Multiple Shock reflection problem

[daddydoodle]

Here's the problem :

Air flows in a passage with an initial Mach No. 2. Determine maximum turning angle A for which 3 regular reflections (i.e. no Mach reflection) of the original oblique shock are possible?

Now, what exactly is a mach reflection? Also, what is the minimum Mach number required for a straight attached shock? From what I have read up, I've worked out that the Mach no. between the 2nd and 3rd (last) reflection should be greater than 1 (which I understood minimum mach number required for a straight attached shock). But I'm not quite sure if what I've understood is right. Could anyone clear this up for me?

Also, if I'm right, then we have the initial and the last (before the 3rd reflection) Mach nos. but then, there are too many unknowns in between to solve the problem. How do I go about that?

 

[PhysicsGuy24]

Have you been able to find a solution to this yet?

 

[Travis_King]

Answer yourself these questions:

1) Can a shockwave be created by an airflow that is less than Mach?
2) What happens to the airflow downstream of a shockwave?

This problem is tough, but not impossible. you will need to work from both sides of the equation to know what you are dealing with. Leaving your angles as variables will help.

Find M2 as a function of A, Find M2's Beta as a function of A, Then you will know the angle M2 is traveling at. You can use the equations you probably have for the x and y components. You do this down the line and you'll have a terribly long equation, but ultimately M5 should be <1.

 

[Travis_King]

This thread might help

https://www.physicsforums.com/showthread.php?p=2537843

 

[alphy]

A Mach reflection occurs when a shock wave reflects off a surface and creates a second shock wave that intersects with the first shock. This creates a complex shock structure and can occur at high Mach numbers. A straight attached shock occurs when the shock wave remains attached to the surface without any reflection.

To determine the maximum turning angle A for which 3 regular reflections are possible, we need to consider the Mach number at each reflection point. As you mentioned, the Mach number between the 2nd and 3rd reflections should be greater than 1 for a straight attached shock. This means that at the 2nd reflection, the Mach number should be greater than 1, and at the 3rd reflection, it should be less than 1.

To solve this problem, we can use the equations for oblique shock waves and the Mach reflection condition. We can also use the fact that the Mach number decreases as the shock wave turns, so the Mach number at the 3rd reflection should be lower than the initial Mach number.

By setting up and solving these equations, we can determine the maximum turning angle A for which 3 regular reflections are possible. It is important to note that this is a theoretical solution and may not be achievable in real-life situations due to factors such as shock wave strength and boundary layer effects.