Effect of the wall temperature on Mach stem transformation in pseudo-steady shock wave reflections

• Published in: International journal of heat and mass transfer Vol. 147; p. 118927
• Main Authors: Wu, Kexin, Raman, Senthil Kumar, Sethuraman, Vignesh Ram Petha, Zhang, Guang, Kim, Heuy Dong
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.02.2020; Elsevier BV
• Subjects: Compressible flow; Computational fluid dynamics; Computer simulation; Conservation laws; Criteria; Heat flux; K-omega turbulence model; Longitudinal waves; Mach reflection; Mathematical models; MUSCL schemes; Pseudo-steady shock wave reflection; Ramps; Reflection; Reynolds averaged Navier-Stokes method; Shock waves; Temperature effects; Transformations; Turbulence models; Unsteady simulation; Wall temperature; Wall temperature; Pseudo-steady shock wave reflection; Unsteady simulation; Compressible flow
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2019.118927

•First study on effects of the wall temperature in pseudo-steady shock reflections.•A new theoretical model is established to analyze the Mach stem transformation.•A series of new Mach stem transformations are numerically captured.•The mechanism of wall temperature effects is clearly expounded. Pseudo-steady shock wave reflections on a compression ramp are recognized as a significant phenomenon in the shock dynamics field. Several investigations have been performed on this phenomenon by shock tube experiments, combined with numerical and theoretical analyses. In addition to the availability of numerous reliable and accurate data on shock reflection patterns in the form of regular reflection, double-Mach reflection, transitional-Mach reflection, and single-Mach reflection, several transitional criteria such as detachment criterion and mechanical-equilibrium criterion are also established. However, none of the research focuses on the influence of the wall temperature on Mach stem transformation in pseudo-steady shock wave reflections. In order to articulate the role played by the wall temperature, a two-dimensional numerical simulation is performed by resolving the unsteady Reynolds-averaged Navier-Stokes equations to investigate the transformation of the Mach stem. Shear-stress transport k-ω turbulence model and third-order Monotonic Upwind Scheme for Conservation Laws scheme are explored to accurately capture various shock structures. Numerical results are initially validated with experimental data in the open literature and it is evident that there is an excellent match between the present simulation and the actual structure. Subsequently, the grid resolution and time step independence analyses are considered to better resolve the shock reflection configuration. Large-scale negative and positive heat fluxes are imposed on the ramp wall, which can simulate the cooling and heating ramps respectively. A new Mach stem transformation that illustrates significant differences in physical structure evolutions caused by the variation of the wall temperature is numerically captured for the first time. The mechanism of wall temperature effects on the transformation of the Mach stem is clearly expounded with the purpose of profound understanding for pseudo-steady shock wave reflections.