Question

Which of these is the linearized perturbation velocity potential equation over a thin airfoil in a supersonic flow?

(a) λ^2(ϕxx + ϕyy) = 0

(b) ϕxx + ϕyy = 0

(c) λ^2ϕxx + ϕyy = 0

(d) λ^2ϕxx + ϕxy = 0

I had been asked this question in semester exam.

My doubt stems from Linearized Supersonic Flow topic in division Linearized and Conical Flows of Aerodynamics

Answer 1

Right answer is (c) λ^2ϕxx + ϕyy = 0

For explanation: For a supersonic flow over a thin airfoil, the two dimensional linearized perturbation velocity potential equation is given by

λ^2ϕxx + ϕyy = 0

In this equation the perturbations are assumed to be small with the value of λ = \(\sqrt {M_∞^2 – 1}\).