WINGS IN COMPRESSIBLE FLOW

4- 1 INTRODUCTION

The theory of the wing in incompressible flow was discussed in Chap. 2 for the two-dimensional problem (infinite span) and in Chap. 3 for the three-dimensional problem (finite span). In this chapter the wing in compressible flow will be treated. Both subsonic and supersonic flows will be considered, depending on whether the flow velocities are lower or higher than the speed of sound, respectively. The connection between these two kinds of flow is formed by the transonic flow. Flows with very high supersonic velocities, so-called hypersonic velocities, are designated as hypersonic flows.

The influence of compressibility must be taken into account at Mach numbers higher than Ma «0.3. Compressible flow is of great significance for flow about wings, because the Mach numbers in aeronautics are, in general, considerably higher than 0.3.

The discussions of this chapter will be organized similarly to those of Chaps. 2 and 3, in that first the airfoil of infinite span in compressible flow (profile theory) and then the wing of finite span in compressible flow will be treated. From gas dynamics it is known that the compressible flows of subsonic and supersonic velocities are basically different; the same is true, naturally, for wing flows (see Fig. 1-9). For the theoretical treatment of compressible wing flow, the so-called linear theories will be applied predominantly, because they yield results that can be interpreted easily and thus aEow the establishment of general validity and of practical conclusions. For the theoretical considerations, mainly inviscid flow will be assumed as in Chaps. 2 and 3.

Besides the textbooks on gas dynamics listed in Section ЇІ of the Bibliography,
basic questions of compressible wing flow are treated by Taylor [94], Prandtl [73, 74], von Karman [101], Howarth [34], Robinson and Laurmann [78], Sears [83], Kuo and Sears [47], Heaslet and Lomax [30], Jones and Cohen [39], and Garrick [26]. Furthermore, more recent results and understanding of the theory of the aerodynamics of wings in compressible flow are presented in progress reports for certain time intervals by, among others, von Karman [102, 104], Ashley et al. [3], Ktichemann [45], Schlichting [81], Landahl and Stark [48], and Hummel [35]. Problems of experimental wing aerodynamics are treated by Frick [24]. In this connection, the comprehensive compilations of experimental data on the aero­dynamics of lift and drag by Hoerner and Borst [32], and Hoerner [31 ] should be mentioned.