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Discrete unified gas kinetic simulation of characteristics of variable temperature wall driven thermal creep flow in cavity

LIU Zanqi LUO Yuan WENG Wanliang HE Qing TAO Shi

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Discrete unified gas kinetic simulation of characteristics of variable temperature wall driven thermal creep flow in cavity

LIU Zanqi, LUO Yuan, WENG Wanliang, HE Qing, TAO Shi
cstr: 32037.14.aps.74.20241334
Article Text (iFLYTEK Translation)
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  • In order to examine the influence of wall temperature change on the flow and heat transfer properties of rarefied gas in restricted space, the discrete unified gas kinetic scheme (DUGKS) is used to simulate the thermal creep flows in a square cavity. All the boundaries of the cavity are stationary diffuse reflection walls. The temperature of left wall and right wall are lower, and the temperature of the upper wall and the lower wall are both subjected to periodic variation. The simulation parameters considered in the present work are set as follows: the Knudsen number Kn is in a range 0.01–10, temperature change frequency St in a range of 0.5–5, and temperature change amplitude Ah in a range of 0.1–0.8. The results indicate that the velocity field and temperature field in the cavity exhibit periodic variations. No inverse Fourier heat transfer phenomenon is observed within the parameter ranges studied. The intensity of the thermal creep flow can be increased by increasing the frequency, temperature, and the Knudsen number. This can also raise the temperature jump and velocity slip close to the temperature change walls. Heat transfer lag and a reduction in the heat transfer capability of the wall are caused by increasing St and Kn. When St is small, say, St = 0.5, a complex vortex structure is seen in the cavity. As the value of St rises to 5, the vortex disappears, the gas travels from the variable temperature wall to the horizontal centerline of cavity, and the region close to the middle of the left wall and right wall changes from an endothermic zone to an exothermic zone. Furthermore, the temperature field and velocity field inside the cavity hardly change, but the degree of heat transfer on the wall decreases with the increase of Ah. The main results are shown in the figure attached below. This work provides helpful recommendations for designing the MEMS devices by using pulsed heating.
      Corresponding author: TAO Shi, taoshi@dgut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 52476148, 51906044).
    [1]

    沈青 2006 力学进展 36 142Google Scholar

    Shen Q 2006 Adv. Mech. 36 142Google Scholar

    [2]

    Frangi A, Frezzotti A, Lorenzani S 2007 Comput. Struct. 85 810Google Scholar

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    梅涛, 陈占秀, 杨历, 朱洪漫, 苗瑞灿 2020 69 224701Google Scholar

    Mei T, Chen Z X, Yang L, Zhu H M, Miao R C 2020 Acta Phys. Sin. 69 224701Google Scholar

    [4]

    Ramadan K M, Qisieh O, Tlili I 2022 Proc. Inst. Mech. Eng. Part C 236 5033Google Scholar

    [5]

    Mousivand M, Roohi E 2022 Phys. Fluids 34 052002Google Scholar

    [6]

    Lan J, Xie J, Ye J, Peng W Z, Jiao X Y 2022 Int. J. Hydrogen Energy 47 19206Google Scholar

    [7]

    韩峰, 王晓伟, 张文青, 张世伟, 张志军 2023 真空科学与技术学报 43 238Google Scholar

    Han F, Wang X W, Zhang W Q, Zhang S W, Zhang Z J 2023 J. Vac. Sci. Technol. 43 238Google Scholar

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    王晓伟, 张志军, 张文青, 苏天一, 张世伟 2020 真空与低温 26 73Google Scholar

    Wang X W, Zhang Z J, Zhang W Q, Su T Y, Zhang S W 2020 Vac. Cryogen 26 73Google Scholar

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    Wu L, Zhang Y H, Li Z H 2017 Sci. Sin. phys. Mech. As. 47 070004Google Scholar

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    Tsimpoukis A, Vasileiadis N, Tatsios G, Valougeorgis D 2019 Phys. Fluids 31 067108Google Scholar

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    Taassob A, Kamali R, Bordbar A 2018 Vacuum 151 197Google Scholar

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    Nabapure D 2021 J. Comput. Sci. Neth. 49 101276.Google Scholar

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    Wu L, Reese J M, Zhang Y 2014 J. Fluid Mech. 748 350Google Scholar

    [14]

    Ogata Y, Kawaguchi T 2011 J. Fluid Sci. Technol. 6 215Google Scholar

    [15]

    Palharini R C, Scanlon T J, White C 2018 Comput. Fluids 165 173Google Scholar

    [16]

    Yang W Q, Tang S, Yang H 2019 Appl. Sci. 9 2733Google Scholar

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    单小东, 王沫然 2013 工程热 34 2159

    Shan X D, Wang M R 2013 J. Eng. Thermophys. 34 2159

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    张帅, 方蜀州, 许阳 2021 推进技术 42 2002Google Scholar

    Zhang S, Fang S Z, Xu Y 2021 J. Propul. Technol. 42 2002Google Scholar

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    Zhang J, Yao S Q, Fei F, Ghalambaz M, Wen D S 2020 Phys. Fluids 32 102001Google Scholar

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    Moghadam E Y, Roohi E, Esfahani J A 2014 Vacuum 109 333Google Scholar

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    Yamaguchi H, Perrier P, Ho M T, Méolans J G, Niimi T, Graur I 2016 J. Fluid Mech. 795 690Google Scholar

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    Barbera E, Brini F 2018 Europhys. Lett. 120 34001Google Scholar

    [23]

    Akhlaghi H, Roohi E, Stefanov S 2018 Sci. Rep. 8 13533Google Scholar

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    Han Y L 2010 Fluid Dyn. Res. 42 045505Google Scholar

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    Zhu M B, Roohi E, Ebrahimi A 2023 Phys. Fluids 35 052012Google Scholar

    [26]

    Roohi E, Shahabi V, Bagherzadeh A 2018 Int. J. Therm. Sci. 125 381Google Scholar

    [27]

    Wang P, Zhu L H, Su W, Wu L, Zhang Y H 2018 Phys. Rev. E 97 043103Google Scholar

    [28]

    Zhu L H, Guo Z L, Xu K 2016 Comput. Fluids 127 211Google Scholar

    [29]

    Wang X W, Su T Y, Zhang W Q, Zhang Z J, Zhang S W 2020 Microsyst. Nanoeng. 6 26Google Scholar

    [30]

    张贝豪, 郑林 2020 69 164401Google Scholar

    Zhang B H, Zheng L 2020 Acta Phys. Sin. 69 164401Google Scholar

    [31]

    Ou Y, Qu F, Wang G Y, Nie M Y, Li Z G, Ou W, Xie C Q 2016 Appl. Phys. Lett. 109 023512Google Scholar

    [32]

    万启坤, 张月, 郭照立 2023 计算物理 40 653

    Wan Q K, Zhang Y, Guo Z L 2023 Chinese J. Comput. Phys. 40 653

    [33]

    Kalempa D, Sharipov F, Silva J C 2019 Vacuum 159 82Google Scholar

    [34]

    Bargatin I, Kozinsky I, Roukes M L 2007 Appl. Phys. Lett. 90 093116Google Scholar

    [35]

    Ilic B, Yang Y, Aubin K, Reichenbach R, Krylov S, Craighead H G 2005 Nano Lett. 5 925Google Scholar

    [36]

    Juvé V, Crut A, Maioli P, Pellarin M, Broyer M, Del Fatti N, Vallée F 2010 Nano Lett. 10 1853Google Scholar

    [37]

    Guo Z L, Wang R J, Xu K 2015 Phys. Rev. E 91 033313Google Scholar

    [38]

    孙喜明, 姚朝晖, 杨京龙 2002 51 1942Google Scholar

    Sun X M, Yao Z H, Yang J L 2002 Acta Phys. Sin. 51 1942Google Scholar

    [39]

    孙佳坤, 林传栋, 苏咸利, 谭志城, 陈亚楼, 明平剑 2024 73 110504Google Scholar

    Sun J K, Lin C D, Su X L, Tan Z C, Chen Y L, Ming P J 2024 Acta Phys. Sin. 73 110504Google Scholar

    [40]

    Huang J C, Xu K, Yu P 2013 Commun. Comput. Phys. 14 1147Google Scholar

    [41]

    Wang Y, Zhong C W, Liu S 2019 Phys. Rev. E 100 063310Google Scholar

    [42]

    Zhu L H, Chen S Z, Guo Z L 2017 Comput. Phys. Commun. 213 155Google Scholar

    [43]

    Vargas M, Tatsios G, Valougeorgis D, Stefanov S 2014 Phys. Fluids 26 057101Google Scholar

  • 图 1  变温壁面驱动方腔流动示意图

    Figure 1.  Schematic diagram of the flow of a variable temperature wall driven cavity.

    图 2  Kn = 0.1时的腔内温度云图和速度场流线结果对比 (a)文献[42]结果; (b)本文结果

    Figure 2.  Comparison of the temperature contour and velocity field streamlines in the cavity at Kn = 0.1: (a) Results of Ref. [42]; (b) the results of this work.

    图 3  通过左侧一级主涡中心的水平和竖直线上的UV速度分布

    Figure 3.  U and V velocity distribution in horizontal and vertical lines through the center of the primary vortex on the left.

    图 4  Kn = 1, Ah = 0.5, t = 0时, 不同St下方腔内温度场和热流线 (a) St = 0.5; (b) St = 1.0; (c) St = 2.0; (d) St = 5.0

    Figure 4.  Temperature field and thermal flow lines in different cavities under different St when Kn = 1, Ah = 0.5 and t = 0: (a) St = 0.5; (b) St = 1.0; (c) St = 2.0; (d) St = 5.0.

    图 5  Kn = 1, Ah = 0.5, t = 0时不同频率St下中心线上的温度分布 (a)竖直中心线X/L = 0.5; (b): 水平中心线Y/L = 0.5

    Figure 5.  Temperature distribution on the centerline at different frequencies St when Kn = 1, Ah = 0.5 and t = 0: (a) Vertical centerline X/L = 0.5; (b) horizontal centerline Y/L = 0.5.

    图 6  Kn = 1, Ah = 0.5, t = 0时不同频率St下方腔内速度云图和流线 (a) St = 0.5; (b) St = 1.0; (c) St = 2.0; (d) St = 5.0

    Figure 6.  Intracavity velocity contours and streamlines below St at different frequencies when Kn = 1, Ah = 0.5 and t = 0: (a) St = 0.5; (b) St = 1.0; (c) St = 2.0; (d) St = 5.0.

    图 7  Kn = 1, Ah = 0.5, t = 0时不同St时左、上壁面处气体温度T、努塞尔数Nu和速度U分布

    Figure 7.  Distributions of gas temperature T, Nusselt number Nu and velocity U on the left and upper walls at different St when Kn = 1, Ah = 0.5 and t = 0.

    图 8  Ah = 0.5, t = 0时不同参数在不同StKn下的变化 (a)左壁面中点温度Tcy; (b)上壁面中点温度Tcx; (c)左壁面中点努塞尔数Nucy; (d)左壁面下半部分平均速度$ {\overline{U}}_{{\mathrm{z}}{\mathrm{x}}} $

    Figure 8.  Variations of different parameters under different St and Kn when Ah = 0.5 and t = 0: (a) Temperature of the midpoint of the left wall Tcy; (b) temperature of the midpoint of the upper wall Tcx; (c) Nussel number of the midpoint of the left wall Nucy; (d) the average velocity of the lower half of the left wall $ {\overline{U}}_{{\mathrm{z}}{\mathrm{x}}} $.

    图 9  不同StKn下, 壁面平均努塞尔数$\overline{Nu} $的时间历程及$\overline{Nu} $的极差$ {\left(\Delta\overline{Nu}\right)}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}} $ (a), (c) Y = 0, 下壁面; (b), (d) X = 0, 左壁面

    Figure 9.  The time history of the average Nussel number $\overline{Nu} $ and the range $ {\left(\Delta\overline{Nu}\right)}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}} $of $\overline{Nu} $ on the wall under different St and Kn: (a), (c) Lower wall surface, Y = 0; (b), (d) left wall, X = 0.

    图 10  Ah = 0.2, Kn = 1, St = 1.0, t = 0时方腔内的温度场和热流线(a)、速度场和流线(b)

    Figure 10.  Temperature field and thermal streamlines (a), velocity field and streamlines (b) in a square cavity at Kn = 1, St = 1.0, Ah = 0.2 and t = 0.

    图 11  Kn = 1, St = 1.0, t = 0时不同振幅Ah的中心线上温度分布 (a)竖直中心线X/L = 0.5; (b)水平中心线Y/L = 0.5

    Figure 11.  Temperature distribution on the centerline of Ah with different amplitudes when Kn = 1, St = 1.0 and t = 0: (a) Vertical centerline X/L = 0.5; (b) horizontal centerline Y/L = 0.5.

    图 12  Kn = 1, St = 1.0, t = 0时不同Ah时左、上壁面处气体温度T, 努塞尔数Nu和速度U分布

    Figure 12.  Distribution of gas temperature T, Nusselt number Nu and velocity U on the left and upper wall surfaces at different Ah when Kn = 1, St = 1.0 and t = 0.

    图 13  St = 1.0, t = 0时, 不同参数在不同AhKn下的变化 (a)左壁面中点温度Tcy; (b)上壁面中点温度Tcx; (c)左壁面中点努塞尔数Nucy; (d)左下半壁面平均速度$ {\overline{U}}_{{\mathrm{z}}{\mathrm{x}}} $

    Figure 13.  Variations of different parameters under different Ah and Kn when St = 1.0 and t = 0: (a) The midpoint temperature of the left wall Tcy; (b) temperature of the midpoint of the upper wall Tcx; (c) Nusselt number of the left wall midpoint Nucy; (d) the average velocity of the lower left half of the wall $ {\overline{U}}_{{\mathrm{z}}{\mathrm{x}}} $.

    图 14  Kn = 10, St = 1.0, t = 0时, 不同Ah下方腔内温度云图和流线 (a) Ah = 0.6; (b) Ah = 0.7; (c) Ah = 0.8

    Figure 14.  Temperature cloud maps and streamlines in the cavity with different Ah values at Kn = 10, St = 1.0, and t = 0: (a) Ah = 0.6; (b) Ah = 0.7; (c) Ah = 0.8.

    图 15  St = 1.0时不同AhKn下, 壁面平均努塞尔数$\overline{Nu} $的时间历程及$\overline{Nu} $的极差$ {\left(\Delta\overline{Nu}\right)}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}} $ (a), (c) X = 0, 左壁面; (b), (d) Y= 0, 下壁面

    Figure 15.  The time history of the average Nussel number $\overline{Nu} $ and the range $ {\left(\Delta\overline{Nu}\right)}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}} $ of $\overline{Nu} $ on the wall under different Ah and Kn when St = 1.0: (a), (c) Left wall, X = 0; (b), (d) lower wall surface, Y = 0.

    Baidu
  • [1]

    沈青 2006 力学进展 36 142Google Scholar

    Shen Q 2006 Adv. Mech. 36 142Google Scholar

    [2]

    Frangi A, Frezzotti A, Lorenzani S 2007 Comput. Struct. 85 810Google Scholar

    [3]

    梅涛, 陈占秀, 杨历, 朱洪漫, 苗瑞灿 2020 69 224701Google Scholar

    Mei T, Chen Z X, Yang L, Zhu H M, Miao R C 2020 Acta Phys. Sin. 69 224701Google Scholar

    [4]

    Ramadan K M, Qisieh O, Tlili I 2022 Proc. Inst. Mech. Eng. Part C 236 5033Google Scholar

    [5]

    Mousivand M, Roohi E 2022 Phys. Fluids 34 052002Google Scholar

    [6]

    Lan J, Xie J, Ye J, Peng W Z, Jiao X Y 2022 Int. J. Hydrogen Energy 47 19206Google Scholar

    [7]

    韩峰, 王晓伟, 张文青, 张世伟, 张志军 2023 真空科学与技术学报 43 238Google Scholar

    Han F, Wang X W, Zhang W Q, Zhang S W, Zhang Z J 2023 J. Vac. Sci. Technol. 43 238Google Scholar

    [8]

    王晓伟, 张志军, 张文青, 苏天一, 张世伟 2020 真空与低温 26 73Google Scholar

    Wang X W, Zhang Z J, Zhang W Q, Su T Y, Zhang S W 2020 Vac. Cryogen 26 73Google Scholar

    [9]

    Wu L, Zhang Y H, Li Z H 2017 Sci. Sin. phys. Mech. As. 47 070004Google Scholar

    [10]

    Tsimpoukis A, Vasileiadis N, Tatsios G, Valougeorgis D 2019 Phys. Fluids 31 067108Google Scholar

    [11]

    Taassob A, Kamali R, Bordbar A 2018 Vacuum 151 197Google Scholar

    [12]

    Nabapure D 2021 J. Comput. Sci. Neth. 49 101276.Google Scholar

    [13]

    Wu L, Reese J M, Zhang Y 2014 J. Fluid Mech. 748 350Google Scholar

    [14]

    Ogata Y, Kawaguchi T 2011 J. Fluid Sci. Technol. 6 215Google Scholar

    [15]

    Palharini R C, Scanlon T J, White C 2018 Comput. Fluids 165 173Google Scholar

    [16]

    Yang W Q, Tang S, Yang H 2019 Appl. Sci. 9 2733Google Scholar

    [17]

    单小东, 王沫然 2013 工程热 34 2159

    Shan X D, Wang M R 2013 J. Eng. Thermophys. 34 2159

    [18]

    张帅, 方蜀州, 许阳 2021 推进技术 42 2002Google Scholar

    Zhang S, Fang S Z, Xu Y 2021 J. Propul. Technol. 42 2002Google Scholar

    [19]

    Zhang J, Yao S Q, Fei F, Ghalambaz M, Wen D S 2020 Phys. Fluids 32 102001Google Scholar

    [20]

    Moghadam E Y, Roohi E, Esfahani J A 2014 Vacuum 109 333Google Scholar

    [21]

    Yamaguchi H, Perrier P, Ho M T, Méolans J G, Niimi T, Graur I 2016 J. Fluid Mech. 795 690Google Scholar

    [22]

    Barbera E, Brini F 2018 Europhys. Lett. 120 34001Google Scholar

    [23]

    Akhlaghi H, Roohi E, Stefanov S 2018 Sci. Rep. 8 13533Google Scholar

    [24]

    Han Y L 2010 Fluid Dyn. Res. 42 045505Google Scholar

    [25]

    Zhu M B, Roohi E, Ebrahimi A 2023 Phys. Fluids 35 052012Google Scholar

    [26]

    Roohi E, Shahabi V, Bagherzadeh A 2018 Int. J. Therm. Sci. 125 381Google Scholar

    [27]

    Wang P, Zhu L H, Su W, Wu L, Zhang Y H 2018 Phys. Rev. E 97 043103Google Scholar

    [28]

    Zhu L H, Guo Z L, Xu K 2016 Comput. Fluids 127 211Google Scholar

    [29]

    Wang X W, Su T Y, Zhang W Q, Zhang Z J, Zhang S W 2020 Microsyst. Nanoeng. 6 26Google Scholar

    [30]

    张贝豪, 郑林 2020 69 164401Google Scholar

    Zhang B H, Zheng L 2020 Acta Phys. Sin. 69 164401Google Scholar

    [31]

    Ou Y, Qu F, Wang G Y, Nie M Y, Li Z G, Ou W, Xie C Q 2016 Appl. Phys. Lett. 109 023512Google Scholar

    [32]

    万启坤, 张月, 郭照立 2023 计算物理 40 653

    Wan Q K, Zhang Y, Guo Z L 2023 Chinese J. Comput. Phys. 40 653

    [33]

    Kalempa D, Sharipov F, Silva J C 2019 Vacuum 159 82Google Scholar

    [34]

    Bargatin I, Kozinsky I, Roukes M L 2007 Appl. Phys. Lett. 90 093116Google Scholar

    [35]

    Ilic B, Yang Y, Aubin K, Reichenbach R, Krylov S, Craighead H G 2005 Nano Lett. 5 925Google Scholar

    [36]

    Juvé V, Crut A, Maioli P, Pellarin M, Broyer M, Del Fatti N, Vallée F 2010 Nano Lett. 10 1853Google Scholar

    [37]

    Guo Z L, Wang R J, Xu K 2015 Phys. Rev. E 91 033313Google Scholar

    [38]

    孙喜明, 姚朝晖, 杨京龙 2002 51 1942Google Scholar

    Sun X M, Yao Z H, Yang J L 2002 Acta Phys. Sin. 51 1942Google Scholar

    [39]

    孙佳坤, 林传栋, 苏咸利, 谭志城, 陈亚楼, 明平剑 2024 73 110504Google Scholar

    Sun J K, Lin C D, Su X L, Tan Z C, Chen Y L, Ming P J 2024 Acta Phys. Sin. 73 110504Google Scholar

    [40]

    Huang J C, Xu K, Yu P 2013 Commun. Comput. Phys. 14 1147Google Scholar

    [41]

    Wang Y, Zhong C W, Liu S 2019 Phys. Rev. E 100 063310Google Scholar

    [42]

    Zhu L H, Chen S Z, Guo Z L 2017 Comput. Phys. Commun. 213 155Google Scholar

    [43]

    Vargas M, Tatsios G, Valougeorgis D, Stefanov S 2014 Phys. Fluids 26 057101Google Scholar

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    [17] FAN TIAN-YOU, LIANG ZHEN-YA. A POSSIBLE MECHANISM OF THE GROWTH OF GRAIN-BOUNDARY CRACK AND AN ESTIMATION OF CREEP RUPTURE TIME. Acta Physica Sinica, 1978, 27(3): 269-275. doi: 10.7498/aps.27.269
    [18] CHEN CHI, DENG ZHI-SHENG, WU BAI-QUN, DING SHU-SHENG. THE CREEP AND STRESS-RUPTURE PROPERTIES OF γ′ CRYSTALS. Acta Physica Sinica, 1974, 23(1): 69-76. doi: 10.7498/aps.23.69
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    [20] LIN HUNG-SUN. ON THE GAS FLOW AND HEAT TRANSFER IN LAMINAR BOUNDARY LAYER FLOW. Acta Physica Sinica, 1954, 10(1): 71-88. doi: 10.7498/aps.10.71
Metrics
  • Abstract views:  472
  • PDF Downloads:  17
  • Cited By: 0
Publishing process
  • Received Date:  22 September 2024
  • Accepted Date:  12 December 2024
  • Available Online:  25 December 2024
  • Published Online:  20 February 2025

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