Question

On which of this parameter is the coefficient of lift over a two – dimensional body at hypersonic flow dependent?

(a) γ.\(\frac {α}{τ}\)

(b) γ, K, M∞

(c) M∞T, \(\frac {α}{τ}\), γ

(d) M∞T, K, γ

I have been asked this question in quiz.

I'm obligated to ask this question of Hypersonic Similarity topic in chapter Transonic and Hypersonic Flows of Aerodynamics

Answer 1

The correct option is (c) M∞T, \(\frac {α}{τ}\), γ

To explain: The lift coefficient over the body at hypersonic flow is obtained by integrating the pressure coefficient over the surface.

cl = \(\frac {1}{l} \int _0^{l}\)(Cpl – Cpu)dx

Where, Cpl – Cpu are coefficient of pressure over the upper and lower surface

l is the length of body

The above equation in terms of x is

cl = \(\int _0^{1}\)(Cpl – Cpu)dx

Diving this equation with the square of slenderness ratio, we get

\(\frac {c_l}{τ^{2}} = \int _0^{1}\)(Cpl – Cpu)dx = f(M∞T, \(\frac {α}{τ}\), γ)

Thus, coefficient of lift is a function of M∞T, \(\frac {α}{τ}\) and γ.