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 Jakirlic and Hanjalic (2002) for incompressible single-phase flows. Two different RSM versions ( Jakirlic and Maduta, 2015 ), both based on the homogeneous dissipation ( e h ) concept that employs the specific dissipation rate ( ω h = e h / 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 - e 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.

中文翻译：

---

由尺度分辨雷诺应力模型计算的方形截面气泡柱中的湍流

摘要 本研究的重点是在非稳态雷诺平均纳维-斯托克斯 (Unsteady Reynolds-averaged Navier-Stokes) 中，利用双流体模型 (TFM) 结合先进的雷诺应力模型 (RSM)，计算方形截面气泡柱中的湍流。 URANS) 框架。将这种先进的建模方法与 TFM 结合使用，很少用于两相流计算，其动机是其解决雷诺应力各向异性和应力耗散各向异性以及相应残余湍流的固有能力。目前采用的 RSM 是基于最初由 Jakirlic 和 Hanjalic (2002) 提出的不可压缩单相流的公式。两个不同的 RSM 版本（Jakirlic 和 Maduta，2015），两者都基于均质耗散 (eh) 概念，该概念采用特定耗散率 (ω h = eh / k ) 作为长度尺度决定变量，在当前工作中得到应用。基线模型版本是在传统的 RANS 框架内制定的，而高级模型代表了一种对不稳定敏感、涡旋分辨的 RSM 变体，能够根据提出的 SAS 方法（尺度自适应模拟）充分捕捉波动的湍流运动。 Menter 和 Egorov (2010)。两个 RSM 获得的结果与 Deen 及其同事提供的相应实验数据库一起讨论 (Deen et al., 2000, 2001; Deen, 2001)。此外，最广泛使用的两相流建模方法是利用标准高雷诺数 k - e 模型进行比较评估。此外，两个 RANS 模型都通过两个不同的模型项提议进行扩展，用于解释所谓的气泡引起的湍流 (BIT)。基于非结构化网格上的有限体积方法，模型方程被实现到开源软件 OpenFOAM® 中。获得的结果与实验参考高度一致，表明两种雷诺应力模型在计算气泡流方面的潜力很大。这特别涉及在这种气泡羽流引起的不稳定流动事件中相应捕获的解析湍流强度，随后导致正确返回的速度场。平均流量不对称，