Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T05:59:51.576Z Has data issue: false hasContentIssue false

Conservative Residual Distribution Method for Viscous Double Cone Flows in Thermochemical Nonequilibrium

Published online by Cambridge University Press:  03 June 2015

Andrea Lani*
Affiliation:
Von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, 1640, Sint Genesius Rode, Belgium
Marco Panesi*
Affiliation:
Institute for Computational Engineering and Sciences, University of Texas, Austin, Texas 78712, USA
Herman Deconinck*
Affiliation:
Von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, 1640, Sint Genesius Rode, Belgium
*
Corresponding author.Email:[email protected]
Get access

Abstract

A multi-dimensionally upwind conservative Residual Distribution algorithm for simulating viscous axisymmetric hypersonic flows in thermo-chemical nonequilibrium on unstructured grids is presented and validated in the case of the complex flow-field over a double cone configuration. The resulting numerical discretization combines a state-of-the-art nonlinear quasi-monotone second order blended scheme for distributing the convective residual and a standard Galerkin formulation for the diffusive residual. The physical source terms are upwinded together with the convective fluxes. Numerical results show an excellent agreement with experimental measurements and available literature.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Barbante, P. F., Degrez, G., and Sarma, G. S. R., Computation of Nonequilibrium High-Temperature Axisymmetric Boundary-Layer Flows, J. Thermophys. Heat Transfer, Vol. 16 (2002), No. 4, pp. 490497.Google Scholar
[2]Bottin, B., Vanden Abeele, D., Carbonaro, M., Degrez, G., and Sarma, G. S. R., Thermodynamic and Transport Properties for Inductive Plasma Modeling, J. Thermophys. Heat Transfer, Vol. 13(1999), pp. 343350.Google Scholar
[3]Candler, G. V. and MacCormack, , Computation of Weakly Ionized Hypersonic Flows in Ther-mochemical Nonequilibrium, J. Thermophys. Heat Transfer, Vol. 5, No. 11 (1991), pp. 266273.CrossRefGoogle Scholar
[4]Ćsik, Á., Upwind Residual Distribution Schemes for General Hyperbolic Conservation Laws and Application to Ideal Magnetohydrodynamics, Ph.D. thesis, Katholieke Universiteit Leuven, Faculteit Wetenschappen Centrum voor Plasma-Astrofysica, Belgium, 2002.Google Scholar
[5]Ćsik, Á, Ricchiuto, M., Deconinck, H., A conservative formulation of the multidimensional upwind residual distribution schemes for general nonlinear conservation laws, J. Comput. Phys., Vol. 179, No. 2(2002), pp. 286312.Google Scholar
[6]Deconinck, H., Ricchiuto, M., Sermeus, K., Introduction to residual distribution schemes and stabilized finite elements, VKI LS 2003-05, 33rdComputational Fluid Dynamics Course, von Karman Institute for Fluid Dynamics, 2003.Google Scholar
[7]Deconinck, H., Roe, P. L., Struijs, R., A multidimensional generalization of Roe’s difference splitter for the Euler equations, Computer and Fluids, Vol. 22, No. 2/3 (1993), pp. 215222.Google Scholar
[8]Degrez, G., van der Weide, E., Upwind residual distribution schemes for chemical nonequilibrium flows, Paper 99-3366, 14th AIAA Computational Fluid Dynamics Conference, Norfolk, USA, June 28-July 1, 1999.Google Scholar
[9]Dobeš, J., Numerical Algorithms for the Computation of Unsteady Compressible Flows over Moving Geometries. Applications to Fluid-Structure Interaction, PhD thesis submitted at Czech Technical University, Prague, Czech Republic, University Libre de Bruxelles, Belgium, November 2007.Google Scholar
[10]Dobeš, J. and Deconinck, H., A Shock Sensor-Based Second-Order Blended (Bx) Upwind Residual Distribution Scheme for Steady and Unsteady Compressible Flow, in Hyperbolic Problems: Theory, Numerics, Applications, 978-3-540-75711-5 (print), 978-3-540-75712-2 (online), pp. 465473, 2008, Springer Berlin Heidelberg.Google Scholar
[11]Gnoffo, P. A., Gupta, R. N., and Shinn, J. L., Conservation equations and physical models for hypersonic air flows in thermal and chemical non-equilibrium. Technical Paper 2867, NASA, 1989.Google Scholar
[12]Gupta, R. N., Yos, J. M., Thompson, R. A., and Lee, K. P., A review of reaction rates and ther-modynamic and transport properties for an 11-species air model for chemical and thermal non-equilibrium calculations to 30 000 K. Reference Publication 1232, NASA, August 1990.Google Scholar
[13]Hirschfelder, J. O., Curtiss, C. F. and Bird, R. B., Molecular theory of gases and liquids, Wiley, New York, 1954.Google Scholar
[14]Issmann, E., Degrez, G., Deconinck, H., Implicit upwind residual distribution Euler and Navier-Stokes solver on unstructured meshes, AIAA Journal, Vol. 34(1996), pp. 20212028.Google Scholar
[15]Knight, D., Longo, J., Drikakis, D., Gaitonde, D., Lani, A., Nompelis, I., Reimann, B. and Walpot, L., Assessment of CFD Capability for Prediction of Hypersonic Shock Interactions, Prog. Aerospace Sci., to appear.Google Scholar
[16]Lani, A., Quintino, T., Kimpe, D., Deconinck, H., Vandewalle, S., Poedts, S., The COOLFluiD Framework: Design Solutions for High-Performance Object Oriented Scientific Computing Software, Computational Science – ICCS 2005, LNCS 3514, Springer-Verlag, Vol. 1(2005), pp. 281286.Google Scholar
[17]Lani, A., Quintino, T., Kimpe, D., Deconinck, H., Vandewalle, S., Poedts, S., Reusable Object-Oriented Solutions for Numerical Simulation of PDEs in a High Performance Environment, Scientific Programming, ISSN 1058-9244, IOS Press, Vol. 14, No. 2 (2006), pp. 111139.Google Scholar
[18]MacLean, M., Holden, M., Wadhams, T. and Parker, R., A computational analysis of thermochemical studies in the lens facilities. ph45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada (US), AIAA 207-121, Jan 2007.Google Scholar
[19]Magin, T. E., Degrez, G., Transport algorithms for partially ionized unmagnetized plasmas, J. Comput. Phys., Vol. 198(2004), pp. 424449.Google Scholar
[20]Magin, T. E., Degrez, G., Transport properties for partially ionized unmagnetized plasmas, Phys. Rev. E, Vol. 70(2004).Google Scholar
[21]Millikan, R. C. and White, D. R., Systematics of vibrational relaxation. J. of Chem. Phys., Vol. 39, No. 12(1963), pp. 32093213.CrossRefGoogle Scholar
[22]Nishikawa, H., A First-Order System Approach for Diffusion Equation. I: Second-Order Residual Distribution Schemes, J. Comput. Phys., 227 (2007), pp. 315352.CrossRefGoogle Scholar
[23]Nishikawa, H., A First-Order System Approach for Diffusion Equation. II: Unification of Advection and Diffusion, J. Comput. Phys., 229 (2010), pp. 39894016.Google Scholar
[24]Nishikawa, H., New-Generation Hyperbolic Navier-Stokes Schemes: (1/h) Speed-Up and Accurate Viscous/Heat Fluxes, AIAA Paper 2011-3043, 20th Computational Fluid Dynamics Conference, June 2011.Google Scholar
[25]Nompelis, I., Drayna, T. W and Candler, G. V., A Parallel Implicit Solver for Hypersonic Reacting Flow Simulation, AIAA 2005-4867, 17th AIAA Computational Fluid Dynamics Conference, Toronto, Canada, June 6-9, 2005.Google Scholar
[26]Nompelis, I., Computational Study of Hypersonic Double-Cone Experiments for Code Validation, PhD Thesis, University of Minnesota, May 2004.Google Scholar
[27]Paillere, H., phMulti-dimensional Upwind Residual Distribution Schemes for the Euler and Navier-Stokes Equations on Unstructured Grids. PhD thesis, Universite Libre de Bruxelles, 1995.Google Scholar
[28]Park, C., Nonequilibrium Hypersonic Aerothermodynamics, John Wiley and Sons, New York, 1989.Google Scholar
[29]Park, C., Review of Chemical-Kinetic Problems of Future NASA Mission, I: Earth Entries, J. Thermophys. Heat Transfer, Vol. 7(1993), pp. 385398.Google Scholar
[30] Argonne National Laboratory: PETSc. Portable, Extensible Toolkit for Scientific Computation, http://www-unix.mcs.anl.gov/petsc, 2004.Google Scholar
[31]Prabhu, R. K., An implementation of a Chemical and Thermal Nonequilibrium Flow Solver on Unstructured Meshes and Application to Blunt Bodies, NASA Contractor Report 194967, Lockheed Engineering and Sciences Co., Hampton, VA, August 1994.Google Scholar
[32]Ricchiuto, M., Construction and Analysis of Compact Resdidual Discretizations for Conservation Laws on Unstructured Meshes, Ph.D. thesis, Université Libre de Bruxelles, 2005.Google Scholar
[33]Ricchiuto, M., Villedieu, N., Abgrall, R., and Deconinck, H., On uniformly high order accurate residual distribution schemes for advection-diffusion, J. Comput. Applied Math., Vol. 215(2007), pp. 547556.Google Scholar
[34]Sarma, G. S. R., Physico-chemical modeling in hypersonic flow simulation, Prog. Aerospace Sci., pp. 281349, 1958.Google Scholar
[35]Sutton, K. and Gnoffo, P. A., Multi-component diffusion with application to computational aerothermodynamics, Technical Paper 98-2575, AIAA, Albuquerque, New Mexico, June 1998.Google Scholar
[36]Van der Weide, E., Deconinck, H., Issmann, E., Degrez, G., A parallel implicit multidimensional upwind residual distribution method forthe Navier-Stokes equations on unstructured grids, J. Comp. Mech., Vol. 23(1999), No. 2, pp. 199208.CrossRefGoogle Scholar
[37]Van der Weide, E., Compressible Flow Simulation on Unstructured Grids using Multidimensional Upwind Schemes, Ph.D. thesis, Delft University of Technology, Netherlands, 1998.Google Scholar
[38]Yos, J. M., Approximate equations for the viscosity and translational thermal conductivity of gas mixtures, Contract Report AVSSD-0112-67-RM, AVCO Corp., Wilmington, MA, 1967.Google Scholar