基于 LES 和 BPBE 的舰船气泡尾流数值分析方法

提出一种基于大涡模拟（LES）和气泡群平衡方程(BPBE)的舰船气泡尾流特征参数研究的数值分析法：首先建立舰船尾流场 LES 控制方程，结合实船初边始条件，对流向的速度进行数值模拟；然后再将 LES 计算得到的速度代入 BPBE 方程进行尾流中气泡数密度分布（BND）的求解。计算结果表明：BND 沿尾流流向的分布基本符合指数分布，在500 m 以内的区域衰减速度很快，500 m 以外的区域衰减速度缓慢；在离船尾越近的地方，小气泡的相对 BND 越大；在3000 m 距离处 BND 最大的气泡尺寸约为70滋m。该方法计算效率较高、占用空间较少，可望为舰船气泡尾流特征的研究提供新的有效手段。

Numerical study method of the ship bubble wake based on LES and BPBE

Based on Large Eddy Simulate (LES) technology and Bubble Population Balance Equation (BPBE), a numerical method is put forward to study the ship’s bubble wake characters: first, a LES equa-tion of the ship’s wake is built, combining the original and boundary conditions, simulating the velocity in flow direction; then this result of the LES is used to calculate the BND. The result indicates that BND changes with flow direction accords to the exponential distribution well, decreases quickly within 500 m and slowly beyond 500 m; the BND of small bubbles increase with the distance decreasing from the stern; bub-bles of 70 μm take up the majority at the position 3 000 m away from stern. The calculation efficiency and space of this numerical method is much sooner and less, and it may afford a new good way to study the bubble wake of the ship.