纤维悬浮流动稳定性研究
摘要
纤维悬浮流是指固体纤维粒子悬浮在液体或气体中形成的混合流动，在化工、纺织、造纸、医疗、环保、复合材料生产、食品加工等许多工业领域都有广泛应用。纤维悬浮流的研究还涉及多个学科分支，具有重要的理论意义。本文运用理论分析、数值计算以及实验的方法，对纤维悬浮流动稳定性相关问题进行了深入研究。
首先综合应用流体动力稳定性理论、细长体理论以及纤维方向张量工具，对纤维悬浮流进行线性稳定性分析，推导槽流和管流的稳定性方程，并对槽流导出在不同的稳定性分析模式以及不同的方向张量封闭格式下的多种形式方程。数值求解稳定性方程得到悬浮流的稳定性特征，发现纤维参数H值和水动力相互作用系数C_1的增加导致流动临界Re数增大，不稳定扰动的最大增长率降低，扰动失稳范围缩小。扰动速度的分布特征与发展规律也说明纤维的综合作用是抑制扰动增长，提高流动稳定性。
然后采用染色线流动显示技术与粒子图像测速技术对槽流悬浮流的扰动波特性进行定性和定量观测。染色线观测显示H值增大使扰动失稳距离增加，扰动衰减率与波数的关系同空间模式稳定性分析的理论结果定性一致。PIV测量得到流场速度矢量图及流线图，扰动波幅与波形特征说明，Re数一定时流动稳定性随H值增大而提高。验证了空间模式稳定性分析的理论结果。
从涡量的角度分析纤维改变悬浮流动稳定性的机理，利用涡量输运方程与涡能平衡方程分析纤维的作用。另外比较纤维的平面与三维取向状态、三种封闭格式对稳定性的影响，通过应力将纤维取向分析同流场涡量分析联系起来。
最后应用稳定性分析结果分析槽流悬浮流失稳阶段的减阻特性。发现当波数大于一定值时流动表现出减阻效应，增大H值可提高减阻率。将结果同部分湍流悬浮流减阻的实验结果进行定性比较。分析减阻机理是流速分布曲线及近壁区速度梯度介于层流与湍流之间，H值增大引起壁面剪应力显著下降。
Fibre suspensions refer to the liquid or gas flows containing suspending fibre particles. To this day they have been very familiar in nature and many fields of industry. On the other hand, researches of them involve many branches of subjects and have great academic values. This thesis researches on the stability of fibre suspensions applying theoretical, numerical and experimental methods.
First the linear stability analysis is performed to fibre suspensions utilizing flow stability, slender-body and orientation tensor theories. The governing equations of channel and pipe suspensions of different stability handling modes and tensor closure approximations are derived. Stability characteristics are obtained through numerical analysis. In general, the influence of fibre additives and their hydrodynamic interactions to the flow results in the increase of critical Reynolds number and the reduction of unstable region of disturbances, therefore reinforces the flow stability.
Qualitative and quantitative measurements of disturbances in channel suspensions are carried out using dye emission and PIV techniques. Traces of dyes indicate that the stable length increases with an augment of H, and the relations between spatial attenuation rates of disturbance and wavenumbers are correspondent with theoretical results by the analysis of spatial mode. Diagrams of velocity vectors and streamlines display waveform and amplitude properties, showing the effect of fibres on enhancing the flow stability. The computational results are tested.
Finally, the mechanisms behind the instability of fibre suspensions are presented from a point of view of vorticity. Effects of fibres are investigated through equations of vorticity transport and enstrophy balance. Then the two orientation states of fibres and three closure approximations are examined. Analyses of fibre orientation and vorticity in the suspension can be contacted by stress features.
In addition, drag reduction characteristics in the transition regime of channel suspensions are studied. It is found that drag reduction occurs with adequate wavenumbers and grows with an increase of H. The mechanisms are revealed through variations of velocity profile and the decrease of wall shear stress.
首先综合应用流体动力稳定性理论、细长体理论以及纤维方向张量工具，对纤维悬浮流进行线性稳定性分析，推导槽流和管流的稳定性方程，并对槽流导出在不同的稳定性分析模式以及不同的方向张量封闭格式下的多种形式方程。数值求解稳定性方程得到悬浮流的稳定性特征，发现纤维参数H值和水动力相互作用系数C_1的增加导致流动临界Re数增大，不稳定扰动的最大增长率降低，扰动失稳范围缩小。扰动速度的分布特征与发展规律也说明纤维的综合作用是抑制扰动增长，提高流动稳定性。
然后采用染色线流动显示技术与粒子图像测速技术对槽流悬浮流的扰动波特性进行定性和定量观测。染色线观测显示H值增大使扰动失稳距离增加，扰动衰减率与波数的关系同空间模式稳定性分析的理论结果定性一致。PIV测量得到流场速度矢量图及流线图，扰动波幅与波形特征说明，Re数一定时流动稳定性随H值增大而提高。验证了空间模式稳定性分析的理论结果。
从涡量的角度分析纤维改变悬浮流动稳定性的机理，利用涡量输运方程与涡能平衡方程分析纤维的作用。另外比较纤维的平面与三维取向状态、三种封闭格式对稳定性的影响，通过应力将纤维取向分析同流场涡量分析联系起来。
最后应用稳定性分析结果分析槽流悬浮流失稳阶段的减阻特性。发现当波数大于一定值时流动表现出减阻效应，增大H值可提高减阻率。将结果同部分湍流悬浮流减阻的实验结果进行定性比较。分析减阻机理是流速分布曲线及近壁区速度梯度介于层流与湍流之间，H值增大引起壁面剪应力显著下降。
Fibre suspensions refer to the liquid or gas flows containing suspending fibre particles. To this day they have been very familiar in nature and many fields of industry. On the other hand, researches of them involve many branches of subjects and have great academic values. This thesis researches on the stability of fibre suspensions applying theoretical, numerical and experimental methods.
First the linear stability analysis is performed to fibre suspensions utilizing flow stability, slender-body and orientation tensor theories. The governing equations of channel and pipe suspensions of different stability handling modes and tensor closure approximations are derived. Stability characteristics are obtained through numerical analysis. In general, the influence of fibre additives and their hydrodynamic interactions to the flow results in the increase of critical Reynolds number and the reduction of unstable region of disturbances, therefore reinforces the flow stability.
Qualitative and quantitative measurements of disturbances in channel suspensions are carried out using dye emission and PIV techniques. Traces of dyes indicate that the stable length increases with an augment of H, and the relations between spatial attenuation rates of disturbance and wavenumbers are correspondent with theoretical results by the analysis of spatial mode. Diagrams of velocity vectors and streamlines display waveform and amplitude properties, showing the effect of fibres on enhancing the flow stability. The computational results are tested.
Finally, the mechanisms behind the instability of fibre suspensions are presented from a point of view of vorticity. Effects of fibres are investigated through equations of vorticity transport and enstrophy balance. Then the two orientation states of fibres and three closure approximations are examined. Analyses of fibre orientation and vorticity in the suspension can be contacted by stress features.
In addition, drag reduction characteristics in the transition regime of channel suspensions are studied. It is found that drag reduction occurs with adequate wavenumbers and grows with an increase of H. The mechanisms are revealed through variations of velocity profile and the decrease of wall shear stress.
引文
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4．林建忠，石兴，邵雪明，黄利忠。2002，纤维悬浮混合层中纤维取向与流场应力的研究。自然科学进展，12，372-376。
5．林建忠，王巍雄。2001b，柱状粒子在液体中沉降的数值模拟。中国工程热物理学会多相流会议论文集，186-190。
6．林建忠，张凌新，吴法理。2001c，纤维悬浮流中的方向分布函数及张量研究。第七届全国工业与环境流体力学会议论文集，5-9。
7．石兴。2002，纤维悬浮混合层及柱状粒子运动直接模拟的研究。浙江大学博士学位论文。
8．余钊圣。1999，三维混合层流场中拟序结构的直接数值模拟。浙江大学硕士学位论文。
9．张卫峰，林建忠。2000，柱状粒子悬浮流中粒子的受力分析。第五届全国多相流、非牛顿流、物理化学流学术会议论文集，8-13。
10．朱泽飞。2000，柱状粒子悬浮流的运动研究。浙江大学博士学位论文。
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2．林建忠。2000，纤维悬浮流场动力学研究综述。力学与实践，22，11-17。
3．林建忠，聂德明。2001a，纤维悬浮两相边界层流场稳定性的研究。中国工程热物理学会多相流会议论文集，285-289。
4．林建忠，石兴，邵雪明，黄利忠。2002，纤维悬浮混合层中纤维取向与流场应力的研究。自然科学进展，12，372-376。
5．林建忠，王巍雄。2001b，柱状粒子在液体中沉降的数值模拟。中国工程热物理学会多相流会议论文集，186-190。
6．林建忠，张凌新，吴法理。2001c，纤维悬浮流中的方向分布函数及张量研究。第七届全国工业与环境流体力学会议论文集，5-9。
7．石兴。2002，纤维悬浮混合层及柱状粒子运动直接模拟的研究。浙江大学博士学位论文。
8．余钊圣。1999，三维混合层流场中拟序结构的直接数值模拟。浙江大学硕士学位论文。
9．张卫峰，林建忠。2000，柱状粒子悬浮流中粒子的受力分析。第五届全国多相流、非牛顿流、物理化学流学术会议论文集，8-13。
10．朱泽飞。2000，柱状粒子悬浮流的运动研究。浙江大学博士学位论文。
11. Acton E. 1976 The modelling of large eddies in a tow-dimensional shear layer. J. Fluid Mech. 76, 561-592.
12． Altan M. C., Guceri S. I. & Pipes R. B. 1992 Anisotropic channel flow of fiber suspensions. J. Non-Newton. Fluid Meck 42, 65-83．
13． Andersson S. R. & Rasmuson A. 1997 Dry and wet friction of single pulp and synthetic fibres. J. Pulp Pap. Sci. 23, 5-11．
14． Azaiez J. 2000a Linear stability of free shear flows of fibre suspensions. .J Fluid Mech, 404, 179-209．
15． Azaiez J. 2000b Reduction of free shear flows instability: Effects of polymer versus fibre additives. J Non-Newtonian Fluid Mech 91, 233-254．
16． Batchelor G. K. 1970a The stress system in a suspension of force-free particles. .J. Fluid Mech. 41,545-570．
17． Batchelor G. K. 1970b Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44． 419-440．
18． Batchelor G. K. 1971 The stress generated in a non-dilute suspension of elongated particles by pure straining motion. J. Fluid Mech. 46, 813-829．
19． Batchelor G. K. 1972 Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52, 245-268．
20． Bernstein O. & Shapiro M. 1994 Direct determination of the orientation distribution function of cylindrical particles immersed in laminar and turbulent flow. J. Aerosol Aci. 25． 113-136．
21． Bibbo M. A. & Armstrong R. C. 1988 Rheology of semi-concentrated fiber suspensions in Newtonian and Non-Newtonian fluids. Proceedings of Manufacturing International '88． Sponsored by: ASME, Council on Engineering, New York, NY, USA.
22． Brown G. L. & Roshko A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775-816．
23． Burgers J. M. 1938 On the motion of small particles of elongated form suspended in a viscous liquid. Chap. 3 of Second Report of Viscosity and Plasticity. Kon. Ned. Akad. Wet., Verhand. 16, 113．
24． Cho H. E., Iribane & Richard W. 1981 On the orientation of ice crystals in cumulonimbus cloud. J. Atmos. Sci. 38, 111-113．
25． Corcos G. M. & Sherman F. S. 1984 The mixing layer: deterministic models of a turbulent flow. Ⅰ . Introduction and the two-dimensional flow. J. Fluid Mech. 139, 29-65．
26． Cox R. G. 1971 The motion of long slender bodies in a viscous fluid. Ⅱ. Shear flow. J. Fluid Mech. 45, 625-657．
27． Crowe C. T., Chung L N. & Troutt T. R. 1988 Particle mixing in free shear flows. Prog. Energy Combust. Sci. 14, 171-194．
28． Crowe C. T., Gore R. A. & Troutt T. R. 1985 Particle dispersion by coherent structures in free shear flows. Paniculate Sci. Tech. 3, 149-158．
29． Dinh S. M. & Armstrong R. C. 1984 Rheological equation of state for semi-concentrated fiber suspensions. J. Rheol. 28, 207-227．
30． Eduljee R. F. & Gillespie J. W. 1990 Analytical solutions for fiber orientation in 2-D flows of dilute suspensions. Polymer Comp. 11, 56-64．
31． Fan X. J., Phan-Thien N. & Zheng R. 1999 Simulation of fibre suspension flows by the Brownian configuration field method. J. Non-Newtonian Fluid Mech. 84． 257-274．
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