AI 中文总结
该研究针对多分散气泡流系综平均模型的热质传递缺失问题，在条件双曲正交矩方法中构建气泡压力与蒸汽质量的常值传递方程，在MFC中实现后经蒙特卡罗和气泡屏计算验证，有效降低压力振荡并得到1.5%的相对均方根误差。
AI 中文摘要
多分散气泡流的系综平均模型需要演化气泡群的统计量。先前基于正交的矩方法用绝热过程关系封闭气泡压力，忽略了气泡壁处的热质传递。我们在条件双曲正交矩方法中构建了气泡压力和蒸汽质量的常值传递方程。二阶条件反演在每个平衡半径区间生成4个联合半径-径向速度节点，每个节点处推进气泡压力和蒸汽质量。节点值封闭系综平均流动方程，无需向输运矩集合中添加混合压力或蒸汽质量矩。该模型在MFC中实现。蒙特卡罗计算验证了谐驱动群的正交节点演化和平均气泡变量；气泡屏计算量化了平衡半径离散化及初始分布变化时的封闭误差。在所考虑的条件下，常值传递计算未出现绝热封闭下观察到的高频压力振荡；三维气泡屏计算得到欧拉-欧拉中心压力与40个体积平均的欧拉-拉格朗日实现均值间的相对均方根误差为1.5%。
英文摘要
Ensemble-averaged models of polydisperse bubbly flows require statistics of the evolving bubble population. Prior quadrature-based moment formulations close bubble pressure with a polytropic relation that omits heat and mass transfer at the bubble wall. We formulate constant-transfer equations for bubble pressure and vapor mass within a conditional hyperbolic quadrature method. Second-order conditional inversion produces four joint radius--radial-velocity nodes per equilibrium-radius bin. Bubble pressure and vapor mass are advanced at each node. The node values close the ensemble-averaged flow equations without adding mixed pressure or vapor-mass moments to the transported moment set. The model is implemented in MFC. Monte Carlo calculations verify the evolution of quadrature nodes and the mean bubble variables for a harmonically forced population. Bubble-screen calculations quantify closure error as the equilibrium radius is discretized and the initial distributions vary. The constant-transfer calculation does not exhibit the high-frequency pressure oscillations observed with the polytropic closure under the conditions considered. 3D bubble-screen calculations give a 1.5% relative root-mean-square error between the Euler--Euler center pressure and the mean of 40 volume-averaged Euler--Lagrange realizations.
Comments17 pages, 8 figures
