Self-similar analysis of gas dynamics for van der Waals gas in slipping flow after normal shock wave

Abstract

A self-similar model of gas dynamics and heat transfer behind the shock wave was developed with allowance for the effects of slippage and dissipation. The model takes into account the impact of the following factors: shock wave intensity (U∞/Us), physical properties (Prandtl number Pr), thermodynamic gas properties (van der Waals numbers Waa, Wab), slippage effects (Knundsen number Kn), and dissipation (Brinkman number Br), as well as the relation of the temperatures of the flow and the wall (T0/Tw). The numerical solution was performed with the help of MATLAB software, as well as an in-house code written using the programming language C++ to verify the accuracy of calculations. The study demonstrated that for the case at hand, the Reynolds analogy holds under the influence of all mentioned factors provided that Pr = 1, except for the conditions when the effects of mechanical energy dissipation become significant. The paper presents the results of calculations of the velocity and temperature profiles, friction, and heat transfer coefficients (Nusselt numbers).