In this paper Roe's flux-difference splitting is applied for the solution of Reynolds-averaged Navier-Stokes equations. Turbulence is modelled using a low-Reynolds number form of the k-ϵ tubulence model. The coupling between the turbulence kinetic energy equation and the inviscid part of the flow equations is taken into account. The equations are solved with a diagonally dominant alternating direction implicit (DDADI) factorized implicit time integration method. A multigrid algorithm is used to accelerate the convergence. To improve the stability some modifications are needed in comparison with the application of an algebraic turbulence model. The developed method is applied to three different test cases. These cases show the efficiency of the algorithm, but the results are only marginally better than those obtained with algebraic models.

References

1 Launder, B. E. and Spalding B., Mathematical models of turbulence, Academic Press, New York, 1972.
Google Scholar
2 Baldwin, B. S. and Lomax, H., Thin layer approximation and algebraic model for separated turbulent flows, AIAA Paper 78–257, Jan., 1978.
Google Scholar
3 Herng, L. and Ching-Chang, C. Comparison of TVD schemes for turbulent transonic projectile aerodynamics computations with a two-equation model of turbulence, Int. j. numer. methods fluids, 16, 365–390 (1993).
10.1002/fld.1650160503
Web of Science® Google Scholar
4 Davidson, L. and Rizzi, A., Navier-Stokes stall predictions using an algebraic Reynolds stress model, J. Spacecraft Rockets, 29, 794–800 (1992).
10.2514/3.25533
Web of Science® Google Scholar
5 Chien, K., Predictions of channel and boundary-layer flows with a low-Reynolds-number turbulence model, AIAA J., 20, 33–38 (1982).
10.2514/3.51043
CAS Web of Science® Google Scholar
6 Roe, P. L., Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Physics, 43, 357–372 (1981).
Google Scholar
7 Lombard, C. K. Bardina, J. and Venkatapathy, E., Multi-dimensional formulation of CSCM—an upwind flux difference eigenvector split method for the compressible Navier-Stokes equations, In Proc. 6th AIAA Computational Fluid Dynamics Conference, Danvers, Massachusetts, 1983.
Google Scholar
8 Siikonen, T., Hoffren, J. and Laine, S., A multigrid LU factorization scheme for the thin-layer Navier-Stokes equations, in Proc. 17th ICAS Congress, Stockholm, 1990.
Google Scholar
9 Vandromme, D., Turbulence modeling for turbulent flows and implementation in Navier-Stokes solvers, in Introduction to the modeling of turbulence, VKI Lecture Series 1991–02.
Google Scholar
10 Jameson, A. and Yoon, S., Multigrid solution of the Euler equations using implicit schemes, AIAA J., 24, 1737–1743 (1986).
10.2514/3.9518
Web of Science® Google Scholar
11 Klebanoff, P. S., Characteristics of turbulence in a boundary layer with zero pressure gradient, NACA Report 1247, 1955.
Google Scholar
12 Houghton, E. L. and Carruthers, N. B., Aerodynamics for engineering students, Edward Arnold, London, 1986.
Google Scholar
13 Holst, T. L., Viscous transonic airfoil workshop compendium of results, J. Aircraft, 25, 1073–1087, (1988).
10.2514/3.45706
Web of Science® Google Scholar
14 Stock, H. W. and Haase, W., Determination of length scales in algebraic turbulence models for Navier-Stokes methods, AIAA J., 270, 5–14 (1989).
10.2514/3.10087
Web of Science® Google Scholar
15 Proceedings of the Symposium on International Vortex Flow Experiment on Euler Code Validation, Edited by A. Elsenaar and G. Eriksson, Stockholm, Sweden, 1986.
Google Scholar
16 Laine, S., Siikonen, T. and Kaurinkoski, P., Calculation of transonic viscous flow around a delta wing, 18th ICAS Congress, Beijing, 1992.
Google Scholar
17 Kaurinkoski, P. and Siikonen, T., Calculation of laminar and turbulent flow past a delta wing, Helsinki University of Technology, Laboratory of Aerodynamics, Report A-13, 1992.
Google Scholar

Citing Literature

Volume21, Issue11

15 December 1995

Pages 1017-1039

An application of Roe's flux-difference splitting for k-ϵ turbulence model

Abstract

References

Citing Literature

References

Information

About Wiley Online Library

Help & Support

Opportunities

Connect with Wiley

An application of Roe's flux-difference splitting for k-ϵ turbulence model

Abstract

References

Citing Literature

References

Related

Information