Isogeometric analysis of multi-phase flows with surface tension and with application to dynamics of rising bubbles
Isogeometric analysis of multi-phase flows with surface tension and with application to dynamics of rising bubbles
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DOI：
10.1016/j.compfluid.2018.04.017
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发表时间：
2019-01
影响因子：
2.8
通讯作者：
Jinhui Yan;Stephen Lin;Y. Bazilevs;G. Wagner
中科院分区：
文献类型：
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作者：
Jinhui Yan;Stephen Lin;Y. Bazilevs;G. Wagner
提出了一种使用基于水平集的界面捕获方法的新型多相流公式，重点解决与表面张力建模相关的数值挑战。表面张力通过连续表面力模型处理。基于残差的变分多尺度 (RBVMS) 公式用于求解耦合纳维-斯托克斯方程和水平集对流方程。 RBVMS 公式使用标准低阶有限元或基于非均匀有理 B 样条 (NURBS) 的等几何分析 (IGA) 进行离散化，后者具有高阶精确性和平滑性。该方法适用于模拟具有大密度和粘度比的粘性液体中的 3D 气泡运动，代表常见的两相流系统。通过将结果与文献中报道的解析解、实验数据和计算结果进行比较来评估所提出方法的准确性。在所有情况下，IGA 都表现出优于标准有限元的性能；这一优势归因于 IGA 的高阶精度及其使用平滑 NURBS 函数直接准确计算曲率项的能力，曲率项是表面张力公式的关键成分。对于单气泡上升问题，所提出的方法可以准确预测终端气泡形状、速度和雷诺数。通过在存在变形自由表面的情况下模拟两个气泡的合并，证明了新的多相流公式的先进性。
A novel multi-phase flow formulation using a level-set-based interface-capturing approach is proposed, focusing on addressing numerical challenges associated with the modeling of surface tension. The surface tension is handled through the continuum surface force model. The residual-based variational multiscale (RBVMS) formulation is employed to solve the coupled Navier–Stokes and level-set convection equations. The RBVMS formulation is discretized using either standard low-order finite elements, or Isogeometric Analysis (IGA) based on Non-Uniform Rational B-Splines (NURBS), which are higher-order accurate and smooth. The proposed method is applied to the simulation of 3D bubbles moving in viscous liquids with large density and viscosity ratios representative of common two-phase flow systems. The accuracy of the proposed method is assessed by comparing the results with analytical solutions, experimental data, and computational results, reported in the literature. In all cases IGA showed superior performance to standard finite elements; this superiority is attributed to the higher-order accuracy of IGA and its ability to directly and accurately compute, using smooth NURBS functions, the curvature term, which is a key ingredient the surface tension formulation. For single-bubble rising problems, the proposed approach produced accurate predictions of the terminal bubble shape, velocity and Reynolds number. The advanced nature of the new multi-phase flow formulation is demonstrated with a simulation of merging of two bubbles in the presence of a deforming free-surface.