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A nonlinear PSE method for two-fluid shear flows with complex interfacial topology

机译：具有复杂界面拓扑的双流体剪切流的非线性PSE方法

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摘要

A nonlinear stability method is developed for laminar two-fluid shear flows which undergo changes in the interface topology. The method is based on the nonlinear parabolized stability equations (PSE) and incorporates a scalar-based interface capturing (IC) scheme in order to track complex deformations of the fluid interface. In doing so, the formulation retains the flexibility and physical insight of instability-wave based methods, while providing hydrodynamic modeling capabilities similar to direct numerical calculations: the new formulation, referred to as the IC-PSE, can capture the nonlinear physical mechanisms responsible for generating large-scale, two-fluid structures, without incurring heavy computational costs. This approach is valid for spatially developing, laminar two-fluid shear flows which are convectively unstable, and can naturally account for the growth of finite amplitude interfacial waves, along with changes to the interfacial topology. We demonstrate the accuracy of the IC-PSE against direct Navier-Stokes calculations for two-fluid mixing layers with density and viscosity stratification. The comparisons show that the IC-PSE can predict the dynamics of the instability waves and capture the formation of Kelvin-Helmholtz vortex rolls and large scale liquid structures, at an order of magnitude less computational cost than direct calculations. The role of surface tension in the IC-PSE formulation is shown to be valid for flows in which Re/We ? 1, and the method accurately predicts the formation and non-linear evolution of flow structures in this limit. This is demonstrated for spatially developing mixing layers which lead to vortex roll-up and ligaments, prior to droplet formation. The pinch-off process itself is a high surface tension phenomenon and in not considered herein. The method also accurately captures the effect of interfacial waves on the mean flow, and the topology changes during the non-linear evolution of the two-fluid structures.
机译：针对层状双流体剪切流的界面拓扑变化，开发了一种非线性稳定性方法。该方法基于非线性抛物线稳定性方程（PSE），并结合了基于标量的界面捕获（IC）方案，以便跟踪流体界面的复杂变形。这样，该公式保留了基于不稳定波的方法的灵活性和物理洞察力，同时提供了类似于直接数值计算的流体动力学建模功能：被称为IC-PSE的新公式可以捕获造成这种情况的非线性物理机制。生成大型的双流体结构，而不会产生大量的计算成本。这种方法适用于对流不稳定的空间发展的层流双流体剪切流，并且自然可以解释有限振幅界面波的增长以及界面拓扑的变化。我们证明了针对具有密度和粘度分层的两流体混合层，针对直接Navier-Stokes计算的IC-PSE的准确性。比较表明，IC-PSE可以预测不稳定性波的动力学并捕获开尔文-亥姆霍兹涡旋辊和大型液体结构的形成，其计算成本比直接计算要低一个数量级。研究表明，表面张力在IC-PSE配方中的作用对于其中Re / We？在图1中，该方法准确地预测了在该极限内的流动结构的形成和非线性演化。这在空间形成的混合层中得到证实，在液滴形成之前，混合层导致涡旋卷起和韧带形成。夹断过程本身是高表面张力现象，因此在本文中未考虑。该方法还可以准确地捕获界面波对平均流量的影响，并且拓扑结构在双流体结构的非线性演化过程中会发生变化。

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