两平行刚性圆盘挤压理想刚塑性介质时压力规律研究

两平行刚性圆盘挤压理想刚塑性介质时,通常考虑圆盘与介质的界面之间存在部分滑移,对库仑摩擦条件下的压力规律做了进一步的研究,同时,引入更合理的速度场,假设圆盘边缘处滑移速度一定,介质的滑移速度随着半径线性变化,得到了压力分布规律,对不同的摩擦条件及用不同方法计算得到的结果进行了对比。     

Transient squeeze flow of viscoplastic materials

The transient, axisymmetric squeezing of viscoplastic materials under creeping flow conditions is examined. The flow of the material even outside the disks is followed. Both cases of the disks moving with constant velocity or under constant force are studied. This time-dependent simulation of squeeze flow is performed for such materials in order to determine very accurately the evolution of the force or the velocity, respectively, and the distinct differences between these two experiments, the highly deforming shape and position of all the interfaces, the effect of possible slip on the disk surface, especially when the slip coefficient is not constant, and the effect of gravity. All these are impossible under the quasi-steady state condition used up to now. The exponential constitutive model, suggested by Papanastasiou, is employed. The governing equations are solved numerically by coupling the mixed finite element method with a quasi-elliptic mesh generation scheme in order to follow the large deformations of the free surface of the fluid. As the Bingham number increases, large departures from the corresponding Newtonian solution are found. When the disks are moving with constant velocity, unyielded material arises only around the two centers of the disks verifying previous works in which quasi-steady state conditions were assumed. The size of the unyielded region increases with the Bingham number, but decreases as time passes and the two disks approach each other. Their size also decreases as the slip velocity or the slip length along the disk wall increase. The force that must be applied on the disks in order to maintain their constant velocity increases significantly with the Bingham number and time and provides a first method to calculate the yield stress. On the other hand, when a constant force is applied on the disks, they slow down until they finally stop, because all the material between them becomes unyielded. The final location of the disk and the time when it stops provide another, probably easier, method to deduce the yield stress of the fluid.     

The squeeze flow of a bi-viscosity fluid between two rigid spheres with wall slip

In this paper, the squeeze flow between two rigid spheres with a bi-viscosity fluid is examined. Based on lubrication theory, the squeeze force is calculated by deriving the pressure and velocity expressions. The results of the normal squeeze force are discussed, and fitting functions of the squeeze and correction coefficients are given. The squeeze force between the rigid spheres increases linearly or logarithmically with the velocity when most or part of the boundary fluid reaches the yield state, respectively. Furthermore, the slip correction coefficient decreases with the increase in the velocity. The investigation may contribute to the further study of bi-viscosity fluids between rigid spheres with wall slip.     

Pressure Distribution in a Curvilinear Thrust Bearing with One Porous Wall Lubricated by a Bingham Fluid

The influence of wall porosity on the pressure distribution of a Bingham fluid flowing in the clearance of a curvilinear thrust bearing is considered. The formulae expressing the pressure distribution are obtained for two cases, namely: an externally pressurized bearing and a squeeze film bearing. The example of a squeeze film between parallel disks is discussed in detail.     

Squeeze flow of a second-order fluid between two parallel disks or two spheres

The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds‘ lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neelected.     

Radial flow velocity profiles of a yield stress fluid between smooth parallel disks

In rock grouting, idealized 2D-radial laminar flow of yield stress fluids (YSF) is a fundamental flow configuration that is used for cement grout spread estimation. A limited amount of works have presented analytical and numerical solutions on the radial velocity profiles between parallel disks. However, to the best of our knowledge, there has been no experimental work that has presented measured velocity profiles for this geometry. In this paper, we present velocity profiles of Carbopol (a simple YSF), measured by pulsed ultrasound velocimetry within a radial flow model. We describe the design of the physical model and then present the measured velocity profiles while highlighting the plug-flow region and slip effects observed for three different apertures and volumetric flow rates. Although the measured velocity profiles exhibited wall slip, there was a reasonably good agreement with the analytical solution. We then discuss the major implications of our work on radial flow.

     

Effect of magnetic field and velocity slip on porous-walled rectangular squeeze films

This is a study of an electrically conducting flow in a squeeze film between two infinite strips where one of the strips has a porous bounding surface backed by a solid wall. The analysis is directed to study the interaction of a transverse magnetic field with the coupled flows in the squeeze film and the porous medium including the slip velocity at the porous bounding surface. Expressions for load capacity and thickness-time are obtained. It is observed that the magnetic field increases the load capacity and response times of squeeze films. This effect is more marked for small values of the permeability K.     

Squeeze flow of a power-law fluid between two rigid spheres with wall slip

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Three dimensional magnetohydrodynamic flow between two porous disks

This is a study of conducting flow in the gap between two parallel co-axial nonconducting disks of which one is rotating and the other stationary in the presence of a uniform axial magnetic field. The effect of uniform suction or injection on the velocity distribution is investigated and asymptotic solutions are obtained for R≪M ². Expressions for the average normal force and the torque on the disks are obtained. We find that all components of velocity are affected by uniform suction or injection and in particular we note that the effect of suction or injection on the radial component of velocity predominates over the effect of rotation for a given Hartmann number.     

Slow motions of a circular cylinder experiencing slip near a plane wall

A theoretical study is presented for the two-dimensional creeping flow caused by a long circular cylindrical particle translating and rotating in a viscous fluid near a large plane wall parallel to its axis. The fluid is allowed to slip at the surface of the particle. The Stokes equations for the fluid velocity field are solved in the quasi-steady limit using cylindrical bipolar coordinates. Semi-analytical solutions for the drag force and torque acting on the particle by the fluid are obtained for various values of the slip coefficient associated with the particle surface and of the relative separation distance between the particle and the wall. The results indicate that the translation and rotation of the confined cylinder are not coupled with each other. For the motion of a no-slip cylinder near a plane wall, our hydrodynamic drag force and torque results reduce to the closed-form solutions available in the literature. The boundary-corrected drag force and torque acting on the particle decrease with an increase in the slip coefficient for an otherwise specified condition. The plane wall exerts the greatest drag on the particle when its migration occurs normal to it, and the least in the case of motion parallel to it. The enhancement in the hydrodynamic drag force and torque on a translating and rotating particle caused by a nearby plane wall is much more significant for a cylinder than for a sphere.     

Model-free inversion of squeeze-flow rheometer data

A method for extracting rheological data from squeeze-flow tests is proposed. The analysis, based upon the lubrication approximation for a generalized Newtonian fluid, differentiates experimental data in order to obtain an estimate of the wall shear rate (as in the Weissenberg–Rabinowitsch correction for the capillary rheometer) and of the wall shear stress. Two examples are discussed. The first is based on an approximate expression for the force required to squeeze a Herschel–Bulkley fluid. The second example concerns a power-law fluid with partial slip at the plates (but non-zero wall shear stress). Second derivatives of the experimental data are required: the interpretation of noisy results is therefore likely to be difficult.     

SQUEEZE FILM FLOW WITH NONLINEAR BOUNDARY SLIP

A nonlinear boundary slip model consisting of an initial slip length and a critical shear rate was used to study the nonlinear boundary slip of squeeze fluid film confined between two approaching spheres. It is found that the initial slip length controls the slip behavior at small shear rate, but the critical shear rate controls the boundary slip at high shear rate. The boundary slip at the squeeze fluid film of spherical surfaces is a strongly nonlinear function of the radius coordinate. At the center or far from the center of the squeeze film, the slip length equals the initial slip length due to the small shear rate. However, in the high shear rate regime the slip length increases very much. The hydrodynamic force of the spherical squeeze film decreases with increasing the initial slip length and decreasing the critical shear rate. The effect of initial slip length on the hydrodynamic force seems less than that of the critical shear rate. When the critical shear rate is very small the hydrodynamic force increases very slowly with a decrease in minimum film thickness. The theoretical predictions agree well with the experiment measurements.     

Surface roughness effects on squeeze film behavior in porous circular disks with couple stress fluid

The effect of surface roughness on squeeze film behavior between two circular disks with couple stress lubricant is analyzed when the upper disk has porous facing which approaches the lower disk with uniform velocity. The modified Stochastic Reynolds equation is derived on the basis of Stokes micro-continuum theory for couple stress fluid and Christensen Stochastic theory for the rough surface. Closed form solution of the Stochastic Reynolds equation is obtained in terms of Fourier–Bessel series. The importance of roughness and couple stress on bearing characteristics are presented in terms of load carrying capacity, squeeze time, and relative percentage of the load. It is observed that, effect of couple stress fluid, and surface roughness is more pronounced compared to classical case. These predictions enable design engineers to choose suitable parameters.     

The behavior of viscoelastic squeeze films subject to normal oscillations, including the effect of fluid inertia

The problem of the squeeze film flow of a viscoelastic fluid between parallel, circular disks is analyzed. The upper disk is subject to small, axial oscillations. Lodge's “rubber-like liquid” is used as the viscoelastic fluid model, and fluid inertia forces are included. An exact solution to the equations of motion is obtained involving in-phase and out-of-phase components of velocity field and load, with respect to the plate velocity. Peculiar resonance phenomena in the load amplitude are exhibited at high Deborah number. At certain combinations of Reynolds number and Deborah number, the in-phase and/or out-of-phase velocity field components may attain an unusual circulating type of motion in which the flow reverses direction across the film. In the low Deborah number limit, and in the low Reynolds number limit, the results of this study reduce to those obtained by other workers.     

载荷作用区域对刚塑性简支梁动力响应的影响

本文研究了载荷作用区域大小对刚塑性简(固)支梁塑性动力响应的影响,得到了中、高载界限值的表达式,并对它进行了详细的讨论。文中还给出了中载和高载情况时各相的具体解答。     

单自由度超弹性SMA减振结构随机振动控制理论研究

利用形状记忆合金（Shape Memory Alloy,简称SMA）丝的超弹性,提出了一种具有复位功能的阻尼器。在SMA丝的Graesser本构模型基础上,建立了阻尼器恢复力的滑移双线性模型;假定滞回面积相等,提出了恢复力的滑移刚塑性模型以近似简化滑移双线性模型。采用等价线性化法建立了单自由度超弹性SMA减振结构在高斯白噪声激励下的平稳随机振动分析公式。通过一算例,考虑不同激励谱密度和结构阻尼比：比较了等价线性法和蒙特卡罗（Monte Carlo）模拟法计算的结构振动响应（位移标准差和速度标准差）,证明了SMA减振结构随机振动控制理论的有效性;比较了等价线性减振结构和无控结构的动力特性（刚度和阻尼比）和振动响应,说明了SMA阻尼器能提高结构的刚度和阻尼比,因而可有效抑制结构的振动。     

The hydrodynamic wall effect for a disperse system

The flow of a highly dilute suspension of spheres (radius α) between two parallel ridid planes (distance L) in slow shearing motion is studied. Even for the limiting situation, (α/L) small but finite, there is a layer-one sphere diameter thick—immediately adjacent to the wall in which bulk quantities are so complicated functionals of the parameters of the microstructure that evaluating them seems out of the question. Nevertheless, it is still simple to obtain average bulk quantifies (e.g. apparent viscosity) and even the evaluation of local bulk quantities far away from the wall poses no problem. The reason being that the customary continuum constitutive equation for the bulk stress can be utilized, although a slip velocity has to supplement it. This applies to any disperse system and can be applied to different flows, too. For the spherical suspension at hand an explicit expression for this slip velocity is obtained.     

Cessation of Newtonian circular and plane Couette flows with wall slip and non-zero slip yield stress

We solve analytically the cessation flows of a Newtonian fluid in circular and plane Couette geometries assuming that wall slip occurs provided that the wall shear stress exceeds a critical threshold, the slip yield stress. In steady-state, slip occurs only beyond a critical value of the angular velocity of the rotating inner cylinder in circular Couette flow or of the speed of the moving upper plate in plane Couette flow. Hence, in cessation, the classical no-slip solution holds if the corresponding wall speed is below the critical value. Otherwise, slip occurs only initially along both walls. Beyond a first critical time, slip along the fixed wall ceases, and beyond a second critical time slip ceases also along the initially moving wall. Beyond this second critical time no slip is observed and the decay of the velocity is faster. The velocity decays exponentially in all regimes and the decay is reduced with slip. The effects of slip and the slip yield stress are discussed.     

Compression behaviors of magnetorheological fluids under nonuniform magnetic field

This work is concerned with an experimental and theoretical study on compression properties of magnetorheological fluids under the nonuniform field. Experimental tests of unidirectional monotonic compression were firstly carried out under constant area operation using a commercial plate–plate magneto-rheometer where the magnetic field radial distribution was nonuniform. Normal forces increased with decreasing of the gap distance, and two regions were found through the normal force versus gap distance curves: elastic deformation and plastic flow. High normal forces could be obtained in the case of high magnetic field, high compression velocity, low initial gap distance, high volume fraction, and high medium viscosity. In the plastic flow region, the normal force with the gap distance could be fitted with a power law relation $F_{\textrm {N}} \propto h^n$ , and the index n was around well in the range (?3, ?2). Taking nonuniform magnetic field into account, the theoretical modeling in the plastic flow was then developed to calculate the normal force under compression based on the continuum media theory. Compared to the uniform field, there existed a magnetic field gradient-induced normal force under nonuniform field. Considering the sealing and squeeze strengthening effect, the gap distance-dependent shear yield stress was proposed, and a good correspondence between the theoretical and experimental results was obtained.     

Particle dynamics calculations of wall stresses and slip velocities for couette flow of smooth inelastic spheres

The objective of this work is to characterize the effects of boundary geometry on the flow of dry granular materials composed of smooth, inelastic spheres between parallel, bumpy walls in the absence of gravity. Particle dynamic simulations are done in which wall stresses and slip velocities are computed over a wide range of parameters, including shear gap height, geometry of the wall particles, wall to free particle diameter ratio, and normal restitution coefficient. Calculated wall stresses and slip velocities are found to be highly sensitive to boundary roughness, which is characterized in terms of the mean spacing value for the wall particles. Most noticeable is a pronounced stress drop for dense flows with an associated large slip velocity in a system having a narrow shear gap height.