Effect of axisymmetric surface protuberance mounted on a spherical nosed body at supersonic speed

In the present work, a laminar supersonic viscous flow over an axi-symmetric surface protuberance mounted on a spherical nosed body has been investigated numerically. The results are computed for two surface protuberances, specifically the triangular and the trapezoidal shaped protuberances. A free stream Mach number ranging from 3 to 8 in steps of 1 at a fixed free stream Reynolds number of 1.8×10⁴has been used in the present study. The steady solutions are obtained using a time marching approach. A newly developed Particle Velocity Upwinding (PVU) scheme has been used for the computation. The scheme employs upwinding of the convective flux based on particle velocity. The PVU scheme is an explicit two step predictor-corrector scheme, in which the convective fluxes are evaluated on cell-faces using a first or the second order upwinding method depending upon the location of discontinuity in the form of shock or contact wave. The spatial flow pattern exhibits a strong bow shock in front of the cylindrical nose which engulfs the entire base body. Near the protuberance, the fluid particle decelerates due to the adverse pressure created by the protuberance and thus the flow separates in front of the protuberance. This point of separation is found to be a function of Mach number and the protuberance shape. The base region of the obstacle is dominated by a low pressure expansion region. The reattachment point for the base separation is also a function of Mach number and protuberances shape. As the Mach number is increased the reattachment point shift toward the protuberances base. A weak recompression shock is also seen in the base region which effects the base separation for both the protuberance shape. The important design parameters such as skin friction, heat transfer, drag, and surface pressure coefficients are reported extensively.