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 引用本文: 韦志龙, 蒋勤. 基于WENO-THINC/WLIC模型的水气二相流数值模拟[J]. 力学学报, 2021, 53(4): 973-985.
Wei Zhilong, Jiang Qin. NUMERICAL STUDY ON WATER-AIR TWO-PHASE FLOW BASED ON WENO-THINC/WLIC MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 973-985.
 Citation: Wei Zhilong, Jiang Qin. NUMERICAL STUDY ON WATER-AIR TWO-PHASE FLOW BASED ON WENO-THINC/WLIC MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 973-985.

## NUMERICAL STUDY ON WATER-AIR TWO-PHASE FLOW BASED ON WENO-THINC/WLIC MODEL

• 摘要: 水气二相流与诸多领域的实际工程问题密切相关. 对二相流运动进行高精度的数值模拟是计算流体力学研究的难点和热点. 针对开敞水域的自由表面流运动问题, 将水和空气均视为不可压缩流体, 采用五阶加权基本无震荡(weighted essentially non-oscillatory, WENO)格式求解描述流体运动的纳维斯托克斯(Navier-Stokes, NS)方程, 利用以加权线性界面算法改进的多维双曲正切函数界面捕捉法(tangent of hyperbola for interface capturing with weighed line interface calculation, THINC/WLIC)追踪水气界面, 建立WENO-THINC/WLIC水气二相流运动数值模型. 模型采用分步计算法离散求解控制方程, 通过压力投影法求解压强场, 并利用三阶总变差递减(total variation diminishing, TVD)龙格库塔(Runge-Kutta, RK)法对时间项进行离散求解. 通过对环境速度场下Zalesak's disk和shearing vortex界面运动问题, 线性液舱晃荡问题以及溃坝问题的模拟结果与理论分析或试验结果的比较, 对所建立的水气二相流数值模型的适用性及模拟精度进行了验证. 结果表明, 本模型的模拟结果与物理模型或理论分析结果吻合良好, 能较为准确地再现不可压缩水气二相流运动现象. 鉴于WENO格式和THINC法本身在算法及应用等方面仍在不断改进, 本研究提出的WENO-THINC耦合模型为后续更高精度的二相流计算模型开发提供了一种研究思路.

Abstract: Water-air two-phase flow can be found in many practical engineering projects in various fields. To simulate water-air two-phase flow with high accuracy has always been a challenging problem and a highlight in the realm of computational fluid dynamics. Based on the assumption that both water and air can be considered as incompressible fluid, for free surface flow in open water areas, the WENO-THINC/WLIC model for water-air two-phase flow is therefore established. In the developed model, the fifth-order accurate weighted essentially non-oscillation (WENO) scheme is used to solve the Navier-Stokes equation for fluid flows, and the improved multi-dimensional tangent of hyperbola for interface capturing scheme with weighted line interface calculation method (THINC/WLIC) is adopted to track the interface. The fractional step method is applied to discretize and solve the governing equations, the pressure projection method is adopted to compute the pressure field, and the third-order accurate total variation diminishing (TVD) Runge-Kutta (RK) method is used to discretize the temporal terms. In order to verify the model, it is applied to simulate two benchmarks of interface evolution subjected to an external velocity field, Zalesak's disk and shearing vortex, the linear sloshing, and the dam-breaking flow problem. Through comparison of the simulated results with the analytical or experimental ones, adaptability and accuracy of the water-air two-phase model are discussed. The analysis indicates that the simulation outputs are in good accordance with theoretical or experimental results, which means the model is capable to simulate incompressible water-air two-phase flows. With the further improved WENO schemes and THINC schemes, more precise prediction results for water-air two phase flow problems can be achieved with the proposed combined WENO-THINC model.

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