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

2019 ◽  
Vol 30 (2) ◽  
pp. 575-606
Author(s):  
Song Gao ◽  
Jory Seguin ◽  
Wagdi G. Habashi ◽  
Dario Isola ◽  
Guido Baruzzi
Keyword(s):  
Heat Flux ◽  
Finite Element ◽  
Hypersonic Flow ◽  
High Speed ◽  
Unstructured Meshes ◽  
Hypersonic Flows ◽  
Anisotropic Mesh ◽  
Content Type ◽  
Edge Based ◽  
Non Equilibrium

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.

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

2019 ◽  
Vol 29 (7) ◽  
pp. 2352-2388
Author(s):  
Jory Seguin ◽  
Song Gao ◽  
Wagdi George Habashi ◽  
Dario Isola ◽  
Guido Baruzzi
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Coupled System ◽  
Hypersonic Flows ◽  
Computational Time ◽  
Content Type ◽  
Stabilized Finite Element ◽  
Loosely Coupled ◽  
Stabilized Finite Element Method ◽  
Non Equilibrium

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.

scholarly journals High-enthalpy hypersonic flows

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Joseph J. S. Shang ◽  
Hong Yan
Keyword(s):  
Hypersonic Flow ◽  
High Speed ◽  
Quantum Physics ◽  
Nonequilibrium Thermodynamic ◽  
Strong Shock ◽  
Hypersonic Flows ◽  
Electrically Conducting ◽  
High Enthalpy ◽  
Speed Range ◽  
Flow Theories

Abstract Nearly all illuminating classic hypersonic flow theories address aerodynamic phenomena as a perfect gas in the high-speed range and at the upper limit of continuum gas domain. The hypersonic flow is quantitatively defined by the Mach number independent principle, which is derived from the asymptotes of the Rankine-Hugoniot relationship. However, most hypersonic flows encounter strong shock-wave compressions resulting in a high enthalpy gas environment that always associates with nonequilibrium thermodynamic and quantum chemical-physics phenomena. Under this circumstance, the theoretic linkage between the microscopic particle dynamics and macroscopic thermodynamics properties of gas is lost. When the air mixture is ionized to become an electrically conducting medium, the governing physics now ventures into the regimes of quantum physics and electromagnetics. Therefore, the hypersonic flows are no longer a pure aerodynamics subject but a multidisciplinary science. In order to better understand the realistic hypersonic flows, all pertaining disciplines such as the nonequilibrium chemical kinetics, quantum physics, radiative heat transfer, and electromagnetics need to bring forth.

Characterization of rotor losses in permanent magnet machines

2020 ◽  
Vol 39 (5) ◽  
pp. 1215-1226
Author(s):  
Antomne Caunes ◽  
Noureddine Takorabet ◽  
Sisuda Chaithongsuk ◽  
Laurent Duranton
Keyword(s):  
Finite Element ◽  
Permanent Magnet ◽  
High Speed ◽  
Permanent Magnets ◽  
Eddy Currents ◽  
Computing Time ◽  
Element Model ◽  
Permanent Magnet Machines ◽  
Content Type ◽  
Rotor Losses

Purpose The purpose of this paper is to present a synthesis of the analysis and modeling of the rotor losses in high speed permanent magnets motors. Design/methodology/approach Three types of losses are as a result of eddy currents in the conductive parts of the rotor. The analysis includes their characterization and the setup of a numerical model using finite element method. The adopted methodology is based on the separation of the losses which allows a better understanding of the physical phenomena. Each type of losses will be modeled and computed separately. Findings It is possible to make a precise estimate of the different losses in the rotor while keeping a relatively short computing time. Research limitations/implications The analysis is applied on a high-speed permanent magnet motor for avionic application. The model is validated with the commercial finite element model (FEM) software Flux2D. Originality/value The developed model allows an important save in terms of CPU-time compared to commercial FEM software while staying accurate. The separation of each losses and their sources is important for motor engineers and was requested for them to improve the designs more easily.

Primary study of a new permanent magnet flux switching machine over straight and spanned rotor configurations

2016 ◽  
Vol 13 (5) ◽  
pp. 441-446 ◽  
Author(s):  
Mahyuzie Jenal ◽  
Erwan Sulaiman ◽  
Hassan Ali Soomro ◽  
Syed Muhammad Naufal Syed Othman
Keyword(s):  
Finite Element ◽  
Performance Analysis ◽  
Permanent Magnet ◽  
High Speed ◽  
Primary Study ◽  
Element Analysis ◽  
Fundamental Study ◽  
Content Type ◽  
Dimensional Finite Element ◽  
And Performance

Purpose The purpose of this paper is to address a fundamental study and performance analysis of a proposed 6Slots-10Poles permanent magnet flux switching machine (PMFSM) using straight rotor (StR) and 6Slots-8Poles PMFSM with spanned rotor (SpR) structure. Design/methodology/approach Design configuration of the proposed machine was developed using commercial finite element analysis package and JMAG-Designer V.14 software, which provides two-dimensional finite element solver throughout the investigation. An electromagnetic performance analysis is carried out and compared over the two proposed topologies which consist of machines no-load and under-load conditions. Findings This paper demonstrates the finding of the proposed StR structure which consist of more favorable three-phase sinusoidal feature, lower cogging torque and higher output torque. Flux density attributes reveal higher established magnetizing flux concentration in StR compared with SpR. Consequently, the StR structure requires low armature current before it may start to rotate and provides better robust construction with less material consumption and cost. Originality/value This paper describes the novel design of a new PMFSM configuration pertinent for high-speed applications.

Asymptotic defect boundary layer theory applied to thermochemical non-equilibrium hypersonic flows

1997 ◽  
Vol 339 ◽  
pp. 213-238 ◽  
Author(s):  
S. SÉROR ◽  
D. E. ZEITOUN ◽  
J.-Ph. BRAZIER ◽  
E. SCHALL
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Wind Tunnel ◽  
Boundary Layer Theory ◽  
Hypersonic Flows ◽  
Navier Stokes ◽  
First Order ◽  
Boundary Layer Equations ◽  
Defect Boundary ◽  
Non Equilibrium

Viscous flow computations are required to predict the heat flux or the viscous drag on an hypersonic re-entry vehicle. When real gas effects are included, Navier–Stokes computations are very expensive, whereas the use of standard boundary layer approximations does not correctly account for the ‘entropy layer swallowing’ phenomenon. The purpose of this paper is to present an extension of a new boundary layer theory, called the ‘defect approach’, to two-dimensional hypersonic flows including chemical and vibrational non-equilibrium phenomena. This method ensures a smooth matching of the boundary layer with the inviscid solution in hypersonic flows with strong entropy gradients. A new set of first-order boundary layer equations has been derived, using a defect formulation in the viscous region together with a matched asymptotic expansions technique. These equations and the associated transport coefficient models as well as thermochemical models have been implemented. The prediction of the flow field around the blunt-cone wind tunnel model ELECTRE with non-equilibrium free-stream conditions has been done by solving first the inviscid flow equations and then the first-order defect boundary layer equations. The numerical simulations of the boundary layer flow were performed with catalytic and non-catalytic conditions for the chemistry and the vibrational mode. The comparison with Navier–Stokes computations shows good agreement. The wall heat flux predictions are compared to experimental measurements carried out during the MSTP campaign in the ONERA F4 wind tunnel facility. The defect approach improves the skin friction prediction in comparison with a classical boundary layer computation.

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