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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.
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Keywords:
- high-speed turbulent channel flows /
- clustering method /
- coherent structures /
- self-similarity /
- wall shear stress and wall heat flux.
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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
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.
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
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 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
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.
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.
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
Figure 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^ + $
Figure 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
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 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
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 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
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.
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 
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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
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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
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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
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