What Are the Key Concepts Behind Compressible Shock Waves and Their Curves?

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SUMMARY

The discussion focuses on the key concepts of compressible shock waves, specifically the theta-beta-Mach (θ-β-M) curves. It establishes that when the angle θ exceeds the maximum value (θ_max), oblique shocks do not occur due to the mathematical solutions becoming imaginary, indicating insufficient space for mass flow continuity. The difference between weak and strong shocks is clarified, with weak shocks resulting in subsonic flow downstream (M_2 < 1) and strong shocks resulting in supersonic flow downstream (M_2 > 1). The terms "extraordinary" and "ordinary" solutions are suggested for better understanding of these shock types.

PREREQUISITES
  • Understanding of compressible flow dynamics
  • Familiarity with shock wave theory
  • Knowledge of the θ-β-M equations
  • Basic principles of fluid mechanics
NEXT STEPS
  • Study the derivation of the θ-β-M equations in compressible flow
  • Explore the characteristics of weak and strong shocks in detail
  • Learn about the physical implications of shock detachment in fluid dynamics
  • Investigate real-world applications of compressible flow and shock wave analysis
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Students and professionals in aerospace engineering, fluid dynamics researchers, and anyone involved in the study of compressible flow and shock wave phenomena.

stephane
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Hi all,

I have some prob to undestand the shock wave in compressible flow, more precisely the "theta, beta, Mach curve)

- Why when "theta" exceeds theta (max) there is no oblique shock? (how we can explain this physicaly)?
- What is the difference betwwen weak shock and strong shock?
- why in weakv shock the flow is supersonic ahead and subsonic when we have a strong shok?

Please could you explain? thanks
 
stephane said:
- Why when "theta" exceeds theta (max) there is no oblique shock? (how we can explain this physicaly)?

Mathematically, the solutions to the ##\theta##-##\beta##-##M## equation become imaginary at this point. Physically, it means that there is no longer enough space between the surface and any attached shock to pass the mass flow required to maintain continuity, so the shock detaches.

stephane said:
- What is the difference betwwen weak shock and strong shock?

One (strong) results in ##M_2>1## downstream and one (weak) results in ##M_2<1## downstream. It may be easier to call these two cases the extraordinary and ordinary solutions, respectively, rather than strong or weak. It isn't as common to do this but it may make more sense to you given that it is almost always the weak shock that develops in the real world.

stephane said:
- why in weakv shock the flow is supersonic ahead and subsonic when we have a strong shok?

I am not really sure what you mean here. Before passing through the shock, the flow must be supersonic in both cases.
 

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