Assessment of Turbulence Models for Unsteady Separated Flows Past an Oscillating NACA 0015 Airfoil in Deep Stall

Document Type : Regular Article

Authors

1 Laboratory of Green and Mechanical Development-LGMD, Ecole Nationale Polytechnique, B.P. 182, El-Harrach, Algiers, 16200, Algeria

2 Department of mechanical engineering, Université de Sherbrooke, 2500 Boulevard de l’Université, Sherbrooke, Québec, J1K2R1 Canada

Abstract

This paper provides 2D Computational Fluid Dynamics (CFD) investigations, using OpenFOAM package, of the unsteady separated fully turbulent flows past a NACA 0015 airfoil undergoing sinusoidal pitching motion about its quarter-chord axis in deep stall regime at a reduced frequency of 0.1, a free stream Mach number of 0.278, and at a Reynolds number, based on the airfoil chord length, , of . First, eighteen 2D steady-state computations coupled with the SST model were carried out at various angles of attack to investigate the static stall. Then, the 2D Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations of the flow around the oscillating airfoil about its quarter-chord axis were carried out. Three eddy viscosity turbulence models, namely the Spalart-Allmaras, Launder-Sharma , and  SST were considered for turbulence closure. The results are compared with the experimental data where the boundary layer has been tripped at the airfoil’s leading-edge. The findings suggest that the  SST performs best among the other two models to predict the unsteady aerodynamic forces and the main flow features characteristic of the deep stall regime. The influence of moving the pitching axis downstream at mid chord was also investigated using URANS simulations coupled with the  SST model. It was found that this induces higher peaks in the nose-down pitching moment and delays the stall onset. However, the qualitative behavior of the unsteady flow in post-stall remains unchanged. The details of the flow development associated with dynamic stall were discussed

Keywords

Main Subjects


Abbas, A., Razak, N., & Zorkipli, M. (2021). Aeroelastic simulation of stall flutter undergoing high and low amplitude limit cycle oscillations. Journal of Applied Fluid Mechanics, 14(6), 1679–1689. https://doi.org/10.47176/JAFM.14.06.32439##
ANSYS, Inc. (2022). ANSYS Fluent Theory Guide (Version 2022 R1). Canonsburg, PA: ANSYS, Inc.##
Bangga, G., & Sasongko, H. (2017). Dynamic stall prediction of a pitching airfoil using an adjusted two-equation URANS turbulence model. Journal of Applied Fluid Mechanics, 10(1), 1–10. https://doi.org/10.18869/ACADPUB.JAFM.73.238.26391##
Beaudet, L. (2014). Etude expérimentale et numérique du décrochage dynamique sur une éolienne à axe vertical de forte solidité. [PhD thesis]. Universite de Poitiers.##
Belkheir, N., Dizene, R., & Khelladi, S. (2012). A numerical simulation of turbulence flow around a blade profile of HAWT rotor in moving pulse. Journal of Applied Fluid Mechanics, 5(01). https://doi.org/10.36884/JAFM.5.01.11953##
Bos, F. M., van Oudheusden, B. W., & Bijl, H. (2013). Radial basis function based mesh deformation applied to simulation of flow around flapping wings. Computers & Fluids,79, 167–177. https://doi.org/10.1016/j.compfluid.2013.02.004##
Carr, L. W., McAlister, K. W., & McCroskey, W. J. (1977). Analysis of the development of dynamic stall based on oscillating airfoil experiments. NASA TN- 8382.##
Catris, S., & Aupoix, B. (2000). Density corrections for turbulence models. Aerospace Science and Technology, 4(1), 1–11. https://doi.org/10.1016/S1270-9638(00)00112-7##
Chan, W. M., & Steger, J. L. (1992). Enhancements of a three-dimensional hyperbolic grid generation scheme. Applied Mathematics and Computation, 51(2-3), 181–205. https://doi.org/10.1016/0096-3003(92)90073-A##
Chitsomboon, T., & Thamthae, C. (2011). Adjustment of k-ω SST turbulence model for an improved prediction of stalls on wind turbine blades. World renewable energy congress.##
Coleman, D. G., Thomas, F. O., Gordeyev, S., & Corke, T. C. (2019). Parametric modal decomposition of dynamic stall. American Institute of Aeronautics and Astronautics Journal 57(1), 176–190. https://doi.org/10.2514/1.J057077##
Ekaterinaris, J. A., & Platzer, M. F. (1998). Computational prediction of airfoil dynamic stall. Progress in Aerospace Sciences, 33(11-12), 759-846. https://doi.org/10.1016/S0376-0421##
Geng, F., Kalkman, I., Suiker, A., & Blocken, B. (2018). Sensitivity analysis of airfoil aerodynamics during pitching motion at a Reynolds number of 1.35×105. Journal of Wind Engineering and Industrial Aerodynamics, 183, 315-332. https://doi.org/10.1016/j.jweia.2018.11.009##
Gharali, K., & Johnson, D. A. (2013). Dynamic stall simulation of a pitching airfoil under
unsteady freestream velocity. Journal of Fluids
and Structures,
42, 228-244. https://doi.org/10.1016/j.jfluidstructs.2013.05.005##
Gharali, K., Gharaei, E., Soltani, M., & Raahemifar, K. (2018). Reduced frequency effects on combined oscillations, angle of attack and free
stream oscillations, for a wind turbine
blade element. Renewable Energy, 115, 252-259. https://doi.org/10.1016/j.renene.2017.08.042##
Greenshields, C., & Weller, H. (2022). Notes on computational fluid dynamics: General principles. Reading, UK: CFD Direct Ltd.##
Gupta, R., & Ansell, P. J. (2018). Investigation of the effects of Reynolds number on the unsteady flow physics of airfoil dynamic stall. 2018 AIAA Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics.##
Hand, B., Kelly, G., & Cashman, A. (2021). Aerodynamic design and performance parameters of a lift-type vertical axis wind turbine: A comprehensive review. Renewable and Sustainable Energy Reviews, 139, 110699. https://doi.org/10.1016/j.rser.2020.110699##
Jasak, H. (2009). Dynamic mesh handling in OpenFOAM. The AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition.##
Jensen, B. L., Sumer, B. M., & Fredsøe, J. (1989). Turbulent oscillatory boundary layers
at high Reynolds numbers. Journal
of Fluid Mechanics,
206, 265–297. https://doi.org/10.1017/S002211208900230##
Kaptein, S. J., Duran-Matute, M., Roman, F., Armenio, V., & Clercx, H. J. (2020). Existence and properties of the logarithmic layer in oscillating flows. Journal of Hydraulic Research, 58(4), 687–700. https://doi.org/10.1080/00221686.2019.1661293##
Kim, Y., & Xie, Z. T. (2016). Modelling the effect of freestream turbulence on dynamic stall of wind turbine blades. Computers & Fluids, 129, 53–66. https://doi.org/10.1016/j.compfluid.2016.02.004##
Ko, S., & McCroskey, W. J. (1997). Computations of unsteady separating flows over an oscillating
airfoil. American Institute of Aeronautics and
Astronautics Journal.
35(7), 1235– 1238. https://doi.org/10.2514/2.226##
Launder, B., & Sharma B. I. (1974). Application of the energy-dissipation model of flow near a spinning disc. Letters in Heat and Mass Transfer, 1(2), 131-137. https://doi.org/10.1016/0094-4548(74)90150-7##
Lee, T., & Gerontakos, P. (2004). Investigation of flow over an oscillating airfoil. Journal of Fluid Mechanics, 512, 313-341. https://doi.org/10.1017/S0022112004009851##
Lee, T., & Su, Y. Y. (2015). Surface pressures developed on an airfoil undergoing heaving and pitching motion. Journal of Fluids Engineering, 137(5). https://doi.org/10.1115/1.4029443##
Leishman, G. J. (2006). Principles of helicopter aerodynamics with CD extra. Cambridge university press.##
Leishman, J. G., & Beddoes, T. S. (1989). A Semi-Empirical model for dynamic stall. Journal of the American Helicopter society, 34(3), 3-17. https://doi.org/10.4050/JAHS.34.3.3##
Li, X., Feng, L. H., & Li, Z. Y. (2019). Flow mechanism for the effect of pivot point on the aerodynamic characteristics of a pitching airfoil and its manipulation. Physics of Fluids, 31(8), 087108. https://doi.org/10.1063/1.5114833##
McCroskey, W. J. (1981). The phenomenon of dynamic stall. NASA-A-National Aeronautics and Space Administration Moffett Field Ca Ames Research Center 8464.##
McCroskey, W. J., McAlister, K. W., Carr, L. W., Pucci, S. L., Lambert, O., & Indergrand, R. F. (1981). Dynamic stall on advanced airfoil sections. Journal of the American Helicopter Society, 26(3), 40-50. https://doi.org/10.4050/JAHS.26.3.40##
Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. American Institute of Aeronautics and Astronautics Journal, 32(8), 1598-1605. https://doi.org/10.2514/3.12149##
Menter, F. R., Kuntz, M., & Langtry, R. (2003). Ten years of industrial experience with the SST turbulence model. Turbulence, Heat and Mass Transfer, 4(1), 625–632.##
OpenCFD. (2022). OpenFOAM version 2112 user guide. Retrieved from https://www.openfoam.com##
Petot, D. (1989). Differential equation modeling of dynamic stall. La Recherche Aerospatiale (English Edition), 5, 59–72.##
Piziali, R. A. (1994). 2-d and 3-d oscillating wing aerodynamics for a range of angles of attack including stall. Technical Report, NASA Ames Research Center, Moffett Field, CA, NASA Tech Memo 4632, USAATCOM Technical Report 94-A-011; September 1994.##
Rhee, M. (2007). Evaluation of grid convergence and turbulence model constant changes for the airfoil flow simulation. The AIAA Aerospace Sciences Meeting and Exhibit.##
Rhee, M. J. (2002). A study of dynamic stall vortex development using two-dimensional data from the AFDD oscillating wing experiment. Ames Research Center, 7, 2002–21185.##
Rumsey, C. L. (2007). Apparent transition behavior of widely-used turbulence models. International Journal of Heat and Fluid Flow, 28(6), 1460-1471. https://doi.org/10.1016/j.ijheatfluidflow.2007.04.003##
Sangwan, J., Sengupta, T. K., & Suchandra, P. (2017). Investigation of compressibility effects on dynamic stall of pitching airfoil Physics of Fluids, 29(7), 076104. https://doi.org/10.1063/1.4995457##
Sharma, A., & Visbal, M. (2019). Numerical investigation of the effect of airfoil thickness on onset of dynamic stall. Journal of Fluid Mechanics, 870, 870-900. https://doi.org/10.1017/jfm.2019.235##
Smith, T. A. & Ventikos, Y. (2019). Boundary layer transition over a foil using direct numerical simulation and large eddy simulation. Physics of Fluids, 31(12), 124102. https://doi.org/10.1063/1.5126663##
Spalart, P. R., & Rumsey, C. L. (2007). Effective inflow conditions for turbulence models in aerodynamic calculations. American Institute of Aeronautics and Astronautics Journal, 45(10), 2544-2553. https://doi.org/10.2514/1.29373##
Spalart, P., & Allmaras, S. (1992). A oneequation turbulence model for aerodynamic flows. In 30th aerospace sciences meeting and exhibit (p. 439). https://doi.org/10.2514/6.1992-439##
Spentzos, A., Barakos, G., Badcock, K., Richards, B., Wernert, P., Schreck, S., & Raffel, M. (2005). Investigation of three-dimensional dynamic stall using computational fluid dynamics. Aeronautics and Astronautics Journal, 43(5), 1023-1033. https://doi.org/10.2514/1.8830##
Storms, B. L., Ross, J. C., Heineck, J. T., Walker, S. M., Driver, D. M., Zilliac, G. G., & Bencze, D. P. (2001). An experimental study of the ground transportation system (GTS) model in the NASA Ames 7-by 10-ft wind tunnel.##
Surekha, RS, D., Khandelwal, A., & Rajasekar, R. (2019). Investigation of flow field in deep dynamic stall over an oscillating NACA 0012 airfoil. Journal of Applied Fluid Mechanics, 12(3), 857–863. https://doi.org/10.29252/JAFM.12.03.29532##
Suvanjumrat, C. (2017). Comparison of turbulence models for flow past NACA0015 airfoil using OpenFOAM. Engineering Journal, 21(3), 207-221. https://doi.org/10.4186/ej.2017.21.3.207##
Tahry, S. H. E. (1983). K-Epsilon equation
for compressible reciprocating engine
flows. Journal of Energy, 7(4), 345-353. https://doi.org/10.2514/3.48086##
Tarzanin, F. J. (1972). Prediction of control loads due to blade stall. Journal of the American
Helicopter Society,
17(2), 33-46. https://doi.org/10.4050/JAHS.17.33##
Thakor, M., Kumar, G., Das, D., & De, A. (2020). Investigation of asymmetrically pitching airfoil at high reduced frequency. Physics of Fluids, 32(5), 053607. https://doi.org/10.1063/5.0006659##
Tseng, C. C., & Cheng, Y. E. (2015). Numerical investigations of the vortex interactions for a flow over a pitching foil at different stages. Journal of fluids and structures, 58, 291-318. https://doi.org/10.1016/j.jfluidstructs.2015.08.002##
Visbal, M. R., & Benton, S. I. (2018). Exploration of high-frequency control of dynamic stall using large-eddy simulations. Aeronautics and Astronautics Journal, 56(8), 2974-2991. https://doi.org/10.2514/1.J056720##
Visbal, M. R., & Garmann, D. J. (2018). Analysis of dynamic stall on a pitching airfoil using
high-fidelity large-eddy simulations. Aeronautics
and Astronautics Journal,
56(1), 46-63. https://doi.org/10.2514/1.J056108##
Visbal, M. R., & Shang, J. S. (1989). Investigation of the flow structure around a rapidly pitching airfoil Aeronautics and Astronautics Journal, 27(8), 1044-1051. https://doi.org/10.2514/3.10219##
Wang, R., & Xiao, Z. (2020). Transition effects on flow characteristics around a static two-dimensional airfoil. Physics of Fluids, 32(3), 035113. https://doi.org/10.1063/1.5144860##
Wang, S., Ingham, D. B., Ma, L., Pourkashanian, M., & Tao, Z. (2010). Numerical investigations on dynamic stall of low Reynolds number flow around oscillating airfoils. Computers & Fluids, 39(9), 1529–1541. https://doi.org/10.1016/j.co##
Wang, S., Ingham, D. B., Ma, L., Pourkashanian, M., & Tao, Z. (2012). Turbulence modeling of deep dynamic stall at relatively low Reynolds number. Journal of Fluids and Structures, 33, 191-209. https://doi.org/10.1016/j.jfluidstructs.2012.04.011##
Volume 16, Issue 8
August 2023
Pages 1544-1559
  • Received: 15 December 2022
  • Revised: 05 March 2023
  • Accepted: 02 April 2023
  • Available online: 31 May 2023