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MAE 5380: Advanced Propulsion

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. NON-IDEAL (“REAL”) CYCLES. Principal deviations from ideal behavior :

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MAE 5380: Advanced Propulsion

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  1. 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, g) 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, f, 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

  4. 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]

  5. 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

  7. THERMODYNAMIC CYCLES [Walsh and Fletcher] Carnot Cycle Non-Ideal Brayton Cycle for turbojet, turboshaft, turboprop, ramjet

  8. 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?

  9. FLOW THROUGH A SCREEN, THROTTLE, OR BLADE ROW

  10. 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

  11. LOSSES IN A THROTTLING PROCESS (II) • Thus for the screen, qrev=Tt1s • So wrev=Tt1s • 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

  12. 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

  13. 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

  14. Along pt2 = const. curve ht2 = ht2 + ht2 - ht2 = ht2 + Dht Isentropic compression At const pt But or Thus at const pt

  15. CONNECTION BETWEEN ENTROPY CHANGESAND COMPONENT EFFICIENCY ht2 = ht2 + Tt2Ds or 2 ; Entropy rise directly tied to efficiency, similarly for turbine ; Turbine

  16. 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

  17. 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

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

  19. REPRESENTATIVE VALUES OF INLET/DIFFUSER STAGNATION PRESSURE RECOVERY AS A FUNCTION OF FLIGHT MACH NUMBER [Kerrebrock]

  20. 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/r 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

  21. 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 Ideal work for pt change: Ideal Dht = ht2s - ht1 Pt2 2s 2 Tt2 Actual work for pt change: Actual Dht = ht2 - ht1 Actual T or h Ideal ht Pt1 Tt1 h= Ideal work/actual work 1 s Ideal work for pt change: Ideal ht= ht25 - ht1 Actual work forpt change: Actual ht = ht2 - ht1

  22. 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

  23. 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/r again • Ideal work/unit mass is cp(Tt3’ - Tt1) [Using notation below] • Actual work/unit mass is cp(Tt2 - Tt1) > cp(Tt3’ - Tt1) hcompressor = Ideal work/Actual work for same pressure ratio = Adiabatic/isentropic efficiency

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

  25. 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  is stagnation temperature ratio: p is stagnation pressure ratio

  26. ACTUAL AND IDEAL WORK FOR A TURBINE pt1 1 ht actual pt2 h ht ideal 2 2s s

  27. 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:

  28. 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

  29. ENGINE CYCLE (THERMAL) EFFICIENCY VARIATIONS [Philpot]

  30. POWER AND CYCLE EFFICIENCY TRENDS WITH TURBINE TEMPERATURE AND COMPONENT EFFICIENCY [Cumpsty] Tt4 / Tt2 Tt4 / Tt2 Tt4 / Tt2

  31. BRAYTON CYCLE FOR SIMPLE GAS TURBINE Pressure ratio 40, inlet temperature =288K, turbine temperature 1700K, turbine and compressor adiabatic efficiencies both 0.9 [Cumpsty]

  32. 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]

  33. 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

  34. 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

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