Evolution, Propagation, Reflection, and Interactions of 1D-normal Shocks in Air and FC70 Using hpk Finite Element Computational Framework

Abstract

In this paper, the mathematical models based on Navier-Stokes equations incorporating physical mechanism of viscosity and conductivity are utilized in h, p, k finite element computational framework to investigate 1-D normal shocks in air and FC70. In the case of air, shock evolution, propagation, repeated reflection and interactions are simulated using ideal gas law with constant viscosity and thermal conductivity. For FC70, numerical studies are presented for initial conditions inside the BZT zone as well as for those away from the BZT zone to investigate the possibility of compression as well as rarefaction shocks. The Van der Waals equation of state with constant transport properties is used for FC70. In all cases, “the rate of production of entropy per unit volume” is used to establish: (i) evolution of shock; (ii) sustained propagation; (iii) repeated reflections and subsequent sustained propagation; and (iv) interactions and sustained propagation of reflected shocks. In all numerical studies care is taken in choosing h, p, k computational parameters to ensure that the computational processes are free of measurable numerical dispersion and that the non-discretized form of the governing differential equations are satisfied accurately in the point wise sense and hence, ensuring time accuracy of the evolutions. 1-D Riemann shock tube is used as a model problem.