基于γ-Reθt转捩模型的低雷诺数翼型数值分析

doi:10.7527/S1000-6893.2015.0278

Abstract

Abstract:

Michel transition criterion and γ-Re_θt transition model have been integrated to complete the aerodynamics analysis of low Reynolds number airfoil. In this paper, Michel transition criterion and laminar separation position are used to estimate transition momentum thickness Reynolds number, then critical Reynolds number and transition length that controls the length of the transition region are computed by Langtry and Tomac empirical correlation, respectively. The three empirical correlation values are read into Fluent by User-Defined Functions (UDF) to implement the numerical analysis for E387 airfoil (Reynolds number is 3×10⁵), then the results are compared with experiment. The results demonstrate that Michel-based criterion has more accurate transition prediction position than laminar separation, which gives the transition onset position ahead of experiment value, while aerodynamic forces obtained with both methods agree with those with experiment. Meanwhile, there is a little discrepancy between Langtry and Tomac correlation; however, Toamc correlation can display the separation bubble, which is identical with oil-flow experiment by Selig.

Key words: low Reynolds number, laminar separation, Michel transition criterion, γ-Re_θt transition model, transition prediction, E387 airfoil

CLC Number:

V211.3

CHEN Lili, GUO Zheng. Numerical analysis for low Reynolds number airfoil based on γ-Re_θt transition model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(4): 1114-1126.

References

[1] HORTON H P. Laminar separation bubbles in two and three dimensional incompressible flow[D]. London:University of London, 1968.
[2] SELIG M S, MCGRANAHAN B D. Wind tunnel aerodynamic tests of six airfoils for use on small wind turbines:NREL/SR-500-34515[R]. 2004.
[3] KARASU, GEN M S, AIKEL H H, et al. An experimental study on laminar separation bubble and transition over an aerofoil at low reynolds number:AIAA-2012-3030[R]. Reston:AIAA, 2012.
[4] 白鹏, 李锋, 詹慧玲, 等. 翼型低Re数小攻角非线性非定常层流分离现象研究[J]. 中国科学:物理学力学天文学, 2015, 45(2):024703 BAI P, LI F, ZHAN H L, et al. Study about the non-linear and unsteady laminar separation phenomena around the airfoil at low Reynolds number with low incidence[J]. Scientia Sinica:Physica, Mechanical & Astronomica, 2015, 45(2):024703(in Chinese).
[5] 杨中. 基于湍流模型的转捩流动数值计算研究[D]. 北京:中国科学院大学, 2011. YANG Z. Numerical investigation of transitional flows based on turbulence model[D]. Beijing:University of Chinese Academy of Sciences, 2011(in Chinese).
[6] 陈奕, 高正红. Gamma-Theta转捩模型在绕翼型流动问题中的应用[J]. 空气动力学学报, 2009, 27(4):411-418. CHEN Y, GAO Z H. Application of Gamma-Theta transition model to flows around airfoils[J]. Acta Aerodynamica Sinica, 2009, 27(4):411-418(in Chinese).
[7] 孟德虹, 张玉伦, 王光学, 等. γ-Re_θt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-Re_θttransition model to two-dimensional low speed flows[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(5):792-801(in Chinese).
[8] MENTER F R, LANGTRY R B, LIKKI S R, et al. A correlation-based transition model using local variables-Part I:Model formulation[J]. ASME Journal of Turbomachinery, 2006, 128(3):413-422.
[9] 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]. ASME Journal of Turbomachinery, 2006, 128(3):423-434.
[10] 王刚, 刘毅, 王光秋, 等. 采用γ-Re_θt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-Re_θt transition model[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(1):70-79(in Chinese).
[11] 张玉伦, 王光学, 孟德虹, 等. γ-Re_θt转捩模型的标定研究[J]. 空气动力学学报, 2011, 29(3):295-301. ZHANG Y L, WANG G X, MENG D H, et al. Calibration of γ-Re_θt transition model[J]. Acta Aerodynamica Sinica, 2011, 29(3):295-301(in Chinese).
[12] 牟斌, 江雄, 肖中云, 等. γ-Re_θt转捩模型的标定与应用[J]. 空气动力学学报, 2013, 31(1):103-109. MOU B, JIANG X, XIAO Z Y, et al. Implementation and caliberation of γ-Re_θt transition model[J]. Acta Aerodynamica Sinica, 2013, 31(1):103-109(in Chinese).
[13] 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.
[14] TOMAC M, PETTERSSON K, RIZZI A. Calibration and verification of a γ-Re_θt transition prediction method for airfoil computations:AIAA-2013-0407[R]. Reston:AIAA, 2013.
[15] MICHEL R. Determination du point de transition et calcul de la trainee de profil incompressible:ONERA Report 1/1578A[R]. Paris:ONERA, 1951.
[16] ALTHAUS D. Profilpolaren fur den modellflug windkanalmessungen an profilen im kritischen Reynoldsza Mbereich[R].[s.n.]:Neckar-Verlag VS-Villingen, 1980.
[17] VOLKERS D F. Preliminary results of wind tunnel measurements on some airfoil sections at reynolds numbers between 0.6×10⁵ and 5.0×10⁵[D]. Delft:Delft University of Technology, 1977.
[18] MCGHEE R J, WALKER B S, MILLARD B F. Experimental results for the Eppler 387 airfoil at low Reynolds numbers in the Langley Low-Turbulence Pressure Tunnel:TM-4062[R]. Washigton, D.C.:NASA, 1988.
[19] COLE G M, MUELLER T J. Experimental mesurements of the laminar separation bubble on an Eppler 387 airfoil low Reynolds numbers:UNDAS-1419-FR[R]. 1990.
[20] SPALART P R, ALLMARAS S A. One-equation turbulence model for aerodynamic flows[J]. La Recherche Aéros-patiale, 1992, 439(1):5-21.
[21] LANGTRY R B. A correlation-based transition model using local variables for unstructured parallelized CFD codes[D]. Stuttgart:Universität Stuttgart, 2006.

Numerical analysis for low Reynolds number airfoil based on γ-Re_θt transition model

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	NIE Han, SONG Wenping, HAN Zhonghua, CHEN Jianqiang, DUAN Maochang, WAN Bingbing. Automatic transition prediction for natural-laminar-flow wing design of supersonic transports [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(11): 526342-526342.
[2]	JIANG Lihong, RAO Hanyue, LAN Xiayu, YANG Tihao, GENG Jianzhong, BAI Junqiang. Aerodynamic design and comprehensive benefit impact of hybrid laminar flow wing [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(11): 526791-526791.
[3]	TANG Songxiang, LI Jie, ZHANG Heng, NIU Xiaotian. Stall separation optimization and analysis of middle wing section on specially configured laminar flight [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(11): 526765-526765.
[4]	CHEN Yifu, WANG Yiwen, DENG Yiju, WANG Bo, BAI Junqiang, LU Lei. Experiment and numerical simulation of natural laminar flow wing glove [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(11): 526793-526793.
[5]	CAO Fan, ZHANG Meifang, HU Xiao, TANG Zhili. Natural laminar flow optimization and transition sensitivity analysis of axisymmetric nacelle [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(11): 527330-527330.
[6]	ZHU Zhibin, SHANG Qing, BAI Peng, LIU Qiang. Evolution of laminar separation phenomenon on low Reynolds number airfoil at different Reynolds numbers [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(5): 122528-122528.
[7]	WANG Kelei, ZHOU Zhou, ZHU Xiaoping, XU Xiaoping. Multi-propeller/wing coupled aerodynamic design at low Reynolds number [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(8): 121918-121918.
[8]	ZHU Zhen, SONG Wenping, HAN Zhonghua. Automatic transition prediction for wing-body configurations using dual e^N method [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(2): 121707-121707.
[9]	LI Guanxiong, MA Dongli, YANG Muqing, GUO Yang. Unsteady aerodynamic characteristics of airfoil with local oscillation at low Reynolds number [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(1): 121427-121427.
[10]	SUN Junlei, WANG Heping, ZHOU Zhou, LEI Shan. Effects of propeller slipstream on aerodynamic performance of diamond joined-wing configuration UAV [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(1): 121431-121431.
[11]	WANG Hongbo, ZHU Xiaoping, ZHOU Zhou, XU Xiaoping. Aerodynamic interactions at low Reynolds number slipstream with unsteady panel/viscous vortex particle method [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(4): 120412-120412.
[12]	LIU Qiang, LIU Qiang, BAI Peng, LI Feng. Aerodynamic characteristics of airfoil and evolution of laminar separation at different Reynolds numbers [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(4): 120338-120338.
[13]	LIU Xiaochun, ZHU Xiaoping, ZHOU Zhou, WANG Kelei. Research on low Reynolds number airfoils based on application of solar-powered aircraft [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(4): 120459-120459.
[14]	LI Guojun, BAI Junqiang, TANG Changhong, LIU Nan, QIAO Lei. Characteristics of laminar separation flutter of two-dimensional airfoils at low Reynolds numbers [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(11): 121280-121280.
[15]	HAN Zhonghua, WANG Shaonan, HAN Li, LIU Fangliang, XU Jianhua, SONG Wenping. A novel method for automatic transition prediction of flows over airfoils based on dynamic mode decomposition [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(1): 120034-120034.

Numerical analysis for low Reynolds number airfoil based on γ-Reθt transition model

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

Numerical analysis for low Reynolds number airfoil based on γ-Re_θt transition model