Review of Components Analysis Aerospace Engineering, International School of Engineering (ISE) Academic year : (August – December, 2012) Jeerasak Pitakarnnop, Ph.D. Aircraft Propulsion2November 17, 2012

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 November 17, 2012Aircraft Propulsion3

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 November 17, 2012Aircraft Propulsion4

Free Stream to Diffuser Inlet November 17, 2012Aircraft Propulsion5 π o represents loss from free stream to the inlet. Subsonic Flow π o ≈ 1 (= 1: ideal isentropic flow) Supersonic Flow  Shock π o < 1

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. Oct. 13, 2012Aircraft Propulsion6

Ex 1: Normal Shocks A standing normal shock occurs on an aircraft flying at Mach The internal recovery factor of the diffuser is 0.98, and the specific heat ratio is Find the total recovery factor of the diffuser. Oct. 13, 2012Aircraft Propulsion7

Ideal Diffuser November 17, 2012Aircraft Propulsion8 Isentropic & Adiabatic Flow Constant Total Pressure p ta = p t1 = p t2 Constant Total Temperature T ta = T t1 = T t2 (h ta = h t1 = h t2 )

Isentropic Flow Oct. 13, 2012Aircraft Propulsion9 Mach Number and Local Speed of Sound Stagnation Relations Area Ratio

Limit on Pressure Rise Separation is one of the limits of the diffuser operation. Oct. 13, 2012Aircraft Propulsion10 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.

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. Oct. 13, 2012Aircraft Propulsion11

Non Ideal Diffuser November 17, 2012Aircraft Propulsion12 To quantify loss from the free stream to the diffuser exit, we introduce: Total Pressure Recovery Factor: where π r is the diffuser pressure recovery factor, and π o represents loss from free stream to the inlet. High Speed/Flow decelerates/ Pressure increases Low Speed/Flow accelerates/Pressure decreases Nearly Adiabatic Flow, assume: Constant Total Enthalpy h ta = h t1 = h t2 Constant Total Temperature T ta = T t1 = T t2

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. Oct. 13, 2012Aircraft Propulsion13

Fanno Line Flow Adiabatic Flow of a Calorically Perfect Gas in a Constant- Area Duct with Friction Oct. 13, 2012Aircraft Propulsion14

Engine with Inlet Cone Oblique Shock – Oblique Planar Shock – Oblique Conical Shock Mode of Operation – Design Condition – Off Design Condition November 17, 2012Aircraft Propulsion15

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. Oct. 13, 2012Aircraft Propulsion16

Oblique Planar Shocks Oct. 13, 2012Aircraft Propulsion17 δ = deflection angle σ = shock angle

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. Oct. 13, 2012Aircraft Propulsion18 Spike on BlackBird

Oblique Conical Shocks Oct. 13, 2012Aircraft Propulsion19

Oblique Conical Shocks Oct. 13, 2012Aircraft Propulsion20

Oblique Conical Shocks Oct. 13, 2012Aircraft Propulsion21

Modes of Operation Oct. 13, 2012Aircraft Propulsion22 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!! Flow rate increases  Pressure in the diffuser drops  Shock moves into the diffuser 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 Acting like a supersonic nozzle  Shock occurs in diverging section with high Mach no.  More total pressure is lost.

Mass Flow or Area Ratio Oct. 13, 2012Aircraft Propulsion23 True ingested mass Mass flow enters the engine Reference Parameter Mass flow ratio

Design Operation November 17, 2012Aircraft Propulsion24

Off-Design Operation When the diffuser operated at off-design conditions, the area should be varied so that it operates efficiently. Oct. 13, 2012Aircraft Propulsion25 In the case of a single planar oblique shock: Inlet area could be determined from:

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 A m is used to decelerate the flow through internal compression. Assume γ = 1.4 and π r = a.Estimate π d on the assumption the inlet starts. Also, find the required A m /A 1 b.Find π d on the assumption the inlet doesn’t start and has a standing normal shock located in front of the spike. Oct. 13, 2012Aircraft Propulsion26

Nozzle Fixed Diverging Nozzle November 17, 2012Aircraft Propulsion27 Converging- Diverging Nozzle

Primary Nozzle Aircraft Propulsion28 In real analysis:  P exit may not match P a due to incorrect nozzle area proportion.  Frictional losses are include but adiabatic process still be assumed. Nozzle Efficiency Constant c p Specific heat Exit Velocity Adiabatic Oct. 20,2012

Primary Nozzle Aircraft Propulsion29 Adiabatic Process Flow: For the ideal case, isentropic process Adiabatic Thus, Oct. 20,2012

Primary Nozzle Aircraft Propulsion30 Choke condition: Then, If p* > p a, the nozzle is choke If p* = p 8, M 8 = 1 If p* < p a, M 8 < 1 and p 8 = p a Oct. 20,2012

Converging Nozzle Oct. 20,2012Aircraft Propulsion31 Exhaust of converging nozzle with matching exhaust and ambient pressures Exhaust of under expanded converging nozzle

Converging-Diverging Nozzle Oct. 20,2012Aircraft Propulsion32

1 st – 3 rd Condition of CD nozzle Case 1: p exhaust = p ambient and Subsonic Flow Through out the nozzle. Case 2: p exhaust = p ambient and Subsonic Flow Through out the nozzle but M throat =1. Case 3: p exhaust = p ambient, Subsonic Flow in the converging section and Supersonic Flow in the diverging section. – MAXIMUM THRUST – Design Condition for the ideal case Oct. 20,2012Aircraft Propulsion33

4 th Condition of CD Nozzle p ambient is slightly above the designed p exhaust – Result in a complex 2D flow pattern outside the nozzle Oct. 20,2012Aircraft Propulsion34 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

5 th Condition of CD Nozzle p ambient is below the designed p exhaust – Result in a complex 2D flow pattern outside the nozzle Oct. 20,2012Aircraft Propulsion35 Considered as “Underexpanded Case” 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.

6 th Condition of CD Nozzle p ambient is significantly above the designed p exhaust But below the 2 nd case – Result in a single normal shock or a series of oblique and normal shocks called λ Oct. 20,2012Aircraft Propulsion36 Also “Overexpanded Case” Result in a subsonic exit Mach no.: LOW THRUST  Totally undesirable

7 th Condition of CD Nozzle p ambient is significantly above the designed p exhaust Limit condition of the 6 th case – Exit pressure causes a normal shock exactly at the exit plane – Case 4 falls between case 7 and 3. Oct. 20,2012Aircraft Propulsion37

Ex4: Converging-Diverging Nozzle A converging-diverging nozzle with an exit area of m2 and a minimum area of m2 has an upstream total pressure of kPa. The nozzle efficiency is and the specific heat ratio is a.At what atmospheric pressure will the nozzle flow be shockless? b.At what atmospheric pressure will a normal shock stand in the exit plane? Oct. 20,2012Aircraft Propulsion38

Axial Flow Compressor November 17, 2012Aircraft Propulsion39

Velocity Polygon November 17, 2012Aircraft Propulsion40

Total Pressure Ratio Power Input to the Shaft October 27, 2012Aircraft Propulsion41 Total Pressure Ratio of the Stage The equations is derived for a single stage (rotor and stator) using 2D planar mean line c.v. approach. “Midway between hub and tip” Control Volume definition for compressor stage

Percent Reaction A relation that approximates the relative loading of the rotor and stator based on the enthalpy rise: October 27, 2012Aircraft Propulsion42

Relationships of Velocity Polygons to Percent Reaction and Pressure Ratio October 27, 2012Aircraft Propulsion43

Limit on Stage Pressure Ratio The rotor is moving, the relative velocity must be used: October 27, 2012Aircraft Propulsion44 For the stator, which is stationary the relative velocity must be used: 1 and 2 refer to the stage inlet and midstage properties.

Limit on Stage Pressure Ratio Rotor October 27, 2012Aircraft Propulsion45 Stator

Axial Flow Turbine November 17, 2012Aircraft Propulsion46

Velocity Polygon November 17, 2012Aircraft Propulsion47

Velocity Polygon November 17, 2012Aircraft Propulsion48

Total Pressure Ratio Power Input to the Shaft November 17, 2012Aircraft Propulsion49 Total Pressure Ratio of the Stage 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:

Percent Reaction A relation that approximates the relative loading of the rotor and stator based on the enthalpy rise: November 17, 2012Aircraft Propulsion50

Relationships of Velocity Polygons to Percent Reaction and Pressure Ratio November 17, 2012Aircraft Propulsion51

Turbine and Compressor Matching 1.Select operating speed. 2.Assume turbine inlet temperature. 3.Assume compressor pressure ratio. 4.Calculate compressor work. 5.Calculate turbine pressure ratio required to produce this work. November 17, 2012Aircraft Propulsion52

Turbine and Compressor Matching 6. Check to see if compressor mass flow plus fuel flow equals turbine mass flow; if it does not, assume a new value of compressor pressure ratio and repeat step 4, 5, and 6 until continuity is satisfied. Note: No need to do the iteration in the exam, I will provide a required values to determine other value. November 17, 2012Aircraft Propulsion53

Turbine and Compressor Matching Note: No need to do the iteration in the exam, I will provide a required values to determine the others from compressor and turbine performance maps. Ex. For given rotational speed, mass flow rate and total pressure ratio across each component, efficiency could be determined. November 17, 2012Aircraft Propulsion54

Good Luck!!! November 17, 2012Aircraft Propulsion55