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本文发展了一种具有壁面模化大涡模拟能力的雷诺平均纳维-斯托克斯 (RANS)和大涡模拟(LES)方法的混合模型(简称WM-HRL模型), 致力于对亚临界区雷诺数钝体绕流相干结构这类复杂流动现象进行高置信度的CFD解析模拟研究. 该方法通过一个仅与当地网格空间分布尺寸有关的湍动能解析度指标参数rk即可实现从RANS到LES的无缝快速转换, 并且RANS/LES混合转换区的边界位置及其各个分区(包括RANS区、LES区及RANS/LES混合转换区)对湍动能的解析能力均可通过两个指标参数
$ n{r_{{\text{k1-Q}}}} $ 和$ n{r_{{\text{k2-Q}}}} $ 准则进行预先设定. 通过对雷诺数Re = 3900下圆柱绕流场的系列数值模拟研究, 获得了能够高置信度解析并捕捉其绕流场中三维时空瞬态发展相干结构特性的湍动能解析度指标参数$ n{r_{{\text{k1-Q}}}} $ 和$ n{r_{{\text{k2-Q}}}} $ 准则的组合条件. 研究表明, 该WM-HRL模型不仅能够准确获取圆柱绕流场中剪切层小尺度K-H不稳定性结构的精细谱结构, 而且在同一套网格系统下通过变化湍动能解析度指标参数$ n{r_{{\text{k2-Q}}}} $ 和$ n{r_{{\text{k1-Q}}}} $ 准则的组合条件, 还可以精细解析圆柱绕流场中两类不同回流区的长度结构特征, 及其对应的圆柱尾部近壁面处V和U形两个平均流向速度剖面的分支结构特性.-
关键词:
- 圆柱绕流 /
- 相干结构 /
- Kelvin-Helmholtz不稳定性 /
- 混合RANS/LES模型
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.-
Keywords:
- flow around a cylinder /
- coherent structures /
- Kelvin-Helmholtz instability /
- hybrid RANS/LES model
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图 3 剪切层小尺度K-H不稳定性结构监测点分布
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 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 
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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
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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^ + } $值P1 (0.20, 0.560) 30.5 P2 (0.30, 0.572) 47.1 P3 (0.40, 0.584) 67.0 P4 (0.50, 0.595) 89.4 P5 (0.60, 0.607) 114.0 P6 (0.70, 0.619) 140.1 P7 (0.80, 0.631) 167.4 P8 (0.90, 0.643) 195.5 P9 (1.00, 0.655) 224.3 P10 (1.10, 0.666) 253.5 P11 (1.20, 0.678) 283.3 P12 (1.30, 0.690) 313.5 P13 (0.71, 0.660) 151.4 P14 (0.69, 0.520) 117.4 P15 (2.00, 0.590) 511.4 P16 (1.00, 0.0) 161.3 P17 (2.00, 0.0) 483.9 P18 (3.00, 0.0) 806.5
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表 4 当$ {\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
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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
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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
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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
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