电流变液及屈服应力流体动力学分析
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摘要
电流变液是一种新型智能材料，在外加电场作用下呈现出屈服应力流体特性，自20世纪40年代以来，电流变液的研究曾一度处于低谷，但随着材料科学的发展，电流变液的潜在应用领域越来越广阔，近20年来电流变液的研究受到越来越多的关注。
本文首先从微观的角度，分析电流变链在Poiseuille流动中的受力以及变形，分析过程中推导了矩形截面管内Poiseuille流动速度分布的Galerkin近似解，并采用理论力学软索模型对电流变变链的受力进行分析，从而避免了点偶极子近似在粒子相距较近情况下引起的误差。分析结果可作为进一步讨论电流变液屈服应力以及临界电场强度的基础。
其次本文从运用的角度，在考虑电流变液屈服特性的前提下，分析了两种典型电流变器件（圆桶型电流变离合器和平板电流变阀）稳态以及瞬态动力学特性。对圆桶型电流变离合器动力学特性的分析发现，在离合器关闭时突加电场瞬间，流场中并未瞬时产生未屈服区，而存在滞后时间，且随外加电场强度的增大而减小；电流变液屈服应力方程中，参数以2.0为界，和时，离合器动力学特性具有显著区别。
论文第三部分对电流变液非零压力梯度平板剪切流动的稳定性进行了分析，提出流场对屈服应力达到饱和的概念；并得出平板壁面剪切运动以及电流变液屈服应力的提高，都将使流动稳定性增强的结论。
在论文第四部分中，对同心圆桶间宾汉流体螺旋T-C（Taylor-Couette）流动的稳定性进行分析，并采用有限体积法对失稳后的螺旋T-C流动，即螺旋T-V（Taylor-vortex）流动进行了数值模拟。研究发现对于螺旋T-C流动，屈服应力对流动稳定性具有双重影响；外桶旋转始终使流动趋于稳定；内桶轴向剪切运动能够增强流动对轴对称小扰动的抑制能力，但对非轴对称小扰动情况却不相同，即内桶轴向剪切运动仅对流动稳定性起有限增强作用；此外内、外桶半径比（0到1之间）增大，也将使流动趋于稳定。通过对螺旋T-V流动的数值模拟发现，屈服应力增大将使流场中Taylor涡减弱，且当屈服应力足够大时，螺旋T-V流动重新恢复螺旋T-C流动；内桶轴向剪切运动在使Taylor涡发生轴向迁移的同时也使其强度减弱。
Electrorheological fluid (ERF) is a new kind of "smart" material. When extra electric field is applied, it behaves just like a yield-stress fluid. The reports of research with ERF appeared sporadically since it was firstly reported in 1940's. But recently, with the development of materials science, the potential application region of ERF becomes more and more wide. And the number of investigations increased dramatically and researchers begin to pay more and more attentions to it.
In present dissertation, firstly an analytical study on the force and deformation of an ER single chain under Poiseuille flow is presented from the point of microscopic view. An approximate solution of the Poiseuille flow in a tube with rectangular cross is derived from Galerkin approach. The balance equation of moment for the ER chain is established to avoid using point-dipole model, which is not accurate enough in the case that dielectric particles are adjacent to each other. The result can be used in further study about the yield-stress and critical electric field strength.
Secondly, the steady and transient characteristics of concentric cylinder ER clutch and plane ER valve are studied with the consideration of yield. It can be found that when the extra electric field is suddenly applied, non-yield region in the clutch dose not generate synchronously. There is a retardation time which becomes shorter while the extra electric field becomes stronger. The demarcation point of, which is the parameter in ERF's yield stress equation, is 2.0. For, the dynamic characteristics of the clutch are remarkably different from those for.
Thirdly, the linear stability of plane shearing flow with non zero pressure gradient is studied. The conception of yield stress saturation is proposed. It can be found that the flow is stabilized by both plane shearing and the increment of yield stress.
The study about the linear stability of spiral Taylor-Couette flow is the fourth part of the dissertation. The numerical simulation of the Taylor-vortex
flow, which is the unstable pattern of the Taylor-Couette flow, is also achieved here. It can be found that yield stress plays a dual role in fluid stability and the rotation of the outer cylinder has stabilizing effect on the flow. The effect of the inner cylinder's sliding is slightly stabilizing on the disturbance of axisymmetric mode but destabilizing on the disturbance of non-axisymmetric mode. So the inner cylinder sliding just has a finite stabilizing effect on the spiral Taylor-Couette flow. Besides these, the increment of the radius ratio of the inner and outer cylinder also has stabilizing effect on the flow. It can be found from the analysis of the Taylor-vortex flow, that both the increment of yield stress and the sliding of the inner cylinder have the effect of weakening Taylor vortex. When the yield stress is high enough, the flow pattern will evolve from Taylor-vortex flow to Taylor-Couette flow and the Taylor vortex has a migration movement along the axial because of the existence of sliding.
本文首先从微观的角度，分析电流变链在Poiseuille流动中的受力以及变形，分析过程中推导了矩形截面管内Poiseuille流动速度分布的Galerkin近似解，并采用理论力学软索模型对电流变变链的受力进行分析，从而避免了点偶极子近似在粒子相距较近情况下引起的误差。分析结果可作为进一步讨论电流变液屈服应力以及临界电场强度的基础。
其次本文从运用的角度，在考虑电流变液屈服特性的前提下，分析了两种典型电流变器件（圆桶型电流变离合器和平板电流变阀）稳态以及瞬态动力学特性。对圆桶型电流变离合器动力学特性的分析发现，在离合器关闭时突加电场瞬间，流场中并未瞬时产生未屈服区，而存在滞后时间，且随外加电场强度的增大而减小；电流变液屈服应力方程中，参数以2.0为界，和时，离合器动力学特性具有显著区别。
论文第三部分对电流变液非零压力梯度平板剪切流动的稳定性进行了分析，提出流场对屈服应力达到饱和的概念；并得出平板壁面剪切运动以及电流变液屈服应力的提高，都将使流动稳定性增强的结论。
在论文第四部分中，对同心圆桶间宾汉流体螺旋T-C（Taylor-Couette）流动的稳定性进行分析，并采用有限体积法对失稳后的螺旋T-C流动，即螺旋T-V（Taylor-vortex）流动进行了数值模拟。研究发现对于螺旋T-C流动，屈服应力对流动稳定性具有双重影响；外桶旋转始终使流动趋于稳定；内桶轴向剪切运动能够增强流动对轴对称小扰动的抑制能力，但对非轴对称小扰动情况却不相同，即内桶轴向剪切运动仅对流动稳定性起有限增强作用；此外内、外桶半径比（0到1之间）增大，也将使流动趋于稳定。通过对螺旋T-V流动的数值模拟发现，屈服应力增大将使流场中Taylor涡减弱，且当屈服应力足够大时，螺旋T-V流动重新恢复螺旋T-C流动；内桶轴向剪切运动在使Taylor涡发生轴向迁移的同时也使其强度减弱。
Electrorheological fluid (ERF) is a new kind of "smart" material. When extra electric field is applied, it behaves just like a yield-stress fluid. The reports of research with ERF appeared sporadically since it was firstly reported in 1940's. But recently, with the development of materials science, the potential application region of ERF becomes more and more wide. And the number of investigations increased dramatically and researchers begin to pay more and more attentions to it.
In present dissertation, firstly an analytical study on the force and deformation of an ER single chain under Poiseuille flow is presented from the point of microscopic view. An approximate solution of the Poiseuille flow in a tube with rectangular cross is derived from Galerkin approach. The balance equation of moment for the ER chain is established to avoid using point-dipole model, which is not accurate enough in the case that dielectric particles are adjacent to each other. The result can be used in further study about the yield-stress and critical electric field strength.
Secondly, the steady and transient characteristics of concentric cylinder ER clutch and plane ER valve are studied with the consideration of yield. It can be found that when the extra electric field is suddenly applied, non-yield region in the clutch dose not generate synchronously. There is a retardation time which becomes shorter while the extra electric field becomes stronger. The demarcation point of, which is the parameter in ERF's yield stress equation, is 2.0. For, the dynamic characteristics of the clutch are remarkably different from those for.
Thirdly, the linear stability of plane shearing flow with non zero pressure gradient is studied. The conception of yield stress saturation is proposed. It can be found that the flow is stabilized by both plane shearing and the increment of yield stress.
The study about the linear stability of spiral Taylor-Couette flow is the fourth part of the dissertation. The numerical simulation of the Taylor-vortex
flow, which is the unstable pattern of the Taylor-Couette flow, is also achieved here. It can be found that yield stress plays a dual role in fluid stability and the rotation of the outer cylinder has stabilizing effect on the flow. The effect of the inner cylinder's sliding is slightly stabilizing on the disturbance of axisymmetric mode but destabilizing on the disturbance of non-axisymmetric mode. So the inner cylinder sliding just has a finite stabilizing effect on the spiral Taylor-Couette flow. Besides these, the increment of the radius ratio of the inner and outer cylinder also has stabilizing effect on the flow. It can be found from the analysis of the Taylor-vortex flow, that both the increment of yield stress and the sliding of the inner cylinder have the effect of weakening Taylor vortex. When the yield stress is high enough, the flow pattern will evolve from Taylor-vortex flow to Taylor-Couette flow and the Taylor vortex has a migration movement along the axial because of the existence of sliding.
引文
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