Satyvir Singh
Applied and Computational Mathematics, RWTH Aachen University, Aachen, Germany.

Bidesh Sengupta
School of Computer Science and Engineering, Nanyang Technological University, Singapore.

Mukesh Kumar Awasthi
Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow, India.

Vinesh Kumar
Department of Computer Science, Bharati College, University of Delhi, New Delhi, India.

DOI https://doi.org/10.33889/IJMEMS.2024.9.1.001

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Abstract

This article investigates the effects of Atwood numbers on the flow physics of shock-driven elliptical gas inhomogeneity based on numerical simulations. We examine five different gases—He, Ne, Ar, Kr, and SF6—that are filled inside an elliptical bubble and surrounded by N2 in order to study flow physics. A high-order modal discontinuous Galerkin finite element approach is used to solve compressible Euler equations for all numerical simulations. In terms of validation studies, the numerical outcomes match the existing experimental data quite well. The findings show that the Atwood number has a significant impact on the characteristics of flow, including wave patterns, the development of vortices, the generation of vorticity, and bubble deformation. When the value of At is greater than zero i.e. At > 0, there is a notable divergence between the incident wave outside the bubble and the transmitted shock wave inside the bubble. Complex wave patterns, including reflected and newly transmitted shock, are seen during the encounter. Interestingly, the transmitted shock and incident shock waves move with the same rates at At ≈ 0. While, compared to the incident shock wave, the transmitted shock wave moves more quickly for At < 0. The influence of Atwood number is then investigated in depth by looking at the vorticity production at the elliptical interface. Furthermore, in the analysis of vorticity production processes, the important spatial integrated domains of average vorticity, dilatational and baroclinic vorticity production terms, and evolution of enstrophy are extended. Finally, a quantitative research based on the interface qualities delves deeply into the influence of the Atwood number on the flow mechanics.

Keywords- Shock wave, Elliptical bubble, Atwood number, Vorticity generation.

Citation

Singh, S., Sengupta, B., Awasthi, M. K. & Kumar, V. (2024). Insight on the Flow Physics of Shock-driven Elliptical Gas Inhomogeneity with Different Atwood Numbers. International Journal of Mathematical, Engineering and Management Sciences, 9(1), 1-22. https://doi.org/10.33889/IJMEMS.2024.9.1.001.