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2D Flow Applications2D Flow Applications
1. Shock Interactions
2. Engine Intakes2. Engine Intakes
3. Supersonic Jets
1. Shock fl
βB1
3
βCReflection
δ=12oβA
23
M1 =6
Find M2, M3, p2/p1, p3/p1δ=12oβA
TABLES
βBM1 =6
M3 =3.41
1
2
3
1
βC
δ=12oβA δ 12βA
More Reflections?More Reflections?
TABLES
1b. Shock βB
3
δB=5o
Intersection1
OPPOSITE FAMILIES
δ 12β
1
2M1 =3
δA=12oβA
1b. Shock βB
3
δB=5o
Intersection1
OPPOSITE FAMILIES
4
5
φ
δ 12β
1
2M1 =3
4
δA=12oβA
1c. Shock Intersection
1
SAME FAMILY
ββB
1
2
3
M1 =3 δB=6o
δ 12βA δA=12o
2. Supersonic Engine Intakes2. Supersonic Engine Intakes
• Designed toDesigned to– Compress the flow– Decelerate it to subsonic speed
– Minimum p0 loss
• Most intakes are designed to direct the flow more than one shock wave
Why Multiple Shocks?Why Multiple Shocks?Consider deceleration of a Mach 2 flow to subsonic….
SINGLE NORMAL SHOCKSINGLE NORMAL SHOCK
M=2
OBLIQUE / NORMAL SHOCK COMBINATION
1 2
OBLIQUE / NORMAL SHOCK COMBINATION
M=2
1 2
3M 2
45o
Two‐Dimensional InletTwo Dimensional Inlet
M∞M∞
Wind‐Tunnel VisualizationMach number 1.95
history.nasa.gov/SP‐4302/ch2.12.htm
Northrup F‐5
F‐4 Phantom
Concorde/ Olympus 563Concorde/ Olympus 563TAKE OFF
http://www.concordesst.com/powerplant.html
SUPERSONIC CRUISE
Axisymmetric InletAxisymmetric Inlet
M∞ = MDESIGN
M∞ < MDESIGN
M∞ > MDESIGNDESIGN
Mirage F1
General Dynamics F‐111
SR‐71
SR‐71 InletSR 71 Inlet
3. Supersonic Jets SATURN V ROCKET(APOLLO 15, 11, 11)
TAKEOFF 39 MILES ALTITUDETRANSONIC
XCOR 5M15 Liquid Methane/Oxygen Rocket EngineRocket Engine
http://www.xcor.com/
2D Over‐Expanded JetREGULAR REFLECTION
E i M 1
pbAmbient
Exit Me>1p=pe>pb p=pb p>pb
p=pb
P i i d f i l h l b• Pressure is raised from pe to pb as it leaves the nozzle by an oblique shock.
• Shock also deflects flow down toward plane of symmetry.• Deflection can’t be sustained at symmetry plane so a 2nd
shock is formed to deflect the flow parallel to the symmetry plane once more.
• This also raises the pressure above pb• To bring the pressure back down to pb the shock as to
reflect from the jet edge as an expansion wave, but this j g p ,then deflects the flow away from the plane of symmetry.
pb=0.2pcAmbientExampleMe=2pe=0.1278pc p=pb p>pb
p=pbFind pressures, Mach numbers and flow directions
1
2
3
4
pb=0.2pcAmbientExampleMe=2pe=0.1278pc p=pb p>pb
p=pbFind pressures, Mach numbers and flow directions
1
2
3
4M2=1.702
M3=1.409p3=0.3pc
2D Over Expanded JetMACH REFLECTION
E i M 1
pbAmbient
Exit Me>1p=pe>pb
p=pbp>pb
p=pb
• Occurs when the Mach number downstream of the 1stshock is too low for regular reflection (i e theshock is too low for regular reflection (i.e. the maximum turn angle for the second wave would be less than the deflection produced by the first.)B k i t th th t f l fl ti• Back pressure is greater than that for regular reflection, and less than that for a shock at the exit.
pbAmbientExampleMe=2pe=0.1278pc p>pb
p=pbFind back pressure at which Mach reflection first appears
1
2
3
4p=pb
appears
TABLES
Axisymmetric Over‐Expanded Jet
http://www.aerospaceweb.org/ Space Shuttle Main Engine
2D Under‐Expanded JetpbAmbient
p=pbp=pb
Exit Me>1p=pe<pb
p=pb
P<pb
p=pb
• Pressure is reduced from pe to pb as it leaves the nozzle by an expansion wave centered on the nozzle lipW l d fl fl f h l f• Wave also deflects flow up away from the plane of symmetry.
• Deflection can’t be sustained at symmetry plane so a another expansion is formed to deflect the flow parallel to the symmetry plane once moreplane once more.
• This also lowers the pressure below pb• To bring the pressure back up to pb the expansion reflects from the
jet edge as an compression wave, but this then deflects the flowjet edge as an compression wave, but this then deflects the flow toward the plane of symmetry.
ExampleAmbientpb=0.05pc
Exit Me=2pb=0.1278
p=pb
P<p
p=pbCompute angle and Mach number of flow after first turn
1
2
P<pb1
Axisymmetric Under‐Expanded Jet
http://www.aerospaceweb.org/
Kinki University, Japan
