Perturbation methods/linearized flow theory

Question 1

Describe requirements to the flow allowing application of perturbation methods based on small deflection
angles (i.e., the linearized flow theory)

Question 2

Explain the difference between boundary conditions at an airfoil in subsonic and supersonic flow. Explain the
causal principle used in the boundary condition for supersonic flow

Question 3

Solving the boundary value problem, calculate the velocity filed in the wavy wall, 𝑦𝑏 = ℎ sin 𝑘𝑥, in a
subsonic flow

Question 4

Solving the boundary value problem, calculate the velocity filed in the wavy wall, 𝑦𝑏 = ℎ sin 𝑘𝑥, in a
supersonic flow

Question 5

Derive a formula which relate the pressure perturbation with the velocity perturbation in the approximation
of the linearized flow

Question 6

Explain what causes the drag and lift forces acting on an object moving with supersonic velocity

Question 7

Explain why the drag force acting on a wavy wall in a subsonic flow is absent in the approximation of
linearized flow theory.

Question 8

Explain why in the linearized flow theory, the drag and lift coefficients grow to infinity if the flow Mach
number tends to one. How to avoid this?

Question 9

Infinitesimally thin flat-plate airfoil has the lift coefficient 𝐶𝐿 = 0.2 at the angle of attack 𝛼 = 10°. Find its
drag coefficient 𝐶𝐷 at this angle of attack.