About incorrect representation of the shock process on shock polars in a viscous heat-conducting gas

The shock gas-dynamic processes, which have found wide application in rocket and space technology in the design and optimization of devices and power plants, were considered. An analysis of the known exact and asymptotic relations/conditions on the shock wave were carried out, in particular, generalized differential relations (GDR) on a curvilinear oblique shock wave for a model of a viscous heat-conducting gas at large Reynolds numbers. The advantages of using the discrete-analytical approach were shown, for example: 1) the ability to make the most of smoothness of the shock gas-dynamic formation (jump) in the tangential direction; 2) build efficient computational algorithms devoid of the negative action of approximation/ artificial viscosity on a schematized discontinuity. At the same time, a very widespread graphical method for displaying the results of gas-dynamic calculations on the plane of shock polars, proposed by Busemann, and a volumetric (3D) polaroid, proposed by V. N. Uskov, was reviewed. The mathematical method of shock polars was built on exact relations of the Rankine – Hugoniot type and was proven itself quite well even in the simulation of viscous heat-conducting gas flows. However, in numerous literary sources there are assisting results (shock solutions) of both physical and computational experiments, which are not strictly reflecting in shock polars. In this abstract, it was shown that in rare cases this and a very widespread way of such a mapping may be incorrect. It was proved that the main reasons for such a defect are the combined action of three main factors: non-uniformity of the flow before the shock formation, the edge effect behind it, the action of the external viscosity factor and the mechanism of heat conductivity.