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Abstract
Scope of present work covers implementation to validation of the Langtry-Menter two equation γ-Reθt Local Correlation based Transition Model (LCTM) in CERANS code for modeling subsonic to hypersonic flow transition. The LCTM is coupled with SST k-ω turbulence model. The governing equations of γ-Reθt model is discretized in finite volume framework similar to the RANS model and implicitized using the point Jacobi method. Transition correlations based on freestream as well as local turbulence intensity and critical momentum thickness Reynolds number were integrated with the model, and the code is validated for several standard transition test cases involving low subsonic to hypersonic high enthalpy flows covering a wide range of turbulent intensities.
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References
- Di Pasquale, D., Rona, A. and Garrett, S. J., "A Selective Review of CFD Transition Models", 39th AIAA Fluid Dynamics Conference, 22-26 June 2009, San Antonio, Texas, AIAA 2009-3812.
- Tapan K. Sengupta., "Theoretical and Computational Aerodynamics", Wiley Aerospace Series, First Edition, Published by John Wiley and Sons Ltd, 2015.
- Dhawan, D. and Narasimha, R., "Some Properties of Boundary Layer Flow During Transition from Laminar to Turbulent Motion", Journal of Fluid Mechanics, Vol.3, pp.418-436, 1958.
- Abu-Ghannam, B.J. and Shaw, R., "Natural Transition of Boundary Layers - the Effects of Turbulence, Pressure Gradient and Flow History", Journal of Mechanical Engineering Science, Vol.22, No.5, pp.213228, 1980.
- Mayle, R.E., "The Role of Laminar-turbulent Transition in Gas Turbine Engines", Journal of Turbomachinery, Vol.113, pp.509-537, 1991.
- Suzen, Y.B. and Huang, P.G., "Model of Flow Transition Using and Intermittency Transport Equation", Journal of Fluid Engineering, Vol.122, pp.273-284, 2000.
- Suzen, Y., Xiong, G. and Huang, P., "Prediction of Transitional Flows in low-pressure Turbines Using an Intermittency Transport Equation", AIAA Journal, Vol.40, No.2, pp.254-266, 2002.
- Wilcox, D.C., "Simulation of Transition with a Twoequation Turbulence Model", AIAA Journal, Vol.32, No.2, 1994.
- Walters, D.K. and Leylek, J.H., "A New Model for Boundary Layer Transition Using a Single PointRANS Approach", Journal of Turbomachinery, Vol.126, pp.193-202, January 2004.
- Steelant, J. and Dick, E., "Modeling of Bypass Transition with Conditioned Navier-Stokes Equations Coupled to Intermittency Transport Equations", Int.J. Numer. Methods Fluids, Vol.23, pp.193-220, 1996.
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- Langtry, R. B. and Menter, F. R., "Correlation-based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes", AIAA Journal, Vol.47, No.12, pp.2894-2906, 2009.
- Langtry, R.B., "A Correlation-based Transition Model Using Local Variables for Unstructured Parallelized CFD Codes", Ph.D. Thesis, University of Stuttgart, 2006.
- Menter, F., "Two-equation Eddy Viscosity Turbulence Models for Engineering Applications", AIAA Journal, Vol.32, No.8, pp.1598-1605, 1994.
- Krause, M., Behr, M. and Ballmann, J., "Modeling of Transition Effects in Hypersonic Intake Flows Using a correlation-based Intermittency Model", 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Dayton,Ohio, AIAA 2008-2598, April-May 2008.
- Frauholz, S., Reinartz, B.U., Muller, S. and Behr, M.,"Transition Prediction for Scramjets Using
- γ − Reθ t Model Coupled to Two Turbulence Models", Journal of Propulsion and Power, Vol.31, No.5,
- pp.1404-1415, September-October 2015.
- Medida, S. and Baeder, J.D., "Application of the Correlation-based γ − Reθ t Transition Model to the
- Spalart-Allmaras Turbulence Model" , 20th AIAA Computational Fluid Dynamics Conference, AIAA
- -3979, Honolulu, HI, June 2011.
- Balasubramanian, R. and Anandhanarayanan, K., "Viscous Computations for Complex Flight Vehicles
- Using CERANS with Wall Function", CFD Journal, Vol.16. No.4, pp.386-390, 2008.
- Spalart, P.R. and Allmaras, S.R., "A One Equation Turbulence Model for Aerodynamic Flows", 30th
- Aerospace Sciences Meeting and Exhibit, AIAA Paper 92-0439, Reno, NV, 1992.
- Schubauer, G.B. and Klebanoff, H.K., "Contribution on the Mechanics of Boundary Layer Transition",
- NACA TN 3489, 1955.
- Kaynak, Ü., "Supersonic Boundary-layer Transition Prediction Under the Effect of Compressibility Using
- a Correlation Based Model", Proceedings of the Institution of Mechanical Engineers, Part G: Journal of
- Aerospace Engineering, Vol.226, No.7, pp.722-739, June 2012.
- Thornber, B., Mosedale, A., Drikakis, D., Youngs, D. and Williams, R.J.R., "An Improved Reconstruction Method for Compressible Flows with Low Mach Number Features", Journal of Computational Physics, Vol.227, pp.4873-4894, 2008.
- Kim, S.S., Kim, C., Rho, O.H. and Hong, S.K., "Cures for Shock Instability: Development of a
- Shock-stable Roe Scheme", Journal of Computational Physics, Vol.185, pp.342-374, 2003.
- Gatski, T. B. and Erlebacher, G., "Numerical Simulation of a Spatially Evolving Supersonic Turbulent
- Boundary Layer", NASA/ TM-2002-211934,2002.
- Mee, D., "Boundary-layer Transition Measurements in Hypervelocity Flows in a Shock Tunnel", AIAA
- Journal, Vol.40, No.8, pp.1542-1548, 2002.
- Xia Chenchao and Chen Weifang., "Boundary-layer Transition Prediction Using A Simplified Correlation-based model", Chinese Journal of Aeronautics, Vol.29, No.1, pp.66-75, 2016.
- Eisfeld, B., "Advanced Turbulence Modeling and Stress Analysis for the DLR-F6 Configuration", 23rdAIAA Applied Aerodynamics Conference, Toronto,Ontario Canada, AIAA 2005-4727, June 2005.
- Haase, W., Chaput, E., Elsholz, E., Leschziner, M. and Mueller, U.R, "ECARP- European Computational Aerodynamics Research Project: Validation of CFD Codes and Assessment of Turbulence Models", Notes on Numerical Fluid Mechanics, Vol.58, 1997.
- McKeel, S.A., "Numerical Simulation of the Transition Region in Hypersonic Flow", Ph.D Thesis, Aerospace Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, February
References
Di Pasquale, D., Rona, A. and Garrett, S. J., "A Selective Review of CFD Transition Models", 39th AIAA Fluid Dynamics Conference, 22-26 June 2009, San Antonio, Texas, AIAA 2009-3812.
Tapan K. Sengupta., "Theoretical and Computational Aerodynamics", Wiley Aerospace Series, First Edition, Published by John Wiley and Sons Ltd, 2015.
Dhawan, D. and Narasimha, R., "Some Properties of Boundary Layer Flow During Transition from Laminar to Turbulent Motion", Journal of Fluid Mechanics, Vol.3, pp.418-436, 1958.
Abu-Ghannam, B.J. and Shaw, R., "Natural Transition of Boundary Layers - the Effects of Turbulence, Pressure Gradient and Flow History", Journal of Mechanical Engineering Science, Vol.22, No.5, pp.213228, 1980.
Mayle, R.E., "The Role of Laminar-turbulent Transition in Gas Turbine Engines", Journal of Turbomachinery, Vol.113, pp.509-537, 1991.
Suzen, Y.B. and Huang, P.G., "Model of Flow Transition Using and Intermittency Transport Equation", Journal of Fluid Engineering, Vol.122, pp.273-284, 2000.
Suzen, Y., Xiong, G. and Huang, P., "Prediction of Transitional Flows in low-pressure Turbines Using an Intermittency Transport Equation", AIAA Journal, Vol.40, No.2, pp.254-266, 2002.
Wilcox, D.C., "Simulation of Transition with a Twoequation Turbulence Model", AIAA Journal, Vol.32, No.2, 1994.
Walters, D.K. and Leylek, J.H., "A New Model for Boundary Layer Transition Using a Single PointRANS Approach", Journal of Turbomachinery, Vol.126, pp.193-202, January 2004.
Steelant, J. and Dick, E., "Modeling of Bypass Transition with Conditioned Navier-Stokes Equations Coupled to Intermittency Transport Equations", Int.J. Numer. Methods Fluids, Vol.23, pp.193-220, 1996.
Papp, J. L. and Dash, S. M., "A Rapid Engineering Approach to Modeling Hypersonic Laminar to Turbulent Transitional Flows for 2D and 3D geometries", 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, AIAA Paper 2008-2600, 2008.
Langtry, R. B. and Menter, F. R., "Correlation-based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes", AIAA Journal, Vol.47, No.12, pp.2894-2906, 2009.
Langtry, R.B., "A Correlation-based Transition Model Using Local Variables for Unstructured Parallelized CFD Codes", Ph.D. Thesis, University of Stuttgart, 2006.
Menter, F., "Two-equation Eddy Viscosity Turbulence Models for Engineering Applications", AIAA Journal, Vol.32, No.8, pp.1598-1605, 1994.
Krause, M., Behr, M. and Ballmann, J., "Modeling of Transition Effects in Hypersonic Intake Flows Using a correlation-based Intermittency Model", 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Dayton,Ohio, AIAA 2008-2598, April-May 2008.
Frauholz, S., Reinartz, B.U., Muller, S. and Behr, M.,"Transition Prediction for Scramjets Using
γ − Reθ t Model Coupled to Two Turbulence Models", Journal of Propulsion and Power, Vol.31, No.5,
pp.1404-1415, September-October 2015.
Medida, S. and Baeder, J.D., "Application of the Correlation-based γ − Reθ t Transition Model to the
Spalart-Allmaras Turbulence Model" , 20th AIAA Computational Fluid Dynamics Conference, AIAA
-3979, Honolulu, HI, June 2011.
Balasubramanian, R. and Anandhanarayanan, K., "Viscous Computations for Complex Flight Vehicles
Using CERANS with Wall Function", CFD Journal, Vol.16. No.4, pp.386-390, 2008.
Spalart, P.R. and Allmaras, S.R., "A One Equation Turbulence Model for Aerodynamic Flows", 30th
Aerospace Sciences Meeting and Exhibit, AIAA Paper 92-0439, Reno, NV, 1992.
Schubauer, G.B. and Klebanoff, H.K., "Contribution on the Mechanics of Boundary Layer Transition",
NACA TN 3489, 1955.
Kaynak, Ü., "Supersonic Boundary-layer Transition Prediction Under the Effect of Compressibility Using
a Correlation Based Model", Proceedings of the Institution of Mechanical Engineers, Part G: Journal of
Aerospace Engineering, Vol.226, No.7, pp.722-739, June 2012.
Thornber, B., Mosedale, A., Drikakis, D., Youngs, D. and Williams, R.J.R., "An Improved Reconstruction Method for Compressible Flows with Low Mach Number Features", Journal of Computational Physics, Vol.227, pp.4873-4894, 2008.
Kim, S.S., Kim, C., Rho, O.H. and Hong, S.K., "Cures for Shock Instability: Development of a
Shock-stable Roe Scheme", Journal of Computational Physics, Vol.185, pp.342-374, 2003.
Gatski, T. B. and Erlebacher, G., "Numerical Simulation of a Spatially Evolving Supersonic Turbulent
Boundary Layer", NASA/ TM-2002-211934,2002.
Mee, D., "Boundary-layer Transition Measurements in Hypervelocity Flows in a Shock Tunnel", AIAA
Journal, Vol.40, No.8, pp.1542-1548, 2002.
Xia Chenchao and Chen Weifang., "Boundary-layer Transition Prediction Using A Simplified Correlation-based model", Chinese Journal of Aeronautics, Vol.29, No.1, pp.66-75, 2016.
Eisfeld, B., "Advanced Turbulence Modeling and Stress Analysis for the DLR-F6 Configuration", 23rdAIAA Applied Aerodynamics Conference, Toronto,Ontario Canada, AIAA 2005-4727, June 2005.
Haase, W., Chaput, E., Elsholz, E., Leschziner, M. and Mueller, U.R, "ECARP- European Computational Aerodynamics Research Project: Validation of CFD Codes and Assessment of Turbulence Models", Notes on Numerical Fluid Mechanics, Vol.58, 1997.
McKeel, S.A., "Numerical Simulation of the Transition Region in Hypersonic Flow", Ph.D Thesis, Aerospace Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, February