AASCIT - Journal - All Issues

ISSN Print: 2381-1072 ISSN Online: 2381-1080

Engineering and Technology

The Journal

Manuscript Information

Assessment of Several Turbulence Models as Applied to Supersonic Flows in 2D – Part I

Engineering and Technology
Vol.2 , No. 4, Publication Date: Jun. 28, 2015, Page: 220-234

1281 Views Since June 28, 2015, 664 Downloads Since Jun. 28, 2015

Paper in PDF (3204K)

Follow on

Authors

[1]	Edisson S. G. Maciel, Aeronautical Engineering Division, ITA (Aeronautical Technological Institute), SP, Brazil.

Abstract

In the present work, the Van Leer flux vector splitting scheme is implemented to solve the two-dimensional Favre-averaged Navier-Stokes equations. The Cebeci and Smith and Baldwin and Lomax algebraic models and the Jones and Launder and Launder and Sharma k-ε two-equation models are used in order to close the problem. The physical problem under study is the supersonic flow around a simplified version of the VLS (Brazilian “Satellite Launcher Vehice”) configuration. The results have demonstrated that the stagnation pressure ahead of the VLS configuration is better predicted by the Baldwin and Lomax turbulence model.

Keywords

Cebeci and Smith Model, Baldwin and Lomax Model, Jones and Launder Model, Launder and Sharma Model, Reynolds Averaged Navier-Stokes Equations, Algebraic and k-ε Turbulence Models

Reference

[01]	P. Kutler, “Computation of Three-Dimensional, Inviscid Supersonic Flows”, Lecture Notes in Physics, vol. 41, pp. 287-374, 1975.
[02]	B. Van Leer, “Flux-Vector Splitting for the Euler Equations”, Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics, E. Krause, Editor, Lecture Notes in Physics, vol. 170, pp. 507-512, Springer-Verlag, Berlin, 1982.
[03]	R. Radespiel, and N. Kroll, “Accurate Flux Vector Splitting for Shocks and Shear Layers”, Journal of Computational Physics, vol. 121, pp. 66-78, 1995.
[04]	M. Liou, and C. J. Steffen Jr., “A New Flux Splitting Scheme”, Journal of Computational Physics, vol. 107, pp. 23-39, 1993.
[05]	E. S. G. Maciel, and N. G. C. R. Fico Jr., “Estudos de Escoamentos Turbulentos Utilizando o Modelo de Baldwin e Lomax e Comparação entre Algoritmos Explícitos e Implícitos”, Proceedings of the III National Congress of Mechanical Engineering (III CONEM), Belém, PA, Brazil, 2004. [CD-ROM]
[06]	B. S. Baldwin, and H. Lomax, “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows”, AIAA Paper 78-257, 1978.
[07]	R. W. MacCormack, “The Effect of Viscosity in Hypervelocity Impact Cratering”, AIAA Paper 69-354, 1969.
[08]	T. H. Pulliam, and D. S. Chaussee, “A Diagonal Form of an Implicit Approximate-Factorization Algorithm”, Journal of Computational Physics, vol. 39, pp. 347-363, 1981.
[09]	A. Jameson, W. Schmidt, and E. Turkel, “Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes”, AIAA Paper 81-1259, 1981.
[10]	E. S. G. Maciel, and N. G. C. R. Fico Jr., “High Resolution Algorithms Coupled with Three Turbulence Models Applied to an Aerospace Flow Problem – Part I”, AIAA Paper 06-0292, 2006. [CD-ROM]
[11]	T. Cebeci, and A. M. O. Smith, “A Finite-Difference Method for Calculating Compressible Laminar and Turbulent Boundary Layers”, Journal of Basic Engineering, Trans. ASME, Series B, vol. 92, no. 3, pp. 523-535, 1970.
[12]	P. R. Sparlat, and S. R. Allmaras, “A One-Equation Turbulence Model for Aerodynamic Flows”, AIAA Paper 92-0439, 1992.
[13]	A. Harten, “High Resolution Schemes for Hyperbolic Conservation Laws”, Journal of Computational Physics, vol. 49, pp. 357-393, 1983.
[14]	E. S. G. Maciel, and N. G. C. R. Fico Jr., “Comparação Entre Modelos de Turbulência de Duas Equações Aplicados a um Problema Aeroespacial”, Proceedings of the Primer Congreso Argentino de Ingeniería Mecánica (I CAIM), Bahía Blanca, Argentina, 2008. [CD-ROM]
[15]	F. Jacon, and D. Knight, “A Navier-Stokes Algorithm for Turbulent Flows Using an Unstructured Grid and Flux Difference Splitting”, AIAA Paper 94-2292, 1994.
[16]	Y. Kergaravat, and D. Knight, “A Fully Implicit Navier-Stokes Algorithm for Unstructured Grids Incorporating a Two-Equation Turbulence Model”, AIAA Paper 96-0414, 1996.
[17]	W. P. Jones, and B. E. Launder, “The Prediction of Laminarization with a Two-Equation Model of Turbulence”, International Journal of Heat and Mass Transfer, vol. 15, pp. 301-304, 1972.
[18]	B. E. Launder, and B. I. Sharma, “Application of the Energy Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc”, Letters in Heat and Mass Transfer, vol. 1, no. 2, pp. 131-138, 1974.
[19]	E. S. G. Maciel, “Analysis of Convergence Acceleration Techniques Used in Unstructured Algorithms in the Solution of Aeronautical Problems – Part I”, Proceedings of the XVIII International Congress of Mechanical Engineering (XVIII COBEM), Ouro Preto, MG, Brazil, 2005. [CD-ROM]
[20]	E. S. G. Maciel, “Analysis of Convergence Acceleration Techniques Used in Unstructured Algorithms in the Solution of Aerospace Problems – Part II”, Proceedings of the XII Brazilian Congress of Thermal Engineering and Sciences (XII ENCIT), Belo Horizonte, MG, Brazil, 2008. [CD-ROM]
[21]	R. W. Fox, and A. T. McDonald, Introdução à Mecânica dos Fluidos, Ed. Guanabara Koogan, Rio de Janeiro, RJ, Brazil, 632 p, 1988.
[22]	L. N. Long, M. M. S. Khan, and H. T. Sharp, “Massively Parallel Three-Dimensional Euler/Navier-Stokes Method”, AIAA Journal, vol. 29, no. 5, pp. 657-666, 1991.
[23]	C. Hirsch, Numerical Computation of Internal and External Flows – Computational Methods for Inviscid and Viscous Flows, John Wiley & Sons Ltd, 691p, 1990.
[24]	E. S. G. Maciel, “Extension of the Steger and Warming and Radespiel and Kroll Algorithms to Second Order Accuracy and Implicit Formulation Applied to the Euler Equations in Two- Dimensions – Theory”, Proceedings of the VI National Congress of Mechanical Engineering (VI CONEM), Campina Grande, PB, Brazil, 2010. [CD-ROM]
[25]	D. J. Mavriplis, and A. Jameson, “Multigrid Solution of the Navier-Stokes Equations on Triangular Meshes”, AIAA Journal, vol. 28, no. 8, pp. 1415-1425, 1990.
[26]	E. S. G. Maciel, “Comparação entre os Modelos de Turbulência de Cebeci e Smith e de Baldwin e Lomax”, Proceedings of the 5th Spring School of Transition and Turbulence (V EPTT), Rio de Janeiro, RJ, Brazil, 2006. [CD-ROM]
[27]	E. S. G. Maciel, “Estudo de Escoamentos Turbulentos Utilizando os Modelos de Cebeci e Smith e de Baldwin e Lomax e Comparação entre os Algoritmos de MacCormack e de Jameson e Mavriplis”, Proceedings of the 7th Symposium of Computational Mechanics (VII SIMMEC), Araxá, MG, Brazil, 2006. [CD-ROM]
[28]	A. Jameson, and D. Mavriplis, “Finite Volume Solution of the Two-Dimensional Euler Equationson a Regular Triangular Mesh”, AIAA Journal, vol. 24, no. 4, pp. 611-618, 1986.
[29]	E. S. G. Maciel, “Simulação Numérica de Escoamentos Supersônicos e Hipersônicos Utilizando Técnicas de Dinâmica dos Fluidos Computacional”, Doctoral Thesis, ITA, CTA, São José dos Campos, SP, Brazil, 2002.
[30]	J. D. Anderson Jr., Fundamentals of Aerodynamics, McGraw-Hill, Inc., EUA, 563p, 1984.