Thermodynamics for gas turbine cycles 1of2

Introduction to Thermodynamics for Gas Turbine Cycles & Cycle Simulation Tools

A Cycle Innova-ons Tutorial Session by

Pavlos K. Zachos -‐ Luis Sanchez de LeonDepartment of Power & Propulsion

Cranfield University, UK

ASME Turbo Expo 2013San Antonio, US

CRANFIELD UNIVERSITYDEPARTMENT OF POWER & PROPULSION

These slides have been prepared by Cranfield University for the personal use of tutorial attendees. Accordingly, they may not be communicated to a third party without the express permission of the author(s). The slides are intended to support the tutorial in which they are to be presented. However the content may be more comprehensive than the presentations they are supporting.

Some of the data contained in the notes/slides may have been obtained from public literature. However, in such cases, the corresponding manufacturers or originators are in no way responsible for the accuracy of such material.

All the information provided has been judged in good faith as appropriate for the course. However, Cranfield University accepts no liability resulting from the use of such information.

Disclaimer

Who we are...

Pavlos K. ZachosLecturer in Aerothermal Performance of TurbomachineryDepartment of Power & PropulsionCranfield University, UKp.zachos@cranfield.ac.uk

Luis Sanchez de LeonDoctoral Researcher in Advanced Cycle Performance

Department of Power & PropulsionCranfield University, UK

l.sanchezdeleon@cranfield.ac.uk

Thermodynamics for Gas Turbine Cycles & Cycle Simulation ToolsASME Turbo Expo San Antonio, Texas, 6th June 2013

PART I - Thermodynamics in our every day life.

PART II - A little bit of modelling.

PART III - A whole lot of modelling.

Why do you care ?

The science.

The people.

The product.

Thermo dynamics

θέρμη (therme)

δυναμική

=theory of relationship between heat and mechanical energy

Aeolipile (or Hero engine)Hero of Alexandria

1st century AD[source: Encyclopedia Britannica]

source: WikipediaThermodynamics for Gas Turbine Cycles & Cycle Simulation Tools

ASME Turbo Expo San Antonio, Texas, 6th June 2013

Otto von Guericke invents the vacuum pump

Boyle & Hookenotice a correlation betweenpressure, temperature and volume

18501750

Carnotcorrelates heat , power, energy & engine efficiency

Rankine - Clausius - Lord Kelvin1st & 2nd Laws of Thermodynamics

Saverybuilds the first steam piston engineto be later improved by Watt

Father of Thermodynamics

equation of state

Entropy, s

34Entropy, s

Entropy, s

v = co

v = const.

P = const.

v = co

Entropy, s

P = const.

Carnot cycle Ideal Otto cycle

Ideal Diesel cycle Ideal Brayton cycleThermodynamics for Gas Turbine Cycles & Cycle Simulation ToolsASME Turbo Expo San Antonio, Texas, 6th June 2013

Why do you care ?

BREATH.

TRAVEL.

Case study:London to New York5,526 km

100 days in 1866 by sailing ship

15 days in 1910 by early steam ships

3 days in 1960 by the fastest steam ship

< 8 hrs today by plane !!

= £475 per kg[source: http://www.bullionbypost.co.uk on 21.5.2013]

Courtesy of Rolls-Royce

per kg

aerodynamics materials

emissions

mechanical integrity

market research&

logistics

system integration

cycle thermodynamics

controls

Entropy, s

P = const.

George Brayton1830 - 1892

Sir Frank Whittle1907 - 1996

Dr Hans von Ohain1911 - 1998

Courtesy of Rolls-Royce

Here’s to the crazy ones.The misfits.The rebels.The troublemakers.The ones who see things differently.They are not fond of rules.And they have no respect for the status quo.You can praise them, disagree with them, quote, disbelieve them, glorify or vilify them.

About the only thing you can’t do...

Apple advertising campaignSeptember 1997

...is ignore them...

...because they change things

...and also the way WE see things...22

Let’s talk about today...

6 Trillion kg CO2

source: ClimateCrisis.netThermodynamics for Gas Turbine Cycles & Cycle Simulation ToolsASME Turbo Expo San Antonio, Texas, 6th June 2013

20,000 kg CO2 per year and person

4,500 kg CO2 per year and person

450 ppm

10% less rainfall

Dust storm approaching Stratford, TEXAS - April 1935source: http://www.weru.ksu.edu

aerodynamics materials

emissions

mechanical integrity

market research&

logistics

system integration

cycle thermodynamics

controls

PART II

Families of thermodynamic cycles

Powercycles

Refrigerationcycles

Gascycles

Vaporcycles

Closedcycles

Opencycles

Families of thermodynamic cycles

Powercycles

Refrigerationcycles

Gascycles

Vaporcycles

Closedcycles

Opencycles

Basic considerations in the analysis of power cycles

1. Study the ideal cycle first

No frictionNo heat lossesQuasi-equilibrium compressions & expansions

2. Neglect kinetic and potential energies

3. Use P-v or T-s diagrams

• Air as working fluid

• Ideal gas

Air standard assumptions

Equation of State: PV = RT

Cv=γ R = Cp - Cv

• Semi-perfect gas

Cp / Cv

Constant Cp / Cv

functions of Temperature

γ= 1.33 - Turbinesγ= 1.40 - Compressors

Internal Energy=

The total energy contained by a thermodynamic system

Internal Energy = u(T)

u(T) + pV = Enthalpy

u(T) + RT = Enthalpy = h(T)

Specific Heat Capacity at Constant Volume

Specific Heat Capacity at Constant Pressure

Ideal Gas Model

PV = RT

Internal Energy = u(T) = Cv T

Enthalpy = u(T) + RT = h(T) = Cp T

γ= 1.33 - Turbines

γ= 1.40 - Compressors

Wilcock R. C., Young J. B., and Horlock J. H., 2002, “Gas properties as a limit to gas turbine performance.”

Kyprianidis K., Sethi V., Ogaji S. O., PILIDIS P., Singh R., and KALFAS A. I., 2009, “Thermo-Fluid Modelling for Gas Turbines-Part I: Theoretical Foundation and

Uncertainty Analysis.”

Kyprianidis K., Sethi V., Ogaji S. O., PILIDIS P., Singh R., and KALFAS A. I., 2009, “Thermo-Fluid Modelling for Gas Turbines-Part II: Impact on Performance

Calculations and Emissions Predictions at Aircraft System Level.”

Entropy, s

P2 = co

P1 = const.

heat in

heat out

work in

maximum cycle pressure

limited by compressor

technology

maximum cycle temperaturelimited by turbine technology

work out

Useful work(Net)

Entropy, s

P2 = co

P1 = const.

heat in

heat out

work in

work out

Compressor Turbine

Combustionchamber

Ideal Brayton cycle processes:

1-2: Isentropic compression2-3: Constant pressure heat addition3-4: Isentropic expansion4-1: Constant pressure heat rejection

InletEnthalpy

OutletEnthalpy

(qin - qout) + (win - wout) = 0

= -wnet

wnet = qin - qout

Steady-flow process energy balance on a unit-mass basis:

wnet = qin - qout

qin = h3 - h2 = cp (T3 - T2)

qout = h4 - h1 = cp (T4 - T1)

Entropy, s

P2 = co

P1 = const.

heat in

heat out

work in

work out

Compressor Turbine

Combustionchamber

Fresh air

Exhaust gases

work out

wnet = qin - qout

qin = h3 - h2 = cp (T3 - T2)qout = h4 - h1 = cp (T4 - T1)

ηthermal =wnet

qin= 1-

using...

( )γ-1/γ

ηthermal = 1- 1

γ-1/γ

Entropy, s

P2 = co

P1 = const.

heat in

heat out

work in

work out

Compressor Turbine

Combustionchamber

Fresh air

Exhaust gases

work out

ηthermal = 1- 1

γ-1/γ

alPressure ratio

Is this right ?

Entropy, s

2s4s2a

in reality...- no compression/expansion is isentropic &- some pressure loss is inevitable

ηcompr

ηturb

h2s - h1

h2a - h1

h3 - h4a

h3 - h4s

Component isentropic efficiencies:

for preliminary cycle modelling component

efficiencies can be guessed or estimated

Case study #1:Effect of compressor efficiency on cycle performance

Compressor Turbine

Combustionchamber

- Standard air assumptions- Standard ISA conditions: 288.15K @ 1 bar- Constant ηt,is

- T3 = 1600K - Combustion efficiency=0.98- Account for cooling flows

isentropic

Isentropic

0.90.85

1 3 5 7 9 11 13 15OVERALL PRESSURE RATIO

POLYTROPIC EFFICIENCY = 0.90

Case study #2:Effect of Turbine Entry Temperature on cycle performance

Compressor Turbine

Combustionchamber

- Standard air assumptions- Standard ISA conditions: 288.15K @ 1 bar- Constant ηt,is

- Combustion efficiency=0.98- Account for cooling flows

Assuming a value for the polytropic efficiency of our compressor a new isentropic efficiency is calculated for every pressure ratio based on:

TET = 1000 K

1200 K1400 K

1600 K 1800 K

Cycle design in a gas turbine performance solverUse of “BRICKS”

Compressor Turbine

Combustionchamber

Thrust per unit flow

IntakeFreshair

ALTITUDE

MACH No.

Rel. Humidity

PRESSURE RECOVERYFACTOR

PRESSURE RATIO

POLYTROPICEFFICIENCY

BLEED FLOWS

COMBUSTION EFFICIENCY

PRESSURE LOSS

TURBINE ENTRY TEMPERATURE

ISENTROPICEFFICIENCY

COOLINGFLOWS

Nozzle

Cycle design in a gas turbine performance solverUse of “BRICKS”

Compressor Turbine

Combustionchamber

IntakeFreshair

ALTITUDE

MACH No.

Rel. Humidity

PRESSURE RATIO

BLEED FLOWS

PRESSURE LOSS

COOLINGFLOWS

Output Powerper unit flow

Case study #3:Single spool gas generator design space exploraIon

Compressor Turbine

Combustionchamber

IntakeFreshair

ALTITUDE

MACH No.

Rel. Humidity

PRESSURE RATIO

BLEED FLOWS

PRESSURE LOSS

COOLINGFLOWS

Output Powerper unit flow

5% 0.91

SpecificFuel

Consumption=

Fuel flow [kg/s]def

initio

nsor SFC

SpecificPower =

Net Output [J/s]

Mass flow [kg/s]Thermodynamics for Gas Turbine Cycles & Cycle Simulation Tools

ASME Turbo Expo San Antonio, Texas, 6th June 2013

PR = 3

PR = 6

PR = 15 TET = 1000 K TET = 1200 K

TET = 1400 K TET = 1600 K Large sizeHigh weight

Small sizeLow weight

Lowtechnology

Hightechnology

Compressor Turbine

Combustionchamber

IntakeFreshair

ALTITUDE

MACH No.

Rel. Humidity

PRESSURE RATIO

BLEED FLOWS

PRESSURE LOSS

COOLINGFLOWS

Thrust per unit flow

Nozzle

High Pressure

Compressor

Combustionchamber

Low Pressure

Compressor

Low Pressure Turbine

High Pressure Turbine

COMING UP NEXT...

High Pressure

Compressor

Combustionchamber

Low Pressure

Compressor

COMING UP NEXT...

High Pressure

Compressor

Combustionchamber

Low Pressure

Compressor

COMING UP NEXT...

High Pressure

Compressor

Combustionchamber

Low Pressure

Compressor

Combustionchamber

COMING UP NEXT...

High Pressure

Compressor

Combustionchamber

Low Pressure

Compressor

Combustionchamber

COMING UP NEXT...

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