Reflection of Oblique Shocks

P M V SubbaraoProfessor

Mechanical Engineering DepartmentI I T Delhi

A Train of Waves ….. Where to End ???

Reflection of Oblique Shocks

If there exists a situation of reflection of flow with M2 such that, is <

The angle required to bring the flow parallel to the reflecting wall is less than wedge angle !!!!

xy

Weak And Strong Oblique Shock

Minimum Allowable Oblique Shock Angle

• It was proved that for normal shock to exist, Mx > 1, i.e., the upstream flow should be supersonic.

• For the occurrence of Oblique shock Mnx > 1.

1sin min xnx MM

xM

1sin min

xM

1sin 1

min

min

• Normal Component of Free stream mach Number at minimum shock angle

•

(NO COMPRESSION!)

1sin minmin, xnx MM

111

21 2

min,min,

nx

x

y Mp

p

Wedge Angle at Minimum Shock Angle

• For an Oblique shock My can be greater or less than one.

• In general My >1 is mostly possible.

1sin min yny MM

yM

1sin min

• It was proved that for a normal shock, My < 1, i.e., the downstream flow should be subsonic.

• For a Oblique shock Mny < 1.

)2cos(2

1sinM2cottan

2

22x

xM

But :

)2cos(2

1sinM2cottan

min2

min22

xminmin

xM

yM

1sin 1

min

minat min

Minimum Flow turning angle is min

The minimum flow turning angle increases with decreasing Mach number.

Minimum Flow Turning Angle

• A point source moving at super sonic speeds will turn the flow through a Mach Angle.

• This is the minimum unavoidable turning due to a supersonic object.

If there exist a situation of reflection of flow with M2 such that, is <

The angle required to bring the flow parallel to the reflecting wall is less than wedge angle !!!!

For a given M2, there exists a minimum allowable flow turning angle.

This is min.

Occurrence of Mach Reflection

Flow will not be parallel to the the reflecting wall!A special curved shock isolates the wall and incident oblique shock.The flow just behind this curved shock is found to be subsonic, near the wall.Since this is subsonic flow, it will not follow the rules of reflection.

• The flow downstream of reflected shock is divided from the flow downstream of curved shock.

• The line of separation is called as slip line.

• A difficult situation to solve analytically.

Effect of Changing Wall direction on Reflections

• The system is designed so that the wall changes direction sharply at the point of shock impingement.

• A positive change is called as convex corner.

• The turning angle produced by the reflected wave is

Less turning than that of a flat wall.Lesser the turning, less will be the strength of the reflected shock.

If is equal to , then the reflection will not occur!

If , then !?!?!?!

Weak And Strong Oblique Shock

angle egiven wedg afor 1

1

12

M

MM

Interaction of Oblique Shock Waves

A concave wall can be constructed using several small angular changes of equal magnitudes.

M>1

Interaction of Dissimilar Oblique Shocks

Flow Visualization Studies

66.0,

designb

b

p

p

85.0,

designb

b

p

p

Design Back Pressure

0.1,

designb

b

p

p

Steady Cruising Design Conditions

Back Pressure Lower than the design conditions

0

,

0 p

p

p

p designbb

Back Pressure Lower than the design conditions

Turning of Flow

• So if>0 .. Compression around corner

Mx

My

• If 0 .. Mach Wave……

Expansion Waves

• Then it follows that<0 .. We get an expansion wave

• Next

Prandtl-Meyer Expansion waves