ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Construction and Its Application of a New One-equation Turbulence Model
Received date: 2013-08-29
Revised date: 2013-12-23
Online published: 2014-01-08
Supported by
National Natural Science Foundation of China
In order to enhance the predictive precision of the influence of Reynolds stress constitutive relation on non-equilibrium turbulent flow and preserve computational efficiency as well, a turbulent kinetic energy k based one-equation (KDO) turbulence model is proposed in this paper. The basic idea of the turbulence model is to recalibrate the original Bradshaw assumption results using the flat plate direct numerical simulation (DNS) data, which makes the local turbulence kinetic energy adaptively adjustable according to the local flow conditions. Meanwhile, the turbulence dissipation rate equation in the standard k-ε model is modeled by using the algebraic type and then a one-equation turbulence model has been completely constructed. The results of test cases showed that the KDO turbulence model could acceptably reflect the log-law. In the cases RAE-2822, ONERA-M6 and DLR-F6 with shock waves or component interferences, the KDO turbulence model is able to control the augmentations and decay of turbulence kinetic energy. Furthermore, comparing with the Spalart-Allmaras and Menter k-ω shear stress transport (SST) models, the KDO turbulence model evidently improved the calculation results.
BAI Junqiang , ZHANG Yang , XU Jinglei , HUA Jun . Construction and Its Application of a New One-equation Turbulence Model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014 , 35(7) : 1804 -1814 . DOI: 10.7527/S1000-6893.2013.0502
[1] Hoyas S, Jiménez J. Scaling of the velocity fluctuations in turbulent channels up to Retau=2003[J]. Physics of Fluids, 2006, 18(011702): 1-4.
[2] Spalart P R. Strategies for turbulence modelling and simulations[J]. International Journal of Heat and Fluid Flow, 2000, 21(3): 252-263.
[3] Prandtl L. Bericht uber untersuchungen zur ausgebildeten turbulenz[J]. Zeitschrift Für angewandte Mathematik und Mechanik, 1925, 5(1): 136-139.
[4] Spalart P, Allmaras S. A one-equation turbulence model for aerodynamic flows[J]. La Recherche Aerospatiale, 1994, 1(2): 5-21.
[5] Menter F R. Eddy viscosity transport equations and their relation to the k-ε model[J]. Journal of Fluids Engineering, 1997, 119: 876-884.
[6] Edwards J, Roy C, Blottner F, et al. Development of a one-equation transition/turbulence model[J]. AIAA Journal, 2001, 39(9): 1691-1698.
[7] Wilcox D. Reassessment of the scale-determining equation for advanced turbulence models[J]. AIAA Journal, 1988, 26(11): 1299-1310.
[8] Abid R. Evaluation of two-equation turbulence models for predicting transitional flows[J]. International Journal of Engineering Science, 1993, 31(6): 831-840.
[9] Rotta J. Statistische theorie nicht-homogener turbulenz I and II [J]. Journal of Physics, 1951, 129(6): 547-572.
[10] Launder B, Sharma B. Application of the energy-dissipation model of turbulence to the calculation of flow near spinning disc[J]. Letter Heat Mass Transfer, 1974(1): 131-138.
[11] Patel V C, Rodi W, Scheuerer G. Turbulence models for near-wall and low Reynolds number flows-A review[J]. AIAA Journal, 1985, 23(9): 1308-1319.
[12] Menter F. Improved two-equation k-ω turbulence models for aerodynamic flows, NASA-TM 103975. Washington D.C.: NASA, 1992.
[13] Bradshaw P, Ferriss D, Atwell N. Calculation of boundary-layer using the turbulent energy equation[J]. Journal of Fluid Mechanics, 1967, 28(3): 593-616.
[14] Wen X Q, Liu Y W, Fang L, et al. Improving the capability of k-ω SST turbulence model for predicting stall characteristics of airfoil[J]. Journal of Beijing University of Aeronautics and Astronautics, 2013, 31(8): 1127-1132. (in Chinese) 文晓庆, 柳阳威, 方乐, 等. 提高k-ω SST模型对翼型失速特性的模拟能力[J]. 北京航空航天大学学报, 2013, 31(8): 1127-1132.
[15] Liu J Y. An improved SST turbulence model for hypersonic flows[J]. Acta Aeronautica et Astronautica Snica, 2012, 33(12): 2193-2201. (in Chinese) 刘景源. SST湍流模型在高超声速绕流中的改进[J]. 航空学报, 2012, 33(12): 2193-2201.
[16] She Z S, Chen X, Wu Y, et al. New perspective in statistical modeling of wall-bounded turbulence[J]. Acta Mechanica Sinica, 2010, 26: 847-861.
[17] She Z S, Leveque E. Universal scaling laws in fully developed turbulence[J]. Physics Review Letter, 1997, 72(3): 336-339.
[18] Menter F, Kuntz M, Langtry R. Ten years of industrial experience with the SST turbulence model[J]. Turbulence Heat and Mass Transfer, 2003, 4(1): 625-632.
[19] Spalart P, Jou W, Strelets M, et al. Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach//Liu C Q, Liu Z N. Advances in DNS/LES, 1st AFOSR International Conference on DNS/LES. Los Angles: Greyden Press, 1997: 137-147.
[20] Menter F. The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 1: theory and model description[J]. Flow Turbulence Combust, 2010, 85(5): 113-138.
[21] Wilcox D. Turbulence modeling for CFD[M]. California: DCW Industries, Inc., 1994: 90.
[22] Xu J L, Yan C. A one-equation scale-adaptive simulation model[J]. Physics of Gases, 2010, 5(1): 79-82.(in Chinese) 徐晶磊, 阎超. 一个一方程Scale-Adaptive simulation模型的构造[J]. 气体物理, 2010, 5(1): 79-82.
[23] Zhang Y, Bai J Q, Hua J, et al. Improvement and assessment of the SST equation based on karman scale and filter method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 442-446. (in Chinese) 张扬, 白俊强, 华俊, 等.基于卡门尺度和滤波方法的SST方程改进和评估[J]. 力学学报, 2013, 45(3): 442-446.
[24] Xu J L, Zhang Y, Bai J Q, et al. A transition model based only on turbulence kinetic equation//Hu H Y. Chinese Congress of Theoretical and Applied Mechanics 2013. Xi'an: Chinese Journal of Theoretical and Applied Mechanics, 2013: 142. (in Chinese) 徐晶磊, 张扬, 白俊强, 等.一个方程驱动转捩的湍动能一方程模型//胡海岩. 中国力学大会文集2013. 西安: 中国力学学会, 2013: 142.
[25] White F. Viscous fluid flow[M]. New York: McGraw-Hill, Inc., 1991: 430.
[26] Spalding D B. A single formula for the "law of the wall" [J]. Journal of Applied Mechanics, 1961, 28(3): 455.
[27] Cook P, McDonald M, Firmin M. Aerofoil RAE-2822 pressure distributions, and boundary layer and wake measurements, AR-138, AGARD. : Experimental Data Base for Computer Program Assessment, 1979.
[28] Schmitt V, Charpin F. Pressure distributions on the ONERA-M6 wing at transonic mach numbers, AR-138, AGARD. : Experimental Data Base for Computer Program Assessment, 1979.
[29] Laflin R, Klausmeyer M, Zickuhr T, et al. Data summary of data from the second AIAA computational fluid dynamics drag prediction workshop[J]. Journal of Aircraft, 2005, 42(5): 1165-1178.
[30] Rumsey C L, Rivers S M, Morrison J H, et al. Study of CFD variation on transport configurations for the second drag prediction workshop[J]. Computers and Fluids, 2005, 34(7): 785-816.
[31] Wang Y T, Wang G X, Zhang Y L. Validation of TRIP 2.0: numerical simulation of DPW II complex configuration[J]. Acta Aeronautica et Astronautica Sinica, 2008, 29(1): 34-40. (in Chinese) 王运涛, 王光学, 张玉伦. TRIP 2.0软件的确认: DPW II复杂组合体的数值模拟[J]. 航空学报, 2008, 29(1): 34-40.
/
| 〈 |
|
〉 |
CJA