一种改进的浸入运动边界算法

An improved algorithm for immersed moving boundary

  • 摘要: 浸入运动边界是数值处理流固耦合作用的主要方法之一,其原始权重函数根据经验确定且形式固定,难以准确地定量描述复杂的流固现象。本文提出了一种新的权重函数对格子Boltzmann方法框架下的浸入运动边界进行修正,通过假定零固含率处的权重因子多阶导数为0,引入可调参数b增强权重函数对固含率的关联,实现了对固体边界渗透性能的改进。对静止圆柱绕流、Taylor-Couette流和振动圆柱绕流3个算例开展数值实验,结果表明:随着雷诺数的增加,原始权重函数预测的升阻力系数均高于文献结果,严重低估了边界处流体组分的作用;当新权重函数中的参数b为3时,改进的浸入运动边界效果最佳;新权重函数增强了固体边界的渗透率,提高了流场的预测精度,使平均误差降低了38.5%;最后,运用新权重函数成功地复现了振动圆柱绕流的锁频现象,表明改进的浸入运动边界在处理复杂的流固耦合问题方面具有广阔的应用前景。

     

    Abstract: Immersed moving boundary is one of the important numerical methods for modeling fluid-structure interaction. However, its original weighting function to determine fluid-solid interaction is empirical and its form is fixed, which is difficult to predict complex fluid-structure phenomena accurately and quantitatively. In this study, a new weighting function is proposed to improve the immersed moving boundary in the framework of the lattice Boltzmann method. By assuming that the multi-order derivative of the weighting factor at zero solid volume fraction is 0, an adjustable parameter b is introduced to enhance the correlation between the weighting function and the solid volume fraction, which improves the permeability performance of the solid boundary. The new weighting function is tested against three benchmark cases namely, flow around a stationary cylinder, Taylor-Couette flow, and flow around an oscillating cylinder. Numerical results show that, with the increase of the Reynolds number, the lift-drag coefficients predicted by the original weighting function are higher than the literature results, which seriously underestimates the effect of fluid components at the boundary. In addition, when the parameter b in the new weighting function is 3, the effect of the improved immersed moving boundary is optimal. Furthermore, the new weighting function enhances the permeability of the solid boundary, improves the prediction accuracy of the fluid field, and reduces the averaged error up to 38.5%. Finally, the frequency-locking phenomenon encountered in flow around an oscillating cylinder is successfully reproduced by using the new weighting function, demonstrating the improved immersed moving boundary is promising in dealing with complex fluid-structure interaction problems.

     

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