Non-newtonian power law fluid lubrication of lightly loaded cylinders with normal and rolling motion

The lubrication of lightly loaded cylinders with rotating and normal motion was investigated using a non-newtonian power law fluid under cavitation boundary conditions. The load capacity and frictional drag increase as the squeeze velocity increases. This increase is enhanced by an increase in the flow behaviour index of the lubricant. However, when the two surfaces move apart these results are reversed. The effect of the flow behaviour index on the location of the point of cavitation does not seem to be very significant.     

Non-Newtonian Lubrication of Asymmetric Rollers with Thermal and Inertia Effects

This research work explores the effects of thermal and inertia on hydrodynamic lubrication of asymmetric rigid rollers by incompressible non-Newtonian power law fluids and assesses the contribution of inertia to the system under consideration. The consistency of the power law lubricants is assumed to vary with the pressure and mean film temperature. The governing equations are solved first analytically and then numerically by the Runge-Kutta-Fehlberg method together with some reasonable tolerance. The results obtained confirm that there is significant increase in load and traction due to inertia. In addition, the effect of inertia shifts the pressure peak and the cavitation points toward the left.     

Power law fluid model incorporated into elastohydrodynamic lubrication theory of line contact

An algorithm is developed for the study of the infinitely long slider bearing in general form, considering the lubricant to be an incompressible power law fluid in isothermal conditions. The earlier works on this topic were considered by taking cavitation boundary conditions when a cylinder moves over a plane lubricated with a power law fluid and in EHL solution in a particular case, viz. pure rolling of a cylinder over an identical cylinder. We have considered a general solution including elastohydrodynamic lubrication (EHL) for different values of power law exponent. Deviation of values of central film thickness for different values of power law exponent from those for Newtonian lubricants are presented. The effects of the power law exponent on the central film thickness, minimum film thickness and load capacity are analysed. The effects of rolling and sliding velocities of contact surfaces are also analysed in terms of an equivalent radius of a cylinder moving over a moving plane. Film shapes and pressure distributions are also calculated numerically and presented graphically for various values of central film thickness considered in this paper. A number of observations obtained here with pseudoplastic nature of lubricants are in good agreement with the experimental results. The theoretical observations suggest the behaviour of common lubricants as pseudoplastic fluids in the cases of slowly moving surfaces and motion under heavy load.     

Numerical analysis of journal bearings lubricated with micropolar fluids including thermal and cavitating effects

A numerical study of the non-Newtonian behavior for a finite journal bearing lubricated with micropolar fluids is undertaken considering both thermal and cavitating effects. The modified Reynolds equation and energy equation are derived based on Eringen's micropolar fluid theory. The solution to the modified Reynolds equation is determined using the Elord's cavitation algorithm. The effects of the size of material characteristic length and the coupling number on the thermohydrodynamic performance of a journal bearing are investigated. It is shown, compared with Newtonian fluids, that micropolar fluids exhibit the increase in load capacity and temperature, but the decrease in coefficient of friction and side leakage flow. It is also indicated that, in the full film region, micropolar fluids increase the values of non-dimensional density, while in the cavitated region, both micropolar fluids and Newtonian fluids yield the same values of the fractional film content.     

Numerical simulation of cavitation surge and vortical flows in a diffuser with swirling flow

The strong swirling flow at the exit of the runner of a Francis turbine at part load causes flow instabilities and cavitation surges in the draft tube, deteriorating the performance of the hydraulic power system. The unsteady cavitating turbulent flow in the draft tube is simplified and modeled by a diffuser with swirling flow using the Scale-adaptive simulation method. Unsteady characteristics of the vortex rope structure and the underlying mechanisms for the interactions between the cavitation and the vortices are both revealed. The generation and evolution of the vortex rope structures are demonstrated with the help of the iso-surfaces of the vapor volume fraction and the Qcriterion. Analysis based on the vorticity transport equation suggests that the vortex dilatation term is much larger along the cavity interface in the diffuser inlet and modifies the vorticity field in regions with high density and pressure gradients. The present work is validated by comparing two types of cavitation surges observed experimentally in the literature with further interpretations based on simulations.     

Different Magnetic Models in the Design of Hydrodynamic Journal Bearings Lubricated with Non-Newtonian Ferrofluid

This work is concerned with theoretical study of hydrodynamic journal bearings lubricated with ferrofluids exhibiting non-Newtonian behavior. Based on the momentum and continuity equations for ferrofluid under an applied magnetic field, a modified Reynolds equation has been obtained. Assuming linear behavior for the magnetic material of the ferrofluid, the magnetic force was calculated. The Reynolds equation has been derived to be able to apply to any magnetic field distribution model. Using different magnetic field models, the equation has been solved numerically by the finite-difference technique with appropriate iterative technique and pressure distributions have been obtained. The boundary shape of the load-carrying active regions (positive-pressure regions) and cavitation regions (zero-pressure regions) could be then determined. The solution renders the bearing performance characteristics, namely: load-carrying capacity, attitude angle of the journal center, frictional force at the journal surface, friction coefficient and bearing side leakage. The results indicated that the flow-behavior index has a large effect on the bearing performance. When the bearing operates at high eccentricity ratios, the increase of flow-behavior index gives higher load capacity, lower attitude angle, higher frictional force, lower friction coefficient and higher side leakage. At low eccentricity ratios where the magnetic effects are significant, the effect of the flow-behavior index depends mainly on the magnetic field distribution model used.     

Characteristics of flow through small sharp-edged cylindrical orifices

The discharge coefficients for flow through small sharp-edged cylindrical orifices of diameters between 0.3 and 2 mm and aspect ratios between 1 and 50 are evaluated. The characteristics of flow in the separated, attached and cavitated flow regions are determined. It is shown that while the discharge coefficient scales with the Reynolds number and aspect ratio in the attached flow regions, the diameter influences the discharge coefficient in the separated flow region. The onset of cavitation in the orifice is also seen to be dependent on the diameter and aspect ratio. The hysteresis in the flow and the violent disintegration of the jet observed for an aspect ratio of about 5 are discussed.     

The role of sand particles on the rapid destruction of the cavitation zone of hydraulic turbines

Metal surfaces in the cavitation zone of hydraulic turbines working in sandy water are damaged rapidly. The damage is much more severe than that caused either by sand erosion or by cavitation alone. This paper presents an analysis of a worn surface of 18Cr-8Ni steel tested in a Venturi device at a hydroelectric power station in the flood season. Two types of damage were found. The first was a smooth erosion in the area of regular fluid flow. The second was in the regions where cavitation occurred. In the latter regions, the sand particles gain high velocities under the action of cavitation, impinge upon the metal surface and cause severe surface deformation and rapid damage. Embedded sand particles, cavities, cracks, cutting scars and fatigue patterns were found on the sponge-like worn surface.     

空化对液膜密封流场特性及密封性能的影响

为进一步探索液膜空化对密封性能的影响，以螺旋槽液膜密封为研究对象，基于JFO空化模型及坐标变换建立其数学模型并采用有限体积法离散求解。探讨Reynolds和JFO两空化边界下的密封速度场和流量场分布规律以及空穴压力对密封性能如承载能力和摩擦扭矩等影响。结果表明：空穴区的形成具有动态性，速度矢量在空穴区内部为0，在液膜始破边界和靠近内径处的液膜重生边界上速度矢量朝向空穴区，而在靠近外径处的液膜重生边界上速度矢量远离空穴区；液膜流量场主要集中于槽区内且JFO空化边界下的流量场分布比Reynolds空化边界下值更为密集；空穴压力的增加可提升液膜承载能力但增幅较小，而对摩擦扭矩的影响可忽略不计。     

Calculation of a Safety Margin for Hydrogenerator Thrust Bearings

The purpose of this paper is to present the two-dimensional linear stability analysis considering the fluid flow in both full film and cavitation regions for a plain cylindrical journal bearing. The Lund's infinitesimal perturbation procedure is applied to Elrod's universal equation for evaluation of unsteady pressure gradients. Based on JFO theory, the pressure distribution, film rupture, and reformation boundaries can be obtained using Elrod's universal equation, for a given operating position of the journal. In this work, it is assumed that for infinitesimal perturbation of a journal about the equilibrium position, the film rupture and film reformation boundaries are the same as those obtained for steady state. However, the unsteady pressure gradients in the full film region are evaluated taking into consideration the perturbed flow parameters in the cavitation region, i.e., at both rupture and reformation boundaries. The linearized stiffness and damping coefficients, whirl frequency ratio, and threshold speed for various values of eccentricity and L/D ratios are obtained for a plain cylindrical journal bearing with an axial groove along the load line. Measured data of dynamic coefficients for a 120° partial arc bearing are chosen for comparison with this work. Results show good agreement between the theoretical and experimental results.     

倒角阀座式水压锥阀空化射流动态行为数值模拟

使用可压缩的VOF空化两相流算法对倒角型阀座水压锥阀的空化射流进行了三维瞬态流场仿真。模拟结果揭示,空化结构首先在狭窄的倒角阀座流道内以附着空化的形式出现;在压差为4.4 MPa的工况条件下,空化分布集中在3个区域,阀座流道内及阀芯后沿的附着型空化,阀座流道至阀芯后沿的漩涡空化。射流势核在阀座流道入口及阀芯后沿均有分离流现象,从而诱发附着型空化;而大尺寸漩涡结构主要分布于射流势核的自由剪切层侧,漩涡空化亦相应地集中在自由剪切层侧,壁面侧偶发性形成薄层型漩涡空化。由于整体的空化行为涉及多个不同类型空化的耦合,其动态演变的周期特性受到干扰。阀座流道后部的脱落空化伴有明显的三维漩涡结构,阀芯后沿的漩涡空化与附着空化通过耦合作用形成大尺寸汽泡结构,揭示了后沿下游稀疏分布的大尺寸空化结构的产生过程。通过开展三维瞬态模拟,结合流场结构探索了空化射流的动态特性,从流体力学的层面解释了实验观测到的空化形态及分布规律。     

Dynamically loaded bearings operating with non-Newtonian lubricant films

The behaviour of a laminar non-Newtonian film (power law) was studied for dynamically loaded bearings. The momentum equation for an infinitely long bearing is solved by assuming that the velocity profile is a superposition of couette and Poiseuille flow for power law fluids. An expression for the modified Reynolds equation is obtained for the non-Newtonian fluid film. The load- carrying capacity is obtained for various values of the viscometric exponent of the power law model. It is shown that non-Newtonian lubricants can have a pronounced effect on dynamically loaded bearings.     

重载下非牛顿流体线接触弹性流体动力润滑的数值解

对重载下线接触流体润滑时 ,润滑剂的流变学作用和表面变形进行了理论分析 ,从而导出了非牛顿流体的模型 ,指数模型就是其中之一。当指数 n增大时 ,油膜厚度随之上升 ,并且油膜破裂点向接触区中心移动 ,同时润滑油的等效粘度也随之上升 ,当 n=1时计算结果与牛顿流体基本一致。     

A cavitation algorithm for arbitrary lubricant compressibility

A general cavitation algorithm that accommodates for an arbitrary density–pressure relation is presented. It is now possible to model the compressibility of the lubricant in such a way that the density–pressure relation is realistic throughout the contact. The algorithm preserves mass continuity for cavitation caused by bearing geometry and surface topography. It is a commonly accepted physical assumption that the contribution of the pressure driven flow is negligible in the cavitated region. This phenomenon is adopted in the present algorithm, which is similar to that of Elrod, and is modeled by a switch function that terminates the pressure gradient at the cavitation regions. Results with this algorithm for different density–pressure relations are presented and discussed. The effects of inlet conditions, such as surface roughness and starvation, on the load carrying capacity of the contact are analyzed.     

Thermal and squeezing effects in non-newtonian fluid film lubrication of rollers

Rigid cylindrical rollers, with rolling and squeezing motions, lubricated by a non-newtonian power law fluid are analysed under cavitation boundary conditions. The lubricant consistency is assumed to vary exponentially with pressure and temperature. These pressures and temperatures are found by solving simultaneously the modified Reynolds and energy equations. Various bearing characteristics are presented and discussed. Also presented are the results obtained when the temperature effect on the lubricant consistency is neglected. The effect of temperature on the consistency is to shift the position of the pressure peak slightly towards the centre line of contact. The viscometric exponent n of the power law fluid and the squeezing velocity q are shown to have pronounced effects on the lubrication behaviour of the system under consideration. The consistency variation, especially in the pressure peak region, for dilatant and newtonian fluids, is quite significant.     

考虑抛光垫特性的CMP流动性能

为了研究具有多孔结构抛光垫对化学机械抛光(Chemical mechanical polishing,CMP)性能所起的重要作用, 通过假定孔质层流体服从Darcy规律,即流动速度正比于压力梯度而反比于粘度,从而提出了CMP中考虑抛光垫特性的三维流体模型,并给出了流动方程。利用多重网格技术和线松驰技术求解上述所得的流动方程,用数值模拟方法探求了不同大小抛光垫孔径和不同孔质层厚度下承载能力和运行参数(包括节距高度、转角和倾角等)的关系。计算结果表明,当抛光垫的孔径尺寸较小和其孔质层较厚时有较大的承载能力(包括载荷与转矩),从而将提高CMP的材料去除率。孔隙直径较大的抛光垫由于允许较多的流体流过多孔层而导致其承载能力下降。研究结果有助于了解CMP的作用机理。     

EXPERIMENTAL INVESTIGATIONS OF CAVITATION EFFECTS ON FLOW CHARACTERISTICS OF SMALL ORIFICES AND VALVES IN WATER HYDRAULICS

The flow characteristics and cavitation effects of water passing through small sharp-edged cylindrical orificesand valves of different shapes in water hydraulics are investigated. The test results using orifices with different aspect ratios and different diameters show that the flow coefficients in the case of non-cavitating flow are larger than that of flow inthe case of cavitation occurrence. The flow coefficients of flow with cavitation initially decrease as Reynolds number increases and ultimately tend to be of constant values close to contraction coefficient. Large aspect ratio has an effect ofsuppressing cavitation. The experimental results about disc valves illustrate that the valves with sharp edge at large opening are less affected by cavitation than that at small opening. Throttle with triangle notch has better anti-cavitation abilitythan that with square notch. The flowrate of the throttle with square notch is significantly affected by the flow direction orthe flow passage shape.     

单柱塞泵工作腔流场的数值模拟和实验研究

针对单柱塞泵工作容腔的气穴现象,运用Fluent软件对柱塞泵工作容腔的气穴流场进行了数值模拟,采用了非平衡壁面函数的k-ε模型和带有空化作用的多相流混合模型,得出了不同阀口开度和入口速度下柱塞泵工作容腔的气穴流场的分布规律.在实验方面,采用了不带补油泵和带补油泵两套实验装置来对比测试柱塞泵工作容腔的真空度大小.将仿真和实验结果进行比较,模拟得到的柱塞泵工作容腔的真空度和实验得到的真空度比较吻合,表明非平衡壁面函数的k-ε模型和带有空化作用的多相流混合模型能够有效地预测柱塞泵工作容腔气穴流场的分布规律.     

Inertia effects in laminar radial flow of power law fluids

An approximate expression for the pressure distribution for the radial flow of a non-Newtonian fluid (power law) between two parallel disks is obtained by using the momentum and energy integral methods. It is shown that inertia has a significant effect on the pressure distribution especially for those fluids with a power law index, n 1.     

Fast scaling approach based on cavitation conditions to estimate the speed limitation for axial piston pump design

The power density of axial piston pumps can benefit greatly from increased rotational speeds. However, the maximum rotational speed of axial piston machines is limited by the cavitation phenomenon for a given volumetric displacement. This paper presents a scaling law derived from an analytical cavitation model to estimate the speed limitations for the same series of axial piston pumps. The cavitation model is experimentally verified using a high-speed axial piston pump, and the scaling law is validated with open specification data in product brochures. Results show that the speed limitation is approximately proportional to the square root of the inlet pressure and inversely proportional to the cube root of volumetric displacement. Furthermore, a characteristic constant C_p is defined based on the presented scaling law. This constant can represent the comprehensive capacity of axial piston pumps free from cavitation.