scholarly journals Lubrication Approximation for Fluids with Shear-Dependent Viscosity

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 98 ◽  
Author(s):  
Bruno M.M. Pereira ◽  
Gonçalo A.S. Dias ◽  
Filipe S. Cal ◽  
Kumbakonam R. Rajagopal ◽  
Juha H. Videman
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Type Equation ◽  
Lubrication Approximation ◽  
The Novel ◽  
Governing Equations ◽  
Shear Dependent Viscosity ◽  
Rigid Plane ◽  
Dependent Viscosity

We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of the fluid, the novel equation can either present itself as a higher-order correction to the classical Reynolds equation or as a completely new nonlinear Reynolds type equation. Both equations are applied to two classic problems: the flow between a rolling rigid cylinder and a rigid plane and the flow in an eccentric journal bearing.

A Mass-Conserving Algorithm for Dynamical Lubrication Problems With Cavitation

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Roberto F. Ausas ◽  
Mohammed Jai ◽  
Gustavo C. Buscaglia
Keyword(s):  
Exact Solution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Source Code ◽  
Squeeze Flow ◽  
Complementarity Conditions ◽  
Relaxation Scheme ◽  
Fluid Fraction ◽  
Oscillatory Squeeze Flow

A numerical algorithm for fully dynamical lubrication problems based on the Elrod–Adams formulation of the Reynolds equation with mass-conserving boundary conditions is described. A simple but effective relaxation scheme is used to update the solution maintaining the complementarity conditions on the variables that represent the pressure and fluid fraction. The equations of motion are discretized in time using Newmark’s scheme, and the dynamical variables are updated within the same relaxation process just mentioned. The good behavior of the proposed algorithm is illustrated in two examples: an oscillatory squeeze flow (for which the exact solution is available) and a dynamically loaded journal bearing. This article is accompanied by the ready-to-compile source code with the implementation of the proposed algorithm.

A Contribution to the Analysis of the Thermo-Hydrodynamic Lubrication of Porous Self-Lubricating Journal Bearings

2010 ◽  
Vol 297-301 ◽  
pp. 618-623 ◽  
Author(s):  
S. Boubendir ◽  
Salah Larbi ◽  
Rachid Bennacer
Keyword(s):  
Thermal Effects ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Porous Matrix ◽  
Journal Bearings ◽  
Governing Equations ◽  
Hydrodynamic Analysis ◽  
Result Show

In this work the influence of thermal effects on the performance of a finite porous journal bearing has been investigated using a thermo-hydrodynamic analysis. The Reynolds equation of thin viscous films is modified taking into account the oil leakage into the porous matrix, by applying Darcy’s law to determine the fluid flow in the porous media. The governing equations were solved numerically using the finite difference approach. Obtained result show a reduction in the performance of journal bearings when the thermal effects are accounted for and, this reduction is greater when the load capacity is significant.

Modified Reynolds Equation for Non-Newtonian Fluid With Rheological Model in Frequency Domain

2005 ◽  
Vol 127 (4) ◽  
pp. 893-898 ◽  
Author(s):  
Chen Haosheng ◽  
Chen Darong
Keyword(s):  
Frequency Domain ◽  
Newtonian Fluid ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Pressure Profile ◽  
Thickness Variation ◽  
Lubrication Equation ◽  
Shear Dependent Viscosity ◽  
Modified Reynolds Equation ◽  
Dependent Viscosity

The purpose of this paper is to provide a lubrication equation for non-Newtonian fluid. Three nonlinear functions instead of common power law model are used to describe non-Newtonian properties more completely. They are shear dependent viscosity, first normal stress difference and stress relaxation. After the coordinate conversion which is needed for the lubricant film thickness variation, the functions are involved in the modified Reynolds equation and show their effects on the lubrication results. As the principle factor in lubrication, viscosity is expressed by a first order transfer function in frequency domain. Its variation process is described by the function’s amplitude frequency response curve, which is validated by rheological experiment. Numerical results of the modified Reynolds equation show that non-Newtonian lubricant’s load capacity is not always higher or lower than Newtonian lubricant’s, and non-Newtonian lubricant has flatter pressure profile at high working speed.

scholarly journals Flow of fluids with pressure- and shear-dependent viscosity down an inclined plane

2012 ◽  
Vol 706 ◽  
pp. 173-189 ◽  
Author(s):  
K. R. Rajagopal ◽  
G. Saccomandi ◽  
L. Vergori
Keyword(s):  
Reynolds Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Inclined Plane ◽  
Shear Dependent Viscosity ◽  
Order Of Magnitude ◽  
The Mean ◽  
Breaking Time ◽  
Propagation Of Waves ◽  
Dependent Viscosity

AbstractIn this paper we consider a fluid whose viscosity depends on both the mean normal stress and the shear rate flowing down an inclined plane. Such flows have relevance to geophysical flows. In order to make the problem amenable to analysis, we consider a generalization of the lubrication approximation for the flows of such fluids based on the development of the generalization of the Reynolds equation for such flows. This allows us to obtain analytical solutions to the problem of propagation of waves in a fluid flowing down an inclined plane. We find that the dependence of the viscosity on the pressure can increase the breaking time by an order of magnitude or more than that for the classical Newtonian fluid. In the viscous regime, we find both upslope and downslope travelling wave solutions, and these solutions are quantitatively and qualitatively different from the classical Newtonian solutions.

Modeling Lubricated Revolute Clearance Joints in Multibody Mechanical Systems

2003 ◽  
Author(s):  
P. Flores ◽  
H. M. Lankarani ◽  
J. Ambro´sio ◽  
J. C. P. Claro
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Hydrodynamic Forces ◽  
Dynamic Loads ◽  
Governing Equations ◽  
Clearance Joints ◽  
Revolute Joints ◽  
System A

This work is concerned with the modeling of lubricated revolute clearance joints in multibody mechanical systems. The existence of the clearance at revolute joints is inevitable in all mechanical systems, and most of them are designed to operate with a lubricant fluid. It is known that the use of lubricant at revolute joints is demonstrated to be an effective way to ensuring better performance of the mechanical systems. The long journal-bearing theory for dynamic loads is used to evaluate the resulting hydrodynamic forces of the pressure distribution in the lubricated revolute joints. These hydrodynamic forces are included into the governing equations of motion of the system. A numerical example is presented in order to demonstrate the efficiency and accuracy of the methodology and procedures adopted. The results are close to those obtained with ideal joints even when simulated in a high-speed mechanism.

Influence of the Thermo-Piezo-Viscous Effect on the THD Lubrication in Porous Self- Lubricating Bearings

2011 ◽  
Vol 312-315 ◽  
pp. 659-664
Author(s):  
S. Boubendir ◽  
Rachid Bennacer ◽  
Salah Larbi
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Numerical Study ◽  
Journal Bearings ◽  
Load Carrying Capacity ◽  
Viscous Effect ◽  
Governing Equations ◽  
Viscous Effects ◽  
Load Carrying ◽  
Variation Versus

A numerical study of the behavior for a finite porous journal bearing lubricated with Newtonian fluid is undertaken considering both thermal and piezo-viscous effects. The modified Reynolds equation is obtained by using the thermo-hydrodynamic aspect to account for the viscous variation versus pressure and temperature where Barus law has been used for the visous formulation. To determine the flow in the porous media, the Darcy’s law has considered. The governing equations were solved numerically using a finite difference approach. Obtained results compared with the case of a thermo-viscous aspect, the piezo-viscous parameter increases the load carrying capacity significantly and improves the characteristics of the journal bearings.

The Rheology of Saliva

1987 ◽  
Vol 66 (1_suppl) ◽  
pp. 660-666 ◽  
Author(s):  
W. H. Schwarz
Keyword(s):  
Salivary Gland ◽  
Rheological Properties ◽  
Medical Management ◽  
Artificial Saliva ◽  
Salivary Gland Dysfunction ◽  
Shear Dependent Viscosity ◽  
Saliva Analysis ◽  
Whole Saliva ◽  
Saliva Substitutes ◽  
Dependent Viscosity

The rheology of saliva affects the coating and lubrication of oral surfaces and the consistency of ingested foods. Salivary gland dysfunction can cause tissue damage and dysphagia. Therefore, we have considered the problem of designing a synthetic saliva for medical management. Also, we have measured certain rheological properties [shear-dependent viscosity η (k)] and the frequency-dependent moduli [G′(f) and η′(f)] of normal stimulated whole saliva. Analysis of the rheological data and consideration of requirements for using artificial saliva have resulted in a better understanding of the rheological functions of natural saliva and the desirable characteristics of synthetic saliva. In addition, we have measured rheological properties of two commercial saliva substitutes for comparison.

A General Solution of Reynolds’ Equation for a Full Finite Journal Bearing

1967 ◽  
Vol 89 (2) ◽  
pp. 203-210 ◽  
Author(s):  
R. R. Donaldson
Keyword(s):  
Fourier Series ◽  
Series Solution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Separation Of Variables ◽  
Hill Equation ◽  
Eigenvalues And Eigenvectors ◽  
General Series ◽  
Bearing Load

Reynolds’ equation for a full finite journal bearing lubricated by an incompressible fluid is solved by separation of variables to yield a general series solution. A resulting Hill equation is solved by Fourier series methods, and accurate eigenvalues and eigenvectors are calculated with a digital computer. The finite Sommerfeld problem is solved as an example, and precise values for the bearing load capacity are presented. Comparisons are made with the methods and numerical results of other authors.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

Stability of Shear-Thickening Liquids Between Rotating Cylinders

2010 ◽  
Author(s):  
Nariman Ashrafi ◽  
Habib Karimi Haghighi
Keyword(s):  
Couette Flow ◽  
Dynamical Behavior ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Taylor Vortex ◽  
Shear Dependent Viscosity ◽  
Shear Thinning Fluids ◽  
Shear Thickening Fluids ◽  
The Stability ◽  
Dependent Viscosity

The effects of nonlinearities on the stability are explored for shear thickening fluids in the narrow-gap limit of the Taylor-Couette flow. It is assumed that shear-thickening fluids behave exactly as opposite of shear thinning ones. A dynamical system is obtained from the conservation of mass and momentum equations which include nonlinear terms in velocity components due to the shear-dependent viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of Couette flow becomes higher as the shear-thickening effects increases. Similar to the shear thinning case, the Taylor vortex structure emerges in the shear thickening flow, however they quickly disappear thus bringing the flow back to the purely azimuthal flow. Naturally, one expects shear thickening fluids to result in inverse dynamical behavior of shear thinning fluids. This study proves that this is not the case for every point on the bifurcation diagram.

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