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A finite element solver for hypersonic flows in thermo-chemical non-equilibrium, Part II

Song Gao (Department of Mechanical Engineering, McGill University, Montreal, Canada)
Jory Seguin (Department of Mechanical Engineering, McGill University, Montreal, Canada)
Wagdi G. Habashi (Department of Mechanical Engineering, McGill University, Montreal, Canada)
Dario Isola (Department of Fluids Aerospace Technology, ANSYS Canada, Montreal, Canada)
Guido Baruzzi (Department of Fluids Aerospace Technology, ANSYS Canada, Montreal, Canada)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 29 August 2019

Issue publication date: 16 January 2020

Abstract

Purpose

This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a two-part series that concerns the application of the solver introduced in Part I to adaptive unstructured meshes.

Design/methodology/approach

The governing equations are discretized with an edge-based stabilized finite element method (FEM). Chemical non-equilibrium is simulated using a laminar finite-rate kinetics, while a two-temperature model is used to account for thermodynamic non-equilibrium. The equations for total quantities, species and vibrational-electronic energy conservation are loosely coupled to provide flexibility and ease of implementation. To accurately perform simulations on unstructured meshes, the non-equilibrium flow solver is coupled with an edge-based anisotropic mesh optimizer driven by the solution Hessian to carry out mesh refinement, coarsening, edge swapping and node movement.

Findings

The paper shows, through comparisons with experimental and other numerical results, how FEM + anisotropic mesh optimization are the natural choice to accurately simulate hypersonic non-equilibrium flows on unstructured meshes. Three-dimensional test cases demonstrate how, for high-speed flows, shocks resolution, and not necessarily boundary layers resolution, is the main driver of solution accuracy at walls. Equally distributing the error among all elements in a suitably defined Riemannian space yields highly anisotropic grids that feature well-resolved shock waves. The resulting high level of accuracy in the computation of the enthalpy jump translates into accurate wall heat flux predictions. At the opposite end, in all cases examined, high-quality but isotropic unstructured meshes gave very poor solutions with severely inadequate heat flux distributions not even featuring expected symmetries. The paper unequivocally demonstrates that unstructured anisotropically adapted meshes are the best, and may be the only, way for accurate and cost-effective hypersonic flow solutions.

Originality/value

Although many hypersonic flow solvers are developed for unstructured meshes, few numerical simulations on unstructured meshes are presented in the literature. This work demonstrates that the proposed approach can be used successfully for hypersonic flows on unstructured meshes.

Keywords

Citation

Gao, S., Seguin, J., Habashi, W.G., Isola, D. and Baruzzi, G. (2020), "A finite element solver for hypersonic flows in thermo-chemical non-equilibrium, Part II", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 2, pp. 575-606. https://doi.org/10.1108/HFF-12-2018-0725

Publisher

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Emerald Publishing Limited

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