A Robust Bubble Growth Solution Scheme for Implementation in CFD Analysis of Multiphase Flows
A Robust Bubble Growth Solution Scheme for Implementation in CFD Analysis of Multiphase Flows
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DOI：
10.3390/computation11040072
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发表时间：
2023-03
期刊：
影响因子：
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通讯作者：
Hao Pang;G. Ngaile
中科院分区：
文献类型：
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作者：
Hao Pang;G. Ngaile
尽管瑞利-普莱塞 (RP) 方程的完整形式比其简化形式更准确地描述了空化流中的气泡行为，但由于其高刚度，在计算流体动力学 (CFD) 模拟中的应用比后者少得多。完整形式 RP 方程的传统变时间步方案很难与 CFD 程序集成，因为它需要在奇点处很小的时间步长才能收敛，并且此步长可能与守恒方程的时间推进不兼容。本文提出了两种基于有限差分法和欧拉法的稳定高效的数值求解方案，使得完整形式的RP方程能够更好地被CFD程序所接受。通过采用截断气泡半径来近似崩溃阶段的最小气泡尺寸，所提出的方案以显式方式求解气泡半径和壁速度。与传统方案相比，所提出的解决方案对于各种环境压力分布更加稳健，并且避免了对奇点处的时间步长的过度细化。由于所提出的解决方案可以计算二阶项、液体粘度和表面张力对气泡演化的影响，因此它为汽化或冷凝速率提供了更准确的壁速度估计，广泛应用于CFD模拟中的空化模型中。解决方案的合法性通过这些方案的结果与文献中已建立的结果之间的一致性来体现。所提出的解决方案在面对各种环境压力分布时更加稳健。
Although the full form of the Rayleigh–Plesset (RP) equation more accurately depicts the bubble behavior in a cavitating flow than its reduced form, it finds much less application than the latter in the computational fluid dynamic (CFD) simulation due to its high stiffness. The traditional variable time-step scheme for the full form RP equation is difficult to be integrated with the CFD program since it requires a tiny time step at the singularity point for convergence and this step size may be incompatible with time marching of conservation equations. This paper presents two stable and efficient numerical solution schemes based on the finite difference method and Euler method so that the full-form RP equation can be better accepted by the CFD program. By employing a truncation bubble radius to approximate the minimum bubble size in the collapse stage, the proposed schemes solve for the bubble radius and wall velocity in an explicit way. The proposed solution schemes are more robust for a wide range of ambient pressure profiles than the traditional schemes and avoid excessive refinement on the time step at the singularity point. Since the proposed solution scheme can calculate the effects of the second-order term, liquid viscosity, and surface tension on the bubble evolution, it provides a more accurate estimation of the wall velocity for the vaporization or condensation rate, which is widely used in the cavitation model in the CFD simulation. The legitimacy of the solution schemes is manifested by the agreement between the results from these schemes and established ones from the literature. The proposed solution schemes are more robust in face of a wide range of ambient pressure profiles.