## Fluids

#### Oblique shock

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Ansys Employee

Hello Friends,

I am looking for some help on properly estimating the flow properties behind an oblique shock wave. Thank you in advance.

• prajput
Ansys Employee

An oblique shock is a type of shock-wave. Its name is strictly connected to the shock orientation with respect to the flow direction. Indeed, the shock is at a certain angle "beta" with respect to the flow direction. A particular case of oblique shock is when beta=90 deg., in this case the oblique shock becomes a normal shock. In order to analyze the properties of a flow passing through an oblique shock the normal shock equations can be used combined with the theta-beta-Mach relation to close the problem. The theta-beta-Mach relation is generally presented in a form of a plot that defines what would be the shock angle based on the body geometry and the flow Mach number.

The oblique shock can have two solutions per case: the strong shock and the weak shock solutions. Weak shocks are the majority of the phenomena that can be seen, while strong shocks are generally enforced by particular operating conditions. For a flow passing through a strong oblique shock the mach number past the shock is always subsonic. If the flow passes through a weak shock, in most of the cases the Mach number would be still supersonic, but there are specific situations where the flow will become subsonic past the shock.

Ansys Employee

Hello. Thank you for the very detailed explanation.

I see that you mentioned theta-beta-Mach relation. Can you elaborate a bit more on that if possible?

• prajput
Ansys Employee

The Theta-Beta-Mach relation specifies the deflection angle as function of the oblique shock angle and the upstream Mach number:

tan(theta) = 2 cot(beta) {[M^2 sin^2(beta)-1]/[M^2(gamma+cos(2 beta))+2]}

The results of this relation are often represented as a plot chart. The relation gives us more insight on the effect of different parameters on the oblique shocks:

- For each Mach number the deflection angle has a maximum value past which the oblique shock detaches from the body and forms a bow shock.

- For each deflection angle there are up to two solutions, namely, a strong shock and a weak shock. The first has larger shock angle than the second. Weak shocks are more common to be found in nature.

- For a fixed deflection angle, an increase of the Mach number would decrease (increase) the shock angle for a weak (strong) shock.

-At a fixed Mach number, an increase of deflection angle would increase (decrease) the weak (strong) shock angle.