Slipstream formed by a supersonic source in a hypersonic stream

Abstract

These results may now be applied to that disturbance gen- erated by a viscous boundary layer. The displacement thickness in a compressible fluid is a function of several parameters. Since we only wish to illustrate the theory, the displacement thickness for an incompressible flow is used. For an external flow with a Reynolds number of 10 5/cm, the displacement thickness corresponding to an incompressible laminar boundary layer is 6* = 6 X 10-V2 (x -cm) Similarly, the displacement thickness for a turbulent boundary layer is: 6* = 4 X 10-3(z)°-86 The density perturbations behind a shock attenuated by laminar and turbulent boundary layers in a Mach 4 flow are illustrated in Fig. 2. A schematic diagram of the shock waves is also presented. The laminar results are applicable beyond the boundary-layer transition length because the waves from the boundary layer require a finite time to reach the shock. The origin of the waves striking the shock at xs is indicated in Fig. 3.f Transition to turbulence at a Reynolds number of 10 5 would correspond to xw = 1 cm. Figure 3 indicates that this would be felt by the shock about 2 m downstream. Thus, the laminar results in Fig. 2 are appro- priate for xs «> and it is not an accurate description of the flow just downstream of the point where the two shocks coalesce. Conclusions Whitham's area rule has been applied to disturbances generated by power law bodies in an otherwise uniform two- dimensional flow. It has been shown that the shocks pro- duced by such bodies decay more slowly than those from bodies of finite extent. The results have been applied to disturbances generated by a viscous boundary layer. For the case cited previously, the application of acoustics is valid for xs > 1 cm (Ap/p|» < 0.1) and density disturbances of the order of a few percent are shown to exist for several meters. References