A particle-center-averaged Euler-Euler model for monodisperse bubbly flows

Abstract

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.