The standard Euler-Euler model is based on the phase-averaging method and each bubble force is a function of the local gas volume fraction. As a result, the coherent motion of each bubble as a whole is not enforced when the bubble diameter is larger than the size of a computational cell. However, the bubble force models are typically developed by tracking the bubbles’ centers of mass and assuming that the forces act on these locations. In simulations, this inconsistency can lead to a nonphysical gas concentration in the center or near the wall of a channel when the bubble diameter is larger than the cell size. Besides, a mesh-independent solution may not exist in such cases.

In the present contribution, a particle-center-averaging method is used to average the solution variables for the disperse phase, which allows to represent the bubble forces as forces that act on the bubbles’ centers of mass. An Euler-Euler approach for bubbly flow simulation is formed by combining this averaging method with a Gaussian convolution method to represent the spatial extent of the bubbles. The remediation of the inconsistency in the standard Euler-Euler model by the particle-center-averaging method is demonstrated using a simplified two-dimensional test case. The test results illustrate that the particle-center-averaging method can recover the bubble force consistency and provide mesh independent solutions. Furthermore, a comparison of the standard Euler-Euler model and the particle-center-averaged Euler-Euler model is shown for several bubbly pipe flow cases where experimental data are available. The results show that the particle-center-averaging method can alleviate the over-prediction of the gas volume fraction peaks for wall-peaking and finely dispersed flow cases. The gas velocities simulated by both approaches are similar.

标准 Euler-Euler 模型基于相位平均法，每个气泡力都是局部气体体积分数的函数。因此，当气泡直径大于计算单元的大小时，不会强制每个气泡作为一个整体的相干运动。然而，气泡力模型通常是通过跟踪气泡的质心并假设力作用在这些位置上来开发的。在模拟中，当气泡直径大于单元尺寸时，这种不一致会导致通道中心或通道壁附近出现非物理气体浓度。此外，在这种情况下可能不存在与网格无关的解决方案。

在目前的贡献中，粒子中心平均方法用于平均分散相的解变量，这允许将气泡力表示为作用在气泡质心上的力。通过将这种平均方法与高斯卷积方法相结合来表示气泡的空间范围，形成了一种用于气泡流模拟的 Euler-Euler 方法。使用简化的二维测试用例演示了通过粒子中心平均方法对标准 Euler-Euler 模型中的不一致性进行的补救。测试结果表明，粒子中心平均法可以恢复气泡力的一致性，并提供网格无关的解决方案。此外，标准 Euler-Euler 模型和粒子中心平均 Euler-Euler 模型的比较显示了几个有实验数据的气泡管流动情况。结果表明，粒子中心平均法可以缓解壁峰和细分散流情况下气体体积分数峰的过度预测。两种方法模拟的气体速度是相似的。