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CHAPTER 3

CHAPTER 3. Gas Turbine C ycl es f or Aircraft Propulsion. Simple Turbojet Cycle. T. 03. ( Δ T 0 ) turb. p 03. V 5 ² / 2 c p. 04. p 04. 5. Δ p b. p 5. 02. ( Δ T 0 ) comp. p 02. V a ² / 2 c p. 01. p 01. p a. s. Simple Turbojet Cycle. 3.3.1 Optimisation of a Turbojet Cycle

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CHAPTER 3

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  1. CHAPTER3 Gas Turbine Cycles for Aircraft Propulsion

  2. Simple Turbojet Cycle T 03 (ΔT0)turb p03 V5²/ 2cp 04 p04 5 Δpb p5 02 (ΔT0)comp p02 Va²/ 2cp 01 p01 pa s Chapter2 Shaft Power Cycles

  3. Simple Turbojet Cycle • 3.3.1 Optimisation of a Turbojet Cycle • When considering the design of a turbojet, the basic thermodynamic parameters at the disposal of the designer are the Turbine Inlet Temperature and the compressor pressure ratio (t, rc) • It is common practice to carry out a series of design point calculations covering a suitable range of these two variables (t, rc) using fixed polytropic efficiencies for the compressor and the turbine and plot sfc vs Fs with " TIT“(T03) and " rc " as parameters. Chapter2 Shaft Power Cycles

  4. Fig. 3.8 Typical Turbojet Cycle Performance Chapter2 Shaft Power Cycles

  5. Optimisation of a Turbojet Cycle • Fs= f (T03) strong function • high T03 is desirable for a given Fs • a small engine means small rcor small ṁ • At rc = const. T03↑sfc↑! Fs↑(i.e. fuel increase ), ( opposite in shaft power ws↑sfc ↓). • This is because as T03↑Vjet↑, • ηp↓↓( Fs↑), ηe↑ηo↓and sfc↑but Fs↑. • Gain in sfc is more important since smaller engine size is more desirable Chapter2 Shaft Power Cycles

  6. Optimisation of a Turbojet Cycle • rc↑ sfc↓ ; at a fixed T03 • Fs first ↑ then ↓( Optimumrc↑ for best Fs) as T03 ↑ • At the same altitude Z , but higher Crusing Speed Va : • i.e Va↑ ; for given rc and T03sfc↑, Fs↓ becauseMomentum Drag↑ , (wcomp↑, since T01↑ ) • At different altitudes Z↑Fs↑ , sfc ↓ since T01↓ and ws↓. • As Va↑rcopt↓due torRAM↑ at the intake Chapter2 Shaft Power Cycles

  7. Optimisation of a Turbojet Cycle • Thermodynamic optimization of the turbojet cycle can not be isolated from mechanical design considerations and the choice of cycle parameters depend very much on the TYPE of the aircraft. Chapter2 Shaft Power Cycles

  8. Fig.3.9. Performance and Design Considerations for Aircraft Gas Turbines Chapter2 Shaft Power Cycles

  9. Optimisation of a Turbojet Cycle • high TIT thermodynamically desirable • causes complexity in mechanical design, • such as expensive alloys & cooled blades. • high rcincreased weight • large number of compressor-turbine stages • i.e multi spool engines. Chapter2 Shaft Power Cycles

  10. 3.3.2 Variation of Thrust & sfc with Flight Conditions • The previous figures represent design point calculations. • At different flight conditions, • both thrust & sfc vary due to the change in ma with ra • and variation of Momentum Drag with forward speed Va. • As altitude Z↑ , FNet↓ due to ra decrease as Pa↓ • Although Fs↑ since T01↓ , sfc↓ a little • At a fixed altitude Z, • as M↑FN↓at first due to increased momentum drag, then FNetdue to benefical effects of Ram pressure ratio. • For M >1 increase in FNet is substantial for M↑ Chapter2 Shaft Power Cycles

  11. Fig.3.10.1 Variation of Thrust with Flight Speed for a TypicalTurbojet Engine Chapter2 Shaft Power Cycles

  12. Fig.3.10.1 Variation of sfcwith Flight Speed for aTypicalTurbojet Engine Chapter2 Shaft Power Cycles

  13. 3.4 THE TURBOFAN ENGINE • The Turbofan engine was originally conceived as a method of improving the propulsive efficiency of the jet engine by reducing the Mean Jet Velocity particularly for operation at high subsonic speeds. • It was soon realized that reducing jet velocity had a considerable effect on Jet Noise , a matter that became critical when large numbers of jet propelled aircraft entered commercial service. Chapter2 Shaft Power Cycles

  14. The Turbofan Engine • In Turbofan engines ; a portion of the total flow by-passespart of the compressor, combustion chamber, turbine and nozzle, before being ejected through a seperate nozzle. • Turbofan Engines are usually decribed in terms of "by-pass ratio" defined as : the ratio of theflow through the by-pass duct (cold stream) to that through the high pressure compressor (HPC) (hot stream). Chapter2 Shaft Power Cycles

  15. FIG.3.11.Twin - Spool Turbofan Engine Vjc Va Vjh Chapter2 Shaft Power Cycles

  16. The Turbofan Engine • By pass ratio is given by; • Then; and ṁ = ṁc + ṁh • If Pjc = Pjh = Pa , (no pressure thrust) then ; • F = (ṁcVjc + ṁhVjh ) - ṁ Vafor a by-pass engine Chapter2 Shaft Power Cycles

  17. The Turbofan Engine • The design point calculations for the turbofan are similar to those for the turbojet. • In view of this only the differences in calculations will be outlined. • a)Overall pressure ratio ( rc) and turbine inlet temperature ( TIT) are specified as before ;but it is also necessary to specify the bypass ratio B and the fan pressure ratio FPR. Chapter2 Shaft Power Cycles

  18. The Turbofan Engine • b) From the inlet conditions and FPR; the pressure and temperature of the flow leaving the fan and entering the by-pass duct can be calculated. • The mass flow down the by-pass duct ṁc can be established from the total mass flow rateṁand B. • The cold stream thrust can then be calculated as for the jet engine noting that the working fluid isair. • It is necessary to check whether the fan nozzle is choked or unchoked. • If choked the pressure thrust must be calculated. Chapter2 Shaft Power Cycles

  19. The Turbofan Engine • c)In the 2-spool configurations the FAN is driven by LP turbine Calculations for the HP compressor and the turbine are quite standard, then inlet conditions to the LP turbine can then be found. Considering the work requirement of the LP rotor ; Chapter2 Shaft Power Cycles

  20. The Turbofan Engine • The value of B has a major effect on the temperature drop and the pressure ratio required from the LP turbine • Knowing T05, ht and T056 , LP turbine pressure ratio can be found, and conditions at the entry to the hot stream nozzle can be established. Chapter2 Shaft Power Cycles

  21. The Turbofan Engine • d)If the two streams are mixed it is necessary to find the conditions after mixing by means of an enthalpy and momentum balance. • Mixing is essential for a reheated turbofan. Chapter2 Shaft Power Cycles

  22. The Turbofan Engine 3.4.1 Optimization of the Turbofan Cycle • There are 4 thermodynamic parameters the designer can play with. • i) Overall pressure ratio rp • ii) Turbine inlet temperature TIT • iii) By-pass Ratio B • iv) Fan pressure ratio FPR Chapter2 Shaft Power Cycles

  23. Optimization of the Turbofan Cycle • At first fix; • a) the overall pressure ratio, rp • b) By pass ratio, B. • Note that optimum values for each TIT ( minimum sfc&maxFs) coincide because of thefixed energy input. • Taking the values of sfc and Fs for each of these FPR values inturn, a curve of sfc vs. Fs can be plotted. • Note that each point on this curve isthe result of a previous optimization and it is associated with a particular value of FPR and TIT. Chapter2 Shaft Power Cycles

  24. Fig.3.11. Optimization of a Turbofan EnginePerformance Chapter2 Shaft Power Cycles

  25. Optimization of the Turbofan Cycle • Note that optimum values for each TIT ( minimum sfc&maxFs) coincide because of the fixed energy input. • Taking the values of sfc and Fs, for each of these FPR values inturn, a curve of sfc vs. Fs can be plotted. • Note that each point on this curve isthe result of a previous optimizationand it is associated with a particular value of FPR and TIT. Chapter2 Shaft Power Cycles

  26. Optimization of the Turbofan Cycle Chapter2 Shaft Power Cycles

  27. Optimization of the Turbofan Cycle • The foregoing calculations may be repeated for a series of B, still at the same rp to give a family of curves. • This plot yields the optimum variation of sfc with Fs for the selected rp as shown by the envelope curve. • The procedure can be repeated for a range of rp. Chapter2 Shaft Power Cycles

  28. Optimization of the Turbofan Cycle • The quantitative results are summarized as: a)B improvessfc at the expense of significant reduction in Fs, b) Optimum FPR with TIT , c) Optimum FPR with B . Chapter2 Shaft Power Cycles

  29. The Turbofan Engine • Long range subsonic transport,sfcis important • B = 4-6 ; high rp high TIT. • Military Aircraft; with supersonic dash capability & good subsonic sfc B = 0.5 -1to keep the frontal area down, optional reheat. • Short Haul Commercial Aircraft, sfc is not as critical B= 2-3 • Thrust of engines of high B is very sensitive to forward speed due to large intake ṁ and momentum drag Chapter2 Shaft Power Cycles

  30. Mixing in a Constant Area Duct Chapter2 Shaft Power Cycles

  31. 3.5 AFT - FAN CONFIGURATION • Some early turbofans were directly developed from existing turbojets, • A combined turbine-fan was mounted downstream of the Gas Generator turbine. Vjc Vjh Chapter2 Shaft Power Cycles

  32. 3.6 TURBO PROP ENGINE • The turboprop engine differs from the shaft power unit in that some of the useful output appears as jet thrust. • Power must eventually be delivered to the aircraft in the form of thrust power (TP) . • This can be expressed in terms of equivalentshaft Power (SP), propeller efficiency hp, and jet thrust F by TP = (SP)pr + FVa • The turboshaft engine is of greater importance and is almost universally used in helicopters because of its low weight. Chapter2 Shaft Power Cycles

  33. 3.7 Thrust Augmentation • If the thrust of an engine has to be increased above the original design value, several alternatives are available. i)Increase of turbine inlet temperature , TIT ii)Increase of mass flow rate through theengine • Both of these methods imply there-design of the engine, and either of them or both may be used to update the existing engine. Chapter2 Shaft Power Cycles

  34. Thrust Augmentation • Frequently there will be a requirement for a temporary increase in thrust. e. g. for take off, for an acceleration from subsonic to supersonic speeds or during combat manoeuvres. • The problem then becomes one of thrust augmentation. • Two methods most widely used are: i)Liquid injection (water+methanol) ii)Reheat (after burner) • Spraying water to the compressor inlet results in a drop in inlet temperature in net thrust Chapter2 Shaft Power Cycles

  35. Cycle of Turbojet with Afterburning Chapter2 Shaft Power Cycles

  36. DESIGN POINT PERFORMANCE CALCULATION FOR TURBOJET & TURBOPROP ENGINES. A Turbojet & Turboprop unit may be considered as consisting of 2 parts: • Thus:- i /GAS GENERATOR ii /POWER UNIT a) Turbojet  Jet Pipe & Final Nozzle b) Turboprop  Power Turbine Jet Pipe & Final Nozzle Chapter2 Shaft Power Cycles

  37. Air intake Compressor Combustion Compressor Chamber Turbine 0 1 2 3 4 The Gas Generator Chapter2 Shaft Power Cycles

  38. TurbojetTurboprop 5 4 5 6 6 Chapter2 Shaft Power Cycles

  39. Problem : Turbojet & Turboprop Engines • DATA: • Altitude Z = 0 ISA (101.325 kPa; 288.0 K) • True Airspeed (Va) = 0 Static • Power Output turbojet= 90 kN Thrust • Power Outputturboprop= 4.5 MW Shaft Power • Compressor Pressure Ratio (P02/P01)= 10 • TIT (total) T03= 1500K • Jet Velocity V6= 220 m/s (turboprop) • Compressor Isentropic efficiency h12= 88% • Turbine Isentropic efficiencyh34 = 90% h45 = 90 % Chapter2 Shaft Power Cycles

  40. Problem :Turbojet & Turboprop Engines ; Data • Jet pipe Nozzle Isentropic efficiency h56 = 100% • Combustion efficiencyh23 = 100% • Mechanical efficiency of Turbo compresordrive hM= 100% • Reduction Gear efficiency hG= 97% • Intake Pressure RecoveryP01/P00=0.98 Chapter2 Shaft Power Cycles

  41. Problem :Turbojet & Turboprop Engines ; Data • Combustion Chamber total pressure loss : ΔP023= 7% of compressor outlet total pressure (P02) • Jet Pipe-Nozzle pressure loss : ΔP056= 3% of turbine outlet total pressure (P04 or P05) • Nozzle discharge Coefficient Cd= 0.98 • Cooling air bleed r= 5% of Compressor mass flow. Chapter2 Shaft Power Cycles

  42. Problem : Turbojet & Turboprop Engines ; Data • Cpa = 1.005 kJ/kg-K for air • Cpg= 1.150 KJ/kg-K for gas • ga = 1.40 for air • gg = 1.33 for gasses Calorific value of fuel • ΔH = 43.124 MJ/kg Chapter2 Shaft Power Cycles

  43. Problem :Turbojet & Turboprop Engines ; Calculations Calculations a) Air Ram Temperature RiseΔT0Ram= Va2/2Cp = 0 K • Toa = (Ta+ΔT0Ram) = 288 + 0 = 288K • P01 = Poa* P01/Poa = 101.3 * 0.98 = 99.3 kPa • No work is done on or by air at the Intake • T01 = Toa = 288K Chapter2 Shaft Power Cycles

  44. Problem :Turbojet & Turboprop Engines ; Calculations • b) Compressor • T02 = T01 + ΔT012= 288. + 304.6 = 592.6 K • P02 = P01 *(P02/P01) = 99.3 * 10 = 993.0 kPa Chapter2 Shaft Power Cycles

  45. Problem :Turbojet & Turboprop Engines ; Calculations • C) Combustion Chamber • ΔP023 =ΔP023* P02 = 0.07* 993.0 = 69.5 kPa • P03 = P02 - ΔP023= 993.0 - 69.5 = 923.5 kPa • By Heat Balance h23 mfΔH = Cp23 (ma+mf) (T03-T02) • defining : f ≡ mf/ma ; ΔT023 = T03-T02 Chapter2 Shaft Power Cycles

  46. Problem :Turbojet & Turboprop Engines ; Calculations • Using the Combustion Curves • Ideal Temperature Rise (Δ T23) vs f • (with T02 as a parameter) • ΔT023' = ΔT023 /h23 = 907.4 K ; (h23 =100%) T02 = 592.6Kf’ = 0.0262 • This takes account of the variation of Cp23 with f and temperature f = 0.0262 / h23 = 0.0262 / 1.00 = 0.0262 Chapter2 Shaft Power Cycles

  47. Problem :Turbojet & Turboprop Engines ; Calculations • d) Compressor Turbine • Compressor Turbine Output *Mechanical efficiency of drive = = Compressor input • ṁ1 Cp12ΔT012 = hmṁ3 Cp34ΔT034 • ṁ1 = Compressor mass flow rate • ṁ3 = Compressor turbine mass flow rate • r = Cooling air bleed = 0.05 • ṁ1 = ṁ2/ (1-r)ṁ3 = ṁ2 (1+f) Chapter2 Shaft Power Cycles

  48. Problem :Turbojet & Turboprop Engines ; Calculations • ṁ1/ ṁ3 = 1 /((1-r)*(1+f)) • ∴ Chapter2 Shaft Power Cycles

  49. Problem :Turbojet & Turboprop Engines ; Calculations Chapter2 Shaft Power Cycles

  50. Problem :Turbojet & Turboprop Engines ; Calculations • P03 / P04 = 2.47 • T04 = T03 - D T034 = 1500 -273.1 =1226.9 K • P04 = P03 / (P03 / P04) = 923.47 / 2.47 • P04 = 373.9 kPa Chapter2 Shaft Power Cycles

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