Compressible Aerodynamic Flows

This chapter will examine the aerodynamics of airfoils, wings, and bodies in compressible flow. Modeling techniques, approximations, and associated solution methods will also be examined, particularly for the important class of small-disturbance flows. Subsonic, transonic, and supersonic flows will be addressed.

8.1 Effects of Compressibility

8.1.1 Compressibility definition

1 V(V[6]) • V

2 a^~

Подпись: a(r) = V ■ V Подпись: -Vp-V p Подпись: 2 ds Подпись: = 0 Подпись: (8.1)

A compressible flow is defined as one with significant density p variations along particle pathlines. The resulting complications for flow-field representation were briefly discussed in Chapter 2. To summarize, a compressible flow has a nonzero field source distribution a(r), which can be related to the density-gradient and velocity fields via the continuity equation and the isentropic density-speed relation.

This field source must be accounted for if source+vorticity superposition is employed to represent the ve­locity field. However, because this a(r) is typically extensive, it cannot be effectively lumped into source sheets, lines, or points, so that actually performing the velocity superposition calculation numerically, or constructing its AIC matrices, becomes impractical for the general case, especially in 3D. Resorting to CFD methods which used grid-based flow-field representation then becomes necessary.

One exception is the case of small-disturbance flows, for which the field source distribution can be approx­imately accounted for via the Prandtl-Glauert coordinate transformation. The superposition approach then becomes effective again for such compressible flows. These will be treated later in this chapter.