






Vol.1 , No. 4, Publication Date: Jul. 7, 2015, Page: 186-200
[1] | Edisson S. G. Maciel, Aeronautical Engineering Division (IEA), Aeronautical Technological Institute (ITA), SP, Brasil. |
In the present work, the Van Leer and the Liou and Steffen Jr. flux vector splitting schemes are implemented to solve the three-dimensional Favre-averaged Navier-Stokes equations. The Granville algebraic model, the Coakley and the Wilcox two-equation models, and the Baldwin and Barth one-equation model are used in order to close the problem. The physical problem under study is the supersonic flow around a blunt body configuration. The results have demonstrated that the Van Leer scheme using the Granville turbulence model has yielded the best value of the stagnation pressure at the blunt body nose.
Keywords
Granville Turbulence Model, Coakley Turbulence Model, Wilcox Turbulence Model, Baldwin and Barth Turbulence Model, Navier-Stokes Equations, Three-Dimensions
Reference
[01] | P. Kutler, “Computation of Three-Dimensional, Inviscid Supersonic Flows”, Lecture Notes in Physics, Vol. 41, 1975, pp. 287-374. |
[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, 1982, pp. 507-512, Springer-Verlag, Berlin. |
[03] | M. Liou, and C. J. Steffen Jr., “A New Flux Splitting Scheme”, Journal of Computational Physics, Vol. 107, 1993, pp. 23-39. |
[04] | E. S. G. Maciel, “Assessment of Several Turbulence Models Applied to Supersonic Flows in Three-Dimensions – Part I”, Computational and Applied Mathematics Journal, Vol. 1, Issue 4, 2015, June, pp. 156-173. |
[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, 1981, pp. 347-363. |
[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] | P. S. Granville, “Baldwin Lomax Factors for Turbulent Boundary Layers in Pressure Gradients”, AIAA Journal, Vol. 25, pp. 1624-1627, 1989. |
[11] | T. J. Coakley, “Turbulence Modeling Methods for the Compressible Navier-Stokes Equations”, AIAA Paper No. 83-1693, 1983. |
[12] | D. C. Wilcox, “Reassessment of the Scale-Determining Equation for Advanced Turbulence Models”, AIAA Journal, Vol. 26, November, pp. 1299-1310, 1988. |
[13] | B. S. Baldwin, and T. J. Barth, “A One-Equation Turbulence Transport Model for High Reynolds Number Wall-Bounded Flows”, AIAA Paper 91-0610, 1991. |
[14] | E. S. G. Maciel, Simulations in 2D and 3D Applying Unstructured Algorithms, Euler and Navier-Stokes Equations – Perfect Gas Formulation. Saarbrücken, Deutschland: Lambert Academic Publishing (LAP), 2015, Ch. 1, pp. 26-47. |
[15] | E. S. G. Maciel, Simulations in 2D and 3D Applying Unstructured Algorithms, Euler and Navier-Stokes Equations – Perfect Gas Formulation. Saarbrücken, Deutschland: Lambert Academic Publishing (LAP), 2015, Ch. 6, pp. 160-181. |
[16] | R. W. Fox, and A. T. McDonald, Introdução à Mecânica dos Fluidos. Ed. Guanabara Koogan, Rio de Janeiro, RJ, Brazil, 632 p, 1988. |
[17] | E. S. G. Maciel, Applications of TVD Algorithms in 2D and 3D, Euler and Navier-Stokes Equations in 2D and 3D. Saarbrücken, Deutschland: Lambert Academic Publishing (LAP), 2015, Ch. 13, pp. 463-466. |
[18] | D. J. Mavriplis, and A. Jameson, “Multigrid Solution of the Navier-Stokes Equations on Triangular Meshes”, AIAA Journal, Vol. 28, No. 8, 1990, pp. 1415-1425. |
[19] | 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] |
[20] | 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] |
[21] | 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. |
[22] | 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. |
[23] | J. D. Anderson Jr., Fundamentals of Aerodynamics. McGraw-Hill, Inc., EUA, 4th Edition, 1008p, 2005. |