Influence of subgrid-scale models on cavitation phenomenon around a 3D twisted hydrofoil
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摘要:
目的 旨在探究三维扭曲水翼空化数值模拟中网格密度及亚格子模型的适应性问题。 方法 为此，使用大涡模拟（LES）方法和Schnerr-Sauer（S-S）空化模型对Delft Twist11N三维扭曲水翼的非定常空化流场进行数值模拟，重点研究3套不同密度的网格和WMLES，SL，WALE这3种亚格子模型对Delft Twist11N水翼空化演变过程、空化脱落频率及时均升阻力系数等的影响。 结果 结果表明：适当的网格加密形式既能够捕捉到较多的细小空泡脱落、马蹄形云空泡的初生与溃灭等非定常空化演变现象，又能够获得具有较高精度的空泡脱落频率、时均升阻力系数和时均压力分布。相较于WMLES和SL亚格子模型， WALE亚格子模型较好地捕捉到了片空泡及云空泡的演变，在预报空泡脱落频率、时均升阻力系数及压力系数方面精度较优。 结论 因此，推荐采用基于WALE亚格子模型的LES方法进行非定常云状空化的数值模拟。 Abstract:Objective This paper aims to explore the suitability of mesh density and subgrid-scale model for the numerical simulation of three-dimensional twisted hydrofoil. Methods The large eddy simulation (LES) method and Schnerr-Sauer (S-S) cavitation model are used to simulate the unsteady cavitation flow of a Delft Twist11N three-dimensional twisted hydrofoil. Three sets of grid with different density and three types of different subgrid-scale models are mainly studied to identify the effects on the Twist11N hydrofoil cavitation evolution process, cavitation shedding frequency and time-averaged lift and drag coefficients. Results The results show that appropriate grid refinement can not only capture more unsteady cavitation evolution phenomena such as the shedding of smaller cavities and the inception and collapse of horse-shoe-shaped cloud cavities, but also obtain more exact cavity shedding frequency, time-averaged lift and drag coefficients, and time-averaged pressure distribution. Among the three subgrid-scale models, compared to the algebraic wall-modeled LES model (WMLES) and Smagorinsky-Lilly (SL) model, the wall-adapting local eddy-viscosity (WALE) model better captures the evolution of sheet and cloud cavitation, and has better accuracy in predicting the frequency of cavity shedding,time-averaged lift, drag and pressure coefficients. Conclusion It is recommended to adopt the LES method with the WALE subgrid-scale model for the numerical simulation of unsteady cloud cavitation. -
图 2 一半Twist11N水翼的计算域示意图
Figure 2. Schematics of computational domain for half-span of Twist11N hydrofoil
图 3 Twist11N水翼周围O型分块网格的划分形式
Figure 3. Grid scheme of the O-shaped block around Twist11N hydrofoil
图 5 不同网格模拟的空化演变过程与试验结果对比
Figure 5. Comparison of cavitation evolution by various grid schemes and experimental results
图 6 不同网格密度下计算的Lc/C值对比
Figure 6. Comparison of cavity length-chord ratio for various grid schemes
图 7 不同网格密度下一个周期内升力系数时历曲线
Figure 7. Time histories of the lift coefficients for various grid schemes in a shedding cycle
图 8 不同网格密度下一个周期内阻力系数时历曲线
Figure 8. Time histories of the drag coefficients for various grid schemes in a shedding cycle
图 9 YC=0.12 m展向位置处水翼表面
$\bar C_{\rm{p}}$ 的分布Figure 9. The time-averaged pressure distribution
$\bar C_{\rm{p}}$ around hydrofoil surface at YC=0.12 m
图 10 YC=0.15 m展向位置处水翼表面
$\bar C_{\rm{p}}$ 的分布Figure 10. The time-averaged pressure distribution
$\bar C_{\rm{p}}$ around hydrofoil surface at YC=0.15 m
图 11 不同亚格子模型计算的空泡脱落频率
Figure 11. Shedding frequency of cavity for various subgrid-scale models
图 12 不同亚格子模型模拟的空化演变过程与试验结果对比
Figure 12. Comparison of cavitation evolution by various subgrid-scale models and experimental results
图 13 不同亚格子模型计算的Lc/C值对比
Figure 13. Comparison of cavity length-chord ratios for various subgrid-scale models
图 14 YC=0.12 m展向位置处水翼表面
$\bar C_{\rm{p}}$ 的分布Figure 14. The time-averaged pressure distribution
$\bar C_{\rm{p}}$ around hydrofoil surface at YC=0.12 m
图 15 YC=0.15 m展向位置处水翼表面
$\bar C_{\rm{p}}$ 的分布Figure 15. The time-averaged pressure distribution
$\bar C_{\rm{p}}$ around hydrofoil surface at YC=0.15 m表 1 Twist11N水翼网格划分参数
Table 1. Grid parameters of Twist11N hydrofoil
网络编号 l1 l2 l3 l4 $ y_{\max }^ + $ $ \Delta x + $ G1 25 63 101 90 0.793 112 G2 30 75 120 90 0.789 94 G3 36 89 143 90 0.803 80 
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表 2 不同网格密度下时均升阻力系数计算结果的对比
Table 2. Numerical results of the time-averaged lift and drag coefficient for various grid schemes
项目 G1 G2 G3 LES[19] $100{\bar C_{\rm{D} } }$ 2.117 2.084 2.116 − $\bar C_{\rm{L}}$ 0.4412 0.4458 0.4503 0.4400 ${\bar C_{\rm{L} } } 误差/\text{%}$ −13.49 −12.59 −11.71 −13.73
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表 3 不同亚格子模型时均升阻力系数计算结果的对比
Table 3. Numerical results of the time-averaged lift and drag coefficients for various subgrid-scale models
项目 WALE WMLES SL LES[19] $100 {\bar C_{\rm{D} } }$ 2.084 2.582 2.564 − $\bar C_{\rm{L} }$ 0.4458 0.4156 0.3660 0.4400 ${\bar C_{\rm{L} }} 误差/\text{%}$ −12.59 −18.51 −28.24 −13.73
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