A-Priori Assessment of Interfacial Sub-grid Scale Closures in the Two-Phase Flow LES Context

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.

Computational and experimental study of an oil jet in crossflow: coupling population balance model with multifluid large eddy simulation

“…In contrast to single-phase LES, additional unclosed SGS terms including diffusive, temporal, surface tension and interfacial terms appear in the filtered form of the multifluid/multiphase LES equations (Saeedipour & Schneiderbauer 2019). The surface tension SGS term was the subject of several studies in the recent decade (Herrmann 2010;Liovic & Lakehal 2012;Saeedipour & Schneiderbauer 2019;Hasslberger, Ketterl & Klein 2020) that investigate the effect of SGS surface tension force on the interfacial flows through different approaches. The subgrid contribution of surface tension force is considered to be proportional to the resolved surface tension force as (Shirani, Jafari & Ashgriz 2006;Saeedipour & Schneiderbauer 2019;Hasslberger et al 2020)…”

“…where ν SGS is the subgrid eddy viscosity and C st is an empirically determined constant (Hasslberger et al 2020). There is not a well-established value for C st in the literature.…”

Sub-grid Scale Modelling and a-Posteriori Tests with a Morphology Adaptive Multifield Two-Fluid Model Considering Rising Gas Bubbles

“…The application of the scale similarity concept to this unclosed term is formulated in terms of explicit volume filtering. In contrast to that, the test filter could be applied based on the concept of surface filtering as well (Hasslberger et al 2020). However, this work focuses on volume-based filtering for the test filter operation.…”

“…Hence, it is possible to observe contributions of the SGS model force in such a large area. The distribution of SGS surface tension over the interfacial region is considered in more detail by Hasslberger et al (2020) in a-priori analysis. The Weber-number models We-KE-0.25 and We-Re reveal resulting model forces, which mainly appear at the lower side of the gas bubble acting in a direction, such that they counteract the curvature of the interface.…”

“…This procedure gives rise to numerous different unclosed terms in the so-called filtered Navier-Stokes equations. The influence of those terms has been assessed with a-priori investigations (Labourasse et al 2004(Labourasse et al , 2007Toutant et al 2006Toutant et al , 2008Toutant et al , 2009aVincent et al 2008;Larocque et al 2010;Chesnel et al 2011;Liovic and Lakehal 2007a;Klein 2016, 2018;Klein et al 2019;Mimouni et al 2017;Hasslberger et al 2020;Saeedipour et al 2019a;Saeedipour and Schneiderbauer 2019). In only a few investigations model formulations for those unclosed terms have been applied in actual multiphase simulations for a-posteriori model assessment Lakehal 2007a, b, 2012;Saeedipour et al 2019a, b;De Villiers et al 2004;Aniszewski et al 2012;Herrmann 2013Herrmann , 2015Ketterl et al 2019).…”