Compressible Unsteady Aerodynamics

The evaluation methods for the sectional as well as the total lift and moment coefficients for unsteady subsonic and supersonic flows will be given in Chap. 5. It is, however, possible to obtain approximate expressions for the amplitude of the sectional lift coefficients at high reduced frequencies and at transonic regimes where M approaches to unity as limiting value. For steady flow on the other hand, the analytical expression is not readily available since the equations are nonlinear. However, local linearization process is applied to obtain approximate values for the aerodynamic coefficients.

Now, we can give the expression for the amplitude of the sectional lift coef­ficient for a simple harmonically pitching thin airfoil in transonic flow

h « 4 (1 + ik)a, k > 1 (1.23)

Here, a is the amplitude of the angle of attack. Let us consider the same airfoil in a vertical motion with amplitude of h.

hl« 8 ikh/b, k > 1 (1.24)

All these formulae are available from (Bisplinghoff et al. 1996).

Aerodynamic response to the arbitrary motion of a thin airfoil in transonic flow will be studied in Chap. 5 with aid of relevant unit response function in different Mach numbers.