LIFT AND DRAG AT HIGH MACH NUMBERS

The preceding material on lift and drag was limited primarily to incompressible flows, that is, to Mach numbers less than approximately 0.4. Compressibility becomes more and more important as the Mach number increases. In the vicinity of a Mach number of unity, airfoils and wings undergo a radical change in their behavior. It is not too surprising, therefore, to find that the equations covering the flow of air undergo a similar change at around М» = 1.0.

Many textbooks are devoted entirely to the subject of compressible flows. References 5.1 and 5.2 are two such examples. Here, the several equations and techniques for the study of gas dynamics are developed in considerable detail. An excellent, lucid, qualitative explanation of com­pressibility effects on wings and airfoils is found in Reference 5.3.

QUALITATIVE BEHAVIOR OF AIRFOILS AS A FUNCTION OF MACH NUMBER

We will consider three regimes of flow around an airfoil. In the first, the flow is everywhere subsonic with a relatively high Mach number. The second regime is referred to as transonic flow. Here the free-stream Mach number is less than unity, but sufficiently high so that the flow locally, as it accelerates over the airfoil, exceeds the local speed of sound; that is, locally the flow becomes supersonic. The lowest free-stream Mach number at which the local flow at some point on the airfoil becomes supersonic is known as the critical Mach number. The third regime is the supersonic flow regime, in which the free-stream Mach number exceeds unity. Even here, a small region of subsonic flow may exist near the leading edge of the airfoil immediately behind a shock wave depending on the bluntness of the leading edge. The sharper the leading edge, the smaller is the extent of the subsonic flow region.