Hosseini Seyed Ali, Safari Hesameddin, Thevenin Dominique
Laboratory of Fluid Dynamics and Technical Flows, University of Magdeburg "Otto von Guericke", D-39106 Magdeburg, Germany.
Department of Mechanical and Process Engineering, ETH Zürich, 8092 Zürich, Switzerland.
Entropy (Basel). 2021 Jan 29;23(2):166. doi: 10.3390/e23020166.
The lattice Boltzmann method, now widely used for a variety of applications, has also been extended to model multiphase flows through different formulations. While already applied to many different configurations in low Weber and Reynolds number regimes, applications to higher Weber/Reynolds numbers or larger density/viscosity ratios are still the topic of active research. In this study, through a combination of a decoupled phase-field formulation-the conservative Allen-Cahn equation-and a cumulant-based collision operator for a low-Mach pressure-based flow solver, we present an algorithm that can be used for higher Reynolds/Weber numbers. The algorithm was validated through a variety of test cases, starting with the Rayleigh-Taylor instability in both 2D and 3D, followed by the impact of a droplet on a liquid sheet. In all simulations, the solver correctly captured the flow dynamics andmatched reference results very well. As the final test case, the solver was used to model droplet splashing on a thin liquid sheet in 3D with a density ratio of 1000 and kinematic viscosity ratio of 15, matching the water/air system at We = 8000 and Re = 1000. Results showed that the solver correctly captured the fingering instabilities at the crown rim and their subsequent breakup, in agreement with experimental and numerical observations reported in the literature.
格子玻尔兹曼方法目前已广泛应用于各种领域，并且还通过不同的公式扩展到对多相流进行建模。虽然该方法已应用于低韦伯数和雷诺数 regime 下的许多不同构型，但在更高的韦伯数/雷诺数或更大的密度/粘度比情况下的应用仍是活跃的研究课题。在本研究中，通过将解耦相场公式（保守的艾伦 - 卡恩方程）与基于累积量的碰撞算子相结合，用于基于低马赫压力的流动求解器，我们提出了一种可用于更高雷诺数/韦伯数的算法。该算法通过各种测试案例进行了验证，首先是二维和三维的瑞利 - 泰勒不稳定性，接着是液滴对液膜的撞击。在所有模拟中，求解器都正确地捕捉到了流动动力学，并且与参考结果非常吻合。作为最后的测试案例，该求解器用于对密度比为 1000 且运动粘度比为 15 的三维薄液膜上的液滴飞溅进行建模，这与韦伯数为 8000 且雷诺数为 1000 时的水/空气系统相匹配。结果表明，求解器正确地捕捉到了冠缘处的指状不稳定性及其随后的破碎，这与文献中报道的实验和数值观察结果一致。
