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雷诺应力模型一直是湍流模式理论研究的前沿和难点, 而提高数值鲁棒性是其广泛开展工程应用的关键. 借鉴经典的
$k$ -$kL$ 湍流模型, 本文构造了一种新的${\nu_{\rm{t}}}$ 尺度方程, 并将其用于耦合SSG/LRR模式从而形成SSG/LRR-${\nu_{\rm{t}}}$ 雷诺应力模型. 通过零压力梯度湍流平板边界层、翼型尾迹流、超声速方腔流和NACA0012翼型45°迎角分离流动4个标准算例对新模型进行了验证与确认. 同时, 为了测试模型的数值鲁棒性, 采用高精度数值格式对模型方程进行了离散求解, 并与SA涡粘模型和SSG/LRR-$\omega$ 雷诺应力模型进行对比. 结果表明:${\nu_{\rm{t}}}$ 尺度方程在黏性壁面边界严格为零, 相比传统的$\omega$ 尺度, 具有更好的数值鲁棒性, 从而可实现新模型与高精度数值格式的匹配并获得更好的网格收敛效率; 新模型具备雷诺应力模型的传统优势, 可对拐角流动进行很好的模拟; 具备尺度自适应能力, 对于非定常分离流动的模拟存在一定的潜力.Reynolds stress model has always been the frontier and challenging problem in turbulence model theory research, where improving numerical robustness is the key to its wide application in engineering. Referring to the classical$k$ -$kL$ turbulence model, a new${\nu_t}$ -scale equation is constructed and used to couple the SSG/LRR model to form a so-called SSG/LRR-${\nu_t}$ Reynolds stress model. Four benchmark cases, including zero pressure gradient turbulent plate boundary layer, airfoil wake flow, supersonic square duck flow and separated flow over NACA0012 airfoil at 45 degree angle of attack, are carried out to test the new turbulence model. At the same time, high-order numerical schemes are used to discretize the turbulence equations in order to assess its numerical robustness. The results are compared with those of SA eddy viscosity model and SSG/LRR-$\omega$ Reynolds stress model. It is shown that the${\nu_t} $ -scale equation is strictly equal to zero at the viscous wall boundary. Compared with the traditional$\omega $ -scale, it has better numerical robustness. Along with this, the new model can be matched with the high-order numerical schemes and obtain a better efficiency in the mesh convergence. Moreover, the new model has the inherent advantage of Reynolds stress model in simulating the corner flow and has the potential in scale adaptive simulation of unsteady separated flow.-
Keywords:
- turbulence flow /
- Reynolds stress model /
- separated flow /
- weighted compact nonlinear scheme
[1] Wilcox D C 2006 Turbulence Modeling for CFD (3rd Ed.) (La Canda: DCW Industries)
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[20] Menter F R, Egorov Y 2010 Flow, Turbulence, and Combustion 85 113Google Scholar
[21] Abdol-Hamid K S, Carlson J R, Rumsey C L 2016 AIAA Paper 3941
[22] Spalart P R, Allmaras S R 1994 Recherche Aerospatiale 1 5
[23] Speziale C G, Sarkar S, Gatski T B 1991 J 1991 J. Fluid Mech. 227 245Google Scholar
[24] 王光学, 王圣业, 葛明明, 邓小刚 2018 物理学报 67 194701Google Scholar
Wang G X, Wang S Y, Ge M M, Deng X G 2018 Acta Phys. Sin. 67 194701Google Scholar
[25] 李昊, 刘伟, 王圣业 2020 物理学报 69 144702Google Scholar
Li H, Liu W, Wang S Y 2020 Acta Phys. Sin. 69 144702Google Scholar
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[29] Strelets M 2001 AIAA Paper 0879
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图 6 方腔流动示意图 (a) 计算网格及边界条件; (b) SA模型在
$ x/D = 50 $ 面上的速度矢量图; (c) SSG/LRR-$ \omega $ 模型在$ x/D = 50 $ 面上的速度矢量图; (d) SSG/LRR-$ {\nu_{\rm{t}}} $ 模型在$ x/D = 50 $ 面上的速度矢量图Fig. 6. Sketch of square duct flow: (a) Mesh and boundary conditions; (b) velocity vector distributions on
$ x/D = 50 $ by SA; (c) velocity vector distributions on$ x/D = 50 $ by SSG/LRR-$ \omega $ ; (d) velocity vector distributions on$ x/D = 50 $ by SSG/LRR-$ {\nu_{\rm{t}}} $ 表 1 再分配项系数
Table 1. Coefficients in redistribution item.
$ {C_1} $ $ {C_1}^* $ $ {C_2} $ $ {C_3} $ $ {C_3}^* $ $ {C_4} $ $ {C_5} $ $ {\phi^\text{(SSG)}} $ 1.7 0.9 1.05 0.8 0.65 0.625 0.2 $ {\phi^\text{(LRR)}} $ 1.8 0 0 0.8 0 0.971 0.578 -
[1] Wilcox D C 2006 Turbulence Modeling for CFD (3rd Ed.) (La Canda: DCW Industries)
[2] 周培源 1940 中国物理学报 4 1Google Scholar
Chou P Y 1940 Chin. J. Phys. 4 1Google Scholar
[3] Chou P Y 1945 Quart. Appl. Math. 3 38Google Scholar
[4] 王圣业, 王光学, 董义道, 邓小刚 2017 物理学报 66 184701Google Scholar
Wang S Y, Wang G X, Dong Y D, Deng X G 2017 Acta Phys. Sin. 66 184701Google Scholar
[5] 王圣业, 符翔, 杨小亮, 郑浩榜, 邓小刚 2021 力学进展 51 29Google Scholar
Wang S Y, Fu X, Yang X L, Zheng H B, Deng X G 2021 Adv. Mech. 51 29Google Scholar
[6] Slotnick J, Khodadoust A, Alonso J, Darmofal D, Gropp W, Lurie E, Mavriplis D 2014 NASA/CR-2014-218178
[7] Eisfeld B, Brodersen O 2005 AIAA Paper 4727
[8] Launder B E, Reece G L, Rodi W 1975 J. Fluid Mech. 68 537Google Scholar
[9] Speziale C G, Abid R, Anderson E C 1992 AIAA J. 30 324Google Scholar
[10] Menter F R 1994 AIAA J. 32 1598Google Scholar
[11] Eisfeld B, Rumsey C, Togiti V 2016 AIAA J. 54 1524Google Scholar
[12] Cecora R D, Radespiel R, Eisfeld B, Probst A 2015 AIAA J. 53 739Google Scholar
[13] Wang S Y, Dong Y D, Deng X G, et al. 2018 J. Aircraft 53 1177Google Scholar
[14] Eisfeld B, Rumsey C, Togiti V, Braun S, Stürmer A 2021 AIAA J. Published online
[15] Togiti V K, Eisfeld B 2015 AIAA Paper 2925
[16] Ilinca F, Pelletier D 1998 AIAA J. 32 44
[17] Abdol-Hamid K S 2019 AIAA Paper 1878Google Scholar
[18] 舒博文, 杜一鸣, 高正红, 夏露, 陈树生 2022 航空学报 43 126385Google Scholar
Shu B W, Du Y M, Gao Z H, Xia L, Chen S S 2022 Acta Aeronautica et Astronautica Sinica 43 126385Google Scholar
[19] Rotta J C 1968 Aerodynamische Versuchsanstalt Göttingen, Rep. 69 A14
[20] Menter F R, Egorov Y 2010 Flow, Turbulence, and Combustion 85 113Google Scholar
[21] Abdol-Hamid K S, Carlson J R, Rumsey C L 2016 AIAA Paper 3941
[22] Spalart P R, Allmaras S R 1994 Recherche Aerospatiale 1 5
[23] Speziale C G, Sarkar S, Gatski T B 1991 J 1991 J. Fluid Mech. 227 245Google Scholar
[24] 王光学, 王圣业, 葛明明, 邓小刚 2018 物理学报 67 194701Google Scholar
Wang G X, Wang S Y, Ge M M, Deng X G 2018 Acta Phys. Sin. 67 194701Google Scholar
[25] 李昊, 刘伟, 王圣业 2020 物理学报 69 144702Google Scholar
Li H, Liu W, Wang S Y 2020 Acta Phys. Sin. 69 144702Google Scholar
[26] Deng X G, Zhang H X 2000 J. Comput. Phys. 165 90Google Scholar
[27] Deng X G, Min Y B, Mao M L, Liu H Y, Tu G H, Zhang H X 2013 J. Comput. Phys. 239 90Google Scholar
[28] Rumsey C Turbulence Modeling Resource https://turbmodels.larc.nasa.gov/
[29] Strelets M 2001 AIAA Paper 0879
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