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Amplification factor transport model based on boundary layer similarity solution
Received date: 2015-04-29
Revised date: 2016-01-14
Online published: 2016-01-15
Supported by
National Basic Research Program of China (2014CB744804)
In order to make the linear stability theory adapt to the modern CFD solver technology, the similarity velocity profiles corresponding to various shape factors is obtained through solving the Falkner-Skan similarity equation. Then the approximate envelope lines of amplification factor can be achieved by analyzing different velocity profiles based on the linear stability theory. Finally, the amplification factor of envelope approximation method is solved locally in the form of scalar transport equation and the transport equation of intermittency factor in the original γ-Reθt transition model is combined to model the prediction of natural transition and separation bubble transition. The transport model has been applied to conducting the transition prediction on the S&K plate flat, S809 airfoil, NLR7301 airfoil and DLR-F5 wing. The successful results verify the rationality and feasibility of the established transport transition model.
XU Jiakuan , BAI Junqiang . Amplification factor transport model based on boundary layer similarity solution[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016 , 37(4) : 1103 -1113 . DOI: 10.7527/S1000-6893.2016.0019
[1] SMITH A M O, GAMBERONI N. Transition, pressure gradient, and stability theory:ES-26388[R]. Long Beach:Douglas Aircraft Company, 1956.
[2] ABU-GHANNAM B J, SHAW R. Natural transition of boundary layers-The effects of turbulence, pressure gradient, and flow history[J]. Journal of Mechanical Engineering Science, 1980, 22(5):213-228.
[3] WILCOX D C. Simulation of transition with a two-equation turbulence model[J]. AIAA Journal, 1994, 32(2):247-255.
[4] WILCOX D C. Turbulence modeling for CFD[M]. La Canada, CA:DCW Industries, 1993.
[5] MENTER F R, ESCH T, KUBACKI S. Transition modeling based on local variables[C]//Proceedings of 5th International Symposium on Engineering Turbulence Modelling and Measurements. Mallorca:Elsevier, 2002:555-564.
[6] MENTER F R, LANGTRY R B, LIKKI S R, et al. A correlation-based transition model using local variables-Part I:Model formulation[J]. Journal of Turbomchinery, 2006, 128(3):413-422.
[7] LANGTRY R B, MENTER F R, LIKKI S R, et al. A correlation-based transition model using local variables-Part Ⅱ:Test cases and industrial applications[J]. Journal of Turbomachinery, 2006, 128(3):423-434.
[8] LANGTRY R B. A correlation-based transition model using local variables for unstructured parallelized CFD codes[D]. Stuttgart:Universität Stuttgart, 2006.
[9] LANGTRY R B, MENTER F R. Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes[J]. AIAA Journal, 2009, 47(12):2894-2906.
[10] 孟德虹, 张玉伦, 王光学, 等. γ-Reθt转捩模型在二维低速问题中的应用[J]. 航空学报, 2011, 32(5):792-801. MENG D H, ZHANG Y L, WANG G X, et al. Application of γ-Reθt transition model to two-dimensional low speed flows[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(5):792-801(in Chinese).
[11] 王刚, 刘毅, 王光秋, 等. 采用γ-Reθt模型的转捩流动计算分析[J]. 航空学报, 2014, 35(1):70-79. WANG G, LIU Y, WANG G Q, et al. Transitional flow simulation based on γ-Reθt transition model[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(1):70-79(in Chinese).
[12] VAN INGEN J L. A suggested semi-emprical method for the calculation of the boundary layer transition region[D]. Delft:Delft University of Technology, 1956.
[13] GLEYZES C, COUSTEIX J, BONNET J L. A calculation method of leading edge separation bubbles[M]. CEBECI T, ed. Numerical and Physical Aspects of Aerodynamic Flows Ⅱ. New York:Springer-Verlag, 1983:173-192.
[14] DRELA M, GILES M B. Viscous-inviscid analysis of transonic and low-Reynolds number airfoils[J]. AIAA Journal, 1987, 25(10):1347-1355.
[15] FALKNER V M, SKAN S W. Some approximate solutions of the boundary layer equations[J]. Philosophical Magazine, 1931(12):865-896.
[16] 章梓雄, 董曾南. 粘性流体力学[M]. 北京:清华大学出版社, 1998:129-134. ZHANG Z X, DONG Z N. Viscous fluid dynamics[M]. Beijing:Tsinghua University Press, 1998:129-134(in Chinese).
[17] CODER J G, MAUGHMER M D. A CFD-compatible transition model using an amplification factor transport equation:AIAA-2013-0253[R]. Reston:AIAA, 2013.
[18] GLEYZES C, COUSTEIX J, BONNET J L. Theoretical and experimental study of low Reynolds number transitional separation bubbles[C]//Conference on Low Reynolds Number Airfoil Aerodynamics. Notre Dame, IN:University of Notre Dame, 1985.
[19] MACK L M. Transition and laminar instability:NASA CR-153203[R]. Washington, D.C.:NASA, 1977.
[20] SOMERS D M. Design and experimental results for the S809 airfoil:NREL/SR-440-6918[R]. Pennsylvania:National Renewable Energy Laboratory, 1997.
[21] BENINI E, PONZA R. Laminar to turbulent boundary layer transition investigation on a supercritical airfoil using the γ-θ transitional model:AIAA-2010-4289[R]. Reston:AIAA, 2010.
[22] SOBIECZKY H. DLR-F5:Test wing for CFD and applied aerodynamics:AGARD FDP AR 303[R]. G ttingen:DLR German Aerospace Research Establishment, 1994.
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