The flow gradients in the vicinity of a shock wave for a thermodynamically imperfect gas

Supersonic rotational planar and axisymmetric flows of a non-viscous, non-heat-conductive gas with arbitrary thermodynamic properties in the vicinity of a steady shock wave are studied. The differential equations describing the gas flow upstream and downstream of the discontinuity surface and the dynamic compatibility conditions at this discontinuity are used. The gas flow non-uniformity in the shock vicinity is described by the spatial derivatives of the gasdynamic parameters at a point on the shock surface. The parameters are the gas pressure, density, and velocity vector. The derivatives with respect to the directions of the streamline and normal to it, and of the shock surface and normal to it, are considered. Spatial derivatives of all gasdynamic parameters are expressed through the flow non-isobaric factor along the streamline, the streamline curvature, and the flow vorticity and non-isoenthalpy factors. An algorithm for determining these factors of the gas flow downstream of a shock wave is developed. Example calculations of these factors for imperfect oxygen and thermodynamically perfect gas are presented. The influence coefficients of the upstream flow factors on the downstream flow factors are calculated. The gas flow in the vicinity of the shock is described by the isolines of gasdynamic parameters. Uniform planar and axisymmetric flows at different distances from the axis of symmetry are examined; the isobars, isopycnics, isotachs and isoclines are used to characterize the downstream flow behind a curved shock in an imperfect gas.