Simulation models for unsteady dispersed multiphase flows

本文用一种新的数值方法研究了小气泡在开口容器底部以短时间间隔释放所引起的二维流动的早期演化。在本方法中，相对液体速度沿着气泡轨迹的变化被近似表示为分段线性，离散气泡的短时运动被描述为恒定流体加速度的完整Basset-Boussinesq-Oseen（B-B-O）方程的精确解。然后假设泡状流体是连续介质，其质量密度和粘度通过运动气泡的间歇存在而在空间和时间上发生波动，通过数值积分Navier-Stokes方程和连续性方程得到泡状流体的速度和压力。本研究提出的数值方法具有以下显著优点：使用B-B-O方程的精确解， ...更多信息 理论和CPU的时间需要数值分析大量气泡的运动。使用完整的B-B-O方程可以考虑历史对气泡行为的影响，这些影响由所谓的Basset项表示，并且由于其数值处理的困难而经常被忽视，没有任何共识。应用该方法对重力作用下二维方形截面容器内的瞬态泡状流进行了数值模拟。数值计算结果与实验结果的对比验证了该方法的有效性。在这个应用中，我们已经表明，整个流变得高度不对称和羽流表现出不稳定的曲折，当相对较小的气泡被释放，其安排是对称的相对于船舶中心线。此外，它是观察到的流动恢复其对称性和羽流稳定，如果我们引入相对较大的气泡到不稳定的上述流通过添加大的对称安排的小的。少

The early-time evolution of two-dimensional flows induced by rising small bubbles, which are released at short intervals on the bottom of an open vessel, has been examined by using a new numerical method. In the present method, the variation of the relative liquid velocity along bubble trajectories is approximately represented to be piecewise linear, and the short-time motion of discrete bubbles is described in terms of the exact solution to the full Basset-Boussinesq-Oseen (B-B-O) equation for constant fluid acceleration. Bubbly fluid is then assumed to be a continuum, the mass desity and the viscosity of which fluctuate in space and time via intermittent existence of moving bubbles, and the velocity and pressure of the bubbly fluid is obtained from numerical integration of the Navier-Stokes and continuity equations. The numerical method to be proposed in this study has the following significant advantages : The use of the exact solution to the B-B-O equation reduces both computer mem … More ory and CPU time necessary to numerically analyze the motion of a large number of bubbles. The use of the full B-B-O equation makes it possible to take into account the historical effects on bubble behavior, which are represented by the so-called Basset term and often neglected without any consensus for the difficulty in its numerical treatment. We applied this method to numerical simulations of the transient bubbly flow in a two-dimensional vessel of a square cross-section under the effect of the gravity. The validity of this method has been confirmed by comparing the numerical results with the experimental ones. In this application, we have shown that the whole flow becomes highly asymmertric and plume exhibits unstable meandering, when relatively small bubbles are released with their arrangement being symmetric with respect to the vessel centerline. In addition, it is observed that the flow recovers its symmetry and the plume is stabilized if we introduce relatively large bubbles into the unstable above flow by adding the large ones to the symmetric arrangement of the small ones. Less