Numerical Solution for the Interaction of a Moving Shock Wave With a Turbulent Mixing Region

Abstract

The objective of this investigation was to provide a method for predicting the interaction between a moving shock wave and a turbulent mixing region. A complete mathematical description of the two-dimensional, turbulent mixing process is given. The turbulent exchange coefficients have been approximated with the aid of the Prandtl-Go¨rtler theory for free turbulence. These were expressed in difference form for application to an Eulerian mesh representing the flow field. The artificial viscosity method was adapted to the requirements of the investigation. A problem which considered a plane Mach 2 jet issuing into a cavity was postulated; and the transient field computed until a steady-state turbulent mixing region was established. Moving shock waves of two different strengths were then introduced into the field and the shock wave-mixing region interaction studied. It was found that the method which has been developed is quite capable of describing a turbulent mixing process. The mixing region velocity profiles which were obtained showed excellent agreement with the experimentally verified Gaussian distribution. The passing of a wave across the turbulent mixing region is characterized by a retardation and change in profile of the wave front, the magnitude of these being dependent upon the strength of the wave. Further, it was found that as a wave passes across a mixing region, pressures can occur which are actually greater than those which existed behind the wave prior to its entry into the high velocity region.