本研究在体积平均理论框架下对气液泡状流进行数学尺度提升，推导了双流体模型及其相关的封闭问题，并针对液体流经均匀单分散变形气泡群的案例求解了该封闭问题。为此，采用含同心气泡的圆柱形晶胞作为表征体元的近似方法，评估的工况范围为：0 < 雷诺数（Re）≤ 675，0 < 气相体积分数（εg）≤ 0.2，7.15×10⁻⁹ ≤ 韦伯数（We）≤ 3.96，莫顿数（Mo）= 2.55×10⁻¹¹。研究以泡状流界面力与等效Re下无界液体中单个气泡的界面力的比值为指标，分析了界面力封闭关系。结果表明，在蠕动流区（0.001 ≤ Re ≤ 0.1），阻力系数之比随εg增大而升高，且与Re无关；在过渡区与惯性区（1 ≤ Re ≤ 650），该比值同样随εg增大而升高，但随Re变化呈现两种不同趋势：过渡区（1 ≤ Re ≤ 50）内比值随Re增大而减小，惯性区（50 < Re ≤ 650）内比值随Re增大而升高，且在Re≈50处存在转变点，该现象可能与边界层的形成有关。本方法得到的变化趋势与现有泡状流直接数值模拟数据的趋势一致，表明在计算成本方面，该方法是获取两相流建模封闭律的优良替代方案。
英文摘要：
The mathematical up-scaling of gas-liquid bubbly flows was carried out under the framework of the volume averaging theory. A two-fluid model and its associated closure problem were deduced. The closure problem was solved for a case study: a liquid flow past an assembly of homogeneous and monodisperse distorted bubbles. To this end, a cylindrical unit cells with concentric bubbles was used as approach of a representative elementary volume. The following conditions were evaluated: 0 < Re <= 675, 0 < εg <= 0.2, 7.15 x 10-9 <= We <= 3.96 and Mo = 2.55 x 10-11. The interfacial force closure was analyzed in terms of the ratio between the interfacial force for bubbly flow and that existing for a single bubble with the equivalent Re (in an unbounded liquid). It was found that, for creeping regime (0.001 <= Re <= 0.1), the ratio between drag coefficients increases as εg increases independently of Re. For intermediate and inertial regimes (1 <= Re <= 650), the ratio also increases as εg increases; however, two different trends were observed with respect to Re: the ratio decreases for the intermediate regime (1 <= Re <= 50) and increases for the inertial regime (50 < Re <= 650). A transition point around Re = 50 was found, which could be related to the boundary layer formation. Similar trends with respect to existing data from direct numerical simulations of bubbly flows were obtained, showing that this approach represents a good alternative, in terms of computing efforts, to obtain closure laws for two-phase flow modeling.
