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Modified Characteristics-Based Schemes for Compressible Flow Past an Airfoil

Published online by Cambridge University Press:  16 October 2012

A. A. Orang  and
A. Paykani
A. A. Orang*
Affiliation:
Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
A. Paykani
Affiliation:
Department of Mechanical Engineering, Parand Branch, Islamic Azad University, Parand, Iran
*
* Corresponding author ([email protected])
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Abstract

In this paper, the numerical study of compressible flow around an airfoil is presented. The flow is analyzed in steady state for subsonic, transonic and even in the supersonic regimes at different angles of attack. In finite-volume method convective fluxes are calculated and compared by two schemes. Modified Jameson flux scheme based on flux averaging with pressure correction is used. Modified Roe scheme which is one of the characteristics-based schemes, with modification in calculation of Jacobian matrix based on Mach number is implemented. Second-order accuracy is used with artificial dissipation to overcome numerical oscillations. The fifth-order Runge–Kutta scheme is used for time discretization. A proper boundary condition based on characteristics is applied. Numerical experiments are performed on the NACA 0012 and also NACA 4412 airfoils. The results confirm the superiority of modified upwind Roe scheme regarding the accuracy, stability and convergence. Results are compared to available results in literature and a good agreement is noticed.

Keywords

Euler equationsCompressible flowFinite-volume methodMethod of characteristicsUpwind schemeNACA 0012 airfoil
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 4 , December 2012 , pp. 627 - 635
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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References

REFERENCES

1.Jameson, A., Schmidit, W. and Turkel, E., “Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping,” AIAA 14th Fluid and Plasma Dynamics Conference. Palo Alto, California, June, pp. 23–25 (1981).Google Scholar
2.Roe, P. L., “Characteristic-Based Schemes for the Euler Equations,” Annual Review of Fluid Mechanics, 18, pp. 337–365 (1986).Google Scholar
3.Lock, R. C., “Test Case for Numerical Methods in Two-Dimensional Transonic Flows,” AGARD REPORT (1970).Google Scholar
4.Jamson, A., “Numerical Calculation of Transonic Flow with Shock Waves,” Symposium Transsonicum, Gottingen, Springer-Verlag (1976).Google Scholar
5.Rizzi, A. and Vivand, H., “Numerical Methods for the Computation of Inviscid Transonic Flow with Shocks,” Proceeding of GAMM Workshop, Stockholm, Viewveg verlag (1981).Google Scholar
6.Razavi, S. E., Ghasemi, J. and Farzadi, A., “Flux Modeling in the Finite-Volume Lattice Boltzmann Approach,” International. Journal of Computational Fluid Dynamics, 23, pp. 69–77 (2009).CrossRefGoogle Scholar
7.Razavi, S. E. and Atashbar, O. A., “A Comparative Investigation of Hydrofoil at Angles of Attack,” International. Journal of Numerical Methods Fluids, 69, pp. 1087–1101 (2012).Google Scholar
8.Pan, D. and Cheng, J. C., “Upwind Finite Volume Navier-Stokes Computations on Unstructured Triangular Meshes,” AIAA Journal, p. 31 (1993).Google Scholar
9.Lyra, P. R. M., Morgan, K., Peraire, J. and Perio, J., “TVD Algorithms of the Compressible Euler Equations on Unstructured Meshes,” International Journal of Numerical Methods in Fluids, 19 pp. 827–847 (1994).Google Scholar
10.Razavi, S. E., Barar, F. and Farhangmehr, V., “Characteristic-Based Finite Volume Solution for Natural Convection Around Horizontal Cylinder,” Journal of Applied Science, 8, pp. 1905–1911 (2008).Google Scholar
11.Nakamura, S. and Holst, T. L., “A New Solution-Adaptive Grid Generation Method for Transonic Airfoil Flow Calculations,” NASA Technical Memorandum, 81330 (1981).Google Scholar
12.Rizzi, R. L. and Eriksson, E., “Transfinite Mesh Generation and Damped Euler Equation Algorithm for Transonic Flow Around Wing-Body Configuration,” 5th AIAA Computational Fluid Dynamics Conference, Palo Alto (1981).CrossRefGoogle Scholar
13.Vivand, H., “Pseudo Unsteady Methods for Transonic Flow Computation,” Proceedings of 7th International Conference on Numerical Methods in Fluid Dynamic, Stanford, (1980).Google Scholar
14.Jameson, A. and Mavriplis, D., “Finite Volume Solution of the Two-Dimensional Euler Equations on a Regular Triangular Mesh,” AIAA 23rd Aerospace Sciences Meeting, Reno, Nevada, January, pp. 14–17 (1985).Google Scholar
15.Katz, A. and Jameson, A., “Meshless Scheme Based on Alignment Constraints,” AIAA Journal, 48, pp. 2501–2511 (2010).Google Scholar
16.Hoffman, A. K. and Chiang, S. T., Computational Fluid Dynamics for Engineers, McGraw-Hill, New York (1994).Google Scholar
17.Swanson, R. C., Turkel, E. C. and Rossow, C., “Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations,” Journal of Computational Physics, 224, pp. 365–388 (2007).Google Scholar
18.Mirzaee, B., Khoshravan, E. and Razavi, S. E., “Finite-Volume Solution of a Cylinder in Cross Flow with Heat Transfer,” International. Journal of Engineering, 15, pp. 303–314 (2002).Google Scholar
19.Mazaheri, K. P. and Roe, L., “New Light on Numerical Boundary Conditions,” AIAA 10th Computational Fluid Dynamics Conference, Honolulu, HI (1991).CrossRefGoogle Scholar