Gas Turbine Cycles for Aircraft Propulsion: Performance Criteria and Efficiency Analysis

1. CHAPTER3 Gas Turbine Cycles for Aircraft Propulsion

2. Gas Turbine Cycles for Aircraft Propulsion • Aircraft GT Cycles differ from Shaft Power Cycles in that the useful power output in the former is produced wholly or in part as a result of expansion in a propelling nozzle wholly in Turbojet and Turbofan engines and partly in Turboprop engines. • A second distinquishing feature is the need to consider the effect of forward speed and altitude on the performance of an aircraft engine. Chapter2 Shaft Power Cycles

3. Gas Turbine Cycles for Aircraft Propulsion3.1Criteria Of Performance For simplicity assume that mass flowṁ is constant (i.e the fuel flow is negligible). The net thrust is then; ṁa Va Vj FIG.3.1 Schematic Diagram of a Propulsive Duct F = ṁj Vj-ṁa Va - ṁf Vf + Aj (Pj-Pa) F = ṁa (Vj - Va ) + Aj (Pj-Pa) ( 3.1 ) Chapter2 Shaft Power Cycles

4. Criteria Of Performance • When the exhaust gasses are expanded completely to Pa in the propulsive duct i.e Pj = Pa ; then; • F = ṁa (Vj-Va) ( 3.2 ) • From this equation , it is clear that the required thrust can be obtained by designing the engine to poduce : • either a high velocity jet of small mass flow • or a low velocity jet of high mass flow. Chapter2 Shaft Power Cycles

5. Criteria Of Performance The most efficient combination of these two variables is povided by the following analysis; Chapter2 Shaft Power Cycles

6. Criteria Of Performance • From eqns. (3. 2) , (3.3); • a)Fis max when Va = 0 ηp = 0 • b)ηpis max when Vj =Va F = 0 • We may conclude that; although Vj must be greater than Va, the difference (Vj-Va) should not be too great. Chapter2 Shaft Power Cycles

7. Criteria Of Performance As a result a family of propulsion units are developed. • FAMILY of PROPULSION ENGINES • 1. Piston Engine • 2. Turboprop • 3. Turbofan • 4. Turbojet • 5. Ramjet • From 1 to 5Vj increases and m decreases, for a fixed Va,F increases and ηpdecreases Chapter2 Shaft Power Cycles

8. Propulsion Engines Piston Engine Turboprop Turbofan Turbojet Ramjet Chapter2 Shaft Power Cycles

9. Criteria Of Performance • Taken in the order shown : Propulsive jets of decreasing massflowrateandincreasing jet velocity • therefore suitable for aircraft of increasing design cruising speed. Chapter2 Shaft Power Cycles

10. Fig 3.2 Flight Regimes Ram-jet Turbojet Chapter2 Shaft Power Cycles

11. Criteria Of Performance • Propulsion efficiency is a measure of the effectiveness with which the propulsive duct is being used for propelling the aircraft. • Efficiency of energy conversion ( 3.4 ) Chapter2 Shaft Power Cycles

12. Criteria Of Performance • From the above definitions; • ( 3.6 ) • Efficiency of an aircraft power plant is inextricably linked to the aircraft speed. • For aircraft engines, Specific fuel consumption = sfc = Fuel Consumption/Thrust [kg/hN] is a better concept than efficiency to define performance. Chapter2 Shaft Power Cycles

13. Criteria Of Performance • Since Qnet,p = const for a given fuel, then • for aircraft plants ; ηo = f (Va/sfc ). • for shaft power units ; ηo = f (1/sfc ). • Another important performance parameter is specific thrust, Fs; • Fs thrust per unit mass flow of air [N.s/kg]. Chapter2 Shaft Power Cycles

14. Criteria Of Performance • This ( Fs) provides an indication of the relative size of engines producing the same thrust, because the dimensions of the engine are primarily determined by the airflow requirements. • Note that; • sfc = ηo/ Fs ( 3.8 ) Chapter2 Shaft Power Cycles

15. ISA (InternationalStandard Atm.) Z (m) • When estimating the cycle performance at altitude one needs to know the variation of ambient pressure and temperature with altitude. • ISA(InternationalStandard Atm.) corresponds to middling lattitudes • Ta decrease by 3.2 K per 500 m up to 11000 m. • After 11000 m Ta = const up to 20 000 m. • Then Ta starts increasing slowly Ta (K) Chapter2 Shaft Power Cycles

16. Criteria Of Performance • For high-subsonic or supersonic aircraft it is more appropriate to use Mach number rather than V (m/s) for aircraft speed, because "DRAG" is more a function of Ma. • Inrease in Mach number with altitude is experienced for a given Va Chapter2 Shaft Power Cycles

17. Criteria Of Performance • Mach Number vs. Flight Velocity Va (m/s) Chapter2 Shaft Power Cycles

18. 3.2 Intake & Propelling Nozzle Efficiencies • FIG 3.4 Simple Turbojet Engine Chapter2 Shaft Power Cycles

19. Intake & Propelling Nozzle Efficiencies • The turbine produces just sufficient work to drive the compressor and remaining part of the expansion is carried out in the propelling nozzle. • Because of the significant effect of forward speed, the intake must be considered as a seperate component. • In studying the performance of aircraft propulsion cycles it is necessary to describe the losses in the two additional components ; i.e. • INTAKE • PROPELLING NOZZLE Chapter2 Shaft Power Cycles

20. 3.2.1 Intakes • The intake is a simple adiabatic duct. • Since Q = W = 0 , the stagnation temperature is constant, • although there will be a loss of stagnation pressure due friction and due to shock waves at supersonic flight speeds. Chapter2 Shaft Power Cycles

21. Intakes • Under static conditions or at very low forward speeds ; intake acts as a nozzle in which the air accelerates from zero velocity or from low Vato V1 at the compressor inlet . • Atcruise speeds, however, the intake performs as a diffuser with the air decelerating from Va to V1 and the static pressure rising from Pa to P1. Chapter2 Shaft Power Cycles

22. Intakes • Inlet isentropic efficiency, “ηi“ defined in terms of temperature rise. • The isentropic efficiency for the inlet ; ( 3.9 ) here; • T01' = Temperature which would have been reached after an isentropic Ram compression to P01. Chapter2 Shaft Power Cycles

23. Intakes V • Fig 3.5 Intake Losses V V V V Chapter2 Shaft Power Cycles

24. Intakes • P01 - Pa = Ram Pressure Rise • RAM efficiency , ηr is defined in terms of pressure rise (pressure rise / inlet dynamic head ). Chapter2 Shaft Power Cycles

25. Intakes • The isentropic efficiency for the INLET ; • ( 3.9 ) Chapter2 Shaft Power Cycles

26. Intakes • The intake presure ratio; • ( 3.10.a ) Chapter2 Shaft Power Cycles

27. Intakes • Noting M= V / (gRT )1/2 and R = Cp( g- 1 ) • ( 3.10.b ) • The stagnation temperature; • ( 3.10.c ) Chapter2 Shaft Power Cycles

28. Intakes • RAM efficiency is defined as; • For supersonic inlets it is more usual to quote values of stagnation pressure ratio P01 / P0a as a function of Mach number. Chapter2 Shaft Power Cycles

29. 3.2.2 Propelling Nozzles Chapter2 Shaft Power Cycles

30. 3.2.2 Propelling Nozzles • Propelling nozzle is the remaining part of the engine after the last turbine stage. • The question is immediately arises, as to whether a simple convergent nozzle is adequate or whether a convergent - divergent nozzle should be employed. • It can be shown that for an isentropic expansion, the thrust produced is maximum when complete expansion to Pa occurs in the nozzle. Chapter2 Shaft Power Cycles

31. Propelling Nozzles • The pressure thrust arising from an incomplete expansion does not entirely compansate for the loss of momentum thrust due to smaller jet velocity. • But this is no longer true when friction is taken into account because the theoretical jet velocity is not achieved. • For values of P04/Pa ( nozzle pressure ratio ) up to 3 • Fconv-div thrust = F simple conv. • Converging-diverging nozzle at off-design condition  Shock wave in the divergent section loss in stagnation pressure. Chapter2 Shaft Power Cycles

32. Propelling Nozzles • With simple convergent nozzles; • a) It easy to employ a variable area nozzle, • b) It is easy to employ a thrust reverser, • c) It is easy to employ a noise suppressor ( i.e. increase the surface area of the jet stream ). • The thrust developed by a propulsive nozzle; • F = ṁ Vj + (Pj -Pa) Aj Chapter2 Shaft Power Cycles

33. Propelling Nozzles • For a given m to determine the nozzle exit area that yields maximum thrust, differentiate the above eqn. • dF = ṁ dVj + AjdPj + Pj dAj - PadAj • but ṁ = AV = rjAjVj • dF = Aj (dPj + rjVj dVj) + (Pj -Pa) dAj Chapter2 Shaft Power Cycles

34. Propelling Nozzles • since momentum equation; • dP + rVdV = 0 --> dF = Aj [0] + (Pj -Pa) dAj • solve for dF/dAj • dF/dAj = Pj- Pa for max thrust(Pj -Pa) =0 • Therefore; the nozzle area ratio must be chosen so that the pressure ratio Pj/Po = Pa/Po • This design criterion is based on planar flow. Chapter2 Shaft Power Cycles

35. Propelling Nozzles • This design criterion is based on planar flow. • If a similar equation is derived for a conical nozzle , it is seen that some under expansion is desirable. • Then the thrust gain is about 2% higher than Pe=Pa. • Variable exit / throat area ratio is essential to avoid shock losses over as much of the operating range as possible, and the additional mechanical complexity has to be accepted. Chapter2 Shaft Power Cycles

36. Variable Area, Thrust Reversal and Noise Suppression Chapter2 Shaft Power Cycles

37. Propelling Nozzles • The main limitations on the design of convergent divergent nozzles are : a) The exit diameter must be within the overall diameter of the engine, otherwise the additional thrust is offset by the increased external drag. b) In spite of the weight penalty; the included angle of divergence must be kept below about 30o, because the loss in thrust associated with the divergence of the jet increases sharply at greater angles. Chapter2 Shaft Power Cycles

38. Propelling Nozzles • In order to allow nozzle losses two approaches are commonly used; • i) Isentropic efficiency : • From definition ofhj; • ( 3.12 ) Chapter2 Shaft Power Cycles

39. Nozzle Loss for Unchoked Flows V Chapter2 Shaft Power Cycles

40. Nozzle Loss for Choked Flows V V Chapter2 Shaft Power Cycles

41. Propelling Nozzles • ii) Specific thrust coefficient : • Kf = actual thrust/Isentropic thrust • For adiabatic flow with w =0 ; • For critical pressure ratio M5 = 1 ( T5 = Tc ); • ( 3.13 ) Chapter2 Shaft Power Cycles

42. Propelling Nozzles • For adiabatic flow with w =0 ; • For critical pressure ratio M5 = 1 ( T5 = Tc ); • ( 3.13 ) Chapter2 Shaft Power Cycles

43. Propelling Nozzles • For choked flow; • Then; Chapter2 Shaft Power Cycles

44. Propelling Nozzles • thus critical pressure ratio is; • (3.14) Chapter2 Shaft Power Cycles

45. Propelling Nozzles • For a given mass flow m; ( 3.15 ) Chapter2 Shaft Power Cycles