Numerical investigation of supersonic turbulent separated flows in the vicinity of oblique steps

Abstract

Prediction of the properties of turbulent separated flows is among the most complicated and pressing problems of fluid mechanics. The lack of a unified and reliable theoretical basis for their analysis impedes the development of computation methods. In this connection present-day computation models call for the use of experimental data. It has been possible to describe some properties of turbulent separation within the limits of ideal gas behavior [1-4]. The approaches that were based on the application of kinetieally consistent difference schemes turned out to be efficient in a number of cases [5]. The development of integral and numerical methods derived from equations for a turbulent boundary layer extended the possibilities of solving applied problems considerably and also made it possible to refine many physical properties discovered in experiments [6-8]. Finally, the improvement of numerical methods for solving the averaged Navier-Stokes equations, which make it possible to obtain detailed information on the different flows under consideration [9-11], is natural and promising. The development of all the above-mentioned lines of inquiry depends to a large measure on information supplied by the experimental investigations which are used for the construction of physical models, the justification of closure relationships (of turbulence models), and the testing of computation procedures as well. The use of the averaged Navier-Stokes equations in solving applied problems requires the development of effective algorithms and the justification of reliable turbulence models. The effectiveness of an algorithm is defined first of all by its efficiency and accuracy. The procedure efficiency depends mainly on the stability of the scheme being used (severity of restriction on a time interval) and the possibility of its stepwise implementation by the simplest procedures (scalar runs) [12]. As a rule, a choice of a turbulence model is justified by the adequacy of the description of characteristic physical processes, mathematical simplicity, and compatibility with the numerical methods employed [13]. The experience gained thus far testifies that the differential models of turbulence with two equations for determining characteristic length and velocity scales are most effective in calculating separated flows. Among them are the well-known models of the k -- e [14], q -- oJ [15], k -- w 2 [16], etc., types. Such models enable one to predict the characteristics of the flows under consideration, including friction and heat-transfer changes in the vicinity of separation zones, more accurately than simpler algebraic ones. At the same time their use calls for additional information on turbulence characteristics to specify the initial conditions which ensure the stability of a computation procedure, especially in the initial stage. Usually, this problem is solved by obtaining numerically calculated parameters for the boundary layer, which develops ahead of interaction zones, or defining the initial airfoils substantiated by reliable experiments. In many instances it is precisely a poor choice of the starting distributions of turbulence characteristics that brings about computation instability. A fairly large number of numerical investigations are devoted to analysis of interactions of the turbulence boundary layer with incident shock waves or the ones generated in a flow past compression corners [17-21]. Flows that are characterized by interaction of the boundary layer with a sequence of different disturbances, for instance, shock and expansion waves, are widely encountered in practice. Their main feature is the possibility of manifestation of relaxation (hereditary) properties, which are attributed to the preceding disturbance in the zone of a subsequent one, in the boundary layer. Such mixed interactions take place, for instance, in a supersonic flow past oblique-side steps or ledges and apparently represent extreme cases for testing numerical computations and turbulence models. The results of detailed experimental investigations into these configurations are presented in [22-25]. They were used to test the parabolized [26] and complete [10, 27-31] two-dimensional Navier-Stokes equations averaged according to Favre and supplemented by different algebraic and differential models of turbulence.