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Article
Publication date: 21 June 2019

Jory Seguin, Song Gao, Wagdi George Habashi, Dario Isola and Guido Baruzzi

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…

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 29 August 2019

Song Gao, Jory Seguin, Wagdi G. Habashi, Dario Isola and Guido Baruzzi

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…

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 1 September 2005

Ghislain Tchuen, Yves Burtschell and David E. Zeitoun

To compute the Navier‐Stokes equations of a non‐equilibrium weakly ionized air flow. This can help to have a better description of the flow‐field and the wall heat…

Abstract

Purpose

To compute the Navier‐Stokes equations of a non‐equilibrium weakly ionized air flow. This can help to have a better description of the flow‐field and the wall heat transfer in hypersonic conditions.

Design/methodology/approach

The numerical approach is based on a multi block finite volume method and using a Riemann's solver based on a MUSCL‐TVD algorithm. In the flux splitting procedure the modified speed of sound, due to the electronic mode, is implemented.

Findings

A good description of the shock standoff distance, of the wall heat fluxes and of the peak of electron density number in the shock layer.

Research limitations/implications

The radiative effects are not included in this paper. For the very high Mach numbers, this can modify the shock layer parameters.

Practical implications

The knowledge of the wall heat transfer in the re‐entry body problems.

Originality/value

The building of a robust numerical code in order to well describe hypersonic air flow in high Mach numbers.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 1 May 1993

ENRICO BERTOLAZZI and VINCENZO CASULLI

A finite difference method for solving the quasi one‐dimensional non‐equilibrium hypersonic flow equations in a diverging nozzle is presented and discussed. In chemically…

Abstract

A finite difference method for solving the quasi one‐dimensional non‐equilibrium hypersonic flow equations in a diverging nozzle is presented and discussed. In chemically reacting flows the system of equations to be solved is very stiff. Some reactions may be several orders of magnitude faster than others and generally, they are much faster than the convective process except for very high Ma numbers. For this reason the development of a numerical scheme whose stability is independent of the chemical reaction rates is of importance. The main advantage of this scheme is the conservation of each chemical component, the positivity of densities and vibrational energies, as well as its relative simplicity, which results in a fast computer code.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 3 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 December 1998

Enrico Bertolazzi

A finite volume, semi‐implicit scheme, is proposed and discussed, which solves the two‐dimensional Euler equations for the hypersonic flow of a mixture of chemically…

Abstract

A finite volume, semi‐implicit scheme, is proposed and discussed, which solves the two‐dimensional Euler equations for the hypersonic flow of a mixture of chemically reactive specie. The present scheme can be applied on a general, unstructured grid. The first order version guarantees non negativity of the densities and of the vibrational energies for arbitrarily large time steps. The semi‐implicit time discretization of advective terms and the fully implicit discretization of the highly nonlinear terms yield a simple and efficient computer algorithm. Numerical tests show that shocks are well captured and the correct profiles for the chemical specie are reproduced at low computational cost.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 8 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 3 July 2020

Mikhail A. Sheremet, Teodor Grosan and Ioan Pop

The purpose of this paper is to study numerically the steady thermal convection in a chamber filled with a nanoliquid affected by a chemical reaction using the…

Abstract

Purpose

The purpose of this paper is to study numerically the steady thermal convection in a chamber filled with a nanoliquid affected by a chemical reaction using the single-phase nanofluid approximation.

Design/methodology/approach

Water was considered as a host fluid while nanoparticles are aluminum oxide. Homogeneous reactions are analyzed. The nonlinear partial differential equations describing the considered problem are simulated using the finite difference technique.

Findings

The results of streamlines, isotherms, isoconcentrations, nanofluid flow rate, mean Nusselt and Sherwood numbers are discussed. The data demonstrate that the mean Sherwood number increases with the homogeneous reaction rate. Further, nanofluid flow rate can be increased with nanoparticles concentration for high Rayleigh numbers owing to the homogeneous chemical reaction inside the cavity.

Originality/value

Searching the existent references illustrates that the homogeneous-heterogeneous reactions influence on the nanoliquid motion and energy transport within enclosures has not been investigated before. The results of this paper are completely original and the numerical results of the present paper were never published by any researcher.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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