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浙江大学学报(工学版)
浙江大学学报(工学版)  2022, Vol. 56 Issue (8): 1606-1621    DOI: 10.3785/j.issn.1008-973X.2022.08.015
机械与能源工程     
时间演化分形流场的直接数值模拟
石均(),邱颖宁,周毅*()
南京理工大学 能源与动力工程学院，江苏 南京 210094
Direct numerical simulation of temporally evolving fractal-generated turbulence
Jun SHI(),Ying-ning QIU,Yi ZHOU*()
School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
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摘要：

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.
关键词： 时间演化;  分形网格湍流;  直接数值模拟;  能量级串;  湍流控制    
Abstract:

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.
Key words: temporal evolution    fractal-generated turbulence    direct numerical simulation    energy cascade    turbulence control
收稿日期: 2021-08-08 出版日期: 2022-08-30
CLC:  O 357.5+1  
基金资助: 国家重点研发计划政府间国际科技新合作重点专项(2019YFE0104800)
通讯作者: 周毅     E-mail: jun@njust.edu.cn;yizhou@njust.edu.cn
作者简介: 石均（1996—），男，硕士生，从事流体力学与空气动力研究. orcid.org/0000-0002-4607-0675. E-mail: jun@njust.edu.cn
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石均
邱颖宁
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引用本文:

石均,邱颖宁,周毅. 时间演化分形流场的直接数值模拟[J]. 浙江大学学报(工学版), 2022, 56(8): 1606-1621.

Jun SHI,Ying-ning QIU,Yi ZHOU. Direct numerical simulation of temporally evolving fractal-generated turbulence. Journal of ZheJiang University (Engineering Science), 2022, 56(8): 1606-1621.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.08.015    或    https://www.zjujournals.com/eng/CN/Y2022/V56/I8/1606

图 1  网格Y-Z平面示意图
工况类型 $ {N_{\text{f}}} $ $ \sigma $ $ R{e_{\text{M}}} $ $ {D_{\text{r}}} $ $ {T_{{\text{end}}}} $
分形网格 3 0.36 1600 9.5 500 $ M/{U_0} $
规则网格 1 0.36 1600 1.0 500 $ M/{U_0} $
表 1  计算模型及条件设置
网格类型 $ {M_0} $ $ {M_1} $ $ {M_2} $ $ {d_0}/{M_0} $ $ {d_1}/{M_1} $ $ {d_2}/{M_2} $ ${L_{X} }/{M_0}$ ${L_{Y} }/{M_0}$ ${L_{Z} }/{M_0}$ ${N_{X} } \times {N_{Y } } \times {N_{Z } }$
分形网格 4M 2M $ M $ 0.19 0.12 0.08 2 2 2 $ 800 \times 400 \times 400 $
规则网格 ? ? $ M $ ? ? 0.2 2 2 2 $ 800 \times 400 \times 400 $
表 2  2类网格的具体参数
图 2  以U0拖曳网格条产生的湍流效果
图 3  TGV的数值结果与解析解误差对比
图 4  中心线上空间分辨率的时间演化
图 5  FGT流向瞬时速度的时间演化
图 6  RGT流向瞬时速度的时间演化
图 7  FGT流向平均速度的时间演化
图 8  RGT流向平均速度的时间演化
图 9  FGT的瞬时涡量和第二不变量
图 10  RGT的瞬时涡量和第二不变量
图 11  RGT的统计特性的时间演化
图 12  中心线上流向平均速度的时间演化
图 13  网格1/4的Y-Z平面不同的(Y, Z)位置
图 14  FGT和RGT不同(Y, Z)位置统计特性的时间演化
图 15  网格中心线上流向均方根速度和泰勒雷诺数的时间演化
图 16  中心线上流向脉动速度偏导数的偏斜度和平坦度的时间演化
图 17  中心线上动能、耗散率、泰勒尺度和Kolmogorov长度尺度的时间演化
图 18  不同时刻下FGT和RGT的三维能谱
图 19  不同波数下动能和耗散率的时间演化
图 20  初始条件对FGT的影响
图 21  初始条件对RGT的影响
图 22  Saffman积分的时间演化
图 23  FGT和RGT的三维能谱与Saffman湍流能谱
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