Fluid Mechanics and Flight Mechanics

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

  • CHEN Lili ,
  • GUO Zheng
Expand
  • College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China

Received date: 2015-06-04

  Revised date: 2015-10-14

  Online published: 2015-10-23

Supported by

National High-tech Research and Development Program of China

Abstract

Michel transition criterion and γ-Reθt 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.

Cite this article

CHEN Lili , GUO Zheng . Numerical analysis for low Reynolds number airfoil based on γ-Reθt transition model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016 , 37(4) : 1114 -1126 . DOI: 10.7527/S1000-6893.2015.0278

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-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-Reθttransition 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-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).
[11] 张玉伦, 王光学, 孟德虹, 等. γ-Reθt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-Reθt transition model[J]. Acta Aerodynamica Sinica, 2011, 29(3):295-301(in Chinese).
[12] 牟斌, 江雄, 肖中云, 等. γ-Reθt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-Reθt 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-Reθt 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.

Outlines

/