Frequency-domain analysis of non-Newtonian fluid behavior in head-disk interface lubrication

A lubricant in a head-disk interface is considered as a non-Newtonian fluid. Properties of non-Newtonian lubricants are specified by three nonlinear functions and a modified Reynolds equation is derived for the varied film thickness in the interface. The shear dependent viscosity is the principal factor and it is expressed by a first order transfer function. Its amplitude frequency response describes the process of the viscosity variation and indicates that the shear dependent viscosity is affected not only by the lubricant material parameters, but also by the shear frequency. Based on the modified Reynolds equation, the numerical result of lubrication is given. The load capacity is not always higher or always lower than that of the Newtonian fluid. The effect of the first normal stress difference is enlarged with the slider flying height varies.     

适用于非牛顿介质的雷诺方程的普遍形式

本文发展了一种更为普遍的雷诺方程。这个方程是在同时考虑了粘弹性的非牛顿介质的剪应力特性、记忆特性与第一正应力差特性的基础上提出来的方程中涉及三个非线性函数,即剪应力函数、第一正应力差函数与差分粘度。对于不同特性的非牛顿介质,这三个非线性函数应有不同的解。     

The First Normal Stress Difference in a Shear-Thinning Motor Oil at Elevated Pressure

Currently, the only aspect of non-Newtonian behavior being modeled in lubrication is the shear dependence of viscosity. However, shear thinning is accompanied by a large difference between the normal stress in the flow direction and the cross-film direction. This stress difference can increase the load capability of a lubricant film without increased frictional penalty.

A commercial 10W-40 motor oil was characterized at elevated pressures. Three different high-pressure instruments were employed: a falling-body viscometer, a thin-film Couette viscometer, and a parallel-plate rheogoniometer. Ordinary shear thinning with a second Newtonian inflection was observed. A first normal stress difference of 0.6 MPa was measured under what may be mild conditions for a crankshaft journal bearing. Elevated pressures are essential to the measurement of rheological properties that govern hydrodynamic film thickness and friction in automotive components.

Time–temperature–pressure superposition was validated for the first normal stress difference. The first normal stress difference in the terminal regime may be estimated from the upper-convected Maxwell model, where the shear modulus is assumed to be equal to the Newtonian limit shear stress obtained from a measurement of shear thinning. The first normal stress difference in the shear-thinning regime may be estimated from an extant empirical rule.

These results will be of substantial importance when analytical techniques are developed for hydrodynamic lubrication with real non-Newtonian shear response. The results are immediately useful for calculating the shear stress for cavitation in ambient pressure high-shear viscometers.     

Effects of surface geometry and non-newtonian viscosity on the flow field in arterial stenoses

Hemodynamics including flow pattern, shear stress, and blood viscosity characteristics has been believed to affect the development and progression of arterial stenosis, but previous studies lack of realistic physiological considerations such as irregular surface geometry, non-Newtonian viscosity characteristics and flow pulsatility. The effects of surface irregularities and non-Newtonian viscosity on flow fields were explored in this study using the arterial stenosis models with 48% arterial occlusions under physiological flow condition. Computational flow dynamics based on the finite volume method was employed for Newtonian and non-Newtonian fluid. The wall shear stresses (WSS) in the irregular surface model were higher compared to those in the smooth surface models. Also, non-Newtonian viscosity characteristics increase the peak WSS significantly. The dimensionless pressure drop and the time averaged WSS in pulsatile flow were higher than those in steady flow. But pulsatility effects on pressure and WSS were less significant compared to non-Newtonian viscosity effects. Therefore, irregular surface geometry and non-Newtonian viscosity characteristics should be considered in predicting pressure drop and WSS in stenotic arteries.     

动载荷下径向轴承的非牛顿介质润滑

为分析动载荷条件下非牛顿介质的流变特性对径向轴承润滑效果的影响，推导了相应的雷诺方程。在方程中用差分粘度和第一正应力差函数表征非牛顿介质的流变特性，用挤压项表示动载荷作用。轴承润滑的数值计算结果表明，差分粘度的变化是影响承载力的主要因素，它取决于非牛顿介质的动态参数和剪切频率范围，使得非牛顿介质润滑的承载力并不总是高于或低于牛顿介质。在动载荷条件下，第一正应力差效应明显增强了油膜压力和承载力，并对轴心轨迹产生影响。     

Calculated load capacity of non-newtonian lubricants in finite width journal bearings

Starting from the most general type of fluid flow equation connecting cubic shear stress to rate of shear for non-Newtonian lubricants, a modified form of Reynolds' equation was derived for steady finite width journal bearings. The finite difference technique with successive over relaxation was used incorporating Reynolds' boundary conditions for pressure to obtain the pressure distribution and hence the load capacity and the attitude angle. It is shown that the flatter pressure profile and higher load capacity at low eccentricity ratios have practical advantages. The apparent viscosity loss at higher rates of shear decreases the load capacity at higher eccentricity ratios but it is expected that the flatter viscosity temperature slope of the polymer thickened non-Newtonian lubricants will compensate for their apparent viscosity decrease.     

The effect of cooling conditions on convective heat transfer and flow in a steam-cooled ribbed duct

This work presents a numerical and experimental investigation on the heat transfer and turbulent flow of cooling steam in a rectangular duct with 90° ribs and studies the effect of cooling conditions on the heat transfer augmentation of steam. In the calculation, the variation range of Reynolds is from 10,000 to 190,000, the inlet temperature varies from 300°C to 500°C and the outlet pressure is from 0.5MPa to 6MPa. The aforementioned wide ranges of flow parameters cover the actual operating condition of coolant used in the gas turbine blades. The computations are carried with four turbulence models (the standard k-?, the renormalized group (RNG) k-?, the Launder-Reece-Rodi (LRR) and the Speziale-Sarkar-Gatski (SSG) turbulence models). The comparison of numerical and experimental results reveals that the SSG turbulence model is suitable for steam flow in the ribbed duct. Therefore, adopting the conjugate calculation technique, further study on the steam heat transfer and flow characteristics is performed with SSG turbulence model. The results show that the variation of cooling condition strongly impacts the forced convection heat transfer of steam in the ribbed duct. The cooling supply condition of a relative low temperature and medium pressure could bring a considerable advantage on steam thermal enhancement. In addition, comparing the heat transfer level between steam flow and air flow, the performance advantage of using steam is also influenced by the cooling supply condition. Changing Reynolds number has little effect on the performance superiority of steam cooling. Increasing pressure would strengthen the advantage, but increasing temperature gives an opposite result.     

Thin film elastohydrodynamic lubrication—a power-law fluid model

A 1-D modified Reynolds equation for power-law fluid is derived from the viscous adsorption theory for thin film elastohydrodynamic lubrication (TFEHL). The lubricating film between solid surfaces is modeled as three fixed layers, which are two adsorption layers on each surface and a middle layer between them. The comparisons between classical non-Newtonian EHL and non-Newtonian TFEHL are discussed. Results show that the TFEHL model can reasonably calculate the pressure distribution, the film thickness, the velocity distribution and the average viscosity. The thickness and viscosity of the adsorption layer and the flow index influence the lubrication characteristics of the contact conjunction significantly. The film thickness increases with the increase of flow index. As the flow index becomes greater, the dimple in the film shape moves towards the center of the contacts. The effect of flow index produces an obvious difference in the pressure distribution. The greater the flow index, the greater the pressure spike, and the pressure spike tends to move toward the center. The larger the flow index, the more the velocity varies in both the middle layer and adsorption layers along the Z-axis. The greater the thickness and viscosity of the adsorption layer and the flow index, the greater the deviation in central film thickness versus speed between EHL model and TFEHL model produced in the very thin film regime.     

通道形状对活塞冷却油腔内工作流体阻力及流动特性的影响

为揭示通道形状对活塞冷却油腔内工作流体的阻力及流动特性的影响,将冷却油腔的直壁通道改为波壁通道,并采用压力差和可视化的方法对通道内工作流体的阻力及流动特性展开了实验研究。压力差实验结果表明,与水在直壁通道内的流动相比,水在波壁通道内层湍转捩点大大提前,将非牛顿流体替换水作为工作流体后,层湍转捩点再次提前;可视化实验结果表明,波壁通道内工作流体在雷诺数较低时就可呈现不稳定流动形态。为在较低雷诺数下继续强化活塞冷却油腔内的热质传递,进一步开展了脉动流场下非牛顿流体在波壁通道内的流动特性实验和数值模拟研究,结果表明：脉动流场的操作参数对波壁通道内非牛顿流体的流动不稳定率有较大影响,且影响了通道内非牛顿流体的质量传递。     

Effects of lubricant additives on the performance of hydrodynamically lubricated journal bearings

A non-Newtonian rheological model to investigate theoretically the effects of lubricant additives on the steady state performance of hydrodynamically lubricated finite journal bearings is introduced. In this model, the non-Newtonian behavior resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman-extended Darcy equations are utilized to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry, and non-Newtonian behavior of the lubricant on the steady-state performance characteristics such as pressure distribution, load carrying capacity, side leakage flow, and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load carrying capacity and reduce both the coefficient of friction and the side leakage as compared to the Newtonian lubricants.     

The effect of ion slip on the flow of Reiner-Rivlin fluid due a rotating disk with heat transfer

The magnetohydrodynamic rotating disk flow and heat transfer of a non-Newtonian Reiner-Rivlin conducting fluid is studied considering the ion slip. The governing nonlinear equations are solved numerically using finite differences. The results show that the inclusion of the ion slip and the non-Newtonian fluid characteristics have interesting effects on the velocity and temperature distributions.     

Calculated journal bearing lubrication of non-Newtonian medium with surface roughness effects

To analyze the effects of non-Newtonian lubricants and surface roughness in journal bearing lubrication, a modified Reynolds equation is derived. In the equation, differential viscosity and the first normal stress function are defined to specify the rheological properties of non-Newtonian medium. Flow factors are used to specify the effect of surface roughness. The modified Reynolds equation is numerically calculated using super over relaxation method. Numerical results of the lubrication show that the differential viscosity is the principal non-Newtonian property affecting the lubrication, it is determined by the material parameters of the lubricant and is affected by the shearing rate. Under its effect, the load capacity of non-Newtonian lubricants is not always higher or lower than that of Newtonian lubricants’. The effect of the first normal stress difference increases under the conditions of dynamic loading. Surface roughness shows an obvious effect on load capacity when it is greater than one-tenth of the film thickness, and the surface with longitudinal pattern affects the load capacity most. However, surface roughness has less effect on lubrication results than lubricants’ non-Newtonian property. __________ Translated from Tribology, 2005, 25(6) (in Chinese)     

The load capacity of a partial journal bearing with a non-Newtonian film

Lubricating oils with viscosity index improver additives exhibit non-Newtonian behaviour. Starting from the most general type of fluid flow equation, connecting cubic shear stress to rate of shear for non-Newtonian lubricants, a modified form of Reynolds' equation has been derived and solved for the steady state load capacity for finite width full cylindrical journal bearings. The method has been extended to partial journal bearings both for the centrally loaded film and for the film with minimum thickness at the trailing edge. Numerical results are given for bearing arcs of 180° and 120° and length-to-diameter ratios of 1 and $\text{1}\text{2}$.     

发散形通道内的稳定电渗流动

电渗流通过外加电场来驱动液体通过微小通道,同时由于焦耳热效应的存在,也会在流体及通道表面形成热传导现象。应用计算流体力学方法,对矩形发散形微通道内电渗流流动所产生的流场、温度场进行了数值模拟和研究。由于流体的介电常数、电导率、粘性、热导率等属性依赖于温度的变化,焦耳热效应产生的温度场会改变流体的多种属性,并进而影响到流动速度、压力分布等。计算结果表明,焦耳效应在微管道芯片上产生了一个非均匀的热梯度场,并同时影响液体流动。热梯度场的存在在均匀截面通道内可以提高液体的流动速度,但在发散形通道内却不能产生相似的效果,此时的出口速度和体积流速都明显下降,分别达到约16%和60 μl/min。焦耳热效应同时通过降低流速和流动压力减弱了发散形管道的电渗流泵送性能。     

Effect of non-Newtonian lubrication on the separation of a sphere from a flat

A numerical analysis is presented to study the effect of lubrication with non-Newtonian fluid on the separation flow of a fully flooded sphere from a flat under the condition of constant applied load. Different non-Newtonian fluid models were utilized to account for the microstructure and rheology of additives suspended in the film lubricant, namely those models for couple stress, micropolar, and power-law fluids. The equation of motion of the sphere was used to examine the effect of the sphere inertia on accelerating the separation process as the film viscous force decreases. This required solving the film pressure field, which is derived from a modified Reynolds equation and later computed numerically by a forth-order Runge-Kutta integration scheme. Several parameters were examined such as the time to complete separation, the length scale of the additives, the variation in lubricant's viscosity due to the presence of the additives, the sphere mass and radius, and the applied force on the sphere. Compared to the Newtonian fluid case, the results of the numerical solution indicated that there is a delay on the separation time for large non-Newtonian parameters, i.e., parameters representing additives characteristic length, additives concentration, and power-law indices.     

竖直矩形窄通道内水流动沸腾换热特性的研究

建立单面加热垂直矩形窄通道流动沸腾换热试验装置,针对截面250mm×3.5mm的窄缝通道,对水流动沸腾换热特性进行试验研究。通过试验分析可知:(1)随着干度的增加,局部换热系数先增加后减小,有一个最大值,此时处于饱和核沸腾区域,其蒸汽干度也接近于0,同时也接近于沸腾起始点。相应地流体从单相流-泡状-块状流-搅拌-环状流转变。(2)在流动沸腾换热中,热流密度对核态沸腾换热有明显影响,而对流动沸腾液膜蒸发的影响甚小,所以可以认为由热流密度的变化而引起的换热变化,主要表现在核态沸腾。(3)入口温度的变化对单相流动的换热系数有影响,而沸腾换热系数与流型及汽泡的产生及扰动有极大关系,入口温度对流动沸腾局部换热系数基本没有影响。     

Effect of pressure dependent viscosity on squeeze film characteristics of micropolar fluid in convex curved plates

In this paper, the effect of pressure dependent viscosity on the squeeze film characteristics between convex curved plates of a cosine form is presented. Micropolar fluid theory, which is a possible non-Newtonian model of a suspension of rigid particle additives, is applied to the study of the lubrication of cosine form convex curved plates. The modified Reynolds equation is solved for the fluid film pressure and then the cosine form by considering the exponential relationship in the viscosity variation. For iso-viscous lubricants, the effects of pressure dependent viscosities signify an increase in the values of the squeeze film pressure, the load capacity and the elapsed time. It provides useful information in designing the mechanisms of squeeze film plates for engineering application.     

Effect of cyclic internal pressure on the temperature distribution in a viscoelastic cylinder

A modified numerical method is introduced to study the interaction between the heat and dynamic response of viscoelastic bodies with temperature-dependent properties. The method is applied to calculate the stress and temperature distributions in a viscoelastic cylinder subjected to cyclic internal pressures. It is found that a large temperature rise may occur due to the interaction, where the value depends upon the thermal and mechanical properties of the material, cylinder size and the frequency of the applied pressure.     

Rheological measurement of untreated sewage by straight tube

Sewage contains abundant low-grade heat energy, and recycling it using a heat pump system is an effective way to reduce carbon emissions. The particles in sewage will cause untreated sewage to exhibit non-Newtonian characteristics, and accurate rheological measurement is important for sewage transmission and distribution system design. The traditional rotary rheometer deforms, agglomerates, or breaks the solid particles in sewage, which affects the measurement results. Therefore, in this study, a horizontal tube rheological test bench was built for urban sewage. Constitutive equations and viscosity expressions of untreated and prepared urban sewage at different temperatures and particle concentrations were tested. The results show that untreated and prepared sewage conforms to the shear-thinning model of power-law fluids in non-Newtonian fluids even at particle wet mass concentration as low as 0.103%. The flow characteristic index n of sewage is unrelated to temperature, and its influence is mainly reflected in the consistency coefficient k. However, the sewage flow characteristic index n increases with a decrease in particle concentration. In the laminar flow range of 0.02–0.2 m/s, the flow resistance obtained by treating untreated sewage as a Newtonian fluid was approximately 1.36–1.99 times that of the non-Newtonian fluid model, which will result in a larger power system design and higher energy consumption. Under turbulent flow conditions, the drag coefficient of the Newtonian model was approximately 1.13 times that of the non-Newtonian model. This shows that when designing a sewage source heat pump system, the power-law fluid shear-thinning characteristics of untreated sewage must be fully considered, which helps reduce the calculated energy consumption of transportation.     

The influence of couple stresses in squeeze films

A theoretical study of non-Newtonian flow effects in a squeeze film configuration is carried out with special reference to synovial joints. The material model taken is that of the Stokes' couple stress fluid. It is found that the bearings with couple stresss fluid as lubricant provide significant load supporting capacities which result in longer bearing life. The squeeze film time is found to be considerably longer for couple stress fluid than in the case of Newtonian fluid of the same viscosity. These are the most desirable advantages which render the model close to the natural characteristics of synovial joints.