Numerical analysis of pressure oscillations over axisymmetric spiked blunt bodies at Mach 6.80

Abstract

The pressure oscillations over a forward facing spike attached to an axisymmetric blunt body are simulated by solving time-dependent compressible Navier–Stokes equations. The governing fluid flow equations are discretized in spatial coordinates employing a finite volume approach which reduces the equations to semidiscretized ordinary differential equations. Temporal integration is performed using the two-stage Runge–Kutta time stepping scheme. A global time step is used to obtain a time-accurate numerical solution. The numerical computation is carried out for a freestream Mach number of 6.80 and for spike length to hemispherical diameter ratios of 0.5, 1.0 and 2.0. The flow features around the spiked blunt body are characterized by a conical shock wave emanating from the spike tip, a region of separated flow in front of the hemispherical cap, and the resulting reattachment shock wave. Comparisons of the numerical results are made with the available experimental results, such as schlieren pictures and the surface pressure distribution along the spiked blunt body. They are found to be in good agreement. Spectral analysis of the computed pressure oscillations are performed employing fast Fourier transforms. The surface pressure oscillations over the spike and phase plots exhibit a behaviour analogous to that of the Van der Pol equation for a self-sustained oscillatory flow.