Friction Drag on a Flat Plate. in Compressible Flow

In Sec. 2-5-2 the friction drag of wing profiles in incompressible flow was discussed. Particularly, in Fig. 2-48 the influence of the Reynolds number on the drag of a flat plate in chord-parallel incident flow was demonstrated. The insight gained then will now be extended to the case of compressible flow.

Wall flow The compressible boundary layer is decisively affected by the heat transfer between the wall and the streaming fluid. Here, the case of the wall without heat transfer (adiabatic wall) is of particular importance.

The laminar boundary layer of compressible flow can be treated theoretically, but theoretical studies dealing with the turbulent compressible boundary layers are still limited to semiempirical theories of the type of the Prandtl mixing-length hypothesis, in which, however, additional assumptions must be made. Drag coefficients of the flat plate at zero incidence over Reynolds and Mach numbers are given in Fig. 4-4 in comparison with measurements. Agreement between computa­tion and measurement is not satisfactory in all cases. However, some uncertainty of measurement at high Mach numbers should be taken into account. Also, in Fig. 4-5,

Figure 4-3 Heating of a solid wall through friction; W — velocity boundary layer; T = temperature boundary layer.

the ratio of the drag coefficients at compressible and incompressible flow are presented against the Mach number up to very high Mach numbers. The decrease of friction drag is very pronounced at high Mach numbers. Curve 1 of the two theoretical curves is valid for the adiabatic wall, curve 2 for the wall with heat transfer. Measurements of several authors are in good agreement with theory. For completeness, the friction coefficients of the flat plate at zero incidence are also given for compressible laminar flow.