Question

For supersonic flow, which differential equation is obtained for the linearized perturbation potential equation?

(a) Elliptic partial differential equation

(b) Hyperbolic differential equation

(c) Parabolic differential equation

(d) Linear differential equation

I got this question in an online interview.

Question is taken from Application to Supersonic Airfoils in section Subsonic Compressible Flow over Airfoils : Linear Theory, Linearized Supersonic Flow of Aerodynamics

Answer 1

Correct answer is (b) Hyperbolic differential equation

Explanation: The linearized perturation potential equation is given by:

1-M\(_∞^2=\frac {∂^2 \hat {ϕ}}{∂x^2}+\frac {∂^2 \hat {ϕ}}{∂y^2}\)=0

Where, \(\hat {ϕ}\) is ther perturbation potential

M∞ is the free stream Mach number

In case of supersonic flow, 1-M\(_∞^2\) < 0 since Mach number is greater than 1. For this case the equation becomes hyperbolic differential equation which is of the type \( \frac {∂^2 u}{∂x^2}+\frac {∂^2 u}{∂y^2}\).