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

The shock gas-dynamic processes that have found wide application in rocket and space technology in the design and optimization of devices and power plants are considered. The analysis of known exact and asymptotic relations/conditions on a shock wave, in particular, generalized differential relations (GDRs) on a curvilinear oblique shock wave (SW) (COSW) for a model of a viscous heat-conducting gas at high Reynolds numbers is made. The advantages of using the discrete-analytical approach are shown, for exam-ple: 1) the ability to make maximal use of the smoothness of the shock gas-dynamic formation (shock wave) in the tangential direction; 2) to build efficient computational algorithms devoid of the negative effect of approximation/artificial viscosity on the schematized discontinuity. In parallel, a very common graphical method for mapping 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, are considered. The mathematical apparatus of shock polars itself is based on exact relations of the Rankine-Hugoniot type and has proven itself well even in modeling the flows of a viscous heat-conducting gas. However, in numerous literature sources there are results (shock solutions) of both physical and computational experiments, which are not mapped strictly on shock polars. In this paper, we show that in rare cases this very common way of such mapping may be incorrect. It has been proven that the main causes of such a defect are the combined ac-tion of three main factors: the nonuniform flow in front of the shock formation, the edge/boudary effect be-hind it, the action of the external factor of viscosity and the heat conduction mechanism.