Abstract
Due to the continuous increase in available computing power, the Large Eddy Simulation (LES) of two-phase flows started to receive more attention in recent years. Well-established models from single-phase flows are often used to close the sub-grid scale convective momentum transport and recently some modifications have been suggested to account for the jump of density and viscosity at the interface of multi-phase flows. However, additional unclosed terms in multi-phase flows, which are absent in single-phase flows, often remain ignored. This paper focuses on the crucial gaps in literature, namely the modeling of volume fraction advection and surface tension effects on sub-grid level. An a-priori analysis has been conducted for this purpose, i.e. the Direct Numerical Simulation of an academic two-phase flow configuration (single wobbling bubble in a turbulent background flow) has been explicitly filtered (corresponding to implicit filtering in actual LES) for varying filter width and the corresponding sub-grid terms have been compared to potentially suitable model expressions. Besides other approaches, adequately formulated models based on the scale similarity principle emerged to be promising candidates for both sub-grid volume fraction advection as well as sub-grid surface tension effects. In this context, special attention has to be paid to the secondary filter. Owing to the nature of the quasi-singular surface tension term, surface-weighted filtering may be more appropriate and robust than standard volume filtering.
Highlights
Turbulent bubbly flows play an essential role in a large number of technical applications, e.g. for chemical reactors in the process industry
One of a few exceptions is the work of Aniszewski et al (2012) who applied the approximate deconvolution technique to sub-grid surface tension as it has originally been applied to turbulent stresses (Stolz and Adams 1999)
The closure of momentum advection (Eq 4) is of significant importance but a large variety of models is already available from single-phase flows that can be reasonably well modified for two-phase flows (Ketterl and Klein 2018)
Summary
Turbulent bubbly flows play an essential role in a large number of technical applications, e.g. for chemical reactors in the process industry. For all models based on the eddy viscosity concept ( related to the closure of momentum advection), another interesting approach (Saeedipour and Schneiderbauer 2019) accounts for unresolved interfacial work done by surface tension by adding a correction term to increase the turbulent viscosity at the interface. Using the concept of a critical grid-based Weber number, Ketterl et al (2019) recently introduced a sub-grid model which increases the surface tension coefficient depending on the local flow conditions and the local curvature of the interface to ensure a solution that can be well represented by the grid. The process of ligament stretching and rupture, or generally regions of high interface curvature, usually remain under-resolved in such cases In this work, both promising existing models as well as novel models are tested by means of a-priori analysis
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