-
采用聚类连通法, 提取高速槽道湍流中强流向速度脉动与强温度脉动对应的拟序结构. 依据空间位置, 结构被划分为壁面附着型与壁面分离型. 部分壁面附着结构在尺度上呈现自相似性, 符合Townsend附着涡假说, 据此进一步细分为矮结构、自相似结构和高结构. 条件平均结果表明, 流向雷诺正应力和温度脉动在对数区满足对数率, 这一现象同样与附着涡假设相符合; 同时, 附着结构内速度脉动与温度脉动间仍保持强雷诺比拟关系. 基于RD分解恒等式的分析显示, 低速高结构主导了壁面摩阻和热流的生成, 而高温高结构则在法向热流传输中起主要作用.In this study, a clustering method is used to extract the coherent structures associated with intense streamwise velocity fluctuations and temperature fluctuations in high-speed turbulent channel flow. Based on their spatial locations, these structures are categorized into wall-attached type and wall-detached type. A subset of the wall-attached structures exhibits self-similarity in scale, consistent with Townsend’s attached eddy hypothesis, and these structures are further classified as squat structure, self-similar structure, and tall structure. Conditional averaging results indicate that the streamwise Reynolds normal stress and the intensity of temperature fluctuations follow a logarithmic law in the logarithmic layer, a phenomenon that aligns with the attached eddy hypothesis; meanwhile, the strong Reynolds analogy relationship between velocity and temperature fluctuations remains valid within these attached structures. Analysis based on the RD identity decomposition reveals that tall structures related to low streamwise momentum mainly control the generation of wall friction and heat flux, while tall structures related to high-temperature events play a main role in the of wall-normal heat flux transfer.
-
Keywords:
- high-speed turbulent channel flows /
- clustering method /
- coherent structures /
- self-similarity /
- wall shear stress and wall heat flux.
-
图 2 不同α值下高速槽道湍流中提取得到的(a)结构数量和(b)结构体积, 分别用各自的最大值进行无量纲化
Fig. 2. (a) Number of structures and (b) the volume of structures extracted from high-speed turbulent channel flows under different α values, normalized by their respective maximum values.
图 3 高速槽道湍流M8 AW算例中的(a)速度壁面附着结构, (b)速度壁面分离结构, (c)温度壁面附着结构, (d)温度壁面分离结构
Fig. 3. (a) Velocity wall-attached structures, (b) velocity wall-detached structures, (c) temperature wall-attached structures, and (d) temperature wall-detached structures in the M8 AW case of high-speed turbulent channel flow.
图 4 高速槽道湍流M8 CW05算例中的(a)速度壁面附着结构, (b)速度壁面分离结构, (c)温度壁面附着结构, (d)温度壁面分离结构
Fig. 4. (a) Velocity wall-attached structures, (b) velocity wall-detached structures, (c) temperature wall-attached structures, and (d) temperature wall-detached structures in the M8 CW05 case of high-speed turbulent channel flow.
图 5 高速槽道湍流M8 CW02算例中的(a)速度壁面附着结构, (b)速度壁面分离结构, (c)温度壁面附着结构, (d)温度壁面分离结构
Fig. 5. (a) Velocity wall-attached structures, (b) velocity wall-detached structures, (c) temperature wall-attached structures, and (d) temperature wall-detached structures in the M8 CW02 case of high-speed turbulent channel flow.
图 6 高速槽道湍流中的结构数量概率分布 M8 AW算例中的(a)速度结构和(b)温度结构; M8 CW02算例中的(c)速度结构和(d)温度结构; M8 CW05算例中的(e)速度结构和(f)温度结构
Fig. 6. The number of clusters per unit with respect to ${y_{\min }}$and ${y_{\max }}$: (a) Velocity and (b) temperature structures in the M8 AW case; (c) velocity and (d) temperature structures in the M8 CW02 case; (e) velocity and (f) temperature structures in the M8 CW05 case.
图 7 高速槽道湍流中的速度/温度壁面附着结构中的结构尺度关系 (a) $l_x^ + $-$l_y^ + $; (b) $l_z^ + $-$l_y^ + $
Fig. 7. Scale relations in wall attached structures for u and T: (a) $l_x^ + - l_y^ + $; (b) $l_z^ + - l_y^ + $.
图 8 高速槽道湍流中速度壁面附着结构的条件平均结果 M8 AW算例中的(a)流向雷诺正应力和(b)剪切雷诺应力; M8 CW05算例中的(c)流向雷诺正应力和(d)剪切雷诺应力; M8 CW02算例中的(e)流向雷诺正应力和(f)剪切雷诺应力. 其中, p和n分别代表高速和低速结构; ss, s和t分别代表自相似结构、矮结构以及高结构
Fig. 8. Conditional averaging results of velocity wall-attached structures in high-speed turbulent channel flow: (a) Streamwise Reynolds normal stress and (b) shear Reynolds stress in the M8 AW case; (c) streamwise Reynolds normal stress and (d) shear Reynolds stress in the M8 CW05 case; (e) streamwise Reynolds normal stress and (f) shear Reynolds stress in the M8 CW02 case. Here, p and n denote high-speed and low-speed structures, respectively; ss, s, and t represent self-similar, squat, and tall structures, respectively.
图 9 高速槽道湍流中温度壁面附着结构的条件平均结果 M8 AW算例中的(a)温度脉动均方和(b)湍流热通量; M8 CW05算例中的(c)温度脉动均方和(d)湍流热通量; M8 CW02算例中的(e)温度脉动均方和(f)湍流热通量. 其中, p和n分别代表高温和低温结构; ss, s 和 t 分别代表自相似结构、矮结构以及高结构
Fig. 9. Conditional averaging results of temperature wall-attached structures in high-speed turbulent channel flow: (a) Mean square of temperature fluctuations and (b) turbulent heat flux in the M8 AW case; (c) mean square of temperature fluctuations and (d) turbulent heat flux in the M8 CW05 case; (e) mean square of temperature fluctuations and (f) turbulent heat flux in the M8 CW02 case. Here, p and n denote high-temperature and low-temperature structures, respectively; ss, s, and t represent self-similar, squat, and tall structures, respectively.
图 10 高速槽道湍流中的结构条件统计下的强雷诺比拟关系 (a) M8 AW算例; (b) M8 CW05算例; (c) M8 CW02算例
Fig. 10. Strong Reynolds analogy under conditional averaging in high-speed turbulent channel flows: (a) Case M8 AW; (b) Case M8 CW05; (c) Case M8 CW02.
表 1 不同算例的网格与流动参数
Table 1. Grid and flow parameters for different cases.
算例 ${{{T_{\text{w}}}} \mathord{\left/ {\vphantom {{{T_{\text{w}}}} {{T_{\text{r}}}}}} \right. } {{T_{\text{r}}}}}$ $R{e_\tau }$ ${M_{\text{b}}}$ ${M_{\text{c}}}$ $\Delta {x^ + }$ $\Delta y_{\text{w}}^ + $ $\Delta {z^ + }$ M8 AW 1.0 504 4.44 6.93 5.5 0.50 2.7 M8 CW05 0.5 450 4.61 6.15 4.8 0.46 2.4 M8 CW02 0.2 540 4.79 6.03 9.9 0.59 2.9 
下载: 导出CSV
表 2 不同速度结构下湍动能生成项对壁面摩阻的贡献占比$ {{{C_{{\text{f, T}}}}} \mathord{\left/ {\vphantom {{{C_{{\text{f, T}}}}} {{C_{\text{f}}}}}} \right. } {{C_{\text{f}}}}} $
Table 2. Contribution percentage, $ {{{C_{{\text{f, T}}}}} \mathord{\left/ {\vphantom {{{C_{{\text{f, T}}}}} {{C_{\text{f}}}}}} \right. } {{C_{\text{f}}}}} $ of the turbulent kinetic energy production term to wall friction under different velocity structures.
Case ${\text{N, SS}}$ ${\text{N, S}}$ ${\text{N, T}}$ ${\text{P, SS}}$ ${\text{P, S}}$ ${\text{P, T}}$ Total M8 AW 3.22 0.32 6.26 1.88 1.35 5.40 42.11 M8 CW05 3.71 0.13 7.10 1.66 1.27 3.70 38.84 M8 CW02 2.21 0.15 9.61 2.01 0.73 2.70 37.20
下载: 导出CSV
表 3 不同速度结构下生成项对壁面热流的贡献占比$ {{{C_{{\text{h, RS}}}}} \mathord{\left/ {\vphantom {{{C_{{\text{h, RS}}}}} {{C_{\text{h}}}}}} \right. } {{C_{\text{h}}}}} $
Table 3. Contribution percentage, $ {{{C_{{\text{h, RS}}}}} \mathord{\left/ {\vphantom {{{C_{{\text{h, RS}}}}} {{C_h}}}} \right. } {{C_h}}} $ of the production term to wall heat flux under different velocity structures.
Case ${\text{N, SS}}$ ${\text{N, S}}$ ${\text{N, T}}$ ${\text{P, SS}}$ ${\text{P, S}}$ ${\text{P, T}}$ Total M8 CW05 6.66 0.16 14.24 2.33 1.38 6.32 69.21 M8 CW02 3.00 0.10 14.19 2.09 0.58 3.40 50.56
下载: 导出CSV
表 4 不同速度结构下湍流热输运项对壁面热流的贡献占比$ {{{C_{{\text{h, T}}}}} \mathord{\left/ {\vphantom {{{C_{{\text{h, T}}}}} {{C_{\text{h}}}}}} \right. } {{C_{\text{h}}}}} $
Table 4. Contribution percentage, $ {{{C_{{\text{h, T}}}}} \mathord{\left/ {\vphantom {{{C_{{\text{h, T}}}}} {{C_{\text{h}}}}}} \right. } {{C_{\text{h}}}}} $ of the turbulent heat transport term to wall heat flux under different velocity structures.
Case ${\text{N, SS}}$ ${\text{N, S}}$ ${\text{N, T}}$ ${\text{P, SS}}$ ${\text{P, S}}$ ${\text{P, T}}$ Total M8 CW05 –0.21 0.33 –0.62 –0.36 0.11 –3.00 –24.95 M8 CW02 0.00 0.93 –0.24 –0.01 0.08 –1.22 –8.08
下载: 导出CSV
-
[1] Smits A, McKeon B, Marusic I 2011 Annu. Rev. Fluid Mech. 43 353
Google Scholar
[2] Jiménez J 2012 Annu. Rev. Fluid Mech. 44 27
Google Scholar
[3] Kline S, Reynolds W, Schraub F, Runstadler P 1967 J. Fluid Mech. 30 741
Google Scholar
[4] Cheng C, Fu L 2022 Phys. Rev. Fluids 7 114604
Google Scholar
[5] Yu M, Xu C, Chen J, Liu P, Fu Y, Yuan X 2022 Phys. Rev. Fluids 7 054607
Google Scholar
[6] Townsend A 1976 The Structure of Turbulent Shear Flows (Cambridge: Cambridge University Press
[7] Perry A, Chong M 1982 J. Fluid Mech. 119 173
Google Scholar
[8] Marusic I, Monty J. 2019 Annu. Rev. Fluid Mech. 51 49
Google Scholar
[9] Hutchins N, Nickels T, Marusic I, Chong M 2009 J. Fluid Mech. 635 103
Google Scholar
[10] Hultmark M, Vallikivi M, Bailey S, Smits A 2012 Phys. Rev. Lett. 108 094501
Google Scholar
[11] Hutchins N, Chauhan K, Marusic I, Monty J 2012 Boundary-Layer Meteorol. 145 273
Google Scholar
[12] Lee M, Moser R 2015 J. Fluid Mech. 774 395
Google Scholar
[13] Nickels T, Marusic I, Hafez S, Chong M 2005 Phys. Rev. Lett. 95 074501
Google Scholar
[14] Ahn J, Lee J, Kang J, Sung H 2015 Phys. Fluids 27 065110
Google Scholar
[15] Lozano D, Flores O, Jiménez J 2012 J. Fluid Mech. 694 100
Google Scholar
[16] Lozano D, Jiménez J 2014 J. Fluid Mech. 759 432
Google Scholar
[17] Dong S, Lozano D, Sekimoto A, Jiménez J 2017 J. Fluid Mech. 816 167
Google Scholar
[18] Lozano D A, Bae H J 2019 J. Fluid Mech. 868 698
Google Scholar
[19] Jiménez J 2013 Phys. Fluids 25 101302
Google Scholar
[20] 董思卫, 程诚, 陈坚强, 袁先旭, 李伟鹏 2021 力学进展 51 792
Dong S W, Cheng C, Chen J Q, Yuan X X, Li W P 2021 Adv. Mech. 51 792
[21] Hwang J, Sung H 2018 J. Fluid Mech. 856 58
[22] Yang J, Hwang J, Sung H 2019 Phys. Rev. Fluids 4 114606
Google Scholar
[23] Yoon M, Hwang J, Yang J, Sung H 2020 J. Fluid Mech. 885 A12
Google Scholar
[24] Hwang J, Lee J, Sung H 2020 J. Fluid Mech. 905 A6
Google Scholar
[25] Yoon M, Sung H 2022 J. Fluid Mech. 943 A14
Google Scholar
[26] Fukagata K, Iwamoto K, Kasagi N 2002 Phys. Fluids 14 73
Google Scholar
[27] Renard N, Deck S 2016 J. Fluid Mech. 790 339
Google Scholar
[28] Gomez T, Flutet V, Sagaut P 2009 Phys. Rev. E 79 035301
[29] Zhang P, Xia Z 2020 Phys. Rev. E 102 043107
[30] Wenzel C, Gibis T, Kloker M 2021 J. Fluid Mech. 930 A1
[31] Li W, Fan Y, Modesti D, Cheng C 2019 J. Fluid Mech. 875 101
Google Scholar
[32] Sun D, Guo Q, Yuan X, Zhang H, Liu P 2021 Adv. Aerodyn. 3 1
Google Scholar
[33] Yu M, Xu C 2021 Phys. Fluids 33 075106
Google Scholar
[34] Yu M, Liu P, Fu Y, Tang Z, Yuan X 2022 Phys. Fluids 34 065139
Google Scholar
[35] Yu M, Liu P, Fu Y, Tang Z, Yuan X 2022 Phys. Fluids 34 065140
Google Scholar
[36] Huang P G, Coleman G N, Bradshaw P 1995 J. Fluid Mech. 305 185
Google Scholar
下载:
计量
- 文章访问数: 385
- PDF下载量: 4
- 被引次数: 0
