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为了了解水平温度梯度作用下旋转环形浅液池内耦合热-溶质毛细对流基本特征, 采用匹配渐近展开法对旋转环形浅液池内耦合热-溶质毛细对流过程进行了求解, 获得了中心区域的速度、温度和浓度分布,分析了旋转、Soret效应、浮力、溶质扩散 系数和液池的几何尺寸对流动结构的影响.将所得到的渐近解和文献中的已有结果进行对比,证明了所求结果的正确性;在浅液池内,耦合热-溶质毛细力对流体流动起主导作用, 旋转和浮力对流动的影响较小,溶质扩散系数和几何尺寸有较明显影响;当各种耦合的 驱动力作用方向相同时,流动增强;否则, 流动减弱.
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关键词:
- 旋转 /
- 环形浅液池 /
- 耦合热-溶质毛细对流 /
- 渐近解
In order to understand the characteristics of the coupled thermal and solutal capillary convection with the radial temperature gradient in a slowly rotating shallow annular pool with the free surface, the asymptotic solution is obtained in the core region using asymptotical analysis in the limit as the aspect ratio, which is defined as the ratio of the layer thickness to the gap width, goes to zero. The influences of the rotating, Soret effect, solute diffusion coefficient, buoyant force and geometric parameters on fluid flow are analyzed. The results show that when the rotating and the solutal capillary force and the buoyancy induced by the ununiform distribution of solute concentration are not considered, the asymptotic solution is the same as that of the previous work. The influences of the rotating, the buoyancy, solute diffusion coefficient and the geometric parameters on the fluid flow are all small and the coupled thermal and solutal capillary forces play a dominant role in the convection. When the coupled forces are in the same direction, the flow is reinforced, otherwise, the flow is suppressed.-
Keywords:
- rotating /
- shallow annular pool /
- coupled thermal and solutal capillary convection /
- asymptotic solution
[1] Schwabe D, Scharmann A, Preisser F, Oeder R 1978 J. Cryst. Growth 43 305
[2] Cröll A, Mitric A, Aniol O, Schtt S, Simon P 2009 Cryst. Res. Technol. 44 1101
[3] Wang J S, Yan J J, Hu S H, Liu J P 2009 Int. J. Heat Mass Transfer 52 1533
[4] Bergman T L 1986 Phys. Fluids 29 2103
[5] Bergeon A, Henry D, Benhadid L H, Tuckerman L S 1998 J. Fluid Mech. 375 143
[6] Arafune K, Hirata A 1998 Numerical Heat Transfer A 44 421
[7] Arafune K, Yamamoto K, Hirata A 2001 Int. J. Heat Mass Transfer 44 2405
[8] Chen C F, Chan C L 2010 Int. J. Heat Mass Transfer 53 1563
[9] Li Y S, Chen Z W, Zhan J M 2010 Int. J. Heat Mass Transfer 53 5223
[10] Chen Z W, Li Y S, Zhan J M 2010 Phys. Fluids 22 0341006
[11] Zhan J M, Chen Z W, Li Y S, Nie Y H 2010 Phys. Rev. E 82 066305
[12] Li Y R, Wu C M, Wu S Y, Peng L 2009 Phys. Fluids 21 084102
[13] Shi W Y, Ermakov M K, Imaishi N 2006 J. Cryst. Growth 294 474
[14] Zheng L C, Sheng X Y, Zhang X X 2006 Acta Phys. Sin. 55 5298 (in Chinese) [郑连存, 盛晓艳, 张欣欣 2006 55 5298]
[15] Zheng L C, Feng Z F, Zhang X X 2007 Acta Phys. Sin. 56 1549 (in Chinese) [郑连存, 冯志丰, 张欣欣 2007 56 1549]
[16] Zhang Y, Zheng L C, Zhang X X 2009 Acta Phys. Sin. 58 5506 (in Chinese) [张艳, 郑连存, 张欣欣 2009 58 5506]
[17] Cormack D E, Leal L G 1974 J. Fluid Mech. 65 209
[18] Merker G P, Leal L G 1980 Int. J. Heat Mass Transfer 23 677
[19] Leppinen D M 2002 Int. J. Heat Mass Transfer 45 2967
[20] Li Y R, Zhao X X, Wu S Y, Peng L 2008 Phys. Fluids 20 082107
[21] Li Y R, Ouyang Y Q, Wang S C, Wu S Y 2010 J. Eng. Thermophys. 31 1921 (in Chinese) [李友荣, 欧阳玉清, 王双成, 吴双应 2010 工程热 31 1921]
[22] Li Y R, Wang S C, Wu S Y, Peng L 2010 Microgravity Sci. Technol. 22 193
[23] Sen A K, Davis S H 1982 J. Fluid Mech. 12 163
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[1] Schwabe D, Scharmann A, Preisser F, Oeder R 1978 J. Cryst. Growth 43 305
[2] Cröll A, Mitric A, Aniol O, Schtt S, Simon P 2009 Cryst. Res. Technol. 44 1101
[3] Wang J S, Yan J J, Hu S H, Liu J P 2009 Int. J. Heat Mass Transfer 52 1533
[4] Bergman T L 1986 Phys. Fluids 29 2103
[5] Bergeon A, Henry D, Benhadid L H, Tuckerman L S 1998 J. Fluid Mech. 375 143
[6] Arafune K, Hirata A 1998 Numerical Heat Transfer A 44 421
[7] Arafune K, Yamamoto K, Hirata A 2001 Int. J. Heat Mass Transfer 44 2405
[8] Chen C F, Chan C L 2010 Int. J. Heat Mass Transfer 53 1563
[9] Li Y S, Chen Z W, Zhan J M 2010 Int. J. Heat Mass Transfer 53 5223
[10] Chen Z W, Li Y S, Zhan J M 2010 Phys. Fluids 22 0341006
[11] Zhan J M, Chen Z W, Li Y S, Nie Y H 2010 Phys. Rev. E 82 066305
[12] Li Y R, Wu C M, Wu S Y, Peng L 2009 Phys. Fluids 21 084102
[13] Shi W Y, Ermakov M K, Imaishi N 2006 J. Cryst. Growth 294 474
[14] Zheng L C, Sheng X Y, Zhang X X 2006 Acta Phys. Sin. 55 5298 (in Chinese) [郑连存, 盛晓艳, 张欣欣 2006 55 5298]
[15] Zheng L C, Feng Z F, Zhang X X 2007 Acta Phys. Sin. 56 1549 (in Chinese) [郑连存, 冯志丰, 张欣欣 2007 56 1549]
[16] Zhang Y, Zheng L C, Zhang X X 2009 Acta Phys. Sin. 58 5506 (in Chinese) [张艳, 郑连存, 张欣欣 2009 58 5506]
[17] Cormack D E, Leal L G 1974 J. Fluid Mech. 65 209
[18] Merker G P, Leal L G 1980 Int. J. Heat Mass Transfer 23 677
[19] Leppinen D M 2002 Int. J. Heat Mass Transfer 45 2967
[20] Li Y R, Zhao X X, Wu S Y, Peng L 2008 Phys. Fluids 20 082107
[21] Li Y R, Ouyang Y Q, Wang S C, Wu S Y 2010 J. Eng. Thermophys. 31 1921 (in Chinese) [李友荣, 欧阳玉清, 王双成, 吴双应 2010 工程热 31 1921]
[22] Li Y R, Wang S C, Wu S Y, Peng L 2010 Microgravity Sci. Technol. 22 193
[23] Sen A K, Davis S H 1982 J. Fluid Mech. 12 163
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