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

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

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Publication date: 19 June 2019

Abstract

Purpose

This paper aims to describe the physical and numerical modeling of a new computational fluid dynamics solver for hypersonic flows in thermo-chemical non-equilibrium. The code uses a blend of numerical techniques to ensure accuracy and robustness and to provide scalability for advanced hypersonic physics and complex three-dimensional (3D) flows.

Design/methodology/approach

The solver is based on an edge-based stabilized finite element method (FEM). The chemical and thermal non-equilibrium systems are loosely-coupled to provide flexibility and ease of implementation. Chemical non-equilibrium is modeled using a laminar finite-rate chemical kinetics model while a two-temperature model is used to account for thermodynamic non-equilibrium. The systems are solved implicitly in time to relax numerical stiffness. Investigations are performed on various canonical hypersonic geometries in two-dimensional and 3D.

Findings

The comparisons with numerical and experimental results demonstrate the suitability of the code for hypersonic non-equilibrium flows. Although convergence is shown to suffer to some extent from the loosely-coupled implementation, trading a fully-coupled system for a number of smaller ones improves computational time. Furthermore, the specialized numerical discretization offers a great deal of flexibility in the implementation of numerical flux functions and boundary conditions.

Originality/value

The FEM is often disregarded in hypersonics. This paper demonstrates that this method can be used successfully for these types of flows. The present findings will be built upon in a later paper to demonstrate the powerful numerical ability of this type of solver, particularly with respect to robustness on highly stretched unstructured anisotropic grids.

Keywords

Citation

Seguin, J., Gao, S., Habashi, W., Isola, D. and Baruzzi, G. (2019), "A finite element solver for hypersonic flows in thermo-chemical non-equilibrium, Part I", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/HFF-09-2018-0498

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Publisher

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Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited

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