Wall function treatment for bubbly boundary layers at low void fractions

Abstract The present work investigates the role of different treatments of the lower boundary condition on the numerical prediction of bubbly flows. Two different wall function formulations are tested against experimental data obtained for bubbly boundary layers: (i) a new analytical solution derived through asymptotic techniques and (ii) the previous formulation of Troshko and Hassan (IJHMT, 44, 871-875, 2001a). A modified k-e model is used to close the averaged Navier-Stokes equations together with the hypothesis that turbulence can be modelled by a linear superposition of bubble and shear induced eddy viscosities. The work shows, in particular, how four corrections must the implemented in the standard single-phase k-e model to account for the effects of bubbles. The numerical implementation of the near wall functions is made through a finite elements code.

摘要 本研究围绕气泡流的数值预测问题，探讨了下边界条件不同处理方式的影响效果。本研究采用气泡边界层的实测数据，对两种壁面函数（wall function）方案进行对照验证：其一为通过渐近分析法推导得到的新型解析解；其二为Troshko与Hassan（IJHMT, 44, 871-875, 2001a）此前提出的壁面函数方案。本研究采用修正的k-ε湍流模型封闭雷诺平均纳维-斯托克斯（Navier-Stokes）方程，并结合如下假设：湍流可通过气泡诱导与剪切诱导涡粘系数的线性叠加进行建模。本研究特别阐明，为刻画气泡的影响效应，需对标准单相k-ε湍流模型实施四项修正。近壁函数的数值实现通过有限元代码完成。