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Referring to the construction of shear stress transport-improved delayed detached-eddy simulation (SST-IDDES) method, a variant of IDDES method based on the Speziale-Sarkar-Gatski/Launder-Reece-Rodi (SSG/LRR)-ω Reynolds-stress model (RSM) as Reynolds-averaged Navier-Stokes (RANS) background model, is proposed. Through combining high-order weighted compact nonlinear scheme (WCNS), the SSG/LRR-IDDES method is applied to three aeronautic cases and compared with traditional methods:SST-unsteady Reynolds-averaged Navier-Stokes (URANS), SSG/LRR-URANS, and SST-IDDES. To verify the SSG/LRR-IDDES method in simulating airfoil stalled flow, NACA0012 airfoil is adopted separately at attack angles of 17°, 45° and 60°. At the attack angle of 17°, SST-URANS, SSG/LRR-URANS, and SST-IDDES methods each predict a higher lift coefficient than the experimental data, while the SSG/LRR-IDDES method obtains a better lift coefficient result and a higher fidelity vortical flow structure. It indicates that the RSM can improve the prediction of RANS-mode for pressure-induced separations on airfoil surfaces in detached-eddy simulation. At the attack angles of 45° and 60°, the SSG/LRR-IDDES method captures the massively separated flow with three-dimensional vortical structures and obtains a good result, which is the same as that from the traditional SST-IDDES method. To indicate the improvement of the SSG/LRR-IDDES method in simulating airfoil trailing edge separation, NACA4412 airfoil is adopted. At the attack angle of 12° (maximum lift), the trailing edge separation is mainly induced by pressure gradient. The SSG/LRR-IDDES method can predict the separation process reasonably and obtains a good lift coefficient and location of separation compared with experimental results. However, none of other methods can predict trailing edge separation. It confirms that when RSM is adopted as RANS background model in detached-eddy simulation, the ability to predict pressure-induced separation on airfoil surface is improved. For further verifying the SSG/LRR-IDDES method for simulating three-dimensional separated flow, blunt-edge deltawing at the attack angle of 24.6° is adopted. At this attack angle, the primary vortex will break, which is difficult to predict by using the SST-URANS method. For the SSG/LRR-URANS method, it predicts the vortex breakdown successfully, but the breakdown process does not show any significant unsteady characteristic. The SST-IDDES and the SSG/LRR-IDDES methods both predict a significant unsteady vortex breakdown. But in terms of the accuracy of surface pressure and the fidelity of unsteady flow, the result obtained by the SSG/LRR-IDDES method is better than by the SST-IDDES method.
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Keywords:
- turbulence flows /
- Reynolds stress model /
- detached eddy simulation /
- weighted compact nonlinear scheme
[1] Slotnick J, Khodadoust A, Alonso J, Darmofal D, Gropp W, Lurie E, Mavriplis D 2014 CFD Vision 2030 Study:A Path to Revolutionary Computational Aerosciences (Washington, DC:Langley Research Center, NASA) Tech. Rep. NASA/CR-2014-218178
[2] Eisfeld B, Rumsey C, Togiti V 2016 AIAA J. 54 1524
[3] Rumsey C 2014 52nd Aerospace Sciences Meeting National Harbor, Maryland, January 13-17, 2014 AIAA 2014-0201
[4] Tucker P 2006 Int. J. Numer. Meth. Fluids 51 261
[5] Richez F, Pape A, Costes M 2015 AIAA J. 53 3157
[6] Xu G, Jiang X, Liu G 2016 Acta Mech. Sin. 32 588
[7] Spalart P, Jou W H, Strelets M, Allmaras S 1997 Comments on the Feasibility of LES for Wings, and on Hybrid RANS/LES Approach (Columbus:Greyden Press)
[8] Spalart P 2009 Annu. Rev. Fluid Mech. 41 181
[9] Probst A, Radespiel R, Knopp T 2011 20st AIAA Computational Fluid Dynamics Conference Honolulu, Hawaii, June 27-30, 2011 AIAA 2011-3206
[10] Strelets M 2001 39th AIAA Aerospace Sciences Meeting and Exhibit Reno, NV, 8-11 January 2001, AIAA 2001-0879
[11] Greschner B, Thiele F, Gurr A, Casalino D, Jacob M 2006 12th AIAA/CEAS Aeroacoustics Conference Cambridge, Massachusetts, May 8-10, 2006 AIAA 2006-2628
[12] Greschner B, Thiele F, Jacob M, Casalino D 2008 Comput. Fluids 37 402
[13] Cécora R D, Radespiel R, Eisfeld B, Probst A 2015 AIAA J. 53 739
[14] Rumsey C 2015 in Eisfeld B (ed.) Differential Reynolds Stress Modeling for Separating Flows in Industrial Aerodynamics (Springer Tracts Mechanical Engineering) p19
[15] Eisfeld B, Brodersen O 2005 23rd AIAA Applied Aerodynamics Conference Toronto, Ontario Canada, June 6-9, 2005 AIAA 2005-4727
[16] Togiti V, Eisfeld B, Brodersen O 2014 J. Aircraft 51 1331
[17] Dong Y D, Wang D F, Wang G X, Deng X G 2016 J. National Univ. Defense Technol. 38 46(in Chinese)[董义道, 王东方, 王光学, 邓小刚2016国防科技大学学报 38 46]
[18] Shu C 2003 Int. J. Comput. Fluid D 17 107
[19] Wang Z, Fidkowski K, Abgrall R, Bassi F, Caraeni D, Cary A, Deconinck H, Hartmann R, Hillewaert K, Huynh H, Kroll N, May G, Persson P O, van Leer B, Visbal M 2013 Int. J. Numer. Meth. Fluids 72 811
[20] Wang S, Deng X, Wang G, Xu D, Wang D 2016 Int. J. Comput. Fluid D 30 469
[21] Georgiadis N, Rizzetta D, Fureby C 2010 AIAA J. 48 1772
[22] Deng X, Zhang H 2000 J. Comput. Phys. 165 22
[23] Deng X, Liu X, Mao M, Zhang H 2005 17th AIAA Computational Fluid Dynamics Conference Toronto, Ontario Canada, June 6-9, 2005 AIAA 2005-5246
[24] Deng X, Mao M, Tu G, Liu H, Zhang H 2011 J. Comput. Phys. 230 1100
[25] Bellot G, Corrsin S 1971 J. Fluid Mech. 48 273
[26] Spalart P, Deck S, Shur M, Squires K, Strelets M, Travin A 2006 Theor. Comput. Fluid Dyn. 20 181
[27] Shur M, Spalart P, Strelets M, Travin A 2008 Int. J. Heat Fluid Fl. 29 1638
[28] Nonomura T, Fujii K 2009 J. Comput. Phys. 228 3533
[29] Liu H, Ma Y, Yan Z, Mao M, Deng X 2014 8th International Conference on Computational Fluid Dynamics Chengdu, China, July 14-18, 2014 ICCFD8-2014-0082
[30] Gang D D, Yi S H, Zhao Y F 2015 Acta Phys. Sin. 64 054705(in Chinese)[冈敦殿, 易仕和, 赵云飞2015物理学报 64 054705]
[31] Schumann U 1977 Phys. Fluids 20 721
[32] Chassaing J, Gerolymos G, Vallet I 2003 AIAA J. 41 763
[33] Yossef Y 2014 J. Comput. Phys. 276 635
[34] Yang Y, Zha G 2016 46th AIAA Fluid Dynamics Conference Washington, D.C., USA, June 13-17, 2016 AIAA 2016-3185
[35] Shur M, Spalart P, Strelets M, Travin A 1999 Proceedings of the 4th International Symposium on Engineering Turbulence Modelling and Measurements Corsica, France, May 24-26, 1999 p669
[36] Chen M Z 2002 Fundamentals of Viscous Fliud Dynamics (Beijing:Higher Education Press) p239(in Chinese)[陈懋章2002粘性流体动力学基础(北京:高等教育出版社)第239页]
[37] Chen Y, Guo L D, Peng Q, Chen Z Q, Liu W H 2015 Acta Phys. Sin. 64 134701(in Chinese)[陈勇, 郭隆德, 彭强, 陈志强, 刘卫红2015物理学报 64 134701]
[38] Wadcock A 1987 Investigation of Low Speed Turbulent Scparatcd Flow Around Airfoils (Washington, DC:Ames Research Center, NASA) Tech. Rep. NASA-CR-177450
[39] Roy R, Stoellinger M 2015 53rd AIAA Aerospace Sciences Meeting Kissimmee, Florida, January 5-9, 2015 AIAA 2015-1982
[40] Luckring M, Hummel D 2013 Aerosp. Sci. Technol. 24 77
[41] Chu J, Luckring M 1996 Experimental Surface Pressure Data Obtained on 65 deg Delta Wing Across Reynolds Number and Mach Number Ranges. Vol. 3:Medium-Radius Leading Edge (Washington, DC:Ames Research Center, NASA) NASA-TM-4645-Vol-3
[42] Luckring M 2013 Aerosp. Sci. Technol. 24 10
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[1] Slotnick J, Khodadoust A, Alonso J, Darmofal D, Gropp W, Lurie E, Mavriplis D 2014 CFD Vision 2030 Study:A Path to Revolutionary Computational Aerosciences (Washington, DC:Langley Research Center, NASA) Tech. Rep. NASA/CR-2014-218178
[2] Eisfeld B, Rumsey C, Togiti V 2016 AIAA J. 54 1524
[3] Rumsey C 2014 52nd Aerospace Sciences Meeting National Harbor, Maryland, January 13-17, 2014 AIAA 2014-0201
[4] Tucker P 2006 Int. J. Numer. Meth. Fluids 51 261
[5] Richez F, Pape A, Costes M 2015 AIAA J. 53 3157
[6] Xu G, Jiang X, Liu G 2016 Acta Mech. Sin. 32 588
[7] Spalart P, Jou W H, Strelets M, Allmaras S 1997 Comments on the Feasibility of LES for Wings, and on Hybrid RANS/LES Approach (Columbus:Greyden Press)
[8] Spalart P 2009 Annu. Rev. Fluid Mech. 41 181
[9] Probst A, Radespiel R, Knopp T 2011 20st AIAA Computational Fluid Dynamics Conference Honolulu, Hawaii, June 27-30, 2011 AIAA 2011-3206
[10] Strelets M 2001 39th AIAA Aerospace Sciences Meeting and Exhibit Reno, NV, 8-11 January 2001, AIAA 2001-0879
[11] Greschner B, Thiele F, Gurr A, Casalino D, Jacob M 2006 12th AIAA/CEAS Aeroacoustics Conference Cambridge, Massachusetts, May 8-10, 2006 AIAA 2006-2628
[12] Greschner B, Thiele F, Jacob M, Casalino D 2008 Comput. Fluids 37 402
[13] Cécora R D, Radespiel R, Eisfeld B, Probst A 2015 AIAA J. 53 739
[14] Rumsey C 2015 in Eisfeld B (ed.) Differential Reynolds Stress Modeling for Separating Flows in Industrial Aerodynamics (Springer Tracts Mechanical Engineering) p19
[15] Eisfeld B, Brodersen O 2005 23rd AIAA Applied Aerodynamics Conference Toronto, Ontario Canada, June 6-9, 2005 AIAA 2005-4727
[16] Togiti V, Eisfeld B, Brodersen O 2014 J. Aircraft 51 1331
[17] Dong Y D, Wang D F, Wang G X, Deng X G 2016 J. National Univ. Defense Technol. 38 46(in Chinese)[董义道, 王东方, 王光学, 邓小刚2016国防科技大学学报 38 46]
[18] Shu C 2003 Int. J. Comput. Fluid D 17 107
[19] Wang Z, Fidkowski K, Abgrall R, Bassi F, Caraeni D, Cary A, Deconinck H, Hartmann R, Hillewaert K, Huynh H, Kroll N, May G, Persson P O, van Leer B, Visbal M 2013 Int. J. Numer. Meth. Fluids 72 811
[20] Wang S, Deng X, Wang G, Xu D, Wang D 2016 Int. J. Comput. Fluid D 30 469
[21] Georgiadis N, Rizzetta D, Fureby C 2010 AIAA J. 48 1772
[22] Deng X, Zhang H 2000 J. Comput. Phys. 165 22
[23] Deng X, Liu X, Mao M, Zhang H 2005 17th AIAA Computational Fluid Dynamics Conference Toronto, Ontario Canada, June 6-9, 2005 AIAA 2005-5246
[24] Deng X, Mao M, Tu G, Liu H, Zhang H 2011 J. Comput. Phys. 230 1100
[25] Bellot G, Corrsin S 1971 J. Fluid Mech. 48 273
[26] Spalart P, Deck S, Shur M, Squires K, Strelets M, Travin A 2006 Theor. Comput. Fluid Dyn. 20 181
[27] Shur M, Spalart P, Strelets M, Travin A 2008 Int. J. Heat Fluid Fl. 29 1638
[28] Nonomura T, Fujii K 2009 J. Comput. Phys. 228 3533
[29] Liu H, Ma Y, Yan Z, Mao M, Deng X 2014 8th International Conference on Computational Fluid Dynamics Chengdu, China, July 14-18, 2014 ICCFD8-2014-0082
[30] Gang D D, Yi S H, Zhao Y F 2015 Acta Phys. Sin. 64 054705(in Chinese)[冈敦殿, 易仕和, 赵云飞2015物理学报 64 054705]
[31] Schumann U 1977 Phys. Fluids 20 721
[32] Chassaing J, Gerolymos G, Vallet I 2003 AIAA J. 41 763
[33] Yossef Y 2014 J. Comput. Phys. 276 635
[34] Yang Y, Zha G 2016 46th AIAA Fluid Dynamics Conference Washington, D.C., USA, June 13-17, 2016 AIAA 2016-3185
[35] Shur M, Spalart P, Strelets M, Travin A 1999 Proceedings of the 4th International Symposium on Engineering Turbulence Modelling and Measurements Corsica, France, May 24-26, 1999 p669
[36] Chen M Z 2002 Fundamentals of Viscous Fliud Dynamics (Beijing:Higher Education Press) p239(in Chinese)[陈懋章2002粘性流体动力学基础(北京:高等教育出版社)第239页]
[37] Chen Y, Guo L D, Peng Q, Chen Z Q, Liu W H 2015 Acta Phys. Sin. 64 134701(in Chinese)[陈勇, 郭隆德, 彭强, 陈志强, 刘卫红2015物理学报 64 134701]
[38] Wadcock A 1987 Investigation of Low Speed Turbulent Scparatcd Flow Around Airfoils (Washington, DC:Ames Research Center, NASA) Tech. Rep. NASA-CR-177450
[39] Roy R, Stoellinger M 2015 53rd AIAA Aerospace Sciences Meeting Kissimmee, Florida, January 5-9, 2015 AIAA 2015-1982
[40] Luckring M, Hummel D 2013 Aerosp. Sci. Technol. 24 77
[41] Chu J, Luckring M 1996 Experimental Surface Pressure Data Obtained on 65 deg Delta Wing Across Reynolds Number and Mach Number Ranges. Vol. 3:Medium-Radius Leading Edge (Washington, DC:Ames Research Center, NASA) NASA-TM-4645-Vol-3
[42] Luckring M 2013 Aerosp. Sci. Technol. 24 10
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