Wall attached strucures of velocity and tempreture fluctuations in high-speed turbulent channel flows

LI Junyang; ZHOU Qingqing; SUN Dong; YU Ming; YUAN Xianxu; LIU Pengxin

doi:10.7498/aps.74.20250783

Abstract

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 (1976)’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 (Renard-Deck) 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:

Authors and contacts

State Key Laboratory of Aeradynamics, Mianyang 621000, China

Corresponding author: LI Junyang, lijunyang@cardc.cn ; LIU Pengxin, liupengxin@cardc.cn

Funds: Project supported by the Young Talent Lifting Project, China and the National Natural Science Foundation of China (Grant No. 12272396).

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References

[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
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[7]	Perry A, Chong M 1982 J. Fluid Mech. 119 173 Google Scholar
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[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
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图 1 高速槽道湍流物理模型

Figure 1. Physical model of high-speed turbulent channel flows

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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

Figure 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.

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图 3 高速槽道湍流M8AW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

Figure 3. (a) Velocity wall-attached structures, (b) velocity wall-detached structures, (c) temperature wall-attached structures, and (d) temperature wall-detached structures in the M8AW case of high-speed turbulent channel flow.

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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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 6 高速槽道湍流中的结构数量概率分布 M8AW算例中的(a)速度结构和(b)温度结构; M8CW02算例中的(c)速度结构和(d)温度结构; M8CW05算例中的(e)速度结构和(f)温度结构

Figure 6. The number of clusters per unit with respect to ${y_{\min }}$and ${y_{\max }}$: (a) Velocity and (b) temperature structures in the M8AW case; (c) velocity and (d) temperature structures in the M8CW02 case; (e) velocity and (f) temperature structures in the M8CW05 case.

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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^ + $

Figure 7. Scale relations in wall attached structures for u and T: (a) $l_x^ + \text{-} l_y^ + $; (b) $l_z^ + \text{-} l_y^ + $.

DownLoad: Full-Size Img PowerPoint

图 8 高速槽道湍流中速度壁面附着结构的条件平均结果　M8AW算例中的(a)流向雷诺正应力和(b)剪切雷诺应力; M8CW05算例中的(c)流向雷诺正应力和(d)剪切雷诺应力; M8CW02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

Figure 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 M8AW case; (c) streamwise Reynolds normal stress and (d) shear Reynolds stress in the M8CW05 case; (e) streamwise Reynolds normal stress and (f) shear Reynolds stress in the M8CW02 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.

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图 9 高速槽道湍流中温度壁面附着结构的条件平均结果　M8AW算例中的(a)温度脉动均方根和(b)湍流热通量; M8CW05算例中的(c)温度脉动均方根和(d)湍流热通量; M8CW02算例中的(e)温度脉动均方根和(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

Figure 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 M8AW case; (c) mean square of temperature fluctuations and (d) turbulent heat flux in the M8CW05 case; (e) mean square of temperature fluctuations and (f) turbulent heat flux in the M8CW02 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.

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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

Figure 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.

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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

DownLoad: 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

DownLoad: 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	$ \mathit{\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

DownLoad: 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
M8CW05	–0.21	0.33	–0.62	–0.36	0.11	–3.00	–24.95
M8CW02	0.00	0.93	–0.24	–0.01	0.08	–1.22	–8.08

DownLoad: 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

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