弯曲水流中固液两相运动夹角的研究
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摘要
自上世纪九十年代开始,国内外学者对弯曲水流中固液两相运动开展了大量研究,尤其是数值模拟的研究,并得到了一些成果,然而,弯曲水流中固液两相运动的夹角如何,尚无人涉及,有待研究。固体颗粒在弯曲水流中会由于密度不同和水流作用力的变化而产生与水流的分离运动。这种与水流的分离运动有利有弊,在多种因素的综合作用下可以衍生出多种自然灾害、险情与工业设备损毁;另外,这一特性也被广泛应用于水利、环境保护、冶矿等领域。研究这种运动特性是把握其致害规律,推进相关应用技术发展的关键。本文旨在通过数值计算和实验方法研究固体颗粒在弯曲水流中发生分离运动的特性,并提出以分离角作为量化标准的计算公式。
数值部分作为辅助工具,通过4阶龙格-库塔格式求解颗粒运动方程,获得了颗粒分离运动要素的变化过程,分析讨论了各种水流作用力对颗粒分离运动的影响,并求出不同时刻颗粒运动方向与水流运动方向的分离角度,分析了影响颗粒分离角的三大主要因素。在数值计算的基础上,针对3个主要参数:颗粒粒径、密度和平台转速进行了27个不同参数组合的实验。分析了设备水平、图像观测和照片扭曲等主要误差来源,通过特定的修正方法,减小了照片扭曲产生的误差,并运用螺旋线来拟合观测数据,获得了连续有效的分离角实验数据。实验结果与数值解吻合良好。研究表明,在床面上的静止颗粒在水流作用下开始运动后,颗粒运动迅速得到发展,颗粒与水流运动方向的分离角亦迅速增大,然后随时间的推移逐步减少;颗粒运动充分发展以后的分离角与当地水流流速、水流运动曲率半径和颗粒的大小及比重有关;在实验范围内,颗粒运动的分离角最大不超过20°。最后,利用多元回归方法,提出了分离角计算公式。
Since the 1990s, extensive research was carried out regarding solid-liquid two-phase movement in curvilinear flows, especially the study of numerical simulation. However, none of it was involved in deviation angle between 2-phase movements.
In curvilinear flows, deviation motion of particle due to its different density and hydrodynamic force can lead to varieties of natural disaster and dangers in industrial process. However, it can be applied to water conservancy and mining industry. Studying its rule is necessary to control its damage and promote the development of corresponding technology. This thesis aims to propose a formula of deviation angle, a quantitative standard of deviation characteristics, through numerical and experimental method. As an auxiliary tool, numerical part aim to analyze the effect of hydrodynamic force on deviation angle and find out the main corresponding parameters. In case of 2D rotational flow (steady along streamline), the kinematic equation is solved through 4th order Runge-Kutta method to get the deviation angle induced by hydrodynamic forces. Based on the numerical result, 27 experiments with different particle diameter, density or rotational speed were carried out on a rotational platform. Three main errors are considered such as device’s leveling, observational error and photos’distortion. Through specific approach, the error induced by distorted photos was narrowed down to minimum. Series of effective data was achieved by fitting observed data with spiral lines. The numerical simulations were consistently compared with the experimental results.
Based on the multiple regression method, a formula was proposed to predict the deviation angle. The study shows that the motion of the particle resting on the bed developed very fast after initiating its movement, the deviation angle dramatically increased and reached a peak, and thereafter decreased gradually. The maximum deviation angle did not exceed 20 degree in the present tests.
数值部分作为辅助工具,通过4阶龙格-库塔格式求解颗粒运动方程,获得了颗粒分离运动要素的变化过程,分析讨论了各种水流作用力对颗粒分离运动的影响,并求出不同时刻颗粒运动方向与水流运动方向的分离角度,分析了影响颗粒分离角的三大主要因素。在数值计算的基础上,针对3个主要参数:颗粒粒径、密度和平台转速进行了27个不同参数组合的实验。分析了设备水平、图像观测和照片扭曲等主要误差来源,通过特定的修正方法,减小了照片扭曲产生的误差,并运用螺旋线来拟合观测数据,获得了连续有效的分离角实验数据。实验结果与数值解吻合良好。研究表明,在床面上的静止颗粒在水流作用下开始运动后,颗粒运动迅速得到发展,颗粒与水流运动方向的分离角亦迅速增大,然后随时间的推移逐步减少;颗粒运动充分发展以后的分离角与当地水流流速、水流运动曲率半径和颗粒的大小及比重有关;在实验范围内,颗粒运动的分离角最大不超过20°。最后,利用多元回归方法,提出了分离角计算公式。
Since the 1990s, extensive research was carried out regarding solid-liquid two-phase movement in curvilinear flows, especially the study of numerical simulation. However, none of it was involved in deviation angle between 2-phase movements.
In curvilinear flows, deviation motion of particle due to its different density and hydrodynamic force can lead to varieties of natural disaster and dangers in industrial process. However, it can be applied to water conservancy and mining industry. Studying its rule is necessary to control its damage and promote the development of corresponding technology. This thesis aims to propose a formula of deviation angle, a quantitative standard of deviation characteristics, through numerical and experimental method. As an auxiliary tool, numerical part aim to analyze the effect of hydrodynamic force on deviation angle and find out the main corresponding parameters. In case of 2D rotational flow (steady along streamline), the kinematic equation is solved through 4th order Runge-Kutta method to get the deviation angle induced by hydrodynamic forces. Based on the numerical result, 27 experiments with different particle diameter, density or rotational speed were carried out on a rotational platform. Three main errors are considered such as device’s leveling, observational error and photos’distortion. Through specific approach, the error induced by distorted photos was narrowed down to minimum. Series of effective data was achieved by fitting observed data with spiral lines. The numerical simulations were consistently compared with the experimental results.
Based on the multiple regression method, a formula was proposed to predict the deviation angle. The study shows that the motion of the particle resting on the bed developed very fast after initiating its movement, the deviation angle dramatically increased and reached a peak, and thereafter decreased gradually. The maximum deviation angle did not exceed 20 degree in the present tests.
引文
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[44]李国美,王跃社,亢力强,突扩圆管内液—固两相流固体颗粒运动,工程热物理学报,2008,29(12):2062~2064.
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[2]王随继,黄河流域河型转化现象初探[J],地理科学进展,2008,27(2):11~16
[3]曹连喜,论固体物料水力输送中的管道磨损[J],有色金属,1997,4:19~22
[4]张开泉刘焕芳,涡管分水排沙规律的研究及其工程应用[J],泥沙研究,1991,4:3~12
[5]刘小兵,张家川,程良骏,旋转流场中沙粒运动的数值模拟[J],水动力学研究与进展,1998,13(3):339~345
[6]罗中平,分选水力旋流器的研究与应用[J],国外金属矿选矿,1993,11:16~18
[7] Nikkam Sures等,水介质旋流器[J],国外锡工业,1990,18(4):16~19
[8]刘凡清,范德顺,黄钟.固液分离与工业水处理[M].北京:中国石化出版社,2001(1):1-17
[9] Poisson, S. A. Memoire sur les Mouvements Simultanes d’un Penduleet de L’air Environnemant, 9, Paris, Mem. Acad. Sci., 1831: 521–523.
[10] Green, G. Researches on the Vibration of Pendulums in Fluid Media. Trans. R. Soc. Edinbrgh, 1833, 13: 54–68.
[11] Stokes, G. G. On the Theories of Internal Friction of the Fluids in Motion, Trans. Cambridge Philos. Soc., 1845, 8: 287–319.
[12] Stokes, G. G. On the Theories of Internal Friction of the Fluids in Motion, Trans. Cambridge Philos. Soc., 1845, 8: 287–319.
[13] Boussinesq, V. J. Sur la Resistance qu’Oppose un Liquide Inde′fini en Repos . . . , C. R., Acad. Sci., 1885, 100: 935–937.
[14] Whitehead, A. N. Second Approximation to Viscous Fluid Motion. A Sphere Moving Steadily in a Straight Line[J], Q. J. Math., 1889, 23: 143–152.
[15] Oseen, C. W. Uber die Stokes’sche Formel und Uber eine verwandte Aufgabe in der Hydrodynamik, Ark. Mat., Astron. Fys., 1910: 6~29.
[16] Oseen, C. W. Uber den Goltigkeitsbereich der Stokesschen Widerstandsformel,Ark. Mat., Astron. Fys. , 1913: 9~19.
[17] Faxen, H. Der Widerstand gegen die Bewegung einer starren Kugel in einer zum den Flussigkeit, die zwischen zwei parallelen EbenenWinden eingeschlossenist, Ann. Phys. Leipzig, 1922, 68: 89–119.
[18] Tchen, C. M. Mean Values and Correlation Problems Connected With the Motion of Small Particles Suspended in a Turbulent Fluid, doctoral dissertation, Technical University of Delft, Delft, The Netherlands, 1949.
[19] Corssin, S. and Lumley, J. L., On the Equation of Motion of a Particle in a Turbulent Fluid, Appl. Sci. Res., Sect. A, 1957, 6: 114–116.
[20] Sy, F., Taunton, J. W., and Lightfoot, E. N. Transient Creeping Flow Around Spheres, AIChE J., 1970, 16: 386–391.
[21] Proudman, I., and Pearson, J. R. A. Expansions at Small Reynolds Numbers for the Flow Past a Sphere and a Circular Cylinder[J], J. Fluid Mech., 1956, 2: 237–262.
[22] Sano, T., Unsteady Flow Past a Sphere at Low Reynolds Number[J], J. Fluid Mech., 1981, 112: 433–441.
[23] Maxey, M. R., and Riley, J. J. Equation of Motion of a Small Rigid Sphere in a Non-Uniform Flow, Phys. Fluids, 1983, 26: 883–889.
[24] Mei, R., Lawrence, C. J., and Adrian, R. J. Unsteady Drag on a Sphere at Finite Reynolds Number With Small Fluctuations in the Free-Stream Velocity[J], J. Fluid Mech., 1991, 233: 613–631.
[25] Lovalenti, P. M., and Brady, J. F. The Hydrodynamic Force on a Rigid Particle Undergoing Arbitrary Time-Dependent Motion at Small Reynolds Numbers[J], J. Fluid Mech., 1993, 256: 561–601.
[26] Hinch, E. J. The Approach to Steady State in Oseen Flows, J. Fluid Mech., 1993, 256: 601–603.
[27] Odar, F., and Hamilton, W. S. Forces on a Sphere Accelerating in a Viscous Fluid, J. Fluid Mech., 1964, 18: 302–303.
[28] Schiller, L., and Nauman, A. Uber die grundlegende Berechnung bei der Schwekraftaufbereitung, Ver. Deutch. Ing., 1933, 44: 318–320.
[29] Al-taweel, A. M., and Carley, J. F. Dynamics of Single Spheres in Pulsated Flowing Liquids: Part I. Experimental Methods and Results, AIChE Symp. Sr., 1971, 67(116):114–123.
[30] Al-taweel, A. M., and Carley, J. F. Dynamics of Single Spheres in Pulsated Flowing Liquids: Part II. Modeling and Interpretation of Results, AIChE Symp. Ser., 1972, 67(116): 124–131.
[31] Tsuji, Y., Kato, N., and Tanaka, T. Experiments on the Unsteady Drag and Wake of a Sphere at High Reynolds Numbers, Int. J. Multiphase Flow, 1991, 17: 343–354.
[32] Bataille, J., Lance, M., and Marie, J. L. Bubbly Turbulent Shear Flows, J. Kim, U. Rohatgi, and M. Hashemi, eds., FED-Vol. 99, ASME, New York, 1990: 1–7.
[33] Darwin, C. A Note on Hydrodynamics, Proc. Roy. Soc., 1953, 49: 342–353.
[34] Rivero, M., Magnaudet, J., & Fabre, J. Quelques Resultats Nouveaux Concernants les Forces Exerce′es sur une Inclusion Spherique par Ecoulement Accelere, C. R. Acad. Sci., Ser. II: Mec., Phys., Chim., Sci. Terre Univers, 1991, 312, ser. II: 1499–1506.
[35] Auton, T. R., Hunt, J. R. C., and Prud’homme, M. The Force Exerted on a Body in Inviscid Unsteady Non-Uniform Rotational Flow[J], J. Fluid Mech., 1988, 197: 241–257.
[36] Kim, I., Elghobashi, S., and Sirignano, W. A. On the Equation for Spherical Particle Motion: Effect of Reynolds and Acceleration Numbers[J], J. Fluid Mech., 1998, 367: 221–253.
[37] Chaplin, J. R. History Forces and the Unsteady Wake of a Cylinder[J], J. Fluid Mech., 1999, 393: 99–121.
[38] Kim, I., Elghobashi, S., and Sirignano, W. A. Three-Dimensional Flow Over Two Spheres Placed Side by Side[J], J. Fluid Mech., 1993, 246: 465–488.
[39] Chiang, H., and Kleinstreuer, C. Numerical Analysis of Variable- Fluid-Property Effects on the Convective Heat and Mass Transfer of Fuel Droplets, Combust. Flame, 1993, 92: 459–464.
[40] Feng, J., and Joseph, D. D. The Unsteady Motion of Solid Bodies in Creeping Flows[J], J. Fluid Mech., 1995, 303: 83–102.
[41]黄远东,吴文权,张红武,王光谦,非定常不稳定液固两相流动中旋涡对颗粒运动影响的数值研究,水科学进展,2002,13(1):2~8.
[42]朱彤,野崎勉,徐成海,张世伟,旋转型分离器流场中粒子运动的数值解析,化学工程,2007,35(8):38~41.
[43]刘娟,许洪元,唐澍,陆力,离心泵内固体颗粒运动规律与磨损的数值模拟,农业机械学报,2008,39(6):55~59.
[44]李国美,王跃社,亢力强,突扩圆管内液—固两相流固体颗粒运动,工程热物理学报,2008,29(12):2062~2064.
[45]冯旺聪,郑士琴,粒子图像测速PIV技术的发展,仪器仪表用户,2003,10(6):1~3.
[46]于建文,刘晓东,黄金瑞,几种先进测量技术浅析,锅炉制造,2002,3:79~80.
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