COMPUTER SIMULATION OF SUPERSONIC FLOW ABOUT BLUNT BODIES GIVEN ENERGY RELEASE SOURCES IN THE FLOW

N.E. Afonina, V.G. Gromov, P.Yu. Georgievsky, V.A. Levin
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 38.

      A technique and software are developed for complete Navier-Stokes equation system base computation of flow about blunt bodies given energy release sources in the flow. The technique is implemented for models of constant adiabatic exponent perfect gas and air of constant chemical composition at thermal equilibrium. For numerical integration of the Navier-Stokes equations a finite-difference Riemann problem type UNO-scheme constructed with the finite volume method is used. Required methodical computations are conducted in order to evaluate and verify the computational technique and software system. These computations were used as a basis for selection of optimal values of the computational scheme parameters.
      To find the basic mechanisms for the class of flows under consideration, a series of parametric computations for flow about bodies of a simple geometric shape were conducted. For illustration some computed results for supersonic flow about a spherical blunt entity R_s, in radius at the Mach number M∞ = 3, the Reynolds number Re= 8300, the temperature factor T_w/T_∞ = 1,2 and the adiabatic exponent γ = 1,4 are presented. The obtained results correspond to two modes of flow in the region of energy release whose intensity was given in the cylindric coordinate system (x, r) with the formula of the form
      .
      In the first case, ; x_q/R_s = -1; R_g/R_s = 0,1 - the flow in the energy release region remains supersonic. At = 2000 and the same values of x_q and R_q the second mode of flow is realized when ahead of the energy release region a jump arises where the flow is decelerated down to the subsonic speed, then accelerated up to the supersonic speed and again decelerated in the leading shock wave ahead of the blunt entity. In both the cases a stagnation zone filled with low-mobility gas is formed ahead of the body. A similar result was obtained for a sphere by the invicid flow-about model in terms of Eulerian equations. The computed results were used to construct pressure, temperature, Mach number isolines, as well as the flow line picture using the code ISOLIN of the graphic program package Grafor. The analysis of distribution of pressure and friction factors, as well as the Stanton number over the sphere surface showed a considerable increase in heat exchange in the region of flow attachment which takes place in both the modes of flow.