycles about 8-8.5°C, above the cooling

water temperature.

18. The optimum condensing temperatures fall around 15 to

18°C higher than the cooling water temperature.

19. Optimization using models I and II are simpler, hence,

should be used for the systems already designed and

installed.

20. Model II should be prefered especially for the LiBr-H20

cycles because large amount of heat/being released from

its absorber and condenser.

21. For designing a new system, Model III should be used,

which calculates the dimensions of the various

components along v/ith the optimization of nearly all the

parameters involved in the operation of the cycle,

22. The generalised computer program and the procedure for

240

the design of absorption systems would enable the users

to have a multiple choice for selecting the refrigerant-

absorbent combinations and the operating conditions,

6.2 Recommendations

1. Models I and II, in the present study, may be further

studied by assigning different values of the condenser

and absorber temperatures, instead of taking them as

equal.

2. All the three models may be tried with other

refrigerant-absorbent combinations.

3. The present study may be extended for multistage cycles.

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Appendix Al

Saturated enthalpy

Lithium nitrate-ammonia solution

h-"- = d + (d, + d_x)t + (d^+ d,x)t^/2 + d.x t^/3 m o 1 ^ J 4 D

+ d,(0.54-x)^ + d^(x-0.54)-'-*^

for X < 0.54, d = 0 and for x > 0.54, dg = 0

Sodium t h i o c y a n a t e - a m m o n i a s o l u t i o n

h^ = A , t + A „ t ^ / 2 + A ^ t ^ / 3 + A . { l - x ) / 8 1 . 0 8 m 1 2 3 4 "

3 ^ 3 . 3 . A, = 2^ e . x , A^ = 2^ f . x , A-, = '5! g-x and

1 = 0 1 = 1 1 = 1

2 A. = 2 h . x ^ 4 .-^„ 1

i = 0

Lithium bromide-water solution

h^ = B^ + B2(t + 17.778) + B3{t + 17.778)^

4 . 4 4 . B. = 5 k x , B = 2! i.x and B^ = m.x^

i=0 ^ ^ i = 0 ^ ^ i--=0 ^

Range: 16 £ t <_ 165°C and 40 <_ x <_ 70%

where d., e., f,, g , h., k , 1 and m. are constants given

in Table Al.1

257

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r-i in CM

o o

00

o o 1

CM r-i 1X3

o o

r-i

o o o o 1

CO

o o o o

rH

o o o o 1

o '3'

1X5

00 ro

o in " o 00 1

r in

CM

CO CM

O r-0) 0)

C N C O r H t N C O r H C N C O O r H C N

01 ( p i w i H i w t P t n t P x l j : : ^

o • H 4-1 P

rH O o

in rH (M 1

O in CM r~i in r-{

rH

00

r->X5 CM 00

ro n

CN

1 w 00

en rH CN

o

CN

1 w CO

en r~ ' o

CO

1 W o 00 r-i r-\

O

O

O r in rH

o en CO ix>

o • H O r H c N r o ' * i n i X ) r ^

258

Superheated enthalpy of water

^sup ^ 1,925 t - 0.126 t + 2500.0 w q c

Equilibrium pressures


P = exp{s^ + S2(l-x)^ + [S3 + s^(l-x)^]/T}


P = exp(s^ + SgX + [s_, + Sgd-x) ]/T}

Water-ammonia

P = exp{Sg + S^QX + [s^^ + s^^{l~x}^]/T]

Pure ammonia

P := exp{s^3 + s^^/T^ + SJ,3/T2)

Pure water

^^^10^ = ^16 ^ ^17/Tr + is/' r

Range: 273.16 <. T £ 283.16 K

where s^ are constants given in the Table Al.1

259

Density


0.5 P^ = - 0.1409653E+4 x + 0.2046222E+4 - 0.13463E+1 t ' m

- 0.39E-2 t^


/o = 0.1707519E+4 - 0 . 2 4004348E+4 x + 0. 2 25 65083E+4 x" m

- 0.9300637E+3 x" + t (-0.36341E+1 x + 0.54552E+lx^

- 0.31674E+1 x- ) + t^(0.5lE-2 x - 0.36E-2 x'

- 0.54E-2 x^)

Viscosity


u^ = ! (-0.51835E+1 t + 0.992337E+3) ^m

,^_^>[0.8333E-1 t + 0.68333E+1]

+ exp(-0.1147E-l t - 0.1744E+1)) O.lE-2


>i = {(-0.5289E+0 t + 0.29695E+2)

,(l_x)["°'128E-l t + 0.39493E+1]

+ 0.219E-10 (0.12E+3 - t ) ^ - " ^ ^ ^^^j O.lE-2

260

Thermal conductivity


K- = 0.2093E+1 + 0.47E-8 t + (-0.15478E+1 m

- 0.7612E-3 t - 0.15353E-4 t^)x


K"'' = (-0.105E-1 t + 0.7655E+1) m

J-0.75E-2 t + 0.305E+1] .(1-x)

+ 0.693E-7 (t-0.5E+2)^ + 0.547

Specific heat


C^ = 0.115125E+1 + 0.3382678E+1 x + (0.2198E-2 m

+ 0.4793E-2 x) t + 0.118E-3 x t^


C^ = 0.24081E+1 - 0.22814E+1 x + 0.79291E+1 x^ m

- 0.35137E+1 x^ + (0.251E-1 x - 0.8E-1 x^

+ 0.612E-1 x^) t + (-0.1E-3 x + 0.3E-3 x^

- O.lE-3 x^) .t^

2 6 i

C r y s t a l l i z a t i o n l i n e

L i t h i u m n i t r a t e - a m m o n i a

X = 0 . 3 0 2 1 - 0 . 3 4 E - 3 t - 0 . 2 7 2 E - 5 t ; 0 . 0 < x < 0 . 2 9 1 1 c

X = x ; 0 . 2 9 1 1 < X < 0 . 3

X = - 0 . 6 0 8 E - 3 t + 0 . 3 1 5 2 ; 0 . 3 < x < 0 . 3 0 7 6 c

X = 0 . 1 4 3 E - 1 t + 0 . 1 2 8 8 5 ; 0 . 3 0 7 6 < x < 0 . 3 3 6 2 c

X = - 0 . 5 4 0 2 E - 2 t + 0 . 4 1 3 1 8 ; 0 . 3 3 6 2 < x < 0 . 4 3 0 4 c

X = 0 . 4 4 3 4 1 3 + 0 . 6 9 E - 2 t + 0 . 8 5 4 E - 3 t ; c

0 . 4 3 0 4 < X < 0 . 5 0 7 2

X = 0 . 5 2 7 6 4 3 - 0 . 3 1 2 6 E - 2 t - 0 . 1 9 E - 4 t ;

0 . 5 0 7 2 < X < 0 . 6 4 3 4

x^ = - 0 . 4 6 0 5 E - 2 t + 0 . 4 0 7 6 1 ; 0 . 6 4 3 4 < x < 0 . 6 6 4 9

x^ = 0 . 3 0 9 E - 4 t + 0 . 5 7 4 5 2 ; 0 . 6 6 4 9 < x < 0 . 7 8 2 6

x^ = G . 7 3 7 8 E - 2 t + 0 . 6 7 2 1 4 ; 0 . 7 8 2 6 < x < 1.0

Sodium thiocyanate

X = 0.360207 - 0.1285E-3 t - 0.30158E-5 t^

+ 0.1058E-7 t^ - 0.39364E-10 t^; 0.0 < x < 0.36

262

X = 0.4924 + 0.124E-1 +• 0.3E-3 t ; c

0.36 < X < 0.430

X = 0.386 - 0.94E-2 t - O.lE-3 t ; 0.43 < x < 0.565

X = 0.2198 - 0.6444E-2 t; 0.565 < x < 0.735

x^ = 0.72395E+1 + 0.80303E-1 t; 0.735 < x < 1.0

Appendix A2

Equationsfor the J-factors in baffled exchangers

The various factors affecting the processess of heat

transfer and fluid flow due to the application of baffles in

the shell and tube type heat exchangers, have been

correlated in terms of the known parameters and presented

below :

The values of J, , taken from the curves drawn for an k

ideal tube bank in Ch. 10-19 of Perry Handbook [80], for

19 < d < 25.4 mm and p^ = 1.25 d , have been related within — o — ' t o

an error of about +_ 5% in the following form :

J, = 1.994005/(Re°''^^-^^°^^^) + 0 .147 07004E-1; K S

for 2 < Re < 200, and — s —

J, = 0.42119741/(Re°''*-^^^"^^^^) + 0 .154686 636E-2 ; K S

for 200 < Re < 10^ s —

The correction factors for baffle configuration

effects J are obtained from Fig. ].0-20 [80] and related

as :

J^ = 0.560199 + 0.48667145/F^ c c

for 0.9 < F <_ 1.0 (with error <_ 2%)

264

and

J = 0.5367916 + 0.8451404 F - 0.16066799 F^;

for 0.0 <_ F 1 0.9 (with error <_ 1%).

The correction factors for baffle-leakage effects J-^

from Fig. 10-21 [80] are related as :

J^ = 1.0267256 exp(-0.893 XI) - 0,29482067 Zl;

for 0.0 £ Zl <_ 0.5 (with error _< 2%), and

J^ = 1.1521969 exp(-l.1748871 XI) - 0.29167184 Zl;

for 0.5 < Zl <_ 1.0 (with error <_ 5%)

where, XI = (S , + S^, )/S , Zl = S , / (S , + S^, ). sb tb^ rn sb^ sb tb

The correction factors for bundle-by-passing effects J,

from Fig. 10-22 [80] are related as follows :

J^ = 0.8311313164 exp[{5.6415639(N /N )

- 1.4684484) F ] + 0.4141877(N /N ) bP s s c

+ 0 . 1 4 2 2 7 8 7 2 ;

f o r Re < 100 a n d 0 . 0 < N /N < 0 , 1 6 7 , ( e r r o r < 10%) S ~~ S S C *~"

Jj = 0.93244755 exp[ {1, 321601 (N /N )

- 0.65427411) F, ] + 0 .1614025 6E-1 (N ,/N ,) Dp S S C

+ 0.62875688E-1;

265

for Re < 100 and 0.167 <_ N /N < 0.5, (error < 2%)

J, = 0.85548401 exp[{4.853734(N/N )

- 1.2855592} F ] + 0.40404823(N^^/N^)

+ 0.11725316;

for Re > 100 and 0.0 < N /N < 0.167, (error < 10%) s — — s s c —

J^ = 0.9351809 exp[{1.2358679(N /N ) b ss c

- 0.6101917} F, ] + 0.62873801E-2 (N /N ) ' bp ss' c

+ 0.64867899E-1

for Re > 100 and 0.167 < N /N < 0.5, (error < 2%) s — — ss' c —

^b = 1-0

for all values of Re and N /N > 0.5 s ss c —

Correction factors for adverse temperature-gradient

build up at low Reynolds number J from Fig. 10-23 [80] are

correlated for Re < 100 as : s

Jj. = 0.84239239 exp (-0 . 6 664867E-2 N )

- 0.10521576E-1 (N +N ); c cw' '

for 3 £ (N +N ) < 20, (with error <_ 10%)

266

J* = 0.66249645 exp(-0.7401456E-2 N^)

- 0.2591331E-2 (N^+N^, ); c cw

for 20 < (N +N ) < 50, (with error < 3%). — c cw — —

Correction factor for adverse temperature gradient at

intermediate Reynolds Number J from Fig. 10-24 [80] are

related as :

J = 0.68852085 exp[(-0.92011122E-2 Re r s

+ 1.0511966) J*] + 0.10599804E-1 Re IT S

- 0.78492123;

for 20 < Re < 100, (with error < 3%) s —

J = J ; for Re < 2 0 r r s —

J = 1.0; for Re > 100, r s —

Equation for the friction factors

The shell side friction factor f obtained from Fig. 29 s ^

of Kern presented in refs [90], for ideal tube bank with 25%

cut segmented baffles, are related with Reynolds number as :

f = 1.8759024 Re'^'^^^^-*-^^^ + 0 .1884 4184E-01; s s

for 200 < Re £ 10^ (with error _< 2%)

267

f = 79.839706 Re"^ * " ^ " ^ + 0.49372697; s s

for 10 £ Re <_ 200, (with error <_ 0.7%)

The friction factor f for tubes and pipes obtained

from Fig. 30 [90] are related as :

cc QQQ1oo o -0.9853048 f = 66.889122 Re ;

for 56 <_ Re < 1000, (with error <_ 2%).

For 1000 <_ Re <_ 10 , the friction factor f for tubes,

f = 0.51 Re~°"^^^^^^^^ + 2.9176E-3; (with error £ 1%),

and for pipes,

f^ - 0.58672 Re; *- -'- ^ + 9.768657E-3; (error £ 2%)

Equations for the R-factors

The correction factors for the effect of baffle leakage

on pressure drop, R, are obtained from Fig. 10-26 [80] and

related as :

R^ = 0.9269 exp[-(1.732.SRB + 1.1444452) .SRM]

- 0.165.SRB - 0.8843305E-1;

for 0,0 < SRB < 0.5, (with error < 7%)

R^ = 0.8312866 exp[-(3.5384.SRB + 1.141776 ).SRM;

- 0.139956.SRB + 0.53258E-1;

268

for 0.5 < SRB <_ 1.0, (with error <_ 5%)

where, SRB = S^^/{ S^^-^S^^) . SRM = (S^^-^S^^)/S^.

Correction factor on pressure drop for bypass flow Rj_

are obtained from Fig. 10-27 [80] and correlated,

If N /N =0.0; ss c

R^ = 0.9906574 exp(-4 . 46 32335 F ^ ) ;

for Re < 100, (with error _< 2%), and

R, = 0.992722 exp(-3.769 F, ); b " bp

for Re > 100, (with error < 1%). s — —

If 0 < N /N < 0.1, ss c —

R, = 0.963 exp[{4.792(N /N ) - 2.6487} F^ ] b " ' ' s s' c bp

+ 1.08(Ngg/N^) - 0.44767E-1;

for Re < 100, (with error <_ 2%), and

R, = 0.9673 exp[(9.0853(N /N ) - 2.547} F^ ] t) s s c bp -

+ 0.3232(N /N ) + 0.341244E-2; ss c

for Re^ >_ 100, (with error £ 1 % ) ,

I f 0 . 1 < N /N <0.5, ss c —

2G9

R = 1.0074 exp[{4.0297(N /N ) - 2.0224} F^ ] b ' s s' c bp

+ 0.152364(N /N ) - 0 . 493172E-1; ss c '

for Re, < 100, (with error _< 7%).

R. = 0.98446 exp[ {3.61752(N /N ) - 1.8037} I' 1 b ^^ ss c ' bp-"

+ 0.962E-1(N /N ) - 0.1110422E-1; ss' c '

for Re^ >_ 100, (with error <_ 6%)

Appendix A3

Table A3.1 Recommended dimensions for tray towers [102]

Weir length Fractions of A used Distance from

(W) by one downspout (A ) centre of tower

0.55 T 3.877% 0.4181 T

0.60 T 5.257% 0.3993 T

0.65 T 6.899% 0.2516 T

0.70 T 8.808% 0.3562 T

0.75 T 11.255% 0.3296 T

0.80 T 14.145% 0.1991 T

Appendix A4

The data for the emissivity of carbon dioxide obtained

from Fig. 4.13 of refs [110] have been correlated in the

following form :

.^ = 1 - 0.97265 e-0-93425E-06 T^^ ^ 2.052169 (P^L);

for [388 < T <_ 888 K] and [0.0046 £ P L<. 0.019 m-bar],

(with error £ i 6%)

c = 1 - 0.9437 e^'^^^""^ " gs + 1.38744 (P L) ; c - c

for [888 < T < 2000 K] and (0.0046 < P L < 0.019 m-bar]; gs — — c —

(with error <_ + 10%) .

The emissivities of water vapour, obtained from Fig.

4-15 of refs [110], have been related in the mathematical

form as given below :

fe = [0.2633 + 326.593 (P L) ] .T~°' -"" ^ - 2.60525 (P L) w v/ gs w

for [0.00463 < P L < 0.0108 m-bar],

e = [0.4545 + 444.67 (P L) ] .T'° ' " ^ ^ - 1.57525 (P L) W W gs W

for [0.0108 < P L < 0.0185 m-bar]. w ~~

The values of change in emissivities, a , a , and b , ^ ' c' w c

b with (PL) and T , respectively are taken from Fig. 4-18 w gs

272

of refs [110] and related as follows within an error of

about + 10% :

a = 0.611 + 0.54475E-4 T - 5.44112 € + 17.98443 i^ c gs c c

a = 0.7986 + 0.757E-4 T - 4.0448 e + 9.3686 a^ w gs _w w

b = 0.881 + 1.808 e + [0.334657E-2 e - 0.165E-2] T c c c gs

b = 2.656 + 2.554 e + [0.20235E-2 g - 0.1014E-2] T w w w gs

The correction factors C and C are obtained from c w

Figs (4.14) and (4.16) of refs [110] respectively, and

related within an error of about j 5% as follows :

C = 0.937 PS'^"^^ + 3.344(P L), for P L > 0.00618 m-bar c T c c

C^ = 0.937 P " " ^ + 0.0206653, for P L ^ 0.00618 m-bar

C = 0.159 + 1.9054 (P +P^)/2 w w T

- 0.4742764 {(P +P^)/2}^.

In the above relations, L is the Mean beam length. The

mean-beam-length, in the absence of information for a

specific geometry, can be obtained from [95] :

L = 3.6 (Volume of the gas)

Surface area of the enclosure"

Appendix A5

For calculating solar flux on an inclined flat plate

collector located at Aligarh, the following procedure

presented by Sukhatme [116] has been used. The empirical

equations for predicting the availability of solar radiation

on a horizontal surface are

Global radiation,

H /H = a + b (S/S ) g' o max

where,

H = (24/A).I [1+0.033 cos (360 n/365)

[w sin d) sin S + cos d) cos & sin w ] '• s ^ s -

S = (2/15). cos (-tan d) tan g)

S = 23.45 sin [3 60 (284 + n)/365]

-1 w = cos (- tan (|) tan S)

Diffuse radiation [118],

H^/H = 1 . 4 1 1 - 1 . 6 9 6 (H /H ) ; f o r 0 . 3 < H / H < 0 . 7 d g g ' o g^ o

Thus, beam radiation which is the difference of the

global and diffuse radiation will be given by

274

H^ = H - H , b g d

The angle of incidence, for the solar beam falling on

an inclined surface facing south, is calculated from

Cos e = sin S sin ((t)-B) + cos S cos w cos ((J)-B)

while for a horizontal surface, from

Cos e = sin & sin d) + cos £ cos w cos (J) ^ • s

The monthly average of daily radiation, falling on a tilted

surface, proposed by Liu and Jordan [119] is

H„, = H, F, + H-iF-, + H F T b b d d g o

v;here F, , F., and F are the tilt factors for beam, diffused b d P

and reflected radiations, respectively and are obtained from

the following relations :

F, - cos e/cos e b ' z

F = (1 + cos p)/2

F = P{\ - cos p)/2,

Thus, the solar flux per unit area, falling on an

inclined solar collector at an angle equal to the latitude

at Aligarh (p = (|)) is calculated from the above e<3uation

which comes out to be

275

S = H^/S

The values of the constants a and b, have been obtained

from the plots presented by Mani and Rangarajan [120].

Their values for Aligarh come out as :

a = 0.25 and b = 0.456

The sunshine hours(S) at Aligarh for different months

of the year have been obtained from the graphs plotted in

Figs (2.4) to (2.15) by Mani et al. in refs [120], and are

tabulated below :

Table A5.1 Sunshine hours and solar flux(S) at Aligarh

Month No. of the days

n

Sunshine hour Solar flux

(S) S(kJ/hm )

January

February

March

April

May

June

July

August

September

October

November

December

1-31

32-59

60-90

91-120

121-151

152-181

182-212

213-243

244-273

274-304

305-334

335-365

8.21

9.13

8.85

9.61

9.57

7.31

5.81

6.42

7.56

9.48

9.25

8.29

2260.27

2280.92

2 3 34.70

2245.00

2179.05

2463.62

2799.17

2666.96

2450.91

2254.51

2230.19

2230.14

Appendix A6

Table A6.1 Tube count entry allowance [90]

Shell diameter Nozzle diameter

(D in mm) (D in mm) s z

D < 304.92 50.82 s

304.92 < D < 438.32 76.23 — s —

489.14 1 D £ 539.96 101.64

590.78 < D < 736.89 152.46 — s —

7 8 7 . 7 1 1 D^ £ 9 4 0 . 1 7 2 0 3 . 2 8

Dg > 9 9 0 . 9 9 2 5 4 . 1 0

( START )

277

Read

AT, gs

the values of: Xd^ (M) ,Xd^(M) ,0^ , S , ^ t^ , ^t^, A t^ , ^t^^

' ^gb' gl' s,o' s,t' ' st' '^st' 'în' 'gk' wi' sp' am

Assign : t ,=4.5, t ,=t .+8, y,=l. ^ I el al wi •'3

11

12

Set tel=êl^°-^

Calculatei x„,x^{= x,),x^{*x-,) C o i. C] /

Yes

Initialize: t =t„,-0.5,t =t .+11 e el c yu I

/ D O 1 1 N = 1 , 1 2 \ \ DO 12 J = l.NNS/

t =t +0.5 _Q P.

Calculate : t ,t ,P ,P ,P ,P ,P I a g' a c e g r

DATA FILE

0 =12600KJ/h; S'=2 4 3 0 . 5 " 7KJ/r e At„ = 10°C, At = At Ât ^'"-c a e gc

t .=t, =20,25,30°C, AT 10 WI am GS

UC'C/145':-

K ^ = 16 . 3 , w/n'-C; p , -1196.:K-: St I g K

Pst=^817, p^^-80.lKg/n"

MR = 6 to 24; NNS = 7, -.. ;

T„K=T ,-523.15K,t 2b~C gb gl sj.

t =90=0,t s , o s , t

Set : t . =t „-3;t =t^ cie sp r c

ICompute : H^ , H^.H^,Hg.H^^,H^^,H^3,H^^,y^3 , x^J

I from the respective subtxiutines 1 I Q^,COP,HCP, ACP,CCP,W^,W^,W^,Wg^,Wg2,W^Vj^,V^,A^,2^

I Design: Absorber, Condenser, Evaporator, Rectifier __. Analyser, Generator,Preheater & Precooler |

^ 1 1 rn ,n 10 the w<i Ler ,

amount of material required and cost of each component with the cost of source of energy, pumps, valves and refrigerant absorbent solution .C ,C ,C ,C . ,C ,C ,C. ,C,,C ,C ,C ,C ,C ) ' --£ - e g ph pc' w' b' 1' s' ae' eg' sy' syt

(STOP )

Fig. A7.1 Flow chart for the Main Program

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PAPERS PUBLISHED · 3.2.3 Falling film absorbers VI 3.2.3.1 Tube side heat transfer coefficient 71...

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Transcript of PAPERS PUBLISHED · 3.2.3 Falling film absorbers VI 3.2.3.1 Tube side heat transfer coefficient 71...