MAE 5380: Advanced Propulsion

GAS TURBINE PERFORMANCE:NON-IDEAL BEHAVIOR IN COMPONENTS AND

CYCLES

Mechanical and Aerospace Engineering Department

Florida Institute of Technology

D. R. Kirk

2

NON-IDEAL (“REAL”) CYCLES

Principal deviations from ideal behavior:– Imperfect diffusion of free-stream flow in engine inlet– Non-isentropic compression and expansion in the

turbomachinery (compressors and turbines)– Stagnation pressure change in combustor– Incomplete combustion in combustor– Variation of gas properties (specific heat, ) through the

engine– Incomplete expansion, or over expansion, in the nozzle– Extraction of compressor discharge air for turbine cooling

and for airframe use (bleeds)

3

SOME COMMENTS ON THE WORKING FLUID

• We have assumed that the working fluid can be approximated as a perfect gas with constant specific heats

• In reality the specific heats, and specific heat ratio, , vary through the engine

• The effect of pressure is small (on the order of 0.1% for 20kPa to 45 Mpa [Cumpsty]) but the effect of temperature is appreciable

• The variation in cp and is given in the next chart, which shows the dependence on temperature, for different values of the

equivalence ratio, , which is the ratio of the fuel air-ratio to the fuel air ratio for stoichiometric combustion– For simplicity, the values of will be taken to be different but

constant in the different components. They will be denoted by subscripts

– The value for the compressor is denoted by c, the value for the turbine by t.

– Appropriate values are 1.4 and 1.3, respectively

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VARIATION IN SPECIFIC HEAT AT CONSTANT PRESSURE, cp, AND SPECIFIC HEAT RATIO, , WITH TEMPERATURE FOR AIR AND FOR

COMBUSTION PRODUCTS OF KEROSENE; is the Equivalence Ratio [Cumpsty]

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DEPARTURE FROM IDEAL BEHAVIOR: LOSSES IN ENGINE COMPONENTS

• Component efficiency has a large impact on cycle performance

• Characterizing losses in components (departures from ideal reversible processes) is a key aspect of real cycle analysis

• We will examine basic mechanisms and measures developed for assessing loss

• In this, it will be seen that entropy generated due to irreversibility is the most useful measure of loss (inefficiency)

• For an adiabatic flow the entropy increase translates to a stagnation pressure change pt can thus often be used as a loss indicator

6

LOSS SOURCES

• Viscous dissipation– Boundary layers– Shear layers (mixing)

• Heat transfer across a finite temperature difference

• Shocks

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THERMODYNAMIC CYCLES [Walsh and Fletcher]

Carnot Cycle

Non-Ideal Brayton Cycle for turbojet, turboshaft, turboprop, ramjet

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LOSSES AND STAGNATION PRESSURE CHANGES

• Consider a medium that undergoes an irreversible process 1--->2– Example: flow through a screen or throttle

– No work done, no heat transfer, therefore ht = constant

• Represent the states on a T-s diagram

• It is “conventional” to think about losses in terms of changes in stagnation pressure. Why?

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FLOW THROUGH A SCREEN, THROTTLE, OR BLADE ROW

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LOSSES IN A THROTTLING PROCESS (I)

• Losses are often expressed as a decrease in stagnation pressure– Directly measurable quantity– Related to the minimum work required to reverse the process to its

original state 2 ---> 1 – Lost work

• For the flow through a screen, examine the work required to reverse the process using an ideal process

• First Law of Thermodynamics: e = q - w, neglecting changes in all forms of energy except internal energy

• For perfect gas e = e(T) only, so for our example of the screen: e(Tt1) = e(Tt2) q = w

• For a reversible process, the heat received per unit mass is: dqrev=Tds

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LOSSES IN A THROTTLING PROCESS (II)

– Thus for the screen, qrev=Tt1s

– So

wrev=Tt1s

– THE WORK REQUIRED TO RETURN THE SYSTEM TO INITIAL STATE (THE “LOST WORK”) IS DIRECTLY RELATED TO THE CHANGE IN ENTROPY

• Now we relate this entropy change to the change in total pressure

– If TT = constant and cp and cv are constant then

Tdsdh

1

dp ds dht

Tt

dpt

tTt

ds Rdpt

pt

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LOSSES IN A THROTTLING PROCESS (III)

• The minimum work required to restore the fluid to its initial state is thus directly connected to the change in stagnation pressure for a flow with constant stagnation temperature

w rev RTt lnpt2

pt1

pt1 pt 2

pt1

1 lnpt2

pt1

pt1 pt2

pt1

w rev pt1

pt2

t

pt

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CONNECTION BETWEEN ENTROPY CHANGESAND TURBOMACHINERY COMPONENT EFFICIENCY

• Efficiency for compressor: For given pt2 / pt1 , how much shaft work is done

• Shaft work / unit mass flow rate = ht2 - ht1 (assuming adiabatic)

Compressor Turbine

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Along pt2 = const. curve

ht2 = ht2 + ht2 - ht2 = ht2 + ht

Isentropic compression

ht ht

s

pt

s

At const pt

But

Tds dh 1

dp

or

Ttds dht 1

t

dpt

Thus at const pt

ht

s

pt

Tt

15

ideal work

actual work

ht 2 ht1

ht2 ht1

ht2

ht1

ht2 ht1

ht

ht2 ht1

Entropy rise directly tied to efficiency, similarly for turbine

1

Tt2s

ht2 ht1

actual work

ideal work

ht1 ht2

ht1 ht2

ht

ht2 = ht2 + Tt2 s

or 2

Turbine

CONNECTION BETWEEN ENTROPY CHANGESAND COMPONENT EFFICIENCY

1TT2s

workCompressor ;

;

1

1Tt2

s

ht1 ht2

1Tt2swork

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SUMMARY: LOSSES AND STAGNATION PRESSURE

• Entropy is the basic measure of loss - Entropy is not measured directly

• For adiabatic processes, we can relate entropy changes and changes in stagnation pressure - Stagnation pressure is measured

• Stagnation pressure is often used as the figure of merit for component loss (or component efficiency)

• The next several slides show the application for an inlet/diffuser combination

d = pt out / pt in

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INLET AND DIFFUSER LOSS

• Subsonic diffusers– Need to supply air to the engine at the Mach number the

compressor demands– Need to be efficient over range of free-stream Mach numbers

from take-off to cruise – Modern computational tools enable efficient inlets with

stagnation pressure recoveries greater than 0.95• Supersonic diffusers

– Shock waves exist and introduce a loss mechanism– Very large variations in capture stream tube area– Inlet compression is a larger fraction of the overall

compression process and overall cycle efficiency is thus more sensitive to inlet design

• References provide detailed information about inlet design

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SCHEMATIC DIAGRAMS OF SUBSONIC AND SUPERSONIC INLETS AND DIFFUSERS [Kerrebrock]

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REPRESENTATIVE VALUES OF INLET/DIFFUSER STAGNATION PRESSURE RECOVERY AS A FUNCTION OF

FLIGHT MACH NUMBER [Kerrebrock]

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EFFICIENCIES IN TURBOMACHINERY COMPONENTS:COMPRESSOR AND TURBINE

Consider the compression process through a compressor stage

The goal is to achieve a given stagnation pressure ratio, and to do this at minimum work

We need a relation involving dh and dp to capture this

dh = Tds + dp/Apply this to the stagnation conditions:

dht= Ttds + dpt/t

The flow in the compressor is essentially adiabatic

The second law says that for a fluid particle ds > 0 for all real processes

For given change in pt, as ds increases, so does ht , the stagnation enthalpy

Thus, for a given change in stagnation pressure, the change in stagnation temperature, which is a direct measure of the work we must do, reflects how “good” we are at compression

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THE ADIABATIC (OR ISENTROPIC) EFFICIENCY

For a compressor, the comparison of ideal to actual work for a given stagnation pressure rise or ratio furnishes the metric known as adiabatic (or isentropic) efficiency

T or h

s

Pt2

Pt1

ActualIdeal

Tt1

Tt2

1

2s2

Actual work for pt change: Actual ht = ht2 - ht1

Ideal work for pt change:

Ideal ht = ht2s - ht1

= Ideal work/actual work

ht

Ideal work for pt change: Ideal ht = ht25 - ht1

Actual work for pt change: Actual ht = ht2 - ht1

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COMPRESSOR ADIABATIC EFFICIENCY

• The adiabatic (sometimes called isentropic) efficiency is the ratio of the ideal work for a given pt to the actual work needed

• Definition: = Ideal work / Actual work

• There is a difference between this quantity and the cycle efficiency:

- The cycle efficiency can describe an ideal situation

- Cycle efficiency is set by the second law --a fundamental limitation on the conversion of heat to work

- The adiabatic efficiency is a measure of “how well we did the design” and reflects our capabilities

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BEHAVIOR OF STAGNATION PRESSURE AND TEMPERATURE IN A COMPRESSOR STAGE

• Stagnation pressure and temperature rise in rotor– Shaft work is done on fluid

• Stagnation temperature is constant in the stator– Forces on fluid, and angular momentum changes, exist,

but no shaft work is done

• Stagnation pressure falls in stator– Constant stagnation temperature, but entropy rises;

Tds = dh - dp/ again

• Ideal work/unit mass is cp(Tt3’ - Tt1) [Using notation below]

• Actual work/unit mass is cp(Tt2 - Tt1) > cp(Tt3’ - Tt1)compressor = Ideal work/Actual work for same pressure ratio

= Adiabatic/isentropic efficiency

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THERMODYNAMIC STATES IN A COMPRESSOR STAGE[Cohen, Rodgers, Savaranamutoo]

232

Vc

222

Vc

212

Vc

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COMPRESSOR ADIABATIC EFFICIENCY IN TERMS OF PRESSURE AND TEMPERATURE RATIOS

• The adiabatic efficiency (and the corresponding quantity for turbines) is a metric of how effectively we are able to raise the stagnation pressure

• It is useful to put it in terms of the stagnation pressure and temperature ratios, which are the quantities actually measured

compressor (Tt3 Tt 2 )isentropic

(Tt 3 T2 )actual

(Tt3 / Tt 2 )isentropic 1

(Tt3 / Tt2 )actual 1

isentropic 1

1

compressor ( 1) / 1

1

is stagnation temperature ratio: is stagnation pressure ratio

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ACTUAL AND IDEAL WORK FOR A TURBINE

h

s

1

ht ideal

2s

2

pt2

ht actual

pt1

ht1 ht 2

ht 1 ht 25

ht actual

ht ideal

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ADIABATIC EFFICIENCY FOR A TURBINE

• For a turbine the “reverse” situation occurs• For a given pressure ratio (expansion ratio), the work extracted in the

real process is less for the actual process than for the reversible, adiabatic (isentropic process)

• Adiabatic (isentropic) efficiency for the turbine is defined as the ratio of Actual work / Ideal work, i.e., the ratio of the amount we actually received, compared to the amount we could have received in an isentropic process

• In terms of temperature and pressure ratios:

turbine 1

1 isentropic

turbine 1 1 ( 1) /

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PARAMETERS AFFECTING CYCLE POWER AND EFFICIENCY

• The ratio Tt4/Tt2, the ratio of turbine entry temperature to compressor inlet temperature is an important parameter

• For a given , i.e., given cycle pressure ratio, increasing Tt4/Tt2 brings a rapid rise in net power (this is effectively how the engine is controlled)

• Compressor and turbine efficiencies have a marked effect on overall cycle efficiency and work. This is because for a Brayton cycle, much of the turbine work goes to drive the compressor

• The next two pages show plots of net power per unit of enthalpy flow and cycle efficiency for different values of the temperature ratio Tt4/Tt2 as well as the effects of component efficiency on cycle efficiency

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ENGINE CYCLE (THERMAL) EFFICIENCY VARIATIONS [Philpot]

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POWER AND CYCLE EFFICIENCY TRENDS WITH TURBINE TEMPERATURE AND COMPONENT EFFICIENCY [Cumpsty]

Tt4 / Tt2

Tt4 / Tt2

Tt4 / Tt2

Wnet

m

cpT2

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BRAYTON CYCLE FOR SIMPLE GAS TURBINE

Pressure ratio 40, inlet temperature =288K, turbine temperature 1700K, turbine and compressor adiabatic efficiencies both 0.9 [Cumpsty]

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BRAYTON CYCLE FOR GAS TURBINEWITH SEPARATE POWER TURBINE

Pressure ratio 40, inlet temperature =288K, turbine temperature 1700K, turbine and compressor adiabatic efficiencies 0.9 [Cumpsty]

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ENGINE PERFORMANCE SET BY

• Basic cycle selection– Pressure ratio– Turbine inlet temperature– Bypass ratio

• Technology levels available– Achievable component efficiencies– Achievable work per stage– Mechanical design and materials selection

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SUMMARY

• A gas turbine engines can be regarded as “a core with different loads fitted to it” [Cumpsty]– It can be analyzed in an approximate and useful manner

by replacing the combustion by an equivalent heat transfer

• The thermodynamic cycle efficiency, and the cycle power, are strongly dependent on:– Adiabatic component efficiencies– Ratio of turbine entry stagnation temperature (max

temperature in the cycle) to compressor inlet stagnation temperature