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In the present paper, a hybrid RANS/LES model with the wall-modelled LES capability (called WM-HRL model) is developed to perform the high-fidelity CFD simulation investigation for complex flow phenomena around a bluff body with coherent structure in subcritical Reynolds number region. The proposed method can achieve a fast and seamless transition from RANS to LES through a filter parameter rk which is only related to the space resolution capability of the local grid system for various turbulent scales. Furthermore, the boundary positions of the transition region from RANS to LES, as well as the resolving capabilities for the turbulent kinetic energy in the three regions, i.e. RANS, LES and transition region, can be preset by two guide index parameters nrk1-Q and nrk2-Q. Through a series of numerical simulations of the flow around a circular cylinder at Reynolds number Re = 3900, the combination conditions are obtained for such two guide index parameters nrk1-Q and nrk2-Q that have the capability of high-fidelity resolving and capturing temporally- and spatially-developing coherent structures for such complex three-dimensional flows around such a circular cylinder. The results demonstrate that the new WM-HRL model is capable of accurately resolving and capturing the fine spectral structures of the small-scale Kelvin-Helmholtz instability in the shear layer for flow around such a circular cylinder. Furthermore, under a consistent grid system, through different combinations of these two guide index parameters rk1 and rk2, the fine structuresof the recirculation zones with two different lengths and the U-shaped and V-shaped distribution of the average stream-wise velocity in the cylinder near the wake can also be obtained.
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Keywords:
- flow around a cylinder /
- coherent structures /
- Kelvin-Helmholtz instability /
- hybrid RANS/LES model
[1] Zdravkovich M M 1997 Flow Around Circular Cylinders (Vol. 120) (Oxford: Oxford Science Publication) pp2–7
[2] Pereira F S, Eça L, Vaz G, Girimaji S S 2018 J. Comput. Phys. 363 98
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Google Scholar
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Google Scholar
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图 1 计算区域设置
Figure 1. Computational domain schematic.
图 2 计算网格剖面
Figure 2. Computational grid configuration.
图 3 剪切层小尺度K-H不稳定性结构监测点分布
Figure 3. Location configuration of the probes for the small scale K-H instability structure in the shear layer.
图 4 圆柱表面周向压力系数${C_{\text{p}}}$分布特性
Figure 4. Azimuthal distribution characteristics for pressure coefficient along the circular cylinder surface.
图 5 沿尾流中心线平均流向速度剖面特性
Figure 5. Distribution characteristics of mean stream-wise velocities along the wake centerline.
图 6 圆柱后方不同站位处平均流向速度剖面特性
Figure 6. Distribution characteristics of mean stream-wise velocities at different locations in the backside of the circular cylinder.
图 7 圆柱后方不同站位处平均横向速度剖面特性
Figure 7. Distribution characteristics of mean cross-flow velocities at different locations in the backside of the circular cylinder.
图 8 圆柱后方不同站位处各向同性流向雷诺应力剖面特性
Figure 8. Distribution characteristics of isotropic stream-wise Reynolds stresses at different locations in the backside of the circular cylinder.
图 9 圆柱后方不同站位处各向同性横向雷诺应力剖面特性
Figure 9. Distribution characteristics of isotropic cross-flow Reynolds stresses at different locations in the backside of the circular cylinder.
图 10 圆柱后方不同站位处各向异性雷诺应力剖面特性
Figure 10. Distribution characteristics of anisotropy cross-flow Reynolds stresses at different locations in the backside of the circular cylinder.
图 11 在Case CU工况下, 在P1—P12监测点处横向脉动速度的Lomb谱
Figure 11. Lomb spectrums of the cross-stream fluctuation velocities at different probes P1–P12 for the Case CU.
图 12 在Case CV工况下, 在P1—P12监测点处横向脉动速度的Lomb谱
Figure 12. Lomb spectrums of the cross-stream fluctuation velocities at different probes P1–P12 for the Case CV.
图 13 在Case CU (第1和第2列)和Case CV (第3和第4列)工况下, 在P13—P18监测点处流向(第1和第3列)及横向(第2和第4列)脉动速度的Lomb谱
Figure 13. Lomb spectrums of the stream-wise (from the first to third rows) and cross-stream (from the second to fourth rows) fluctuation velocities at different probes P13–P18 for the Case CU (from the first to second rows) and the Case CV (from the third to fourth rows).
图 14 在Case AU—DU(前4行)和Case AV—DV(后4行)工况下, 圆柱绕流涡量(左)及流向速度(右)云图
Figure 14. Contours of the span-wise vorticity (left) and stream-wise velocity (right) for both Case AU–DU (the first four lines) and Case AV–DV (the last four lines).
图 15 在Case AU—DU (左)和Case AV—DV (右)工况下, 圆柱绕流展向三维涡量云图
Figure 15. Contours of the three-dimensional span-wise vorticities both Case AU–DU (left) and Case AV–DV (right).
表 1 在雷诺数Re = 3900下圆柱绕流文献中所用计算模型与网格参数设置情况比较
Table 1. Comparisons of computational models and grid parameters in references for flow around a circular cylinder at Reynolds number Re = 3900.
$ L_3/D $ $ \varDelta_3/D $ 网格量 ($ \times {10^6}$) Lehmkuhl等[10] (DNS) $ {\text{π}} $ $ {\text{π}} $/128 9.30 Tremblay[8] (LES) $ {\text{π}} $ $ {\text{π}} $/64 7.70 Breuer [15] (LES) $ {\text{π}} $ $ {\text{π}} $/64 1.70 Pereira等[2] (PANS) 3.0 $ {\text{π}} $/48 4.55 Luo等[24]
(PANS/SST-DES)$ {\text{π}} $ $ {\text{π}} $/60 2.23 D'Alessandro等[30]
(SA-DES/SA-IDDES/
v2-f DES)$ {\text{π}} $ $ {\text{π}} $/48 3.96 本文(WM-HRL) $ {\text{π }} $ $ {\text{π }} $/64 1.43 
DownLoad: CSV
表 2 文献中雷诺数Re = 3900下圆柱绕流场相关统计量的实验和数值结果
Table 2. Experimental and numerical results for flow statistical characteristics from references for flow around a circular cylinder at Reynolds numbers Re = 3900.
参考文献及方法 $ {\bar f_{{\text{vs}}}} $ ${\bar f_{{\text{kh}}}}$ $ {\phi _{\text{s}}}/({\, ^ \circ }) $ $L_{\text{r}}/D $ $C_{\rm d} $ $ - {C_{{\text{pb}}}} $ 形状 Parnaudeau等[18] (Exp.) 0.208 — 88 1.51 — — U Lourenco和Shih[27] (Exp.) — — 85 1.18 0.98 0.9 V Lehmkuhl等[10] (DNS) (Mode H) 0.214 1.34 88.25 1.26 1.043 0.98 V Lehmkuhl等[10] (DNS) (Mode L) 0.218 — 87.8 1.55 0.979 0.877 U Tremblay[8] (LES) 0.21 — 87.3 1.04 1.14 0.99 V Breuer[15] (LES) 0.215 — 87.4 1.372 1.016 0.941 V Pereira等[2] (PANS) ($ {f_{\text{k}}} $ = 0.25) 0.208 1.48 80.3 1.73 0.927 0.864 U Pereira等[2] (PANS) ($ {f_{\text{k}}} $ = 0.5) 0.214 1.55 81.8 1.12 1.036 1.050 V Luo等[24] (PANS) ($ {f_{\text{k}}} $ = 0.1) 0.201 — 87.2 1.27 1.05 0.94 V Luo等[24] (PANS) ($ {f_{\text{k}}} $ = 0.5) 0.208 — 92.8 0.49 1.35 1.47 V Luo等[24] (SST-DES) 0.203 — 86.4 1.46 1.01 0.89 V D'Alessandro等[30] (SA-DES) 0.215 — 89.28 0.850 1.2025 1.077 V D'Alessandro等[30] (SA-IDDES) 0.222 — 87.0 1.427 1.0235 0.878 U D'Alessandro等[30] (v2-f DES) 0.214 — 86.4 1.678 0.9857 0.829 U
DownLoad: CSV
表 3 监测点坐标信息
Table 3. Coordinate information of the probes.
监测点编号 监测点坐标
$(x_1 /D, x_2/D)$监测点对应
的$ {y^ + } $值P1 (0.20, 0.560) 30.5 P2 (0.30, 0.572) 47.1 P3 (0.40, 0.584) 67.0 P4 (0.50, 0.595) 89.4 P5 (0.60, 0.607) 114.0 P6 (0.70, 0.619) 140.1 P7 (0.80, 0.631) 167.4 P8 (0.90, 0.643) 195.5 P9 (1.00, 0.655) 224.3 P10 (1.10, 0.666) 253.5 P11 (1.20, 0.678) 283.3 P12 (1.30, 0.690) 313.5 P13 (0.71, 0.660) 151.4 P14 (0.69, 0.520) 117.4 P15 (2.00, 0.590) 511.4 P16 (1.00, 0.0) 161.3 P17 (2.00, 0.0) 483.9 P18 (3.00, 0.0) 806.5
DownLoad: CSV
表 4 当$ {\varGamma _{{\text{LES}}}} $位于剪切层小尺度K-H不稳定性结构发生区域内时, 相关流场统计量的数值结果
Table 4. Numerical results for flow statistic characteristics when $ {\varGamma _{{\text{LES}}}} $ is located in the K-H instability region of the shear layer.
$ {\varGamma _{{\text{RANS}}}} $ $ {\varGamma _{{\text{LES}}}} $ $ {\bar f_{{\text{vs}}}} $ ${\bar f_{{\text{kh}}}}$ $ {\phi _{\text{s}}}/({\,^\circ }) $ $ {{{L_{\text{r}}}} \mathord{\left/ {\vphantom {{{L_{\text{r}}}} D}} \right. } D} $ $ {C_{\text{d}}} $ $ - {C_{{\text{pb}}}} $ 形状 $ {r_{{\text{k1}}}} $ $ y_{{\text{RANS}}}^ + $ $ {r_{{\text{k2}}}} $ $ y_{{\text{LES}}}^{+} $ 0.9302 7.9 0.1556 105.8 0.219 1.38 88.1 1.05 1.14 1.12 V 0.6364 13.3 0.221 1.23 88.1 1.07 1.14 1.09 V 0.5951 14.9 0.221 1.35 87.7 1.19 1.12 1.04 V 0.4923 18.4 0.222 1.30 88.1 1.03 1.15 1.08 V 0.4635 20.4 0.222 1.18 87.8 1.22 1.12 1.03 V 0.3898 27.1 0.223 1.23 87.0 1.32 1.12 0.99 U 0.3134 38.4 0.224 1.16 86.6 1.48 1.10 0.96 U 0.2973 41.7 0.220 1.21 87.1 1.32 1.10 1.00 U 0.2546 49.2 0.223 1.00 88.0 1.14 1.13 1.06 V 0.1983 72.7 0.221 1.06 88.1 1.01 1.15 1.12 V 0.1713 91.2 0.226 1.21 86.6 1.46 1.10 0.96 U 0.9302 7.9 0.1484 113.9 0.218 1.13 88.0 1.12 1.14 1.06 V 0.6364 13.3 0.221 1.17 88.4 1.00 1.16 1.13 V 0.5951 14.9 0.220 1.30 87.8 1.18 1.12 1.04 V 0.4923 18.4 0.224 1.23 87.1 1.32 1.15 1.00 V 0.4635 20.4 0.224 1.26 86.5 1.48 1.09 0.97 U 0.3898 27.1 0.224 1.01 87.2 1.22 1.12 1.00 V 0.3134 38.4 0.224 1.11 86.5 1.47 1.08 0.95 U 0.2973 41.7 0.218 1.16 86.5 1.47 1.10 0.96 U 0.2546 49.2 0.222 1.00 87.7 1.23 1.12 1.04 V 0.1983 72.7 0.225 1.14 87.8 1.23 1.14 1.03 V 0.1713 91.2 0.225 0.99 87.8 1.22 1.12 1.03 V
DownLoad: CSV
表 5 当$ {\varGamma _{{\text{LES}}}} $位于剪切层小尺度K-H不稳定性结构发生区域外且在对数律层内时, 相关流场统计量的数值结果
Table 5. Numerical results for flow statistic characteristics when $ {\varGamma _{{\text{LES}}}} $ is located in the log-law layer and outside the K-H instability region of the shear layer.
$ {\varGamma _{{\text{RANS}}}} $ $ {\varGamma _{{\text{LES}}}} $ $ {\bar f_{{\text{vs}}}} $ ${\bar f_{{\text{kh}}}}$ $ {\phi _{\text{s}}}/({\, ^ \circ }) $ $ L_{\text{r}}/D $ $ {C_{\text{d}}} $ $ - {C_{{\text{pb}}}} $ 形状 $ {r_{{\text{k1}}}} $ $ y_{{\text{RANS}}}^ + $ $ {r_{{\text{k2}}}} $ $ y_{{\text{LES}}}^{+} $ 0.9302 7.9 0.2546 49.2 0.220 1.50 87.8 1.20 1.13 1.05 V 0.6364 13.3 0.224 1.51 87.3 1.26 1.12 1.02 V 0.5951 14.9 0.221 1.4 86.7 1.45 1.13 0.98 U 0.4923 18.4 0.224 1.34 87.7 1.18 1.11 1.06 V 0.4635 20.4 0.223 1.43 87.0 1.36 1.11 0.99 U 0.3898 27.1 0.220 1.40 87.7 1.22 1.16 1.04 V 0.3134 38.4 0.222 1.20 87.3 1.26 1.10 1.01 V 0.2973 41.7 0.226 1.13 86.4 1.49 1.08 0.96 U 0.9302 7.9 0.1983 72.7 0.222 1.26 87.2 1.25 1.13 1.02 V 0.6364 13.3 0.223 1.07 86.6 1.44 1.10 0.97 U 0.5951 14.9 0.221 1.39 86.8 1.36 1.11 0.98 U 0.4923 18.4 0.222 1.34 88.1 1.07 1.17 1.10 V 0.4635 20.4 0.22 1.41 88.0 1.16 1.14 1.06 V 0.3898 27.1 0.224 1.34 87.1 1.36 1.11 1.00 U 0.3134 38.4 0.224 1.17 87.8 1.23 1.11 1.03 V 0.2973 41.7 0.224 1.07 86.5 1.50 1.09 0.95 U 0.2546 49.2 0.224 1.13 87.0 1.34 1.11 0.99 U 0.9302 7.9 0.1713 84.6 0.22 1.52 86.5 1.50 1.09 0.97 U 0.6364 13.3 0.221 1.12 86.9 1.25 1.11 0.99 V 0.5951 14.9 0.223 1.45 87.1 1.26 1.12 1.00 V 0.4923 18.4 0.22 1.34 87.5 1.17 1.17 1.04 V 0.4635 20.4 0.22 1.32 87.9 1.16 1.14 1.06 V 0.3898 27.1 0.224 1.33 86.9 1.41 1.11 0.98 U 0.3134 38.4 0.222 1.15 87.0 1.32 1.11 1.00 U 0.2973 41.7 0.223 1.15 87.8 1.16 1.14 1.05 V 0.2546 49.2 0.223 1.27 87.2 1.35 1.13 1.00 U 0.1983 72.7 0.222 1.22 87.8 1.16 1.14 1.05 V
DownLoad: CSV
表 6 当$ {\varGamma _{{\text{LES}}}} $位于过渡层时, 相关流场统计量的数值结果
Table 6. Numerical results for flow statistic characteristics when $ {\varGamma _{{\text{LES}}}} $ is located in the buffer layer.
$ {\varGamma _{{\text{RANS}}}} $ $ {\varGamma _{{\text{LES}}}} $ $ {\bar f_{{\text{vs}}}} $ ${\bar f_{{\text{kh}}}}$ $ {\phi _{\text{s}}}/({\, ^ \circ }) $ $ {{{L_{\text{r}}}} \mathord{\left/ {\vphantom {{{L_{\text{r}}}} D}} \right. } D} $ $ {C_{\text{d}}} $ $ - {C_{{\text{pb}}}} $ 形状 $ {r_{{\text{k1}}}} $ $ y_{{\text{RANS}}}^ + $ $ {r_{{\text{k2}}}} $ $ y_{{\text{LES}}}^{+} $ 0.9302 7.9 0.7333 10.4 0.222 1.48 87.9 1.13 1.12 1.06 V 0.9302 7.9 0.6364 13.3 0.225 1.44 87.6 1.19 1.12 1.02 V 0.7333 10.4 0.217 1.45 87.9 1.15 1.13 1.05 V 0.9302 7.9 0.5235 18.4 0.223 1.32 87.3 1.29 1.14 1.01 V 0.7333 10.4 0.221 1.37 86.9 1.37 1.08 0.99 U 0.5951 14.9 0.225 1.45 87.0 1.39 1.08 0.99 U 0.9302 7.9 0.4635 20.4 0.221 1.44 87.0 1.37 1.12 1.00 U 0.7333 10.4 0.219 1.34 87.6 1.16 1.13 1.03 V 0.5951 14.9 0.224 1.44 87.5 1.25 1.12 1.02 V 0.5235 18.4 0.224 1.47 86.4 1.46 1.12 0.96 U 0.9302 7.9 0.3687 29.6 0.224 1.48 87.4 1.27 1.13 1.02 V 0.5951 14.9 0.224 1.48 87.7 1.24 1.03 1.14 V 0.4635 20.4 0.218 1.40 88.0 1.08 1.08 1.15 V 0.3898 27.1 0.221 1.40 87.1 1.36 1.12 1.00 U
DownLoad: CSV
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[1] Zdravkovich M M 1997 Flow Around Circular Cylinders (Vol. 120) (Oxford: Oxford Science Publication) pp2–7
[2] Pereira F S, Eça L, Vaz G, Girimaji S S 2018 J. Comput. Phys. 363 98
Google Scholar
[3] Prasad A, Williamson C H K 1996 Phys. Fluids 8 1347
Google Scholar
[4] Williamson C H K 1988 Phys. Fluids 31 3165
Google Scholar
[5] Palkin E, Mullyadzhanov R, Hadžiabdić M, Hanjalić K 2016 Flow Turbul. Combust. 97 1017
Google Scholar
[6] Xia M, Karniadakis G E 1997 Proceedings of the First AFOSR International Conference on DNS/LES Ruston, LA, August 4–8, 1997 p129
[7] Ma X, Karamanos G S, Karniadakis G E 2000 J. Fluid Mech. 410 29
Google Scholar
[8] Tremblay F 2001 Ph. D. Dissertation (Munich: Technical University of Munich
[9] Dong S, Karniadakis G E, Ekmekci A, Rockwell D 2006 J. Fluid Mech. 569 185
Google Scholar
[10] Lehmkuhl O, Rodr´ıguez I, Borrell R, Chiva J, Oliva A 2013 Phys. Fluids 25 085109
Google Scholar
[11] Song B Y, Ping H, Zhu H B, Zhou D, Bao Y, Cao Y, Han Z L 2022 Phys. Fluids 34 15109
Google Scholar
[12] Ooi A, Lu W, Chan L, Cao Y, Leontini J, Skvortsov A 2022 Int. J. Heat Fluid Flow 96 108982
Google Scholar
[13] Kim S E 2012 44th AIAA Aerospace Sciences Meeting and Exhibit Reno, Nevada, January 9–12, 2006 p1418
[14] Beaudan P, Moin P 1994 Numerical Experiments on the Flow Past a Circular Cylinder at Sub-critical Reynolds Number (Stanford: Stanford University) p57
[15] Breuer M 1998 Int. J. Numer. Methods Fluids 28 1281
Google Scholar
[16] Kravchenko A G, Moin P 2000 Phys. Fluids 12 403
Google Scholar
[17] Franke J, Frank W 2002 J. Wind Eng. Ind. Aerodyn. 90 1191
Google Scholar
[18] Parnaudeau P, Carlier J, Heitz D, Lamballais E 2008 Phys. Fluids 20 085101
Google Scholar
[19] Wong J, Png E 2010 Adv. Fluid Mech. 8 79
Google Scholar
[20] Afgan I, Kahil Y, Benhamadouche S, Sagaut P 2011 Phys. Fluids 23 075101
Google Scholar
[21] Lysenko D A, Ertesvåg I S, Rian K E 2012 Flow Turbul. Combust. 89 491
Google Scholar
[22] Tian G, Xiao Z 2020 AIP Adv. 10 85321
Google Scholar
[23] 郭志远, 虞培祥, 欧阳华 2021 上海交通大学学报 55 924
Guo Z Y, Yu P X, Ouyang H 2021 J. Shanghai Jiaotong Univ. Sci. 55 924
[24] Luo D H, Yan C, Liu H K, Zhao R 2014 J. Wind Eng. Ind. Aerodyn. 134 65
Google Scholar
[25] 刘跃, 管小荣, 徐诚 2019 空气动力学学报 37 530
Google Scholar
Liu Y, Guan X R, Xu C 2019 Acta Aero. Sin. 37 530
Google Scholar
[26] Kořínek T, Tisovský T, Fraňa K 2021 Int. J. Therm. Sci. 169 106977
Google Scholar
[27] Lourenco L M, Shih C 1993 Characteristics of the Plane Turbulent Near-wake of a Circular Cylinder, A Particle Image Velocimetry Study (Data Taken From Beaudan and Moin, 1994
[28] Spalart P R 2000 Int. J. Heat Fluid Flow 21 252
Google Scholar
[29] Fröhlich J, Von Terzi D 2008 Prog. Aerosp. Sci. 44 349
Google Scholar
[30] D'Alessandro V, Montelpare S, Ricci R 2016 Comput. Fluids 136 152
Google Scholar
[31] Gritskevich M S, Garbaruk A, Schütze J, Menter F R 2012 Flow Turbul. Combust. 88 431
Google Scholar
[32] Menter F R, Kuntz M, Langtry R 2003 Turbul. Heat Mass Transf. 4 625
[33] Spalart P R, Deck S, Shur M L, Squires K D, Strelets M K, Travin A 2006 Theor. Comput. Fluid Dyn. 20 181
Google Scholar
[34] Shur M L, Spalart P R, Strelets M K, Travin A K 2008 Int. J. Heat Fluid Flow 29 1638
Google Scholar
[35] Johansen S T, Wu J, Shyy W 2004 Int. J. Heat Fluid flow 25 10
Google Scholar
[36] Breuer M, Jovičić N, Mazaev K 2003 Int. J. Numer. Methods Fluids 41 357
Google Scholar
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