Abstract A two-fluid model in the Eulerian-Eulerian framework has been implemented for the turbulent gas-liquid bubbly upward flow in a vertical pipe. The transport equations, i.e. Reynolds-Averaged Navier-Stokes equations for the two-fluid model, are discretized using the finite volume method. The effect of the disperse gas phase on the liquid phase turbulence, referred to as turbulence modulation, was accounted for through source terms in the transport equations for a low Reynolds number k - e turbulence closure. The model was used to predict the turbulence kinetic energy and its dissipation rate, mean phasic velocities and volume fraction distribution for a set of test cases selected from the available literature. The focus of the present study was on assessing the model predictions using measurements of the turbulence kinetic energy of the liquid phase. A relatively novel aspect of the present analysis is the use of the budgets of the transport equations for the turbulence kinetic energy and dissipation rate to assess the effect of the turbulence modulation on the liquid turbulence field. Although the present model formulation is shown to adequately predict the effect of bubbles in some flows and perform better than some of the other model formulations, the overall conclusion is that the present approaches for incorporating turbulence modulation are at best partially successful and still need further development.

中文翻译：

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模拟垂直管道中气液气泡流动的气泡诱导湍流

摘要 针对垂直管道中湍流的气液气泡向上流动，实现了欧拉-欧拉框架下的二流体模型。传输方程，即二流体模型的雷诺平均纳维-斯托克斯方程，使用有限体积方法离散化。分散气相对液相湍流的影响，称为湍流调制，通过低雷诺数 k-e 湍流闭合的传输方程中的源项来解释。该模型用于预测从现有文献中选择的一组测试案例的湍流动能及其耗散率、平均相速度和体积分数分布。本研究的重点是使用液相湍流动能的测量来评估模型预测。本分析的一个相对新颖的方面是使用湍流动能和耗散率的传输方程的预算来评估湍流调制对液体湍流场的影响。尽管目前的模型公式已被证明可以充分预测某些流动中气泡的影响，并且比其他一些模型公式表现得更好，但总体结论是，目前结合湍流调制的方法至多是部分成功的，仍需要进一步发展. 本分析的一个相对新颖的方面是使用湍流动能和耗散率的传输方程的预算来评估湍流调制对液体湍流场的影响。尽管目前的模型公式已被证明可以充分预测某些流动中气泡的影响，并且比其他一些模型公式表现得更好，但总体结论是，目前结合湍流调制的方法至多是部分成功的，仍需要进一步发展. 本分析的一个相对新颖的方面是使用湍流动能和耗散率的传输方程的预算来评估湍流调制对液体湍流场的影响。尽管目前的模型公式已被证明可以充分预测某些流动中气泡的影响，并且比其他一些模型公式表现得更好，但总体结论是，目前结合湍流调制的方法至多是部分成功的，仍需要进一步发展.