Review of Components Analysis Aerospace Engineering, International School of Engineering (ISE)...

Aircraft Propulsion 1

Review ofComponents Analysis

Aerospace Engineering, International School of Engineering (ISE)Academic year : 2012-2013 (August – December, 2012)

Jeerasak Pitakarnnop , [email protected]@nimt.or.th

November 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

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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

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Free Stream to Diffuser Inlet

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πo represents loss from free stream to the inlet.

Subsonic Flow• πo ≈ 1 (= 1: ideal isentropic flow)

Supersonic Flow Shock• πo < 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.

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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.

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Ideal Diffuser

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Isentropic & Adiabatic Flow• Constant Total Pressure

pta = pt1 = pt2

• Constant Total TemperatureTta = Tt1 = Tt2

(hta = ht1 = ht2)


Isentropic Flow

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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.

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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.

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Non Ideal Diffuser

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To quantify loss from the free stream to the diffuser exit, we introduce:• Total Pressure Recovery Factor:

where• πr is the diffuser pressure

recovery factor, and• πo 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

hta = ht1 = ht2

• Constant Total TemperatureTta = Tt1 = Tt2


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.

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Fanno Line FlowAdiabatic Flow of a Calorically Perfect Gas in a Constant-Area Duct with Friction

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Engine with Inlet Cone

• Oblique Shock–Oblique Planar Shock–Oblique Conical Shock

• Mode of Operation–Design Condition–Off Design Condition

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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.

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Oblique Planar Shocks

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δ = deflection angleσ = 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.

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Spike on BlackBird



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Modes of Operation

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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 lossSome of the air will be spilled high pressure additive dragShock 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

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True ingested mass

Mass flow enters the engine

Reference Parameter

Mass flow ratio


Design Operation

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Off-Design Operation

When the diffuser operated at off-design conditions, the area should be varied so that it operates efficiently.

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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 Am is used to decelerate the flow through internal compression. Assume γ = 1.4 and πr = 0.98.

a. Estimate πd on the assumption the inlet starts. Also, find the required Am/A1

b. Find πd on the assumption the inlet doesn’t start and has a standing normal shock located in front of the spike.

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NozzleFixed Diverging

Nozzle

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Converging-Diverging Nozzle


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

Exit Velocity

Adiabatic

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Primary Nozzle

Adiabatic Process Flow: For the ideal case, isentropic process

Adiabatic

Thus,

Oct. 20,2012


Primary Nozzle

Choke condition:

Then,

If p* > pa, the nozzle is chokeIf p*= p8, M8 = 1If p* < pa , M8 < 1 and p8 = pa

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Converging Nozzle

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Exhaust of converging nozzle with matching exhaust and ambient pressures

Exhaust of under expanded converging nozzle


Converging-Diverging Nozzle

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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

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4th Condition of CD Nozzle

• pambient is slightly above the designed pexhaust

– Result in a complex 2D flow pattern outside the nozzle

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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



• pambient is below the designed pexhaust

– Result in a complex 2D flow pattern outside the nozzle

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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.


6th Condition of CD Nozzle• pambient is significantly above the designed pexhaust

But below the 2nd case– Result in a single normal shock or a series of oblique

and normal shocks called λ

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Also “Overexpanded Case”• Result in a subsonic exit Mach no.: LOW THRUST Totally

undesirable



• pambient is significantly above the designed pexhaust

Limit condition of the 6th case– Exit pressure causes a normal shock exactly at the exit

plane– Case 4 falls between case 7 and 3.

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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. 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. 20,2012


Axial Flow Compressor

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Velocity Polygon

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Total Pressure Ratio

• Power Input to the Shaft

October 27, 2012

• 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:

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Relationships of Velocity Polygons to Percent Reaction and Pressure Ratio

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Limit on Stage Pressure Ratio

• The rotor is moving, the relative velocity must be used:

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• 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

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Stator


Axial Flow Turbine

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Velocity Polygon

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Total Pressure Ratio

• Power Input to the Shaft

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• 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:

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Relationships of Velocity Polygons to Percent Reaction and Pressure Ratio

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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.

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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.

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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.

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Good Luck!!!

November 17, 2012

Review of Components Analysis Aerospace Engineering, International School of Engineering (ISE)...

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