AASCIT - Journal - All Issues

ISSN Print: 2381-1218 ISSN Online: 2381-1226

Computational and Applied Mathematics Journal

The Journal

Manuscript Information

Assessment of Several Turbulence Models Applied to Supersonic Flows in Three-Dimensions – Part IV

Computational and Applied Mathematics Journal
Vol.1 , No. 5, Publication Date: Jul. 10, 2015, Page: 344-354

1333 Views Since July 10, 2015, 819 Downloads Since Jul. 10, 2015

Paper in PDF (4134K)

Follow on

Authors

[1]	Edisson S. G. Maciel, Aeronautical Engineering Division (IEA), Aeronautical Technological Institute (ITA) São José dos Campos, São Paulo, Brazil.

Abstract

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 Zhou, Davidson and Olsson, the Yoder, Georgiadids and Orkwis, and the Rumsey, Gatski, Ying and Bertelrud two-equation models 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 Yoder, Georgiadids and Orkwis turbulence model has yielded the best value of the stagnation pressure at the blunt body nose.

Keywords

Zhou et al. Turbulence Model, Yoder et al. Turbulence Model, Rumsey et al. 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, Vol. 1, No. 4, 2015, 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]	G. Zhou, L. Davidson, and E. Olsson, “Turbulent Transonic Airfoil Flow Simulation Using a Pressure-Based Algorithm”, AIAA Journal, Vol. 33, No. 1, January, pp. 42-47, 1995.
[11]	D. A. Yoder, N. J. Georgiadids, and P. D. Orkwis, 1996, “Implementation of a Two-Equation K-Omega Turbulence Model in NPARC”, AIAA Paper 96-0383.
[12]	C. L. Rumsey, T. B. Gatski, S. X. Ying, and A. Bertelrud, “Prediction of High-Lift Flows Using Turbulent Closure Models”, AIAA Journal, Vol. 36, No. 5, May, pp. 765-774, 1998.
[13]	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.
[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. 6, pp. 160-181.
[15]	R. W. Fox, and A. T. McDonald, Introdução à Mecânica dos Fluidos. Ed. Guanabara Koogan, Rio de Janeiro, RJ, Brazil, 632 p, 1988.
[16]	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.
[17]	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.
[18]	C. G. Speziale, S. Sarkar, and T. B. Gatski, “Modeling the Pressure-Strain Correlation of Turbulence: An Invariant Dynamical Systems Approach”, Journal of Fluid Mechanics, Vol. 227, pp. 245-272, 1991.
[19]	E. S. G. Maciel, “Assessment of Several Turbulence Models Applied to Supersonic Flows in Three-Dimensions – Part II”, Submitted to Computational and Applied Mathematics (under review).
[20]	J. D. Anderson Jr., Fundamentals of Aerodynamics. McGraw-Hill, Inc., EUA, 4th Edition, 1008p, 2005.