Reflection of Oblique Shocks P M V Subbarao Professor Mechanical Engineering Department I I T Delhi A Train of Waves ….. Where to End ???

Reflection of Oblique Shocks If there exists a situation of reflection of flow with M 2 such that,    is <   The angle required to bring the flow parallel to the reflecting wall is less than wedge angle !!!!    x y

Weak And Strong Oblique Shock 

Minimum Allowable Oblique Shock Angle It was proved that for normal shock to exist, M x > 1, i.e., the upstream flow should be supersonic. For the occurrence of Oblique shock M nx > 1.

Normal Component of Free stream mach Number at minimum shock angle (NO COMPRESSION!)

Wedge Angle at Minimum Shock Angle For an Oblique shock M y can be greater or less than one. In general M y >1 is mostly possible. It was proved that for a normal shock, M y < 1, i.e., the downstream flow should be subsonic. For a Oblique shock M ny < 1.

But :  min  at  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 M 2 such that,    is <  The angle required to bring the flow parallel to the reflecting wall is less than wedge angle !!!! For a given M 2, 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 

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

Design Back Pressure

Steady Cruising Design Conditions

Back Pressure Lower than the design conditions

Turning of Flow So if  >0.. Compression around corner   M x M y If  0.. Mach Wave……

Expansion Waves Then it follows that  <0.. We get an expansion wave Next Prandtl-Meyer Expansion waves