Module 4 : Approximate and exact methods for hypersonic inviscid flows

Lecture 14 : The Hypersonic Small Disturbance Theory

Since the configuration under consideration is slender, the slope at any point is of the order of ratio of length to diameter of the body.

14.2

Hence, = Slenderness Ratio

Therefore,

14.3

However, u' << V, which leads to,

14.4

Let a be the freestream speed of sound,

 

 

14.5

Hence, Strength of the disturbance in the flow relative to  is of the order of . This expression also provides information that  is a hypersonic similarity parameter. This information is fetched only from the boundary conditions.

We can express the steady Euler Equations in terms of the perturbation velocities, u’ and v’ forsteady flow,

14.6


14.7


14.8


14.9


14.10