Abstract The void fraction is a key parameter of the two-phase flow in vertical downward pipes, particularly for calculating the mixture density, mixture velocity, mixture viscosity, heat transfer coefficient, and pressure gradient of the flow. Studies on two-phase flows have focused primarily on vertical upward and horizontal pipe flows, while vertical downward pipe flows have been largely neglected. Compared with the flow characteristics of the gas–liquid two-phase flow in upward pipes, those of a downward pipe flow are more complex under the interaction of the gravity, buoyancy, and inertial forces. In this study, a detailed experimental analysis of the void fraction of the gas–liquid two-phase flow in a vertical downward pipe was conducted with a pipe having an inner diameter of 20 mm. A total of 171 void-fraction data points were measured using the quick-closing valve method, and the performances of 12 commonly used correlations that do not take into consideration the flow pattern were assessed based on experimental data points. Errors were obtained on using some of the correlations for calculating the void fraction of the gas–liquid two-phase. flow in a vertical downward pipe at a low liquid superficial velocity. These models will regularly produce errors in the calculation of the void fraction, mainly because this problem is outside the scope of their application. In addition, a new model that takes into consideration the flow pattern was established based on the drift flux model; this new model overcomes the deficiencies of the conventional correlations in the calculation of the void fraction of the gas–liquid two-phase flow in vertical downward pipes at a low liquid superficial velocity. The reliability of the new method and 12 conventional correlations was assessed using 243 published data points. The mean relative errors of these correlations ranged from −21.65% to 8.65%, and the average absolute errors ranged from 8.57% to 23.17%. The results of the proposed method fit the experimental data in the literature better than those of the 12 existing correlations; the average relative error was −2.80%, and the average absolute error was 6.49%. The proposed model thus improves the prediction of void fractions of the gas–liquid two-phase flow in downward pipes.

中文翻译：

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垂直向下管道气液两相流实验研究及空隙率计算新方法

摘要 空隙率是垂直向下管道两相流动的一个关键参数，尤其是计算流体的混合物密度、混合物速度、混合物粘度、传热系数和压力梯度的关键参数。对两相流的研究主要集中在垂直向上和水平管流，而垂直向下管流在很大程度上被忽视了。与向上管道中气液两相流的流动特性相比，向下管道中的流动特性在重力、浮力和惯性力的共同作用下更为复杂。在这项研究中，使用内径为 20 mm 的管道对垂直向下管道中气液两相流的空隙率进行了详细的实验分析。使用快闭阀法测量了总共 171 个空隙率数据点，并基于实验数据点评估了 12 个不考虑流型的常用相关性的性能。使用一些相关性计算气液两相的空隙率时会出现错误。在垂直向下的管道中以低液体表观速度流动。这些模型在计算空隙率时会经常产生错误，主要是因为这个问题超出了它们的应用范围。此外，在漂移通量模型的基础上建立了考虑流型的新模型；这种新模型克服了传统相关式在低液体表观速度下垂直向下管道中气液两相流的空隙率计算中的不足。使用 243 个已发布的数据点评估了新方法和 12 个传统相关性的可靠性。这些相关性的平均相对误差范围为 -21.65% 至 8.65%，平均绝对误差范围为 8.57% 至 23.17%。所提出的方法的结果比现有的12个相关性更好地拟合了文献中的实验数据；平均相对误差为-2.80%，平均绝对误差为6.49%。因此，所提出的模型改进了对向下管道中气液两相流的空隙率的预测。使用 243 个已发布的数据点评估了新方法和 12 个传统相关性的可靠性。这些相关性的平均相对误差范围为 -21.65% 至 8.65%，平均绝对误差范围为 8.57% 至 23.17%。所提出的方法的结果比现有的12个相关性更好地拟合了文献中的实验数据；平均相对误差为-2.80%，平均绝对误差为6.49%。因此，所提出的模型改进了对向下管道中气液两相流的空隙率的预测。使用 243 个已发布的数据点评估了新方法和 12 个传统相关性的可靠性。这些相关性的平均相对误差范围为 -21.65% 至 8.65%，平均绝对误差范围为 8.57% 至 23.17%。所提出的方法的结果比现有的12个相关性更好地拟合了文献中的实验数据；平均相对误差为-2.80%，平均绝对误差为6.49%。因此，所提出的模型改进了对向下管道中气液两相流的空隙率的预测。所提出的方法的结果比现有的12个相关性更好地拟合了文献中的实验数据；平均相对误差为-2.80%，平均绝对误差为6.49%。因此，所提出的模型改进了对向下管道中气液两相流的空隙率的预测。所提出的方法的结果比现有的12个相关性更好地拟合了文献中的实验数据；平均相对误差为-2.80%，平均绝对误差为6.49%。因此，所提出的模型改进了对向下管道中气液两相流的空隙率的预测。