Non-Newtonian couple stress poroelastic squeeze film

The aim of this paper is to develop a new model of the interaction of a fluid film with a porous medium. The model takes into account the fluid inertia in both the lubricant and the porous matrix. Non-Newtonian behavior of the fluid, viscous effects in the porous matrix, and poroelasticity of the matrix are also considered. The main concerns are modeling and simulation of the squeeze film lubrication between two discs when one has a porous facing. The fluid flow is described using a reduced version of the Navier–Stokes equations in the fluid film, and the Darcy–Brinkman–Forchheimer generalized model in the porous matrix.The present study focuses on the combined effects of the non-Newtonian fluid lubricant and porous matrix deformation. The non-Newtonian behavior of the lubricant is described by the so-called couple stress model. The porous interface deformation is obtained using the thin elastic layer approach. The partial differential equations established in this study are discretized by finite differences. The resulting algebraic equations are solved using the Gauss–Seidel relaxation method.The numerical results of the present simulations show that all these effects have a significant influence on the porous squeeze film performance.     

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.     

Static and dynamic analysis of elastohydrodynamic elliptical journal bearing with micropolar lubricant

In this paper the effect of deformation of the bearing liner on the static and dynamic performance characteristics of an elliptical (two-lobe) journal bearing operating with micropolar lubricant is presented. Lubricating oil containing additives and contaminants is modeled as micropolar fluid. A generalized form of Reynold's equation is derived from the fluid flow and diffusion equations. Finite element technique is used to solve the modified Reynold's equation governing the flow of micropolar lubricant in the clearance space of the journal bearing and the three-dimensional elasticity equations governing the displacement field in the bearing shell. The static and dynamic characteristics of the bearing are computed for a wide range of deformation coefficient which takes into accountant the flexibility of bearing liner by treating operating lubricant as (i) Newtonian and (ii) micropolar. The computed results show that the increasing volume concentration of additives and mass transfer of additives produce significant changes on the performance characteristics.     

Development of a texture averaged Reynolds equation

The application of textured bearing surfaces results in a more complex lubricant flow pattern compared to smooth bearing surfaces. In order to capture the more complex flow pattern and possible inertia effects in the vicinity of the surface pockets, the Navier-Stokes equations should be used to model the flow between textured surfaces instead of the Reynolds equation. In this paper a multi-scale method is presented where the fluid flow in a single micro-scale texture unit cell is modelled using the Navier-Stokes equations, the results of which are then averaged to flow factors to be used in a novel texture averaged Reynolds equation on the macro-scale bearing level. Depending on the local flow conditions the non-linear inertia effects in the flow can either contribute or detract from the local load capacity of the lubricant film. Some results from the micro-scale calculations are presented, followed by the method developed to average these results to the macro-scale. The resulting flow-factors are presented and a load correction term is introduced. Although the method presented does not put restrictions to the texture dimensions, the texture unit cell dimensions are chosen equal to those in an experimental polymer water lubricated bearing. In a follow-up paper these results will be used to determine the efficiency of surface texturing in a lubricated journal bearing application.     

Turbulent flow over thin rectangular riblets

The effect of longitudinal thin rectangular riblets aligned with the flow direction on turbulent channel flow has been investigated using direct numerical simulation. The thin riblets have been modeled using the immersed boundary method (IBM) where the velocities at only one set of vertical nodes at the riblets positions are enforced to be zeros. Different spacings, ranging between 11 and 43 wall units, have been simulated aiming at getting the optimum spacing corresponding to the maximum drag reduction while keeping the height/spacing ratio at 0.5. Reynolds number based on the friction velocityuτ and the channel half depth δ is set to 150. The flow is driven by adjusted pressure gradient so that the mass flow rate is kept constant in all the simulations. This study shows similar trend of the drag ratio to that of the experiments at the different spacings. Also, this research provides an optimum spacing of around 17 wall units leading to maximum drag reduction as experimental data. Explanation of drag increasing/ decreasing mechanism is highlighted.     

Steady state and stability characteristics of a hydrodynamic journal bearing with a non-Newtonian lubricant

The effect of the non-Newtonian behaviour of lubricants, resulting from the addition of polymers, on the performance of hydrodynamic journal bearings was investigated. An empirical fluid flow equation which adequately represents the flow behaviour of lubricant was used to obtain a modified form of Reynolds' equation. Finite difference numerical solutions were obtained for steady state conditions at various width-to-diameter ratios. The results show a strong influence of the width-to-diameter ratio on the load capacity of journal bearings. Linearised stiffness and damping coefficients were evaluated from the fluid film force equations for the unsteady motion of the journal centre and were used to predict the stability limits of a simple rigid rotor-bearing system which showed a reduction in threshold speeds. The steady state load capacity and stability limits were verified experimentally for finite width bearings.     

Effect of riblets on the streaky structures excited by free stream tip vortices in boundary layer

In this study, experimental investigations were made regarding the effect of riblets on the streak instability in boundary layer. The streak instability is now regarded as a major source of the self-regeneration mechanism for the hairpin type coherent structures in turbulent boundary layer flow. Thus, it is important to control the instability to suppress the drag-inducing vortical structure in terms of drag reduction. Toward enhancing the measurement accuracy and spatial resolution, an enlarged version of riblets was applied to a streak which was artificially induced by a microwing in a laminar boundary layer. It is found that the riblets have attenuation effect on the streak instability, i.e., to reduce the spanwise velocity gradient of the quasi-streamwise streak in boundary layer.     

Static and dynamic characteristics of externally pressurized circular step thrust bearings lubricated with couple stress fluids

The combined effects of couple stresses, fluid inertia and recess volume fluid compressibility on the steady-state performance and the dynamic stiffness and damping characteristics of hydrostatic circular step thrust bearings are presented theoretically. Based on the micro-continuum theory, the modified Reynolds equation and the recess flow continuity equation are derived by using the Stokes constitutive equations to account for the couple stress effect resulting from a lubricant blended with various additives. Using a perturbation technique, results in terms of steady-state load-carrying capacity, oil flow rate, stiffness and damping coefficients are presented. A design example is also illustrated for engineering and industrial applications.     

Inertial MHD Couple Stress Effects on Infinitely Wide Slider Bearings

This article presents a numerical study of magnetohydrodynamic (MHD) infinitely wide plane inclined slider bearings including both fluid inertia and non-Newtonian couple stress effects. Fluid inertia forces are considered in the film fluid using a simplified form of the Navier-Stokes equations. The non-Newtonian couple stress behavior of the lubricant is described based on the microcontinuum Stokes theory. The governing equations are discretized by finite differences using a boundary layer–type equations resolution. The resulting algebraic equations are solved using the Gauss-Seidel method. It is found that the couple effects of fluid inertia forces, MHD, and non-Newtonian couple stresses provide a significant improvement in the slider bearing load capacity compared to the case of the noninertia Newtonian nonconducting lubricant. The use of conducting lubricant diminishes the negative effect of inertia forces on the friction coefficient.     

Variable-viscosity effects in externally pressurized spherical oil bearings

Externally pressurized spherical bearings were analysed considering the rotational inertia of the lubricant and the variation of the lubricant viscosity along the flow. The equations of motion expressed in spherical coordinates were suitably reduced to describe the lubricant flow through the bearing clearance. A numerical solution of the resulting equations, in which the variation of viscosity with temperature was considered, was obtained using the finite-difference technique. The effects of bearing geometry, bearing speed, inlet oil temperature, bearing load, lubricant flow rate and frictional torque on pressure and temperature distributions under adiabatic flow conditions were investigated. Satisfactory agreement between experiment and the adiabatic solution was found for a high speed factor. The theory is applicable to both fitted and clearance-type spherical bearings.     

Role of ultrafiltration of synovial fluid in lubrication of human joints

Introducing the concept of mixture theory of two interacting continua for the poroelastic cartilage and the micromorphic approach for the synovial fluid, a two-region flow model has been developed in order to study the lubrication characteristics of synovial joints. The fluid transport in the deformable porous cartilaginous matrix is computed from a simple analysis of the coupled equations of motion and the resulting flow into the intra-articular gap. As the gap closes, ultrafiltration of the suspending medium increases the load carrying capacity and closure time. It ultimately leads to the formation of a lubricant gel on the surfaces when the gap reduces to the order of surface asperities.     

Experimental study of effects of circular-cross-section riblets on the aerodynamic performance of Risø airfoil at transient flow regime

New drag reduction methods have received much attention due to the importance of drag reduction in airplanes and wind turbines. One of the ways for drag reduction is the use of riblets. We investigated the effects of riblets on the aerodynamic performance of the Risø airfoil quantitatively. By installing a load cell and using the one-sided force measurement method, the drag and lift coefficients of the Risø airfoil were measured in two modes: With and without riblets at three different arrangements. The shape of riblets is a circularcross- section and the ratio of riblets’ diameter to the airfoil chord is equal to 0.005. The tests were carried out in transient flow regime (Two Reynolds numbers of 2.02×10⁵ and 1.4×10⁵), and at attack angles from 0 to 20 degrees. The results indicate that the extent of the riblets effect on the aerodynamic performance of the airfoil depends on the angle of attack, Reynolds number, and arrangement of the riblets on the airfoil. The maximum drag reduction at the Reynolds numbers of 2.02×10⁵ and 1.4×10⁵ is about 29.7 % and 54 %, respectively, that occurs at an attack angle of 7 degrees for both two Reynolds numbers.     

Influence of micropolar lubricants on the performance of slot-entry hybrid journal bearing

A theoretical study concerning the slot-entry hybrid journal bearing lubricated with micropolar lubricants is presented. The modified Reynolds equation for micropolar lubricant is solved using finite element method along with equation of lubricant flow through slot-entry restrictors as a constraint together with appropriate boundary conditions. It has been observed that a slot-entry hybrid journal bearing operating with micropolar lubricant shows an increase in the value of minimum fluid film thickness and a reduction in the value of coefficient of friction as compared to a corresponding similar slot-entry hybrid journal bearing operating with Newtonian lubricant.     

Influence of micropolar lubricants on the performance of slot-entry hybrid journal bearing

A theoretical study concerning the slot-entry hybrid journal bearing lubricated with micropolar lubricants is presented. The modified Reynolds equation for micropolar lubricant is solved using finite element method along with equation of lubricant flow through slot-entry restrictors as a constraint together with appropriate boundary conditions. It has been observed that a slot-entry hybrid journal bearing operating with micropolar lubricant shows an increase in the value of minimum fluid film thickness and a reduction in the value of coefficient of friction as compared to a corresponding similar slot-entry hybrid journal bearing operating with Newtonian lubricant.     

A theoretical study of two‐dimensional grease flow in regions with discontinuities

This paper presents a theoretical analysis of two‐dimensional grease flow through an asymmetric discontinuity. The behaviour of the fluid is described using Navier—Stokes equations, numerically solved by the finite‐element method. The FLFI program was used for this purpose. For this type of discontinuity, the velocity profile in the lubricant film, the shape and the dimensions of the stagnant core, the flow capacity, and the pressure distribution have been obtained. The results are useful in the design of bearings, if one considers the discontinuities in the carrying region as orifices, canals, or pockets for lubrication.     

Thermo-Mixed Hydrodynamics of Piston Compression Ring Conjunction

A new method, comprising Navier–Stokes equations, Rayleigh–Plesset volume fraction equation, an analytical control-volume thermal-mixed approach and asperity interactions, is reported. The method is employed for prediction of lubricant flow and assessment of friction in the compression ring–cylinder liner conjunction. The results are compared with Reynolds-based laminar flow with Elrod cavitation algorithm. Good conformance is observed for medium load intensity part of the engine cycle. At lighter loads and higher sliding velocity, the new method shows more complex fluid flow, possessing layered flow characteristics on the account of pressure and temperature gradient into the depth of the lubricant film, which leads to a cavitation region with vapour content at varied volume fractions. Predictions also conform well to experimental measurements reported by other authors.     

Comments on “The unlubricated wear of cast irons”

A numerical solution is developed for the equations governing the laminar hydrodynamic flow in a sector-shaped thrust bearing with its axis parallel to but offset from the rotational axis. The lubricant viscosity is assumed to be a function of the temperature distribution in the fluid film. The rotating plate is assumed to be an isothermal component and the heat conduction equation in the stationary component is solved simultaneously with the governing equations of the fluid film. Thermal effects are shown to be pronounced especially at large values of offset from the rotational axis.     

Lubricant additives effects on the hydrodynamic lubrication of misaligned conical–cylindrical bearings

Conical–cylindrical bearings are used in electrohydraulic servo systems to improve the control accuracy, eliminate the static friction and increase the normal load‐carrying capacity. A non‐Newtonian rheological model to investigate theoretically the effects of lubricant additives on the performance of misaligned conical–cylindrical bearings is proposed in this study. In this model, the non‐Newtonian behaviour 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 utilised to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. The misalignment of the cylinder rod is also considered. 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 behaviour of the lubricant on the steady‐state performance characteristics such as pressure distribution, load‐carrying capacity and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load‐carrying capacity and reduce the coefficient of friction as compared to the Newtonian lubricants. Furthermore, the misalignment of the piston rod has significant effects on the performance of conical–cylindrical bearings. Copyright © 2007 John Wiley & Sons, Ltd.     

NUMERICAL STUDY OF FLOW IN CONICAL DIFFUSER WITH VORTEX GENERATOR JETS

To develop vortex generator jet (VGJ) method for flow control, the turbulence flow in a 144°conical diffuser with and without vortex generator jets are simulated by solving Navier-Stokes equations with κ -ε turbulence model. The diffuser performance, based on different velocity ratio (ratio of the jet speed to the mainstream velocity), is investigated and compared with the experimental study. On the basis of the flow characteristics using computation fluid dynamics (CFD) method observed in the conical diffuser and the downstream development of the longitudinal vortices, attempt is made to correlate the pressure recovery coefficient with the behavior of vortices produced by vortex generator jets.     

Thermal characteristics of a non-newtonian fluid in a porous thrust bearing

A study of the behavior of an externally pressurized circular porous thrust bearing using a non-newtonian fluid lubricant was made. The governing Navier-Stokes equations were reduced to a set of ordinary differential equations and were solved numerically with the cross-flow Reynolds number and the Prandtl number as parameters. The pressure distribution and the lift force were evaluated. The effects of cross-viscosity coefficients on the flow and heat transfer characteristics of the bearing were determined.