Review of Components Analysis

1. Review ofComponents Analysis Aerospace Engineering, International School of Engineering (ISE) Academic year : 2012-2013 (August – December, 2012) Jeerasak Pitakarnnop , Ph.D. Jeerasak.p@chula.ac.th jeerasak@nimt.or.th Aircraft Propulsion

2. Component Analysis • Diffuser • Free Stream to Diffuser Inlet • Diffuser Inlet to Outlet • Nozzle • Fixed Divergent Nozzle • Diverging Converging Nozzle • Axial Flow Compressor • Axial Flow Turbine Aircraft Propulsion

3. Engine without Inlet Cone • Free Stream to Diffuser Inlet • Subsonic Flow • Supersonic Flow with Shock • Diffuser Inlet to Outlet • Ideal Diffuser – Isentropic Flow • Non Ideal Diffuser – Fanno Line Flow Aircraft Propulsion

4. Free Stream to Diffuser Inlet πo represents loss from free stream to the inlet. Supersonic Flow  Shock • πo < 1 Subsonic Flow • πo ≈ 1 (= 1: ideal isentropic flow) Aircraft Propulsion

5. Supersonic Flow with Normal Shocks • Shocks usually occur exterior to, or near, the inlet plane of the diffuser when an aircraft flies supersonically. • The strongest shocks is the normal shocks. Aircraft Propulsion

6. Ex 1: Normal Shocks A standing normal shock occurs on an aircraft flying at Mach 1.50. The internal recovery factor of the diffuser is 0.98, and the specific heat ratio is 1.40. Find the total recovery factor of the diffuser. Aircraft Propulsion

7. Ideal Diffuser Isentropic & Adiabatic Flow • Constant Total Pressure pta = pt1 = pt2 • Constant Total Temperature Tta= Tt1= Tt2 (hta= ht1= ht2) Aircraft Propulsion

8. Isentropic Flow Mach Number and Local Speed of Sound Stagnation Relations Area Ratio Aircraft Propulsion

9. Limit on Pressure Rise Separation is one of the limits of the diffuser operation. Aligned Inlet Flow: for flow without separation. Mis-Aligned Inlet Flow: Upper limit on the pressure coefficient will be reduced appreciably to perhaps 0.1 to 0.2. Aircraft Propulsion

10. Ex 2: Separation Limit Design an ideal diffuser to attain the maximum pressure rise if the incoming Mach no. is 0.8. That is find the diffuser area ratio, pressure ratio and the resulting exit Mach number. Assuming isentropic flow and γ = 1.4. Aircraft Propulsion

11. Non Ideal Diffuser Low Speed/Flow accelerates/Pressure decreases To quantify loss from the free stream to the diffuser exit, we introduce: • Total Pressure Recovery Factor: High Speed/Flow decelerates/ Pressure increases Nearly Adiabatic Flow, assume: • Constant Total Enthalpy hta= ht1= ht2 • Constant Total Temperature Tta = Tt1 = Tt2 where • πr is the diffuser pressure recovery factor, and • πo represents loss from free stream to the inlet. Aircraft Propulsion

12. Friction Flow Viscous flows are the primary means by which total pressure losses occur!! Fanno Line Flow: flow with friction but no heat transfer Fanno Line Flow could be used when: • Exit-to-inlet area ratio is near unity, • The flow does not separate. Aircraft Propulsion

13. Fanno Line Flow Adiabatic Flow of a Calorically Perfect Gas in a Constant-Area Duct with Friction Aircraft Propulsion

14. Engine with Inlet Cone • Oblique Shock • Oblique Planar Shock • Oblique Conical Shock • Mode of Operation • Design Condition • Off Design Condition Aircraft Propulsion

15. Oblique Planar Shocks • 2D planar shock is simpler than conical shock. • Occur when an inlet is attached to the fuselage of the aircraft, the inlet is more or less rectangular, resulting in planar shock. • Flow behind the planar shock is uniformly parallel to the wedge. Aircraft Propulsion

16. Oblique Planar Shocks δ = deflection angle σ = shock angle Aircraft Propulsion

17. Oblique Conical Shocks • Found in many aircraft applications. • A conical ramp is used to generate an oblique shock, which decelerate flow to a less supersonic conditions. • A normal shock further decelerates the flow to a subsonic condition for the internal flow in the diffuser. Spike on BlackBird Aircraft Propulsion

18. Oblique Conical Shocks Aircraft Propulsion

19. Oblique Conical Shocks Aircraft Propulsion

20. Oblique Conical Shocks Aircraft Propulsion

21. Modes of Operation Design Condition: the oblique shock intersects the diffuser cowl  All the air that cross oblique shock enters the engine Flow rate decreases  Pressure in the diffuser decreases  Mach no. in the diffuser decreases  Shock is pushed out!! Shock is stronger  larger total pressure loss Some of the air will be spilled  high pressure additive drag Shock is used to compress air  outside shock wasting power Flow rate increases  Pressure in the diffuser drops  Shock moves into the diffuser Acting like a supersonic nozzle  Shock occurs in diverging section with high Mach no.  More total pressure is lost. Aircraft Propulsion

22. Mass Flow or Area Ratio Reference Parameter True ingested mass Mass flow enters the engine Mass flow ratio Aircraft Propulsion

23. Design Operation Aircraft Propulsion

24. Off-Design Operation When the diffuser operated at off-design conditions, the area should be varied so that it operates efficiently. In the case of a single planar oblique shock: Inlet area could be determined from: Aircraft Propulsion

25. Ex 3: Supersonic Diffuser A diffuser with a spike is used on a supersonic aircraft. The freestream Mach number is 2.2, and the cone half-angle is 24°. The standing oblique shock is attached to the spike and cowl, and a converging inlet section with a throat of area Am is used to decelerate the flow through internal compression. Assume γ = 1.4 and πr = 0.98. • Estimate πd on the assumption the inlet starts. Also, find the required Am/A1 • Find πd on the assumption the inlet doesn’t start and has a standing normal shock located in front of the spike. Aircraft Propulsion

26. Nozzle Fixed Diverging Nozzle Converging-Diverging Nozzle Aircraft Propulsion

27. Primary Nozzle In real analysis: • Pexit may not match Pa due to incorrect nozzle area proportion. • Frictional losses are include but adiabatic process still be assumed. Nozzle Efficiency Constant cp Specific heat Adiabatic Exit Velocity Aircraft Propulsion

28. Primary Nozzle Adiabatic Process Flow: For the ideal case, isentropic process Thus, Adiabatic Aircraft Propulsion

29. Primary Nozzle Choke condition: If p* > pa, the nozzle is choke If p*= p8, M8 = 1 If p* < pa , M8 < 1 and p8 = pa Then, Aircraft Propulsion

30. Converging Nozzle Exhaust of converging nozzle with matching exhaust and ambient pressures Exhaust of under expanded converging nozzle Aircraft Propulsion

31. Converging-Diverging Nozzle Aircraft Propulsion

32. 1st – 3rd Condition of CD nozzle • Case 1: pexhaust = pambient and Subsonic Flow Through out the nozzle. • Case 2: pexhaust = pambient and Subsonic Flow Through out the nozzle but Mthroat =1. • Case 3: pexhaust = pambient ,Subsonic Flow in the converging section and Supersonic Flow in the diverging section. • MAXIMUM THRUST • Design Condition for the ideal case Aircraft Propulsion

33. 4th Condition of CD Nozzle • pambientis slightly above the designed pexhaust • Result in a complex 2D flow pattern outside the nozzle • Considered as “Overexpanded Case” • The flow suddenly is compressed and decelerates outside the nozzle. • A series of compression waves and expand waves are generated. • Can be calculated basing on 2D compressible flow Aircraft Propulsion

34. 5th Condition of CD Nozzle • pambientis below the designed pexhaust • Result in a complex 2D flow pattern outside the nozzle • Considered as “UnderexpandedCase” or “Super Critical Case” • The flow continues to expand and accelerates outside the nozzle. • A series of compression waves and expanded waves are generated resulting in a series of shock diamonds. Aircraft Propulsion

35. 6th Condition of CD Nozzle • pambientis significantly above the designed pexhaustBut below the 2nd case • Result in a single normal shock or a series of oblique and normal shocks called λ • Also “Overexpanded Case” • Result in a subsonic exit Mach no.: LOW THRUST  Totally undesirable Aircraft Propulsion

36. 7th Condition of CD Nozzle • pambientis significantly above the designed pexhaustLimit condition of the 6th case • Exit pressure causes a normal shock exactly at the exit plane • Case 4 falls between case 7 and 3. Aircraft Propulsion

37. Ex4: Converging-Diverging Nozzle A converging-diverging nozzle with an exit area of 0.2258 m2 and a minimum area of 0.1774 m2 has an upstream total pressure of 137.895 kPa. The nozzle efficiency is 0.965 and the specific heat ratio is 1.35. • At what atmospheric pressure will the nozzle flow be shockless? • At what atmospheric pressure will a normal shock stand in the exit plane? Aircraft Propulsion

38. Axial Flow Compressor Aircraft Propulsion

39. Velocity Polygon Aircraft Propulsion

40. Total Pressure Ratio The equations is derived for a single stage (rotor and stator) using 2D planar mean line c.v. approach. “Midway between hub and tip” • Power Input to the Shaft • Total Pressure Ratio of the Stage Control Volume definition for compressor stage Aircraft Propulsion

41. Percent Reaction A relation that approximates the relative loading of the rotor and stator based on the enthalpy rise: Aircraft Propulsion

42. Relationships of Velocity Polygons to Percent Reaction and Pressure Ratio Aircraft Propulsion

43. Limit on Stage Pressure Ratio • The rotor is moving, the relative velocity must be used: • For the stator, which is stationary the relative velocity must be used: 1 and 2 refer to the stage inlet and midstage properties. Aircraft Propulsion

44. Limit on Stage Pressure Ratio Stator Rotor Aircraft Propulsion

45. Axial Flow Turbine Aircraft Propulsion

46. Velocity Polygon Aircraft Propulsion

47. Velocity Polygon Aircraft Propulsion

48. Total Pressure Ratio The equations is derived for a single stage (rotor and stator) using 2D planar mean line c.v. approach. “Midway between hub and tip” The continuity, momentum and energy equations are used for the delivered shaft power: • Power Input to the Shaft • Total Pressure Ratio of the Stage Aircraft Propulsion

49. Percent Reaction A relation that approximates the relative loading of the rotor and stator based on the enthalpy rise: Aircraft Propulsion

50. Relationships of Velocity Polygons to Percent Reaction and Pressure Ratio Aircraft Propulsion