Arbitrary Lagrangian-Eulerian Method for Two-Phase Flows - Applications
Encyclopedia of Two-Phase Heat Transfer and Flow III (World Scientific)
ABSTRACT:
A moving mesh method is presented for the numerical simulation of two-phase flows in 2D and axisymmetric geometries. The incompressible Navier–Stokes equations for two fluid phases are discretized with the finite element method (FEM) in the arbitrary Lagrangian–Eulerian (ALE) framework. In the context of the FEM, several triangular elements are described, which satisfy the inf-sup compatibility condition and can thus be employed for two-phase flow simulations without any additional stabilization terms. The interface between the phases is defined explicitly by an interface adapted mesh consisting of line segments, which are part of the unstructured triangular mesh. This allows for a sharp representation of the interface as a discontinuous transition region between the different fluids. Surface tension is modeled as a volume force and it is discretized in the same manner as the pressure gradient, thus allowing to fulfill an exact balance between these two terms. The important issue of suppressing parasitic currents in computational two-phase flow is addressed by showing that the present approach almost achieves this goal for a spherical droplet moving in a constant velocity field. An exact computation of the interface curvature is shown to be a necessity for the spurious currents to be numerically zero. The adaptive mesh technique developed to preserve mesh quality with the moving interface is described and mesh refinement strategies are also discussed. Accuracy and robustness of the present method are demonstrated on several test problems. Finally, an application of the method to a capillary two-phase flow is presented in the simulation of a slug flow in a microchannel, where the results are compared to experimental data.