时间演化分形流场的直接数值模拟

为了研究分形网格湍流中小尺度结构的运动规律，在具有高分辨率的空间网格中，开展分形流场时间演化的直接数值模拟，并通过模拟具有相同阻塞率的规则流场进行对比研究. 通过给流场中注入合适的能量扰动，促使2类流场从层流初始状态向湍流状态过渡. 数值模拟结果表明，与规则流场相比，分形流场受到初始条件影响的持续时间更久，同时在时间演化的初期，分形流场产生的动能更小，但分形流场在衰减期的大尺度运动起到强化湍流的作用，导致其产生的动能更大、湍流强度更高，有利于实现对流场的被动控制. 分形流场和规则流场均在截断波数 $ kM \approx 20 $时满足能量与耗散水平相等，但有别于能量级串过程中能量传输与耗散的平衡. 当流场达到统计均匀后，规则流场衰减符合Saffman湍流特征的规律.

Direct numerical simulation of temporally evolving fractal-generated turbulence

The direct numerical simulation of temporal evolution of fractal flow field was performed in a high resolution spatial grid to study the characteristics of small scale motions in fractal-generated turbulence. An additional numerical simulation of regular-generated turbulence with the same blockage ratio was also performed for comparison. Random disturbances with appropriate energy distribution were imposed for a quick transition of the two types of flow fields from the laminar initial state to the turbulent state. Numerical results indicated that the fractal-generated turbulence can be significantly affected by the initial velocity conditions for a long time. And in the early stage of the temporally evolution, the kinetic energy generated by the fractal-generated turbulence was smaller, but the large-scale motions of the fractal-generated turbulence in the decay period played an important role in turbulence evolution, resulting in a larger kinetic energy level and a higher turbulence intensity compared with regular-generated turbulence. This observation contributes to the possible passive control of the fractal-generated turbulence. Both fractal-generated and regular-generated turbulence reached the same level of energy and dissipation at the wave number $ kM \approx 20 $, but it was different from the balance of energy transmission and dissipation in energy cascade process. Furthermore, when the regular-generated turbulence became statistically homogenous, the energy decay law was more or less consistent with the Saffman turbulence.