Turbulent flow in a square cross-sectioned bubble column computed by a scale-resolving Reynolds-stress model

Abstract

The present study focuses on the computations of turbulent flow in a square cross-sectioned bubble column by utilizing the two-fluid model (TFM) in conjunction with advanced Reynolds-stress models (RSMs) within the Unsteady Reynolds-averaged Navier–Stokes (URANS) framework. The use of such an advanced modeling approach in combination with the TFM, rarely employed for two-phase flow computations, is motivated by its inherent capability of resolving both Reynolds-stress anisotropy and stress-dissipation anisotropy, also of the corresponding residual turbulence. The presently adopted RSMs are based on the formulation proposed initially by Jakirlić and Hanjalić (2002) for incompressible single-phase flows. Two different RSM versions (Jakirlić and Maduta (2015)), both based on the homogeneous dissipation (εh) concept that employs the specific dissipation rate (ωh=εh/k) as the length-scale-determining variable, are applied in the present work. The baseline model version is formulated within the conventional RANS framework, whereas the advanced model represents an instability-sensitized, eddy-resolving RSM variant, capable of adequately capturing the fluctuating turbulent motion in accordance with the SAS methodology (Scale-Adaptive Simulation) proposed by Menter and Egorov (2010). The results obtained by both RSMs are discussed along with the corresponding experimental database made available by Deen and co-workers (Deen et al., 2000, 2001; Deen, 2001). Additionally, the most-widely used modeling approach for two-phase flows is followed by utilizing the Standard high-Reynolds number k-ε model for the purpose of a comparative assessment. Furthermore, both RANS models are extended by two different proposals for a model term accounting for the so-called bubble-induced turbulence (BIT). The model equations are implemented into the open source software OpenFOAM® based on the finite-volume method on unstructured meshes. The results obtained exhibit high level of agreement with the experimental reference demonstrating high potential of both Reynolds-stress models in computing the bubbly flows. This relates in particular to the correspondingly captured resolved turbulence intensity in this bubble-plume-induced unstable flow event, leading subsequently to a correctly returned velocity field. The mean flow asymmetry, characterizing the baseline Eddy-Viscosity Model (EVM) performance was remedied only after introducing the BIT-related source term contributing appropriately to intensified turbulence production.