Dougs Thermo 2a Complete Course Work Report Final

8/2/2019 Dougs Thermo 2a Complete Course Work Report Final

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Faculty of Engineering

Science and

Built Environment

Course: BEng Building Services Engineering

Mode: Part Time

Level: Two

Unit: Thermofluids 2 A

Tutor: Dr S Ahuja

Unit Code: DTF-2-257

Date: Semester 1, 2010

Prepared By

Douglas Buchan


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Combined Cycle ReportThermofluids 2a

PRODUCED BY

DOUGLAS BUCHAN

2911727

12.12.2010


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COURESEWORK 2 FOR THERMOFLUIDS 2A

(From thermodynamics part of this unit)

A gas-turbine power plant operates on a pressure ratio of 13:1 with compressor and

turbine-inlet temperatures of 290 and 1440 K, respectively. The adiabatic

efficiencies of the compressor and turbine are 84% and 88%, respectively. The

turbine exhaust, used as the energy source for a steam cycle, leaves the boiler at

500 K. The inlet conditions to the 86% efficient turbine in the steam cycle are

160 bar and 560 C. The condenser pressure is 0.08 bar, and the pump is 70%

efficient. Calculate:

a) The required heat input, in kJ/kg of air

b) The mass flow rate ratio of air to steam

c) The net work output of the gas-turbine cycle, in kJ/kg of air

d) The net work output of the steam cycle, in kJ/kg of steam

e) Overall thermal efficiency of the combined cycle

f) Specific volume of air at the inlet of combustor, in m3/kg if air coming into the

Brayton cycle is at 1 atmosphere.

g) Draw a sketch of the complete cycle

h) Show relevant P-v, T-s or h-s diagram for both the cycles

Assume:

1) Cp for air = 1.005 kJ/(kg K)2) Cp for combustion gases = 1.115 kJ/(kg K)

Assessment:

The solution must be presented in a professional report format. Each element of the

Engineering Problem Solving Method must be clearly listed. Each of the above, a

through h, are worth 10 marks each. 10 marks are for assumptions. 10 marks are

for clarity of your work and report presentation.

Submission deadline: 16 December, 2010. Submit your report to FESBE Faculty

Office T 313.


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Contents

Introduction 1

Brayton Cycle Analysis

System Description 2

System Thermodynamics 2

Temperature Analysis 3

PV and TS Diagrams 4

Volumetric Analysis 5

Work Input and Output Analysis 7

Rankine Cycle Analysis



Properties of Steam and Water Analysis 9

Summary of Interpolated Results 11

Thermodynamic Analysis 11

PV and TS Diagrams 12

Combined Cycle Analysis



Thermal Efficiency Analysis 17

Conclusions 18

Further Analysis and Recommendations 18

Bibliography


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Combined Cycle Report

1

Introduction

This report contains an analysis of a combined cycle which has been undertaken in

order to inform the client of the performance, through the various stages, of the

processes involved. The combined cycle involves two processes, firstly the Brayton

Cycle or Gas Cycle, and secondly the Rankine Cycle or Steam Cycle.

Both of these cycles provide a means of generating electrical power. The reason that

the cycles are combined (which is also termed Co-generation) is due to the fact that

the exhaust gasses, which are a product of the Brayton Cycle, can be utilised in the

Rankine cycle in order to produce the steam required to drive a turbine.

The effects of this are obvious; by extracting the heat energy from the exhaust

gasses more electrical energy can be produced, whilst the initial energy input, i.e.

the combustion of fossil fuels, remains constant. This increases efficiency which in

turn reduces the amount of CO2 released into the atmosphere.

The fact that the Brayton Cycle provides the input heat energy for the Rankine cycle

dictated that this cycle was the first to be selected for analysis.


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2

Brayton Cycle Analysis

Fig 1, Schematic Diagram which is representative of the Brayton Cycle.

System Description

Air enters the cycle at the air intake (point 1), the air is then compressed in the

compressor, which in an ideal cycle is an isentropic process, i.e. the entropy remains

constant. This compressed air is then channelled to the combustor (point 2). Fuel is

then mixed with the compressed air before being ignited in the combustor, which is

an isobaric process, i.e. the pressure remains constant. The now heated air reaches

the turbine (point 3) where is velocity is used to turn the turbine which in turn

provides mechanical work which will drive the electrical generator as well as

powering the crankshaft which connects to the Compressor, this process is again

isentropic. The hot exhaust gasses then pass through a heat exchanger (between

points 4-5) where heat is extracted from the gasses for use in the Rankine cycle, this

process is isobaric.

System Thermodynamics

The following conditions were known and were not calculated as part of my analysis.The gas-turbine power plant operates on a pressure ratio of 13:1 with compressorand turbine-inlet temperatures of 290 and 1440 K, respectively. The adiabaticefficiencies of the compressor and turbine are 84% and 88%, respectively. Theturbine exhaust, used as the energy source for a steam cycle, leaves the boiler at

500 K.

Compressor

From Process

Heat Exchanger

Combustor

Turbine

To Process

2

3

4

1

5

Fuel In

Work Out


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The following assumptions have been made;

1. Air is delivered to compressor at atmospheric pressure of 101325 Pa

2. The Fuel used in the combustor is natural gas

3. The process is an ideal cycle

4. The Heat Exchanger is 100% efficient and has no losses

5. The specific Heat Capacity for Air is 1.005 kJ/(kg K)

6. The specific Heat Capacity for Combustion Gases is 1.115 kJ/(kg K)

Temperature analysis

T1 = 290 K (Compressor inlet temp)

T3 = 1440K (Turbine inlet temp)

Heat Capacity Ratio (Cp/Cv) (1.4 from class notes)

Pressure Ratio)

Turbine= 88%

Compressor = 84%

T2 had to be calculated using the following formula;

T2 = 603.5K

T4 was calculated in a similar manner;

T4 = 692K


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4

A temperature entropy diagram can now be plotted using these values.

S

Compression

Q Out

T

Q In

Work Out

Work In

Fig 2 Temperature Entropy Diagram showing the Brayton Cycle

V

Compression

ExpansionIsentropic

Isentropic

Isobaric

Isobaric

Q In

Q Out

P

Fig 3 Pressure Volume Diagram showing the Brayton Cycle


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The temperatures that have been established were also used to assess the requiredheat input to the cycle. The following assumptions were made;

Cp for air = 1.005 kJ/(kg K)

Cp for combustion gases = 1.115 kJ/(kg K)

Using the calculated value for T2 and the value given for T3 the following formula hasbeen used to carry out an assessment of the required heating input;

Qin = 932.7 kj/kg

Volumetric Analysis

In order to establish the specific volume of the air entering the combustor I haveused the Ideal gas law in conjunction with data taken from Thermodynamic andTransport Properties of Fluids fifth Edition;

Formula of Ideal Gas Law

Where:

V = Volume (m3/s)P = Pressure of fluid medium (bar)n = Amount of substance (mol)T = Temperature (Kelvin)V = Specific Volume (m3/kg)

R = Specific Gas Constant = Molar Gas Constant


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GAS CONSTANT

Where:

Entering Pressure

The air pressure entering the Brayton cycle is at 1 atmosphere which is takento be standard atmospheric pressure of 1.01325 bar, it is then compressed inthe compressor at a pressure ratio of 13:1. I have used the following formulato calculate the pressure of air entering combustor;

Specific volume at combustor inlet

T=603.5K

p=1.01325bar=101.325kPa


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Work Input and Output Analysis

The temperatures calculated for the Brayton Cycle have been utilised to calculatethe amount of mechanical work being inputted and outputted to and from the system.

Compressor Work Done (Wc)

This figure represents the work input of the compressor had it been operating at100% efficiency, however the turbine efficiency is stated as 88%.Therefore the actual work input of the compressor has been calculated as follows;

Turbine Work Done (WT)

WT =

This figure represents the output of the turbine had it been operating at 100%efficiency, however the turbine efficiency is stated as 88%.Therefore the actual output of the turbine has been calculated as follows;

WT Actual = 733.92 kj/kg

Net Work Output for Brayton Cycle

WNe t= WT Actual WC Actual = 733.92 kj/kg 375.08 kj/kg

WNet = 358.84 kj/kg


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Rankine Cycle Analysis

Fig 4, Schematic Diagram which is representative of the Rankine Cycle.

System Description

Water enters the pump (point 1), and through the work input of the pump ispressurised to a higher pressure and begins the cycle, which in an ideal cycle is an

isentropic process, i.e. the entropy remains constant. The high pressure water is

then channelled to the Heat Exchanger (point 2). The Heat Exchanger (between

points 2-3) heats the water in the Rankine cycle and thus converts it into steam, the

heat generated during combustion on the Brayton cycle has been utilised as a heat

source in this instance, (This is a similar process to using a boiler, etc) which is an

isobaric process, i.e. the pressure remains constant. The now superheated steam

(dry saturated water vapour) reaches the turbine (point 3) where is velocity (due to

expansion) is used to turn the turbine which in turn provides mechanical work whichwill drive the electrical generator, this process is again isentropic. The wet vapour

(due to the loss of pressure and temperature) then leaves the turbine (point 4) it then

passes through a Condenser where it is converted to a saturated liquid due to the

additional temperature loss (between points 4-1), this process is isobaric.


The following conditions were known and were not calculated as part of my analysis.The inlet conditions to the 86% efficient turbine in the Rankine cycle are 160 bar and560 C. The condenser pressure is 0.08 bar, and the pump is 70% efficient. In order

to carry out an analysis of this system I will be consulting the steam tables providedin Thermodynamic and Transport Properties of Fluids, Fifth Edition.

Work Out

Q out

Q in

41

Turbine

Heat Exchanger

Condenser

2

3

56

Work InPump


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Properties of Water and Steam Analysis

In Order to achieve the correct figure for h1 I have had to interpolate the steam tables

as 0.08bar is not listed. The interpolation of the figures in the table is as follows;

Therefore

In Order to achieve the correct figure for h3 I have had to interpolate the steam tables

as 560oC @160bar is not listed. The interpolation of the figures in the table is as

follows;

Therefore

In Order to achieve the correct figure for h fg @ 0.8bar I have had to interpolate the

steam tables as 0.08bar is not listed. The interpolation of the figures in the table is as

follows;

Therefore


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In Order to achieve the correct figure for S1 I have had to interpolate the steam

tables as 0.08bar is not listed. The interpolation of the figures in the table is as

follows;

Therefore

In Order to achieve the correct figure for S fg @ 0.08bar I have had to interpolate the


follows;

Therefore

In Order to achieve the correct figure for V f @ 0.08bar I have had to interpolate the


follows;

0.0010081Therefore


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Summary of interpolated results

Thermodynamic Analysis

Quality Dryness

Enthalpy @ h4

Work Done Pump

Enthalpy @ h2


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Work Done Turbine

The Pressure Volume Chart can now be plotted.

Liquid VapourLiquid and Vapour

1

4 3

2

V

P

Fig 5. A Pressure volume Chart showing the Ideal Rankine Cycle.


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13

Liquid VapourLiquid and Vapour

1

43

2

S

T

SuperheatedSteam

Fig 6. Temperature Entropy Diagram showing the ideal Rankine Cycle.


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14

Combined Cycle Analysis

Fig 5. Schematic Diagram which is representative of the Combined Cycle.

System Description

The combined cycle is composed of the two component parts that have been shown

in detail in previous chapters of this report. Namely the Brayton Cycle (Gas Turbine)

and the Rankine cycle (Steam Turbine). The Brayton cycle is an open system in that

the cycle requires a fresh intake of air (the fluid medium) for each cycle. The Rankine

cycle is a closed system in that the water (the fluid medium) is constantly recycled.

The way in which the systems operate independently has been described in this

report (see Brayton and Rankine cycle system descriptions), however to summarise,

Q out

Turbine

Heat Exchanger

Condenser

Work Out

Work InPump

Compressor

Heat Exchanger

Combustor

Turbine

Fuel In

Work Out

Brayton Cycle

Rankine Cycle

ExhaustGasses

Air Intake


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the heat input to the Rankine Cycle is provided by the gasses rejected by the

Brayton Cycle turbine. The heat transfer is facilitated by way of a heat exchanger.

The combined cycle produces electricity from both of these cycles and is shown

diagrammatically below; this should help the reader of this report to envisage how

the processes are used.

Fig 6, Diagram which shows the Combined Cycle1.

1Diagram from, http://www.power-technology.com/projects/san_joaquin/san_joaquin3.html


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Heat Rejected From Brayton Exhaust Gas

Exhaust gases leave turbine at 692K and enter the heat exchanger, in which heat is

transferred to the Steam Cycle. Exhaust gases leave the heat exchanger at a

temperature of 500K. I have used the assumed cp of the exhaust gas.

Assuming that 1 kg/s of combusted gas will be circulating then;

Heat Absorbed

I have assumed the heat exchanger to be ideal and as such it shall experience no

losses. Therefore the same amount of heat that was rejected by the Brayton Cycle

through the heat exchanger will be absorbed by the water from the Rankine Cycle. In

the Rankine cycle I will be using the enthalpies instead of temperatures and the

assumed cp value for steam.

From this equation I have calculated the mass flow rate of the steam, which is found

using the following equation;


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Mass Flow Rate Ratio

I have assumed that the mass flow rate of the exhaust gases is 1 kg/s. The ratio of

steam cycle has been calculated through the heat exchanged in the heat exchanger.

The ratio at which air cycles in comparison to that of steam was found to be; 15.4: 1

The net work output of the steam cycle [kJ/kg] of steam

Thermal Efficiency Analysis

Heat Input

Work Done Brayton Cycle

Work Done Rankine Cycle

Thermal Efficiency


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Conclusions

It can be seen, from the results of my calculations, that the Rankine Cycle has

produced 78.9 KW of Energy. Although the work that the pump has put into the

Rankine cycle should be taken into account it is negligible. Therefore for the

purposes of this report it can be assumed that the combined cycle has produced

nearly 80KW of energy during a cycle. Of course the extra capital costs of

implementing a system of this type would need to be taken into account before the

final cost benefit (and payback period) to the client could be assessed.

Further Analysis and Recommendations

The type of turbine fan blades that have been used as well as the pitch angle that

they have been set at is undetermined; as a result further investigation should takeplace. This further work will certainly determine whether efficiency can be improved.

The temperature of the gases being exhausted are currently still at 500 Kelvin, this

heat is being lost. It is recommended that a feasibility study is carried out to ascertain

whether this lost heat could be utilised for other uses such as space heating or other

building services applications, this type of study is outwith the scope of this report.

Frictional losses from rotating machinery have not been taken into account but will

almost certainly be present; it is recommended that the client commission a more in-

depth report into these areas, this type of study is outwith the scope of this report.

The combustion efficiency of the natural gas will also play a major part in the

efficiency of the combined cycle this has been assumed to be ideal for the purpose

of this report.


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Bibliography

Handbook for cogeneration and combined cycle power plants,

By Meherwan P. Boyce

Thermodynamic and transport properties of fluids: SI units

By G. F. C. Rogers, Yon Richard Mayhew

Thermodynamics and Thermal Engineering

By J.Selwin Rajadurai

Fundamentals of engineering thermodynamics

By Michael J. Moran, Howard N. Shapiro

Websites Consulted

http://web.mit.edu/

http://www.cogeneration.net

http://www.power-technology.com
http://www.google.co.uk/search?tbs=bks:1&tbo=p&q=+inauthor:%22G.+F.+C.+Rogers%22http://www.google.co.uk/search?tbs=bks:1&tbo=p&q=+inauthor:%22Yon+Richard+Mayhew%22http://www.google.co.uk/search?tbs=bks:1&tbo=p&q=+inauthor:%22Yon+Richard+Mayhew%22http://web.mit.edu/http://web.mit.edu/http://www.cogeneration.net/http://www.cogeneration.net/http://www.power-technology.com/http://www.power-technology.com/http://www.power-technology.com/http://www.cogeneration.net/http://web.mit.edu/http://www.google.co.uk/search?tbs=bks:1&tbo=p&q=+inauthor:%22Yon+Richard+Mayhew%22http://www.google.co.uk/search?tbs=bks:1&tbo=p&q=+inauthor:%22G.+F.+C.+Rogers%22

Dougs Thermo 2a Complete Course Work Report Final

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