Numerical methods for multi-scale interfacial flows

Abstract

Fluid-fluid interfaces are omnipresent in nature as well as in industrial processes. Yet, the understanding and modelling of their behaviour is limited. The main challenges associated with the numerical modelling of interfacial flows lie in the accurate transport of the fluid-fluid interface and in the stable discrete treatment of surface tension. Numerous numerical methods have been developed to address these issues, however most available methods are specific to Cartesian meshes. Additionally, the multi-scale behaviour of interfacial flows of practical importance is a limiting factor in their modelling, since requiring prohibitively large simulation meshes.

In order to improve the accuracy and stability of interfacial flow simulations on unstructured meshes, two novel methods for the estimation of curvature are presented. The first method relies on the reconstruction of a triangulated interface, from which curvature is estimated using an adaptive fitting approach in conjunction with a partition of unity approximation technique. The second method requires to solve for local volume-fraction-based parabolic reconstruction problems, and extends the height-function curvature evaluation method to unstructured meshes. This method is shown to produce convergent curvature estimations on unstructured meshes, and exhibits a stable behaviour with regard to parasitic currents.

To reduce the costs associated with the modelling of multi-scale interfacial flows, such as atomising sprays, a hybrid Eulerian-Lagrangian method is presented. An interface-capturing scheme is employed to accurately resolve the interface in the primary atomisation region, whereas small liquid elements are tracked using Lagrangian particle tracking. The method relies on a filtering approach, which is shown to allow a consistent modelling of Lagrangian droplets with arbitrary particle diameter to cell size ratios. The hybrid method is applied to a realistic spray atomisation case, and its impacts on the interface dynamics and spray statistics is studied.