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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2022, Vol. 56 Issue (8): 1606-1621    DOI: 10.3785/j.issn.1008-973X.2022.08.015
    
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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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     
Received: 08 August 2021      Published: 30 August 2022
CLC:  O 357.5+1  
Fund:  国家重点研发计划政府间国际科技新合作重点专项(2019YFE0104800)
Corresponding Authors: Yi ZHOU     E-mail: jun@njust.edu.cn;yizhou@njust.edu.cn
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Jun SHI
Ying-ning QIU
Yi ZHOU
Cite this article:

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.

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


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.


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 
Fig.1 Grid Y-Z plane diagram
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} $
Tab.1 Calculation model types and condition settings
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 $
Tab.2 Specific parameters of two types of grid
Fig.2 Turbulence generated by a grid towed with velocity U0
Fig.3 Error comparison between numerical results and analytical solutions of TGV
Fig.4 Temporal evolution of spatial resolution on centerline
Fig.5 Temporal evolution of streamwise instantaneous velocity of FGT
Fig.6 Temporal evolution of streamwise instantaneous velocity of RGT
Fig.7 Temporal evolution of streamwise mean velocity of FGT
Fig.8 Temporal evolution of streamwise mean velocity of RGT
Fig.9 Instantaneous vorticity and second invariant of velocity gradient tensor of FGT
Fig.10 Instantaneous vorticity and second invariant of velocity gradient tensor of RGT
Fig.11 Temporal evolution of statistics of RGT
Fig.12 Temporal evolution of streamwise mean velocity on centerline
Fig.13 Different (Y, Z) locations on 1/4 grid plane Y-Z
Fig.14 Temporal evolution of statistical characteristics at different (Y, Z) locations between FGT and RGT
Fig.15 Temporal evolution of streamwise root mean square of velocity and Taylor Reynolds number on centerline
Fig.16 Temporal evolution of skewness and flatness of streamwise fluctuating velocity partial derivatives on centerline
Fig.17 Temporal evolution of kinetic energy, dissipation rate, Taylor scale and Kolmogorov scale on centerline
Fig.18 3D energy spectrum of FGT and RGT at different timesteps
Fig.19 Temporal evolution of kinetic energy and dissipation rate on different wavenumbers
Fig.20 Effects of initial conditions on FGT
Fig.21 Effect of initial conditions on RGT
Fig.22 Temporal evolution of Saffman integral
Fig.23 3D energy spectrum and Saffman turbulence spectrum of FGT and RGT
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