Understanding Compressible Shock Waves: Exploring Theta, Beta, and Mach Curves

In summary: After passing through, the flow is subsonic in both cases. In a weak shock, the flow slows down more gradually compared to a strong shock, resulting in a smaller change in flow properties. This can be seen in the change in the Mach number (##M_2<1## for a weak shock and ##M_2>1## for a strong shock).
  • #1
stephane
18
0
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
 
  • #3
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.
 

Related to Understanding Compressible Shock Waves: Exploring Theta, Beta, and Mach Curves

1. What is a compressible shock wave?

A compressible shock wave is a type of shock wave that occurs in a gas or fluid where the density and pressure change significantly across the wave front. This is usually caused by a sudden change in the speed or direction of flow, which leads to a rapid increase in pressure and temperature.

2. How is a compressible shock wave different from an incompressible shock wave?

In an incompressible shock wave, the density of the fluid remains constant across the wave front, while in a compressible shock wave, the density changes. This is due to the fact that incompressible fluids, such as liquids, cannot be compressed, while compressible fluids, such as gases, can be compressed.

3. What is the Mach number and how does it relate to compressible shock waves?

The Mach number is a dimensionless number that represents the velocity of an object in relation to the speed of sound in the surrounding medium. In the context of compressible shock waves, the Mach number is used to determine whether the flow is subsonic (Mach number < 1), transonic (Mach number ~ 1), or supersonic (Mach number > 1). Compressible shock waves occur in supersonic flow.

4. What are some practical applications of compressible shock waves?

Compressible shock waves have many practical applications, including in the field of aerodynamics where they are used to generate lift and reduce drag in aircraft design. They are also used in supersonic and hypersonic propulsion systems, in shock tubes for studying high-speed flows, and in shock absorbers for vehicles.

5. How are compressible shock waves studied and analyzed?

Compressible shock waves are studied and analyzed using a variety of tools and techniques, including computational fluid dynamics (CFD) simulations, wind tunnel experiments, and shock tube experiments. These methods allow scientists to measure and analyze the behavior of compressible shock waves in different conditions and environments.

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