Proposal and validation of a model for the dynamic simulation

Mots cles : Refroidisseur a` absorption ; Bromure de lithium ; Performance dynamique ; Simulation ; Resultats experimentaux

1. Introduction

Dynamic simulation plays a very important role in the

description of the real performance of an energy conversion

system, especially during the activation stage or part-load

operation. Such a problem is extremely relevant for absorp-

tion chillers, where the high mass of the internal components

and the accumulation of the fluids inside the vessels usually

make the transient phase longer than in mechanical

compression chillers.

* Corresponding author. Tel.: 33 47 975 88 58; fax: 33 47 975 81 44.s).

Available online at www.sciencedirect.com

e:

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 8E-mail address: nolwenn.le-pierres@univ-savoie.fr (N. Le Pierre`Proposition et validation dun mode`le pour la simulationdynamique dun refroidisseur a` absorption au LiBr / eausolaire monoetageReceived 28 November 2011

Received in revised form

21 September 2012

Accepted 18 October 2012

Available online 1 November 2012

Keywords:

Absorption chiller

Lithium bromide

Dynamic performance

Simulation

Experimental results0140-7007/$ e see front matter 2012 Elsevhttp://dx.doi.org/10.1016/j.ijrefrig.2012.10.013LiBr/water absorption chiller is presented. The model is based on mass and energy

balances applied to the internal components of the machine, and it accounts for the non-

steady behaviour due to thermal and mass storage in the components. The validation of

the mathematical model is performed through experimental data collected on a commer-

cial small-capacity water-cooled unit. Due to the peculiar technology adopted in the real

chiller, a special effort was made to identify the appropriate values of the main physical

parameters. The validation of the model is based on the values of the water temperature at

the outlet of the machine, as no measurement inside the machine was possible; anyway,

a consistency analysis applied to the internal parameters is also presented. The agreement

between experimental and simulated results is very good, both on a daily and on a seasonal

basis.

2012 Elsevier Ltd and IIR. All rights reserved.Article history: In this paper, a general mathematical model for the dynamic simulation of a single-effecta r t i c l e i n f o a b s t r a c tof a solar-assisted single-stage LiBr/water absorption chiller

G. Evola a, N. Le Pierre`s b,*, F. Boudehenn c, P. Papillon c

a LEPMI, CNRS UMR 5279, 50 avenue du lac Leman, 73377 Le Bourget du Lac, Franceb LOCIE, CNRS UMR 5271, Universite de Savoie, Polytech Annecy-Chambery, 73376 Le Bourget du Lac, FrancecCEA LITEN, BP 332, 50 avenue du lac Leman, 73377 Le Bourget du Lac, Francewww. i ifi i r .org

journal homepagier Ltd and IIR. All rightswww.elsevier .com/locate/ i j refr igreserved.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 81016Nomenclature

Variables

A surface (m2)

cp specific heat capacity (J kg1 K1)

Cd discharge coefficient (e)

D diameter (m)

f specific backflow (e)

F fouling factor (m2 kW1)h specific enthalpy (J kg1)H height difference between two components (m)

H daily solar irradiation on the collector plane

(kWhm2 day1)I solar irradiance on the collector plane (Wm2)_m mass flow rate (kg s1)M mass (kg)

Nu Nusselt number (e)

p pressure (Pa)

Pr Prandtl number (e)

Re Reynolds number (e)_Q thermal power (W)

s thickness (m)

S pipe section (m2)

t time (s)Very interesting papers on this topic have been presented

in scientific literature. Jeong et al. (1998) propose a dynamic

model for the simulation of a steam-driven LiBr/water

absorption heat pump that exploits low-grade waste heat. The

model includes storage terms to take into account the thermal

capacity of the container and the solution mass storage in the

components, but no thermal inertia is attributed to the heat

exchangers. Solution and vapour mass flow rates are not

constant, as they are determined as a function of the pressure

difference between the vessels. The simulation time step is

automatically adjusted; the model has been verified, with

good agreement, through operational data, but only by looking

at the thermal power exchanged by the absorber and the

condenser.

Kohlenbach and Ziegler (2008a, 2008b) paid a lot of atten-

tion to the dynamic behaviour, by accounting for heat and

mass storage, as well as to the solution transport delay

between generator and absorber e and the way back; on the

contrary, their model is over-simplified as far as the descrip-

tion of the steady state is concerned: as an example, water and

LiBr/water solution have constant property data, and

a detailed enthalpy calculation for each state of the system is

avoided. Hence, their model is able to describe very accurately

the shape of the dynamic response to a change in the input

conditions, but a low accuracy on the numerical values is

obtained after verification with the experimental measure-

ments on a commercial 10 kW single-stage absorption chiller.

T temperature (K)

U heat transfer coefficient (Wm2 K1)V volume (m3)_V volumetric flow rate (m3 s1)

x concentration (e)

z level of the liquid inside a component (m)Greek letters

a convective coefficient (Wm2 K1)

l thermal conductivity (Wm1 K1)r density (kgm3)z pressure loss coefficient (-)

Subscripts and superscripts

a absorber

abs absorbed

av average value

c condenser

d dissipated

des desorbed

ext external

ev evaporator

g generator

hx heat exchanger

in inlet

int internal

l liquid

max maximum value

o outdoor

out outlet

s solution

sh shellThe work also includes a sensitivity analysis to some internal

parameters, which is not supported by experimental

verification.

The model developed by Shin et al. (2009) applies to high-

capacity double effect absorption chillers. It has been veri-

fied against experimental data collected on a commercial

direct-fired chiller of medium capacity during 370 min of

operation, with an acquisition time step as high as 5 s. On the

whole, the model proved to be quite reliable at steady opera-

tion; on the contrary, during the first 90 min, i.e. when the

transient behaviour was particularly pronounced, differences

up to 10 C were observed between simulated and experi-mental values of the temperatures inside generator and

absorber. Furthermore, during the same period the error on

the determination of the instantaneous capacity reached 20%.

Other works have been recently presented by Gomri (2010)

and Bakhtiari et al. (2011); bothworks are based on a simplified

steady-state model of a single or multiple effect absorption

chiller. In the first case, the model is used for evaluating the

performance sensitivity to the main operating parameters,

even under a second law perspective, but no validation is

presented, whereas in the second work the model is validated

through experimental data and used for the optimization of

the chiller design.

Myat et al. (2011) presented an effective dynamic model for

the evaluation of temperature and concentration profiles in

a single stage LiBr/water absorption chiller; their model also

v vapour

w water

which is not steady, a dynamic model is necessary;

(2008a) and Jeong et al. (1998);

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 8 1017- the aim of the model is not to get an extremely precise

description of the transient response of the machine, but to

describe with good accuracy the time profile of the chiller

behaviour when subject to load variations in the time scale

of a few minutes;

- the model must determine the water outlet temperature

and the thermal power at each section of the absorption

chiller;

- the model should also present good accuracy in the

description of the average chiller performance (daily,

weekly or even seasonal).

For this reason, the validation of the dynamic model is not

based on the application of a load perturbation starting from

a steady state, but it is performed by means of real operating

conditions, with a continuous change of all the external

parameters over several days of operation.

Section 2 describes the equations included in the mathe-

matical model, as well as the hypotheses that justify such

equations. Section 3 presents the calculation of the physical

parameters to be adopted in the mathematical model to

simulate the commercial single-stage absorption unit

considered in this study. Section 4 comments on the experi-

mental data and their comparison with the simulated results.

Section 5 shows a consistency analysis that investigates into

the capability of the model to correctly describe the internal

behaviour of themachine and its response to a sudden change

in the forcing conditions. Section 6 concerns the use of the

proposed model to identify some improvements in the

experimental solar-assisted cooling system.

2. Description of the model

A single-stage LiBr/water absorption chiller is made up of

a generator, an absorber, an evaporator and a condenser;

the circulation of the solution is assured by a solution

pump, and a solution heat exchanger is normally used to

internally recover thermal energy (see Fig. 1). At the gener-

ator, a heat source is supplied, in order to desorb the

refrigerant (water vapour) from the solution; the vapour

moves towards the condenser, where it is condensed at

a high pressure. The remaining solution, called strong as it is

rich in LiBr, flows down via the heat exchanger to theincludes some relations for the calculation of the heat transfer

coefficients and finally leads to an entropy analysis of the

chiller, but it is not validated through experimental results.

The model described in the present paper has been

conceived in the framework of a research project where

a commercial solar-assisted single-stage absorption chiller is

being monitored to verify its performance in the air-

conditioning of an office space. As a consequence, some

specific features are needed:

- the model must be suitable for the simulation of commer-

cial units;

- as the driving water flow is heated through solar energy,absorber; here it is exposed to the vapour coming from the

evaporator, that is absorbed in the solution at low pressuref the LiBr/water solution leaving the generator and the

absorber is saturated (Kohlenbach and Ziegler, 2008a);

g the throttling valves between generator/absorber and

condenser/evaporator are adiabatic;

h the vapour produced in the evaporator is saturated, thus

no superheating is allowed, as remarked by Shin et al.

(2009) and Gomri (2010);

i the volumetric flow rate of diluted solution conveyed by

the solution pump from the absorber to the generator is

assumed constant.

Most of the above simplifying assumptions are quite

reasonable (b, c, g, i) or well established in the literature on the

topic (a, d, e, h). Only the assumption fmight be questionable:

Myat et al. (2011) underline that in a well-designed absorber

the solution inside the component and at its outlet is normally

slightly sub-cooled. However, when simulating commercial

absorption units, it is not possible to access the inside of the

machine, thus there is no way to verify through experimental

measurements the accuracy of this last assumption.

2.1. Generator and absorber

If looking at the scheme described in Fig. 1, the mass balance

for the solution and the vapour in the generator can be

respectively written as follows, by including the storage of

both fluids in the vessel:

_ms;in;g _ms;out;g _mv;des dMs;gdt (1)

_mv;des _mv;out;g dMv;gdt (2)

The ideal gas law can be used for the vapour, Eq. (3). This

position is allowed as the vapour pressure inside a single-

stage LiBr/water absorption chiller is normally between 1

and 10 kPa, i.e. far lower than the critical pressure; in this

conditions, the error made on the evaluation of the specific

volume by using the ideal gas law is lower than 0.1%,whateverand temperature. The diluted solution is then conveyed to

the generator by the solution pump. The cold production

occurs at the evaporator.

In order to simplify the formulation and the consequent

implementation of the model, some assumptions are made:

a temperature, pressure and LiBr concentration are

homogenous inside each component (Myat et al., 2011);

b the pressure inside the generator equals that in the

condenser, and the same relation holds between absorber

and evaporator;

c the cooling water outlet temperature in the absorber

corresponds to the cooling water inlet temperature at the

condenser;

d the fluid transport delay between two components is

neglected;

e each heat exchanger has a constant overall heat transfer

coefficient, as already stated by Kohlenbach and Zieglerthe vapour temperature, as remarked in (Cengel, 1997). In Eq.

(3) the volume Vv occupied by the vapour is calculated by

morp

i n t e r n a t i o n a l j o u r n a l o f r e f r i1018subtracting the volume of the solution from that of the entire

vessel, see Eq. (4).

Q d,c

CONDENSER

M l,c

M v,c

m l

m l,out,c

M l,e

Q d.e

m w,cQ hx,c

m v,in,c

m ev

Q hx,e

M v,e

m w,e

m l,in,e

High pressure

Low pressure m v,out,e

EVAPORATOR

Fig. 1 e Description of the main components inside the absMv;g$Rv$Tg pg$Vv (3)

Vv Vg Ms;g=rs;g (4)Furthermore, the mass balance on LiBr, see Eq. (5), and the

energy balance on the solution, see Eq. (6), hold:

_ms;in;g$xs;in;g _ms;out;g$xs;out;g Ms;g$dxs;gdt

xs;g$dMs;gdt (5)

_Qhx;g _Qd;g _mv;des$hv;des _ms;out;g$hs;out;g _ms;in;g$hs;in;g

ddt

Mcp;g$Tg

(6)

In Eq. (6), the convective and radiative heat transfer

between vapour and solution is neglected. The solution is

assumed to be fully mixed at each simulation step; as

a consequence the enthalpy and the salt concentration in the

solution leaving the vessel correspond to those inside the

vessel. Furthermore, according to Alefeld and Radermacher

(1993) the temperature of the vapour desorbed in the gener-

ator corresponds to the saturation temperature associated

with the diluted solution entering the component; as

a consequence the vapourwill be super-heatedwith respect to

the solution contained inside the vessel.

In addition, the model takes into account the thermal

inertia of the shell; the shell is assumed at thermal equilib-

riumwith the solution (Tsh Tg), thus its thermal capacity canbe composed with that of the solution itself in Eq. (6), where

MMshMs and cp is the average specific heat capacity (Shinet al., 2009), defined as:cp;g Msh$cp;sh Ms$cp;s (7)Msh Ms

Pump

Q hx,g

m s,out,g

M s,a

Q d,a

m w,g

m s,in,gM v,g

m v,in,a

Q hx,a

m s,out,a

M v,a

w,a

m s,in,a

Solution exch

ABSORBER

m v,abs

m v,out,g

m v,des

GENERATOR

Q d,g

M s,g

tion machine (white arrows: vapour, black arrows: liquid).

g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 8The thermal power released into the environment can be

assessed by introducing an overall thermal resistance Rgbetween the solution in the generator and the outdoor air:

_Qd;g Tg To

Rg (8)

Suchaschemecanbeextendedtotheabsorber, justaccounting

for the different direction of the vapour flow, which enters the

component and is absorbed in the solution. The thermodynamic

state of the vapour entering the absorber corresponds to that of

thevapourproduced in theevaporator; itsenthalpy isassessedas

a function of temperature and pressure through the relations

available in (Florides et al., 2003), that are derived by fitting the

data presented in (Rogers andMayhew, 1992).

In the equations previously presented, the thermodynamic

properties of the LiBr/water solution (enthalpy, density,

specific heat, thermal conductivity, viscosity) are calculated

through appropriate polynomial functions reported in

(Florides et al., 2003).

2.2. Condenser and evaporator

Fig. 1 also shows the scheme used to describe the condenser.

In this component the liquid phase is condensed vapour

instead of LiBr/water solution; as a consequence, the mass

balance on the condensate and the vapour can be written as:

_ml _ml;out;c dMl;cdt (9)

_mv;in;c _ml dMv;cdt (10)

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 8 1019In addition, Eqs. (3) and (4) can be rewritten, whereas the

energy balance applied to the vapour yields:

_Qhx;c _Qd;c _mlhl _mv;in;chv;in;c ddt

Mcp;c$Tc

(11)

Furthermore, the vapour and the condensate are saturated;

the enthalpy of the inlet vapour is the same as for the vapour

flowing out of the generator. As described before, the shell is

assumed at thermal equilibrium with the working fluid, thus

the specific heat capacity used in Eq. (11) is an average one

(Shin et al., 2009).

The equations can be easily extended to the evaporator by

looking at the scheme in Fig. 1; as an example, the following

energy balance holds:

_Qhx;e _Qd;e _mev$hev _ml;in;e$hl;in;e ddt

Mcp;e$Te

(12)

Here, the enthalpy of the saturated vapour produced inside

theevaporator isdeterminedbymeansof therelationsavailable

in (Florides et al., 2003) and already used for the generator.

2.3. Heat exchangers

In order to evaluate the heat flux conveyed by the hot water to

the solution inside the generator, a model of the internal heat

exchanger is also required. According to thismodel, a uniform

temperature Thx can be assigned to the metal core of the heat

exchanger, whose thermal capacity is Mchx. A distinction can

then bemade between the heat flux released by the water and

delivered to the surface of the exchanger, see Eq. (13), and that

transferred from the exchanger to the solution, see Eq. (14).

The latter depends on the internal (exchanger solution) heattransfer coefficient UAint, whereas the former can also be

written as in Eq. (15), i.e. as a function of the external

(water exchanger) heat transfer coefficient of the heatexchanger, UAext, and themean logarithmic temperature. The

difference between such fluxes represents the thermal energy

stored on the body of the heat exchanger (see Eq. (16)).

The heat transfer coefficients UAint and UAext can be easily

assessed as shown in Eq. (17); in order to understand this

definition, one must remember that each heat exchanger

consists of a bank of cylindrical tubes, and that a uniform

temperature Thx is attributed to the tube itself. The simplifi-

cation introduced in Eq. (17) is justified by the very low

thermal resistance associated with the conductive heat

transfer through the tube thickness: due to the high thermal

conductivity of copper (l 387Wm1 K1) and the reducedthickness (normally not higher than 1 mm), the contribution

of this term on the overall thermal resistance would be lower

than 1%, as shown by a preliminary analysis carried out by the

authors.

_Qhx;w rw$ _Vw$cp;w$Tw;in Tw;out

(13)

_Qhx UAint$Thx Ts (14)

_Qhx;w UAext$Tw;in Thx

Tw;out Thx (15)

ln

Tw;in ThxTw;out Thx_Qhx;w _Qhx Mcp;hx$dThxdt

(16)

UAextAhx$

0BBBBB@

1ahx;ext

Dhx=2lhx

$lnDhxshx

DhxFext

|{z}overall thermal resistance

1CCCCCA

1

zahx;ext$Ahx

1ahx;ext$Fext

(17)

In the above equations, the density and the specific heat of

water are determined as a function of the inlet temperature,

according to the relations reported by Florides et al. (2003).

Thanks to the model of the heat exchanger, it is possible to

predict the outlet water temperature and the heat flux

released to the solution once the water mass flow and its inlet

temperature are known, as well as the temperature of the

solution inside the generator.

The same approach can be easily extended to the heat

exchanger inside the other components.

2.4. Other devices

As previously stated, the volumetric flow rate of the diluted

solution conveyed by the solution pump is constant, and

imposed as an input value. On the contrary, the strong solu-

tion flow rate from the generator to the absorber cannot be

held constant, as it depends on the pressure and the height

difference between the generator and the absorber. According

to this scheme, the mass flow rate of the strong solution can

be assessed as:

_ms;out;g Cd$S$

2$rs;g$

hpg pa

rs;g$g$H z

i

z

vuut(18)

Here, the pressure losses in the solution heat exchanger and

the corresponding piping are described through a resistance

coefficient z. The level z of the solution inside the generator is

continuously updated, as a function of the mass of solution

actually contained inside the vessel; the vertical distance H

between the bottom of the generator and the solution inlet of

the absorber is also considered. The same expression is used

to calculate the condensate mass flow rate from the

condenser to the evaporator.

In both cases, the pressure loss coefficient is not set

constant, but it is assumed to change as a function of the fluid

height inside the upper vessel.

Such an assumption corresponds to the control logic which

is often adopted in absorption chillers, where an increase in the

resistanceof the throttlingvalve is inducedwhenthe levelof the

liquid gets too low, in order to prevent the vessel from getting

empty. In this work, the following formulation is proposed:

z z0$z0=z2 (19)where z0 and z0 are nominal values. The use of such a condi-

tion is a real novelty if compared to other models available in

the literature, such as those proposed by Kohlenbach and

Ziegler (2008a) or Shin et al. (2009), and it has relevantly

improved the stability and the consistency of the model.As regards the solution heat exchanger between the

generator and the absorber, no thermal inertia has been

proposed by Gnielinski (1976):

adopted (aint 9000 Wm2 K1), as the latter is very similar to

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 81020f 0:079$ ln Re 1:642 (20a)

0:125$f$Re 1000$Pr1 12:7$

0:125f

0:5$Pr2=3 1

(20b)considered. Its heat transfer coefficient UAhx is assumed

constant and assigned as an input; its efficiency can be easily

assessed as a function of UAhx and the solution mass flow,

through well-known relationships valid for counter-flow heat

exchangers (Incropera et al., 2006).

3. Definition of the parameters

The mathematical model presented so far refers to a general

LiBr/water single effect absorption machine. In this work the

model will be applied to a commercial water-cooled unit with

a nominal cooling capacity of 4.5 kW, manufactured by

Rotartica. This chiller is installed at INES (Institut National de

lEnergie Solaire) near Chambery (France), where it is used in

the framework of a national research program aimed at

assessing the performance of different solar-assisted refrig-

eration systems.

Actually, the Rotartica chiller is a very particular one, as the

absorption cycle is carried out into an hermetically welded

spheroid container of approximately 500 mm diameter by

500mm long, rotated at 400 rpm about a horizontal axis, as

described in (Monne et al., 2011) and also in (Gilchrist et al.,

2002) for a similar model. The rotation of the components

improves the heat transfer coefficients and the efficiency of the

cooling production, but an additional electricity consumption

of around 400W has to be accounted for to maintain the rota-

tion. Furthermore, the solution pump is not electrically driven,

as the pumping power is derived from rotation, by converting

the kinetic energy at the outer radius of the vessel into pres-

sure. Further information on the Rotartica chiller is reported by

Izquierdo et al. (2008) and Garcia Cascales et al. (2011).

In order to use the proposed model for the simulation of

the Rotartica chiller, a special effort was devoted to the

parameter identification. As a matter of fact, when dealing

with commercial chillers the internal components are usually

not accessible, thus the only way to determine their geometry

is based on schemes of the chiller available on the technical

sheets which is the approach followed in this work.

In Table 1 the values of all the constant inlet parameters

used in the model are reported.

For the evaluation of the cumulated heat capacities, the

materials are copper in the heat exchangers and iron in the

vessel. The value of the discharge coefficient Cd is quite typical

and commonly accepted in the case of circular sharp-edged

orifices (Massey and Ward-Smith, 1998), whereas the thermal

resistance R between each component and the outdoors was

estimated roughly by knowing the geometry of the machine.

Furthermore, in Eq. (17) the convective heat transfer coef-

ficient aext between thewater flow and the surface of the tubes

in each component is assessed by using the correlationsaext lwDhx (20c)the Rotartica machine.

In addition, the heat transfer coefficient for both water

boiling and condensation on a circular surface can be assessed

through appropriate relations available in the literature

(Incropera et al., 2006).

It must be remembered that the thermodynamic proper-

ties of the LiBr/water mixture as well as those of liquid water

and water vapour can be calculated as a function of the

temperature and pressure, thus they normally vary with time.

However, in the determination of the heat transfer coeffi-

cients a fixed average temperature was considered for each

fluid, in order to get constant values and simplify the imple-

mentation of the model.

Finally, the volumetric flow rate of the diluted solution

conveyed from the absorber to the generator is kept constant

and equal to 0.0185 l s1. The mass flow rate changes at eachtime step as a function of the solution density. No calibration

was applied to optimise the values reported in Table 1.

4. Experimental verification

In order to check the reliability of the proposed model for the

simulation of the Rotartica absorption machine, the authors

used the experimental results collected during a test

campaign carried out at INES in summer 2009, fromMay 27 to

September 10. The results of the simulations were compared

to the experimental data and the agreement between them

was verified.

The Rotartica absorption chiller installed at INES is powered

by thermal energy produced in a solar field composed of 30-m2

flat plate solar collectors; a 400-l tank is used to store the hot

water, and no backup is provided to drive the absorption

machine when solar energy is not sufficient. The heat rejection

is carried out by means of a water flow that is cooled down in

a horizontal ground heat exchanger, made up of twenty-two

polyethylene pipes divided into two layers, buried at a depth of

0.75mand1.1 m, respectively; the lengthof everypipe isaroundAccording to Gnielinsky, the Eqs. (20a) and (20b) can be

applied for Re> 3000, thus they are more general than the

well-known Dittus-Boelter correlation, valid for Re> 10000.

The viscosity and the thermal conductivity of water,

respectively required to determine the Reynolds number and

to solve Eq. (20c), are determined as a function of the

temperature through appropriate relations available in

(Florides et al., 2003).

In addition, the value of the fouling factor F for the internal

and external surface of the tubes can be assumed as high as

0.09 m2 K kW1 (Howell et al., 2005).As concerns the convective heat transfer coefficient on the

solution side in the absorber and the generator, some exper-

imental values have been derived by Rivera and Xicale (2001).

However, these values refer to a geometry that is quite

different from that of the Rotartica chiller, where the heat

exchangers rotate with the vessel at 550 rpm (58 rad s1). Forthis reason, in this work the heat transfer coefficients deter-

mined by Gilchrist et al. (2002) for the Interotex machine are100 m. The chilled water produced by the absorption chiller is

stored ina300-l tankand thenused to feed three fancoils for the

ptio

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 8 1021Table 1 e Constant inlet parameters for the Rotartica absor

Parameter Unit Value

Cd e 0.61

Fint, Fext m2 kW1 0.09 103

Hc m 0

Hg m 0

Mcp,a kJ K1 58.5

Mcp,c kJ K1 33.0

Mcp,e kJ K1 38.0

Mcp,g kJ K1 58.5

Mcp,hx,a kJ K1 4.94

Mcp,hx,c kJ K1 3.04

Mcp,hx,e kJ K1 2.66

Mcp,hx,g kJ K1 2.66

Ra KW1 4

Rc KW1 4

Re KW1 4

Rg KW1 4

Rv J kg1 K1 455

Sc m2 2 105

Sg m2 2 104

UAint,a WK1 13970

UAint,c WK1 9720air conditioning of some office rooms. It is worth mentioning

that the systemwasnot designed for insuring standard comfort

conditions in the offices (e.g. indoor temperature always below

26 C), but rather for refreshing theoffices, sokeeping the indoortemperature at 5e8 C below outdoor air. Hence, no controlsystem has been implemented in the conditioned spaces: the

system keeps working as long as sufficient thermal energy is

available to drive the absorption machine.

During the experimental campaign only the water

temperatures at the inlet and at the outlet of the machine

were measured, together with the water flow rates at each

component. The temperatures were measured by means of

Pt1000 temperature sensors calibrated together with the

whole measurement chain (sensor, wire, acquisition system),

with an absolute uncertainty of 0.15 C. The uncertainty in themeasure of the volumetric flow rates was 2% according to the

manufacturer of the flow meters. All the data were acquired

every 120 s; it was not possible to reduce the acquisition time

step, due to the need of storing the experimental data for long

periods (up to 1 week) without saturating the memory of the

acquisition system.

No data were acquired inside the machine, such as pres-

sure, temperature and LiBr concentration in each component,

UAint,e WK1 6620

UAint,g WK1 7290

UAext,a WK1 4780

UAext,c WK1 3320

UAext,e WK1 2240

UAext,g WK1 2890

UAhx WK1 42

Va m3 0.024

Vc m3 0.014

Ve m3 0.024

Vg m3 0.024

z0,c M 0.2

z0,g M 0.2

z0,c e 1400

z0,g e 1400n machine.

Description

Discharge coefficient

Fouling factors

Height between condenser bottom and evaporator inlet

Height between generator bottom and absorber inlet

Cumulated heat capacity of the absorber

Cumulated heat capacity of the condenser

Cumulated heat capacity of the evaporator

Cumulated heat capacity of the generator

Cumulated heat capacity of the absorber heat exchanger

Cumulated heat capacity of the condenser heat exchanger

Cumulated heat capacity of the evaporator heat exchanger

Cumulated heat capacity of the generator heat exchanger

Thermal resistance between absorber and outdoors

Thermal resistance between condenser and outdoors

Thermal resistance between evaporator and outdoors

Thermal resistance between generator and outdoors

Gas constant for water vapour

Pipe section between condenser and evaporator

Pipe section between generator and absorber

Internal heat transfer coefficient of the absorber

Internal heat transfer coefficient of the condenserbecause the interior of themachine was not accessible and no

internal sensors had been installed by the manufacturers. For

this reason, the agreement between simulated and experi-

mental results was verified based on the outlet water

temperatures and on the thermal power exchanged by the

absorption chiller at each section.

Figs. 2 and 3 report the behaviour of the absorption

machine during two sunny days (14th of August and 8th of

September). These days are representative of the greatest part

of the experimental campaign: actually, during cloudy days

the absorption machine did not normally switch on, because

of the insufficient driving temperature provided by the solar

plant. Themain climatic data registered during both the afore-

mentioned days and the whole experimental campaign are

reported in Table 2.

As shown in the graphs, at around 11:00, as soon as the

water available at the generator inlet reaches 80 C, theabsorptionmachine turns on (see Fig. 2); the cold production is

almost immediate, as can be noticed from the profile of the

inlet and outlet temperatures at the evaporator. The chiller

produces cold water at mild temperatures, with a minimum

value of 13.7 C on August the 14th and 18.1 C on Septemberthe 8th, respectively. The highest driving temperature is

Internal heat transfer coefficient of the evaporator

Internal heat transfer coefficient of the generator

External heat transfer coefficient of the absorber

External heat transfer coefficient of the condenser

External heat transfer coefficient of the evaporator

External heat transfer coefficient of the generator

Overall heat transfer coefficient of the solution exchanger

Volume of the absorber

Volume of the condenser

Volume of the evaporator

Volume of the generator

Nominal height of the liquid inside the condenser

Nominal height of the solution inside the generator

Pressure loss coefficient (condenser/evaporator)

Pressure loss coefficient (generator/absorber)

Te

mp

eratu

re

[C

]

Te

mp

eratu

re

[C

]

Inlet Outlet Inlet Outleta b

r th

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 81022around 90 C. On the heat rejection loop, the water inlettemperature keeps in the range 30e35 C on August the 14thand 37e42 C on September the 8th.

The reason for the different performance during these 2

days is that during a short period of the experimental

campaign (from the 25th of August to the 8th of September),

a section of the ground heat exchanger was closed for exper-

imental reasons. As expected, due to the lower surface avail-

able for heat rejection, the water temperature in the rejection

loop raised in comparison with normal operation days, such

as the 14th of August. This induced a reduction in the cooling

capacity, hence an increase in the outlet temperature of the

chilled water.

The machine eventually stops when the driving tempera-

ture gets lower than 76 C, which occurs at around 17:40 onSeptember the 8th.

In addition, one can notice that the cooling power keeps

almost constant between 11:30 and 15:30 (around 6 kW on

August 14th and 4 kW on September 8th, see Fig. 3), but an

important reduction occurs during the last hours of operation.

Time [h]

Fig. 2 e Experimental inlet and outlet temperature profiles foFurthermore, the thermal COP, defined as the ratio of the

cooling power produced at the evaporator to the thermal

power required at the generator, is quite stable and suffi-

ciently high (0.71e0.75 and 0.65e0.7 in the two representative

days, respectively).

CO

P [-]

Th

erm

alp

ow

er[k

W]

a

Fig. 3 e Experimental energy performance of the absorpHere again, the better performance of the machine in the

first day, where the cooling power is almost 30% higher than

the machine nominal capacity, can be justified by the more

favourable operating conditions (lower temperature on the

heat rejection side).

Afterwards, the same representative days discussed above

were used to run the simulations, by using the water inlet

temperature profiles shown in Fig. 2 as an input to the

mathematical model, as well as the experimental values of

the water flow rate.

Themodel provides as output the values of thewater outlet

temperatures and the thermal powers, calculated as:

_Q j rw$ _Vj$cp;w$Tout Tinj (21)

Here, the density r of water is calculated as a function of the

inlet temperature (Florides et al., 2003). The water flow rates

measured on the real system are:

Hot water flow rate at the generator: _Vw;g 0:82 [m3 h1] Cold water flow rate at the evaporator: _Vw;e 1:34 [m3 h1] Cooling water flow rate at the condenser: _Vw;c 2:20 [m3 h1]

e absorption chiller (a: 14th of August, b: 8th of September).Time [h]Furthermore, the control logic of the absorption machine

were implemented, according to which the machine switches

onwhen the driving temperature gets higher than 80 C, and itturns off below 76 C.

CO

P [-]

Th

erm

alp

ow

er[k

W]

b

tion chiller (a: 14th of August, b: 8th of September).

The system of equations is solved on the simulation tool

SimSpark by using a NewtoneRaphson procedure with

forward finite difference approximation; the simulation is

performed with a time step as long as 5 s.

after calculating the profile of the thermal power exchanged at

each component, one can integrate over time in order to obtain

the overall thermal energy during a certain time interval. Table 3

reports the results of this procedure performed both over the

representative days previously described and over the whole

test campaign (107 days). The results are very encouraging,

as the absolute error on the cumulated daily and seasonal

cold production is lower than 0.3%; the error on the average

thermal COP is also very low. The highest discrepancy e around

5% e between experimental and simulated data occurs on the

heat rejection side (condenser absorber).If lookingmore in detail, one can notice that the sum of the

simulated values of the overall thermal energy provided at the

generator and evaporator does not correspond to that rejected

by the machine, as one would expect, but the latter is around

The results in Table 3 show that the proposed model not

only can be used to followwith a good approximation the daily

Table 2 e Main climatic data for the experimentalcampaign.

Tavext[C]

Tmaxext[C]

Imax

[Wm2]H [kWhm2

day1]

14th of August 23.4 33.5 827.3 6.36

8th of September 18.0 28.6 813.2 5.93

Whole period

(27/05e10/09)

21.8 40.6 1053.0 5.42

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 8 1023The discrepancy between experimental and simulated

results is shown in Figs. 4 and 5. In the first diagram, it is

possible to see the profile of the difference between simulated

andmeasured outlet temperatures during the chosen days. As

regards the evaporator outlet temperature (see Fig. 4), this

discrepancy keeps always very low (between 0.2 C and0.2 C). The precision of the model is also good for the gener-ator and the condenser outlet temperatures, as the discrep-

ancy with the experimental results never exceeds 0.4 C.Furthermore, the percentage error on the evaluation of the

thermal and cooling power is moderate, as shown in Fig. 5.

Here, each point in the graphs allows the comparison between

an experimental acquisition and its corresponding simulated

value (there is one point every 120 s of machine operation).

The deviation between experimental value and simulated

result is measured by the distance from the diagonal line,

where a perfect match between the two values holds. One can

remark that the absolute deviation is always lower than 10%

for all the components, but during the greatest part of the

operation time it is even lower than 5%. The error at the

evaporator (Fig. 5a) and the generator (Fig. 5b) tends to be

higher at low capacity, whereas it is almost negligible at high

capacity. The average error seems to be higher at the heat

rejection section (Fig. 5c). Because of such discrepancies, an

error on the evaluation of the thermal COP is expected, which

keeps however always lower than 5% (Fig. 5d).

Apart from verifying the capability of the model to describe

the dynamic performance of the absorption machine, it is also

important to test its reliability on a long time basis. To this aim,

aErro

r [C

]

Time [h]

Fig. 4 e Discrepancy between simulated and experimental oudynamic behaviour of the Rotartica absorption machine, but

also to evaluate its overall performance over a long period. In

any case, due to the amplitude of the acquisition time step

used in the experimental test rig (120 s), nothing can be said

about the precision of the model for transient phenomena

whose duration is shorter than that.

5. Consistency analysis

As shown before, the verification of the agreement between

simulated and experimental data was carried out through the

temperatures measured at the outlet of the absorption

machine, due to the impossibility to make measurements

inside the chiller. Nonetheless, the model is able to reproduce

the profile of pressure, temperature and LiBr concentration

inside the components, as well as the vapour and solution

Erro

r [C

]

Time [h]

b1e2% lower than the former. As amatter of fact, the process is

not adiabatic, and the thermal energy stored in the generator

is partially dissipated to the environment. On the contrary,

when looking at the experimental data, the thermal energy

rejected by the machine is always higher than the sum of that

measured at generator and evaporator, and the difference can

even reach 5%. This discrepancy might be attributed to the

heat produced by the electricmotor placed inside themachine

to maintain the rotation.tlet temperatures (a: 14th of August, b: 8th of September).

a b

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 81024cmass flow rates. The values of these parameters are shown in

Fig. 6 for the first day used in the previous analysis (14th of

August).

The parameter f represented in Fig. 6c is known as specific

backflow, and is defined as the ratio of the diluted solution e

which is rich in refrigerant e to the vapour produced in the

evaporator (Eicker, 2003):

Fig. 5 e Comparison between simulated and experimental energ

5% error.

Table 3 e Experimental and simulated values for daily and sea

Generator [kWh] Evaporator [kWh] Gene

Daily performance (14th of August)

Experimental 46.8 34.7

Simulated 47.1 34.6

Error 0.6% 0.1%Daily performance (8th of September)

Experimental 34.7 23.4

Simulated 34.0 23.4

Error 2.0% 0.0%Full test campaign (27/05e10/09)

Experimental 3278 2354

Simulated 3251 2362

Error 0.8% 0.3%df _ms;out;amev

xgxg xa (22)

It must be underlined that the diluted solution mass flow

rate pumped from the absorber to the generator is not

constant (see Fig. 6c), even though the volumetric flow rate

was set constant, due to the variation in the solution density.

y performance (both days). Solid line: 10% error; dotted line:

sonal energy performance.

r Evap [kWh] Heat rejection [kWh] Thermal COP [e]

81.5 85.0 0.741

81.7 80.9 0.735

e 4.8% 0.7%

58.1 58.7 0.674

57.4 56.2 0.688

e 4.2% 2.0%

5632 5849 0.718

5613 5559 0.727

e 4.9% 1.2%

a transient period of at least 400 s is needed by the chiller to

reach new steady-state operation.

6. Use of the simulations for the systemimprovement

Themodel presented and validated in the previous sections is

b

c

Fig. 6 e Simulated values for the main internal parameters

(14th of August). (a): Pressure and LiBr concentration, (b):

temperature, (c): mass flow rates.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 8 1025This density is highly influenced by the LiBr concentration,

according to the relation proposed in (Florides et al., 2003).

In order to check the internal consistency of themathemat-

ical model, a further test was carried out (see also Kohlenbach

and Ziegler, 2008b). A new simulation was run by adopting

constant cooling and chilled water inlet temperatures 30 Cand 18 C, respectivelye and a step changefrom80 C to 90 Ce to the driving temperature. In this case the simulation time

step was set at 1 s. The duration of the simulation is 2000 s; the

temperature step occurs at 1000 s after the beginning, as

a certain delay is needed to wait for the system to reach steady

operation in the initial operating conditions. Such an analysis is

alsohelpful to investigate intomassandthermalstorageeffects.

AsshowninFig.7, thetemperaturestep is followedbyasteep

increase of the thermal power released to the solution in the

generator (see graphg), hence by an increase of themassflowof

vapour desorbed (see graph e). As a consequence of the higher

vapour production rate, the LiBr concentration of the diluted

solution inside the generator starts growing (see graph d).

A more important vapour flow rate is then conveyed to the

condenser but actually, due to the storage effects, the increase

of the condensation rate follows in a slower fashion (see the

curvem_l in graph e). Therefore, the condenser pressure rises,

which is also communicated to the generator (see graph d); as

saturation holds in the condenser, such a pressure increase

also induces a temperature rise (see graph b).

Fig. 7g also shows that the thermal power delivered to the

generator tends to decrease after the initial step; such an

effect is due to the growing temperature of the solution (see

graph a), and then to the reduced heat transfer potential. It is

interesting to underline that, despite the reduced thermal

power, the vapour production keeps rising (see graph e): as

a matter of fact, at higher pressure and temperature the

energy needed to release an unit mass of vapour is lower.

Again from Fig. 7e, one can notice that during the transient

stage, the evaporation rate at the evaporator keeps higher

than the liquid production rate at the condenser; this implies

a fall in the evaporator absorber pressure (see graph d) anda consequent reduction in the evaporator temperature (see

graph c). Furthermore, due to the time lag between vapour

production in the generator and in the evaporator, a higher

generator thermal power is not immediately followed by an

equivalent rise in cooling production (see graph g, time 1000),

thus the thermal COP initially shows a sudden decrease.

However, such a fall is progressively recovered as long as the

cooling power grows and the thermal power decreases.

As far as the solution mass flow is concerned, the strong

solution conveyed from the generator to the absorber initially

decreases (see graph f), as a consequence of the higher vapour

production. However, as far as the temperature and the LiBr

concentration at generator rise, the density of the strong

solution gets higher, and this implies, at around 1040 s, an

inversion in the curve representing the strong solution rate

(see graph f). In the absorber, temperature and LiBr concen-

tration also rise (see graphs b and d), due to the same tendency

previously identified at the generator.

The simulated behaviour of the absorption chiller after

a step of 10 K in the driving temperature is then coherent withwhat would be expected from thermodynamics. Such a test

also showed that, due to thermal and mass storage effects,auseful to simulate the performance of the Rotartica chiller

when integrated into a solar-assisted air-conditioning system,

bi n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 81026aas it is able to describe with good accuracy the dynamic

response of the chiller both to load variations and to

a continuous change in the driving temperature. In a solar-

assisted system, the latter are strictly connected with the

c d

e

g

Fig. 7 e Simulated response of the absorption chilleenvironmental conditions, especially if no back-up is avail-

able, as occurs in the plant considered in this study.

In order to show the usefulness of the model in a practical

case, several simulations were carried out to investigate into

f

r to a step variation in the driving temperature.

climatic data registered during the experimental campaign.

The corresponding profiles of the outdoor temperature and of

the solar irradiance on the surface of the collectors are re-

ported in Fig. 8

The results of such parametric analysis are shown in

Table 4. In order to justify them, it is useful to remind that the

absorption unit starts working when the driving temperature

reaches 80 C, and eventually stops when the latter gets lowerthan 76 C.

As a rule, the higher the volume of the hot storage is, the

longer it takes for the hot water to reach theminimumdriving

temperature needed to run the absorption unit: as a conse-

quence, the unit starts working late in the morning. However,

a higher storage volume also allows a slower thermal

In this paper, a dynamic model for the simulation of

Fig. 8 e Experimental values of the climatic data for the

period considered in the simulations (from the 11th to the

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 8 1027the effect of the size of the storage tanks on the chiller

performanceemeasured by its cold production and its thermal

COP e when the chiller is used in a solar-assisted air-condi-

tioning system like the one installed at INES and described in

Section 4. This system contains two storage tanks:

- the hot storage tank (400 l) is used to collect the hot water

produced by the solar section, and provides the hot water

flow that drives the absorption unit;

- the cold storage tank (300 l) is used to store the chilled water

produced by the absorption unit, and provides cold water to

feed the fan-coil units.

More details concerning the layout of the system, the

models used to simulate the other components (solar collec-

tors, storage tanks) and the reliability of such models can be

found in (Evola et al., 2010).

Afirstseriesof simulationswasperformedbyvaryingthesize

of the hot storage tank (from 200 to 1000 l) and keeping the

volume of the cold storage tank at the real value. Then, in

asecondseriesofsimulations, thevolumeof thehotstoragetank

was kept constant (400 l) and the cold storage tank was varied

between 200 and 600 l. In all the simulations an insulating layer

17th of August).madeupof 40mmof polystyrene is applied to the storage tanks.

The simulations were run over one week (from the 11th to

the 17th of August) by using, as input values for themodel, the

Table 4 e Influence of the storage volume (up: hot storage e bochiller.

Storage volume (hot water) [l] 200

Chiller activation time from 10:10

to 17:00

Average daily cold production [kWh/day] 39.2

Average daily thermal COP [] 0.705COP variation 1.0%

Storage volume (cold water) [l] 200

Chiller activation time from 10:50

to 17:30

Average daily cold production [kWh/day] 38.6

Average thermal COP [] 0.708COP variation 0.6%a commercial single-effect LiBr/water absorption chiller has

been described. The structure of the model makes it suitable

for a general use, but in this context it has been applied to the

absorption unit distributed by Rotartica, which is different

from common LiBr absorption chillers as the thermal cycle is

performed inside a rotating vessel. After defining the values of

the parameters which best describe the geometry of the

Rotartica chiller, the reliability of the model has been verified

by comparing the simulated results to those collected in an

experimental installation. The comparison was based on the

values of the outlet water temperature and on the thermal

power exchanged at each section, as no internal parameters

ttom: cold storage) on the performance of the absorption

400 600 800 1000

10:50 11:20 11:50 12:20

17:30 18:00 18:20 18:50

39.0 38.9 38.8 38.7

0.712 0.718 0.724 0.728

d 0.8% 1.6% 2.3%

300 400 500 600

10:50 10:50 10:50 10:50

17:30 17:30 17:30 17:30

39.0 39.2 39.4 39.6

0.712 0.716 0.719 0.722discharge, thus the daily operation has a duration that does

not change noticeably as a function of the hot storage volume.

On the whole, higher storage volume means lower average

temperatures, which induces for the Rotartica absorption unit

a slight decrease in the cold production but also a slight

increase in the average thermal COP.

On the other hand, a variation in the volume of the cold

storage tank does not affect the driving conditions, thus the

chiller activation time stays the same. However, in this case,

higher storage volumemeans higher average temperatures for

the chilled water, which improves the average thermal COP of

the absorption unit and reduces the overall cold production.

7. Conclusionsd 0.5% 1.0% 1.4%

(pressure, salt concentration, temperature) could be Bakhtiari, B., Fradette, L., Legros, R., Paris, J., 2011. A model for

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 6 ( 2 0 1 3 ) 1 0 1 5e1 0 2 81028measured inside the machine.

Themodel shows a good agreement with the experimental

data: the transient performance during two typical operation

days is simulated with a satisfying accuracy, since the devia-

tion between the instantaneous simulated and experimental

values of cooling power and COP never exceeds 5%. The paper

also verifies the capability of the model to describe the system

performance on a long time basis: the results are very

encouraging, as the error on the overall test campaign is

around 1%.

A fundamental condition to obtain such a high reliability

is the good estimation of the chiller design parameters,

based on the availability of design data and schemes

provided by the manufacturers. In the paper, these results

were obtained without any tuning or calibration of the input

parameters.

In addition, a consistency analysis was also performed to

investigate the response of the model to a 10 K temperature

step applied to the driving temperature. According to this test,

the behaviour of the chiller is perfectly consistent with ther-

modynamics; the time needed to reach steady-state operation

after the temperature step is around 8 min.

Finally, an example of practical application of the model is

presented, where simulations are used to investigate into the

influence of the storage volume on the chiller performance,

in the specific case of the solar-assisted air-conditioning

system installed at INES (Institut National de lEnergie Sol-

aire, France) for the air-conditioning of some offices. The

simulations allowed to understand that increasing the

volume of the hot storage is beneficial in order to improve the

average thermal COP, even though a slight reduction in the

cold production and a shift in the operating time must be

accounted for.

The dynamic model presented in this paper is then a reli-

able tool to evaluate the long-term behaviour of a single-effect

LiBr/water absorption chiller, but also to follow its daily

operational profile with good precision. Its use is suggested to

study the interaction of the absorption unit with the other

components of a solar-assisted cooling plant, with the aim of

optimizing both the layout of the system and the control logic

of the chiller.

Acknowledgements

The experimental installation has been financed in the

framework of the European project SOLERA (FP6), coordinated

by Fraunhofer ISE. The study of its performance has been

conducted in the framework of the research project ORASOL

ANR 06-PBAT-009-01.

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Proposal and validation of a model for the dynamic simulation of a solar-assisted single-stage LiBr/water absorption chiller1. Introduction2. Description of the model2.1. Generator and absorber2.2. Condenser and evaporator2.3. Heat exchangers2.4. Other devices

3. Definition of the parameters4. Experimental verification5. Consistency analysis6. Use of the simulations for the system improvement7. ConclusionsAcknowledgementsReferences