Fluid-structure Interaction Simulation and Data-driven Modeling of Tube Bundle Based on OpenFOAM
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摘要: 为实现开源工具OpenFOAM在管束流固耦合行为预测方面的应用，针对OpenFOAM缺乏大涡模拟验证的综合基准案例、缺乏基于OpenFOAM仿真数据的参数辨识方法和数据驱动建模方法问题，首先通过研究基准问题来定量比较OpenFOAM中大涡模拟的性能，重点讨论统计时间长度、计算域大小与形状、网格划分方式、壁面函数对结果的影响规律，并将数值结果与实验数据进行验证，获得了合理的流场分析模型；然后，将运动方程与流场计算相耦合，求解具有移动边界的非定常Navier-Stokes(uRANS)方程，实现管束的流固耦合仿真，成功捕捉到了管束的流固耦合特征，并以流管模型为例，实现了关键参数辨识和数据驱动建模。结果表明，大涡模拟中，达到统计收敛至少需180个漩涡脱落周期；升力、回流长度对网格分辨率较为敏感，漩涡脱落频率、圆柱表面压力对计算域较为敏感；对于尾流区的统计量分布，网格分辨率的影响更为显著；计算域形状的影响可以忽略；通过数据驱动建模方式计算的临界流速与实验值吻合较好。Abstract: In order to realize the application of open-source tool OpenFOAM in the prediction of tube bundle fluid-structure interaction, in view of the lack of comprehensive benchmark cases for large eddy simulation verification in OpenFOAM, the lack of parameter identification methods and data-driven modeling methods based on OpenFOAM simulation data, this study first quantitatively compares the performance of large eddy simulation in OpenFOAM by studying benchmark problems, focusing on the effects of statistical time length, size and shape of calculation domain, meshing method, and wall function on the results, and verifies the numerical results with experimental data to obtain a reasonable flow field analysis model; Then, this study couples the motion equation with the flow field calculation, solves the unsteady Navier-Stokes (uRANS) equation with moving boundary, realizes the fluid-structure interaction simulation of the tube bundle, and successfully captures the fluid-structure interaction characteristics of the tube bundle. Taking the flow-cell model as an example, this study realizes the key parameter identification and data-driven modeling. The results show that at least 180 vortex shedding cycles are required to achieve statistical convergence in large eddy simulation; The lift and recirculation length are sensitive to the grid resolution, while the vortex shedding frequency and cylinder surface pressure are sensitive to the calculation domain; For the statistical distribution of the wake zone, the effect of grid resolution is more significant, the effect of the shape of the calculation domain can be ignored, and the critical velocity calculated by data-driven modeling is in good agreement with the experimental data.
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Key words:
- Fluid-structure interaction /
- Large eddy simulation /
- OpenFOAM /
- Tube bundle
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图 2 流体力系数的主要统计量随统计时间长度的变化
T为漩涡脱落周期
Figure 2. Variation of Main Statistics of Fluid Force Coefficient with Statistical Time Length
图 3 平均流动参数随网格的变化情况
$ {\overline \theta _{\text{s}}} $—分离角；$ - {\overline C_{{\text{pb}}}} $—背压系数负值；$ {\overline u_{{\text{min}}}} $—尾流中心线上平均流向速度的最小值；$ {\overline L_{\text{r}}} $—回流长度。
Figure 3. Variation of Average Flow Parameters with Grid
图 7 不同x/D截面上的
$ \bar u/{U_0} $ x—流向坐标；y—横流方向坐标图例说明：实验数据：
—Lourenco 和 Shih； —Parnaudeau；数值结果： —网格 1； —网格 2； —网格 3； —网格 4 (图 8 图例同此) Figure 7.
$\bar u/{U_0} $ on Different x/D Sections
图 8 不同x/D截面上的
$ \overline {u'u'}/U^2 $ Figure 8.
$ \overline {u'u'} /U^2$ on Different x/D Sections
图 10 临界流速预测结果与实验结果的对比
Figure 10. Comparison between Predicted and Experimental Results of Critical Velocity
表 1 网格细节
Table 1. Details of Grid
网格 Lx Ly Nc Nz NT/106 网格1 20D 10D 316 32 1.13 网格2 20D 10D 316 48 3.94 网格3 40D 20D 316 32 2.40 网格4 40D 20D 316 32 5.27 Nc—圆柱周向网格数；Nz—展向网格数；NT—总网格单元数 
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表 2 壁面函数对结果的影响
Table 2. Effects of Wall Function on Results
工况 字典nut ${\overline C_{\text{d} } }$ $ {C_{{\text{d,Ku}}}} $ $ {C_{{\text{lRMS}}}} $ $ {C_{{\text{l,Ku}}}} $ 工况1 nutkWallFunction 1.01 4.24 0.073 3.04 工况2 nutUWallFunction 1.02 4.68 0.081 3.21 工况3 nutUSpaldingWallFunction 1.04 4.34 0.090 3.60 工况4 fixedValue 1e-10 1.02 3.88 0.081 3.30
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表 3 计算域形状的影响
Table 3. Effects of Calculation Domain Type
计算域形状 ${\overline C_{\text{d} } }$ $ {C_{{\text{d,Ku}}}} $ $ {C_{{\text{lRMS}}}} $ St $ {C_{{\text{l,Ku}}}} $ 矩形域 1.01 4.24 0.073 0.21 3.04 圆形域 0.98 4.51 0.083 0.21 3.35
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