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초음속 유동 해석을 위한 Wilcox к - ω 난류 모델 비교

Comparison between Wilcox к - ω turbulence models for supersonic flows

  • 김민하 (부산대학교 항공우주공학과 대학원) ;
  • 투고 : 2011.12.02
  • 심사 : 2012.04.06
  • 발행 : 2012.05.01

초록

본 연구에서는 초음속 비행체에 나타나는 유동 특성 해석을 위해 1988 Wilcox $\mathcal{k}-{\omega}$ 모델과 2008 Wilcox 모델의 수치 결과를 비교하였다. 충격파 - 경계층 간섭 현상과 램프 주입기 혼합 문제에 대하여 실험결과와 비교, 검토하였다. 또한, 표면 마찰 측정의 기초가 되는 평판 흐름과 전단 층 성장에 대한 상관 관계식도 비교, 분석 하였다. 램프 주입기 케이스에서 최대 주입 질량비는 1988 Wilcox 모델을 이용하였을 때 보다 신뢰성 있는 해석 결과를 예측할 수 있었다. 그러나 충격파 - 경계층 간섭 케이스에 대해서는 2008 Wilcox 모델을 적용하였을 때 더 정확한 해석 결과가 도출됨을 확인하였다.

This paper presents numerical results comparing the performance of the 2008 Wilcox $\mathcal{k}-{\omega}$ turbulence model to the one of the 1988 Wilcox $\mathcal{k}-{\omega}$ model for supersonic flows. A comparison with experimental data is offered for a shock wave/turbulent boundary layer interaction case and two ramp injector mixing cases. Furthermore, a comparison is performed with empirical correlations on the basis of skin friction for flow over a flat plate and shear layer growth for a free shear layer. It is found that the maximum injectant mass fraction of some ramp injector cases is better predicted using the 1988 Wilcox model. On the other hand, the 2008 model performs better in simulating shock-boundary layer cases.

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참고문헌

  1. Parent, B., and Sislian, J. P., "Validation of Wilcox ${\kappa}-{\omega}$ Model for Flows Characteristic to Hypersonic Airbreathing Propulsion," AIAA Journal, Vol. 42, No. 2, 2004, pp. 261-270. https://doi.org/10.2514/1.1989
  2. Wilcox, D. C., "Formulation of the ${\kappa}\;-\;{\omega}$ Turbulence Model Revisited," AIAA Journal, Vol. 46, No. 11, 2008, pp. 2823-2838. https://doi.org/10.2514/1.36541
  3. Wilcox, D. C., 2006, Turbulence Modeling for CFD, Third Ed. DCW Industries.
  4. Settles, G. S., Vas, I. E., and Bogdonoff, S. M., "Details of a Shock Separated Turbulent Boundary Layer at a Compression Corner," AIAA Journal, Vol. 14, No. 12, 1976, pp. 1709-1715. https://doi.org/10.2514/3.61513
  5. Waitz, I. A., Marble, F. E., and Zukoski, E. E., "Investigation of a Contoured Wall Injection for Hypervelocity Mixing Augmentation," AIAA Journal, Vol. 31, No. 6, 1993, pp. 1014-1021. https://doi.org/10.2514/3.11723
  6. Donohue, J. M., McDaniel, J. C., and Haj-Hariri, H., "Experimental and Numerical Study of Swept Ramp Injection into a Supersonic Flowfield," AIAA Journal, Vol. 32, No. 9, 1994, pp. 1860-1867. https://doi.org/10.2514/3.12184
  7. Brown, G. L., and Roshko, A., "On Density Effects and Large Structure in Turbulent Mixing Layers," Journal of Fluid Mechanics, Vol. 64, Issue 04, 1974, pp. 775-781. https://doi.org/10.1017/S002211207400190X
  8. Dimotakis, P. E., "Turbulent Mixing and Combustion," High-Speed Flight Propulsion Systems, edited by S. N. B. Murthy and E. T. Curran, Vol. 137, Progress in Aeronautics and Astronautics, AIAA, Washington D.C, 1991, pp. 265-340.
  9. Macheret, S. O., Shneider, M. N., and Miles, R. B., "Electron-Beam-Generated Plasmas in Hypersonic Magnetohydrodynamics Channels," AIAA Journal, Vol. 39, No. 6, 2001, pp. 1127-1138. https://doi.org/10.2514/2.1426
  10. Jain, S., "Hypersonic Nonequilibrium Flow Simulation over a Blunt Body using BGK Method," Texas A&M University, 2007, Master's thesis.
  11. Macheret, S. O., Martinelli, L., and Miles, R. B., "Shock Wave Propagation and Structure in Non-Uniform Gases and Plasmas," AIAA 99-0598, 37th AIAA Aerospace Sciences Meeting and Exhibit, January 11-14, Reno, NV., 1999.
  12. Dixon-Lewis, G., "Computer Modeling of Combustion Reactions in Flowing Systems with Transport," Combustion chemistry, edited by W. C. Gardiner, Jr.., Springer Verlag, New-York, 1984, Chapter 2.
  13. Vinokur, M., "Conservative Equations of Gas-Dynamics in Curvilinear Coordinate Systems," Journal of Computational Physics, Vol. 14, Issue 2, 1974, pp. 105-125. https://doi.org/10.1016/0021-9991(74)90008-4
  14. Roe, P. L., "Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes," Journal of Computational Physics, Vol. 43, Issue 2, 1981, pp. 357-372. https://doi.org/10.1016/0021-9991(81)90128-5
  15. Yee, H. C., Kloper, G. H., and Montagne, J.-L., "High-Resolution Shock-Capturing Schemes for Inviscid and Viscous Hypersonic Flows," Journal of Computational Physics, Vol. 88, Issue 1, 1990, pp. 31-61. https://doi.org/10.1016/0021-9991(90)90241-R
  16. Beam, R., and Warming, R. F., "An Implicit Factored Scheme for the Compressible Navier-Stokes Equations," AIAA Journal, Vol. 16, No. 4, 1978, pp. 393-402. https://doi.org/10.2514/3.60901
  17. Parent, B. and Sislian, J. P., "The Use of Domain Decomposition in Accelerating the Convergence of Quasihyperbolic Systems," Journal of Computational Physics, Vol. 179, No. 1, 2002, pp. 140-169. https://doi.org/10.1006/jcph.2002.7048