Non Equlibrium Chemistry for Hypersonic Flows Using an Edge-based Finite Element Method PDF Download
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Author: Jory Seguin
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Languages : en
Pages :
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"The development of hypersonic vehicles for civilian transport presents several multi-disciplinary design challenges. The highly energetic conditions in the flow field can lead to chemical and thermal non-equilibrium effects that render complex the estimation of aerothermodynamic quantities such as lift, drag, mechanical stresses and heat fluxes through the body. These calculations are essential for the aerodynamic design of the vehicle as well as the development of thermal protection systems. Thus, there is a need for advanced computational tools to assist in the preliminary design phase.The present work extends the capabilities of the HALO3D simulation software into the non-equilibrium regime. The numerical approach enables accurate and robust computation of hypersonic flows, as well as relatively straightforward coupling with additional physical models. The physical and numerical modeling of several aspects related to chemical non-equilibrium are discussed. The species transport equations are solved in a loosely-coupled manner to reduce computational cost and simplify implementation. Reactions are modeled using laminar finite-rate chemistry, and various vibration-dissociation coupling models account for the effect of thermal non-equilibrium in the chemistry. Varying mixture composition is accounted for in all thermodynamic relations and several mixture transport property models are implemented. All calculations are encapsulated in an edge-based finite element framework that simultaneously incorporates many of the advantages of finite volume and finite element methods.A methodical verification and validation is carried out to isolate the effects and mechanisms in the model. The chemical source term and vibration-dissociation coupling models are first verified through unsteady reactor cases, then the mass diffusion is verified using a mixing layer problem. Subsequently, two-dimensional and three-dimensional flows in thermo-chemical non-equilibrium are simulated and comparisons are made against established codes and experimental data. Overall, the solver is shown to be extremely capable and promising for future hypersonics research. " --
Author: Jory Seguin
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Category :
Languages : en
Pages :
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Book Description
"The development of hypersonic vehicles for civilian transport presents several multi-disciplinary design challenges. The highly energetic conditions in the flow field can lead to chemical and thermal non-equilibrium effects that render complex the estimation of aerothermodynamic quantities such as lift, drag, mechanical stresses and heat fluxes through the body. These calculations are essential for the aerodynamic design of the vehicle as well as the development of thermal protection systems. Thus, there is a need for advanced computational tools to assist in the preliminary design phase.The present work extends the capabilities of the HALO3D simulation software into the non-equilibrium regime. The numerical approach enables accurate and robust computation of hypersonic flows, as well as relatively straightforward coupling with additional physical models. The physical and numerical modeling of several aspects related to chemical non-equilibrium are discussed. The species transport equations are solved in a loosely-coupled manner to reduce computational cost and simplify implementation. Reactions are modeled using laminar finite-rate chemistry, and various vibration-dissociation coupling models account for the effect of thermal non-equilibrium in the chemistry. Varying mixture composition is accounted for in all thermodynamic relations and several mixture transport property models are implemented. All calculations are encapsulated in an edge-based finite element framework that simultaneously incorporates many of the advantages of finite volume and finite element methods.A methodical verification and validation is carried out to isolate the effects and mechanisms in the model. The chemical source term and vibration-dissociation coupling models are first verified through unsteady reactor cases, then the mass diffusion is verified using a mixing layer problem. Subsequently, two-dimensional and three-dimensional flows in thermo-chemical non-equilibrium are simulated and comparisons are made against established codes and experimental data. Overall, the solver is shown to be extremely capable and promising for future hypersonics research. " --
Author: Djaffar Ait-Ali-Yahia
Publisher:
ISBN:
Category : Aerodynamics, Hypersonic
Languages : en
Pages : 0
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This dissertation concerns the development of a loosely coupled, finite element method for the numerical simulation of 2-D hypersonic, thermo-chemical equilibrium and nonequilibrium flows, with an emphasis on resolving directional flow features, such as shocks, by an anisotropic mesh adaptation procedure. Since the flow field of such problems is chemically reacting and molecular species are vibrationally excited, numerical analyses based on an ideal gas assumption result in inaccurate if not erroneous solutions. Instead, hypersonic flows must be computed by solving the gasdynamic equations in conjunction with species transport and vibrational energy equations. The number of species transport equations could be very high but is drastically reduced by neglecting the ionization, thus leaving one to represent the air by only five neutral species: O, N, NO, O$\sb2$ and N$\sb2.$ This system of equations is further simplified by considering an algebraic equation for conservation of the fixed nitrogen to oxygen ratio in air. The chemical source terms are computed according to kinetic models, with reaction rate coefficients given by Park's reaction models. All molecular species are characterized by a single vibrational temperature, yielding the well-known two-temperature thermal model which requires the solution of a single conservation equation for the total vibrational energy. In this thesis, the governing equations are decoupled into three systems of PDEs--gasdynamic, chemical and vibrational systems--which are integrated by an implicit time-marching technique and discretized in space by a Galerkin-finite element method. This loosely-coupled formulation maintains the robustness of implicit techniques, while keeping the memory requirements to a manageable level. It also allows each system of PDEs to be integrated by the most appropriate algorithm to achieve the best global convergence. This particular feature makes a partially-decoupled formulation attractive for the extension of existing gasdynamic codes to hypersonic nonequilibrium flow problems, as well as for other applications having stiff source terms. The hypersonic shocks are resolved in a cost-effective manner by coupling the flow solver to a directionally mesh adaptive scheme using an edge-based error estimate and an efficient mesh movement strategy. The accuracy of the numerical solution is continuously evaluated using a bound available from finite element theory. The Hessian (matrix of second derivatives) of a selected variable is numerically computed and then modified by taking the absolute value of its eigenvalues to finally produce a Riemannian metric. Using elementary differential geometry, the edge-based error estimate is thus defined as the length of the element edges in this Riemannian metric. This error is then equidistributed over the mesh edges by applying a mesh movement scheme made efficient by removing the usual constraints on grid orthogonality. The construction of an anisotropic mesh may thus be interpreted as seeking a uniform mesh in the defined metric. The overall methodology is validated on various relevant benchmarks, ranging from supersonic frozen flows to hypersonic thermo-chemical nonequilibrium flows, and the results are compared against experimental data and, when not possible, to other computational approaches.
Author: Song Gao
Publisher:
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Category :
Languages : en
Pages :
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"The present work extends the capabilities of a compressible Navier-Stokes solver into a thermo-chemical non-equilibrium hypersonic flow solver. Finite-rate chemistry and two-temperature thermal non-equilibrium solvers are implemented to account for the additional non-equilibrium processes. The spatial discretization uses an edge-based Finite Element formulation with flow stabilization achieved using a Roe scheme. The governing equations are solved numerically on both structured and unstructured grids. The steady-state solution is obtained by using an implicit integration in time. The present code is comprised of flow, chemistry, and thermal non-equilibrium solvers, developed primarily by Dario Isola, Jory Seguin, and the author, respectively. A loosely-coupled strategy is used in which each of the systems is solved separately via a generalized minimal residual (GMRES) method with an incomplete LU factorization (ILU) preconditioner provided by the PETSc library. Numerical experiments consisting of flows past blunt cones, cylinders, and spheres are performed to assess the accuracy and efficiency of the approach, and good agreement is found with solutions available in the literature. It is observed that mesh distributions are crucial for simulations on unstructured meshes, and anisotropic mesh optimization is successfully applied. A Jacobian-free Newton-Krylov (JFNK) solver with a lower-upper symmetric Gauss-Seidel (LU-SGS) preconditioner is developed for thermal equilibrium flows with frozen chemistry. The traditional LU-SGS formulation is enriched by including the contributions from viscous fluxes and boundary conditions. The performance of the JFNK solver is subsequently assessed and the enriched LU-SGS is found to be more robust and efficient than the Jacobi preconditioner and the original LU-SGS. Comparisons between JFNK with LU-SGS and GMRES with ILU are carried out and the results show that the present method, despite requiring more computation time, significantly reduces the memory footprint by half. " --
Author: Djaffar Ait-Ali-Yahia
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Category :
Languages : en
Pages :
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Author: Gan Yang
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Category :
Languages : en
Pages :
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"Hypersonic flows over re-entry capsules are characterized by a strong bow shock with the gas seeing a rapid increase in temperature of the order of thousands of Kelvins. Chemical reactions in the resulting hot thermal non-equilibrium gas surrounding the vehicle are thus accelerated, causing ionization reactions that produce free electrons. The properties of such gas plasmas differ from those of neutral gases, causing communication blackouts. It is thus crucial to reliably predict the effects of ionization with Computational Fluid Dynamics (CFD) given its ability to produce results at all stages of the design phase at significantly reduced cost and complexity than experiments. The present work extends the capabilities of the HALO3D hypersonic flow simulation software into the weakly ionized regime, with various aspects of the physical and numerical modeling of weakly ionized flows discussed. The gasdynamic equations of chemical-thermal non-equilibrium air are solved in a loosely coupled manner to increase computational efficiency. Reactions with different controlling temperatures are modeled using laminar finite-rate chemistry, and four vibrational-electronic source terms are modeled for ionization effects. A modified Fick's law with ambipolar diffusion is implemented to account for ionized flows, with binary diffusion coefficients added to model flows at high Mach numbers. The governing equations are discretized with an edge-based stabilized finite element method (FEM) that elegantly combines the many advantages of both finite element and finite volume methods. The finite-rate chemistry solver is verified through 11-species heat baths, while the modified Fick's law accounting for ambipolar diffusion is verified against a 1-D shock tube case. The implementation of the various plasma models is then validated using flight data from the RAM C-II, while code-to-code comparisons are also performed. Finally, HALO3D's results of RAM C-II and FIRE-II vehicles using unstructured and highly anisotropic meshes are optimized using OptiGrid through a series of multi-physics criteria, ensuring verification and validation of the algorithms used"--
Author:
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Category : Aeronautics
Languages : en
Pages : 836
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Author: Ankush Bhatia
Publisher:
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Category :
Languages : en
Pages : 192
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This methodology requires no a priori knowledge of the shock0s location, and is suitable for detached shock problems. r-p adaptivity method has allowed for successful prediction of surface heating rate for hypersonic flow over cylinder. Additionally, good comparisons are made, for non-equilibrium hypersonic flows, to the published results. This tool is also used to determine the effect of micro-second pulsed sinusoidal Dielectric Barrier Discharge (DBD) plasma actuators on the surface heating reduction for hypersonic flow over cylinder. A significant effect, of the plasma actuators, is found on the surface heating for hypersonic flows (with and without thermo-chemistry) and several designs are investigated for optimum heating reduction.
Author: Alain Dervieux
Publisher: Springer Science & Business Media
ISBN: 3322878759
Category : Technology & Engineering
Languages : en
Pages : 369
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Book Description
The numerical simulation of the Euler equations of Fluid Dynamics has been these past few years a challenging problem both for research scientists and aerospace engineers. The increasing interest of more realistic models such as the Euler equations originates in Aerodynamics and also Aerothermics where aerospace applications such as military aircrafts and also space vehicles require accurate and efficient Euler solvers (which can be extended to more complicated modelisations including non-equilibrium chemistry) for su personic and hypersonic flows at high angles of attack and Mach number regimes involving strong shocks and vorticity. This book contains the proceedings of the GAMM Workshop on the Numerical Simu lation of Compressible Euler Flows. that W:LS held at INRIA, Rocquencourt (France), on June 10-13, 1986. The purpose of this event was to compare in terms of accuracy and efficiency several codes for solving compressible inviscid, mainly steady, Euler flows. This workshop was a sequel of the GAMM workshop held in 1979 in Stockholm; this time, though, because of the present strong activity in numerical methods for the Euler equat.ions, the full-potential approach was not included. Since 1979, other Eulpr workshops have been organised, sev eral of them focussed on airfoil calculations; however, many recently derived methods were not presented at these workshops, because, among other reasons, the methods were not far enough developed, or had not been applied to flow problems of sufficient complexity. In fact, the 1986 GAMM workshop scored very high as regards to the novelty of methods.
Author: Benjamin S. Kirk
Publisher: BiblioGov
ISBN: 9781289131937
Category :
Languages : en
Pages : 38
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Presentation topics include background and motivation; physical modeling including governing equations and thermochemistry; finite element formulation; results of inviscid thermal nonequilibrium chemically reacting flow and viscous thermal equilibrium chemical reacting flow; and near-term effort.
Author: Shrutakeerti Mallikarjun Vagishwari
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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"HALO3D (High-Altitude Low-Orbit, 3D) is a multidisciplinary all-Mach CFD system developed by the McGill CFD Lab to simulate flow fields around hypersonic aircraft whose flight path spans low (continuum) to high (rarefied) altitudes. HALO3D uses an unstructured edge-based finite-element Navier-Stokes (NS) flow solver (HALO3D-NS) for the continuum regime that includes complex thermochemistry. This thesis extends the applicability of HALO3D to the rarefied regime through three significant efforts. First, a rarefied flow solver, HALO3D-DSMC (Direct Simulation Monte Carlo), is developed to tackle the high-altitude flow field. It is a 3D unstructured DSMC code capable of simulating thermochemical non-equilibrium and volume chemistry with sub-cell features for collision pair selection. Validation simulations for HALO3D-DSMC are presented. Second, a HALO3D-HYBRID infrastructure is developed to simulate moderate Knudsen number flows. In a domain consisting of continuum and rarefied patches, the hybrid routine transparently steps between NS and DSMC techniques to calculate a global solution with no user intervention. Delineating the DSMC and NS regions is accomplished by using the gradient length local Knudsen number (Kn_GLL) as a continuum breakdown detector. Cell and node masks based on the Kn_GLL distribution are inputs for mesh population, particle insertion, buffer zone creation, and NS-DSMC boundary condition routines. Bird's leading-edge and 2D cylinder cases are used to demonstrate that a finite-element NS-DSMC hybrid algorithm can be successfully built to address high-Mach flows. Consistent treatment of thermochemical non-equilibrium by both continuum and rarefied modules is found to be necessary to accurately simulate complex flows. Third, is the coupling of HALO3D-DSMC and HALO3D-HYBRID with a powerful in-house solution-driven automatic mesh optimizer, OptiGrid, heavily used in the NS context. A thorough investigation is carried out on scalars and constraints needed to optimize DSMC and hybrid meshes, an aspect that is currently lacking in the literature. Three optimization constraints: the minimum and maximum edge lengths, and a target number of node/cells are studied and applied to the leading-edge case and flows over 2D and 3D cylinder geometries for freestream Knudsen numbers ranging from 0.01 to 0.047. It is shown that an adaptation scalar combination of flow variables such as density, velocities, temperatures, pressure, and Mach number automatically converges to a final optimized mesh through a series of mesh iterations. The adapted meshes gradually improve the solution's quality without necessarily increasing the number of mesh points or cells, even reducing them sometimes. The solutions represented by the final adapted mesh are smooth and free of irregularities. The solutions and meshes of adapted full DSMC simulations and adapted hybrid simulations are seen to match, thus validating the hybrid solver and showcasing the solver-independence aspect of OptiGrid. Further, the optimized hybrid mesh generates buffers with smooth boundaries and consists of coarse NS cells and refined DSMC cells. The cell sizes from NS to DSMC are seen to reduce organically in the shock and boundary layer. This coupled DSMC/hybrid-OptiGrid system can thus simulate complex 3D geometries and multiscale flow features while drastically reducing mesh preparation time as these are automatically adapted to the emerging physics during the iterative solutions. Taken altogether, the DSMC, hybrid NS-DSMC, and mesh optimization efforts form an advanced system to simulate hypersonic flows over complex geometries with controlled precision and at a much lower expense both in the pre-processing and solution phases. These contributions are the essential components of a seamless hybrid solution approach within HALO3D, upon which other functionalities could be easily built in the future"--
