Multiple Shock reflection problem

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Discussion Overview

The discussion revolves around a fluid dynamics problem involving shock waves, specifically focusing on determining the maximum turning angle for which three regular reflections of an oblique shock are possible in a flow with an initial Mach number of 2. Participants explore concepts related to Mach reflections, minimum Mach numbers for attached shocks, and the implications of shock wave behavior in airflow.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the definition of Mach reflection and the minimum Mach number required for a straight attached shock, suggesting that the Mach number between the second and third reflections should exceed 1.
  • Another participant proposes that the problem is complex and suggests working with variables for angles to derive relationships between Mach numbers and angles.
  • A third participant emphasizes the need to consider the behavior of airflow downstream of a shockwave and poses questions to guide understanding of the problem.
  • There is a suggestion to reference another thread that may provide additional insights into the problem.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants express uncertainty about the definitions and relationships involved in the problem, and multiple approaches to solving it are suggested.

Contextual Notes

Participants highlight the complexity of the problem, noting the presence of multiple unknowns and the need for assumptions regarding angles and Mach numbers. There is an acknowledgment of the challenge in deriving a solution due to these uncertainties.

Who May Find This Useful

This discussion may be useful for students or professionals interested in fluid dynamics, particularly those studying shock wave phenomena and their mathematical modeling.

daddydoodle
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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?

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

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