Generalized Reynolds Equation for Solid-Liquid Lubricated Bearings

1994 ◽  
Vol 61 (2) ◽  
pp. 460-466 ◽  
Author(s):  
F. Dai ◽  
M. M. Khonsari
Keyword(s):  
Boundary Conditions ◽  
Reynolds Equation ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Continuum Theory ◽  
Solid Particles ◽  
Governing Equations ◽  
Hydrodynamic Bearing ◽  
Solid Liquid ◽  
Generalized Reynolds Equation

The continuum theory of mixture was employed to derive a generalized form of the Reynolds equation for the lubrication problems involving lubricants that contain solid particles. The derivation of the governing equations and the boundary conditions are presented. The governing equations are two coupled partial differential equations that must be solved simultaneously for the solid volume fraction and the pressure distribution in a hydrodynamic bearing. The boundary conditions allow the particles to slip at the boundary surfaces. The formulation takes the interaction between the solid and the fluid constituents into consideration. Extensive numerical results are presented for the performance parameters in finite journal bearings lubricated with granular powder mixed with Newtonian oil.

scholarly journals Integral Solution of Two-Region Solid–Liquid Phase Change in Annular Geometries and Application to Phase Change Materials–Air Heat Exchangers

Energies ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4474 ◽  
Author(s):  
Hamidreza Shabgard ◽  
Weiwei Zhu ◽  
Amir Faghri
Keyword(s):  
Liquid Phase ◽  
Boundary Conditions ◽  
Phase Change ◽  
Phase Change Materials ◽  
Volume Fraction ◽  
Control Volume ◽  
Solid Volume Fraction ◽  
Solidification Time ◽  
Design And Optimization ◽  
Solid Liquid

A mathematical model based on the integral method is developed to solve the problem of conduction-controlled solid–liquid phase change in annular geometries with temperature gradients in both phases. The inner and outer boundaries of the annulus were subject to convective, constant temperature or adiabatic boundary conditions. The developed model was validated by comparison with control volume-based computational results using the temperature-transforming phase change model, and an excellent agreement was achieved. The model was used to conduct parametric studies on the effect of annuli geometry, thermophysical properties of the phase change materials (PCM), and thermal boundary conditions on the dynamics of phase change. For an initially liquid PCM, it was found that increasing the radii ratio increased the total solidification time. Also, increasing the Biot number at the cooled (heated) boundary and Stefan number of the solid (liquid) PCM, decreased (increased) the solidification time and resulted in a greater (smaller) solid volume fraction at steady state. The application of the developed method was demonstrated by design and analysis of a PCM–air heat exchanger for HVAC systems. The model can also be easily employed for design and optimization of annular PCM systems for all associated applications in a fraction of time needed for computational simulations.

A Continuum Theory of a Lubrication Problem With Solid Particles

1993 ◽  
Vol 60 (1) ◽  
pp. 48-58 ◽  
Author(s):  
Fuling Dai ◽  
M. M. Khonsari
Keyword(s):  
Numerical Solutions ◽  
Volume Fraction ◽  
Solid Phase ◽  
Solid Volume Fraction ◽  
Mixture Theory ◽  
Continuum Theory ◽  
Fluid Phase ◽  
Solid Particles ◽  
Mixture Flow ◽  
Particulate Solid

The governing equations for a two-dimensional lubrication problem involving the mixture of a Newtonian fluid with solid particles at an arbitrary volume fraction are developed using the theory of interacting continuua (mixture theory). The equations take the interaction between the fluid and the particles into consideration. Provision is made for the possibility of particle slippage at the boundaries. The equations are simplified assuming that the solid volume fraction varies in the sliding direction alone. Equations are solved for the velocity of the fluid phase and that of the solid phase of the mixture flow in the clearance space of an arbitrary shaped bearing. It is shown that the classical pure fluid case can be recovered as a special case of the solutions presented. Extensive numerical solutions are presented to quantify the effect of particulate solid for a number of pertinent performance parameters for both slider and journal bearings. Included in the results are discussions on the influence of particle slippage on the boundaries as well as the role of the interacting body force between the fluid and solid particles.

scholarly journals Numerical Analysis of Nanofluids in Differentially Heated Enclosure Undergoing Orthogonal Rotation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
H. Saleh ◽  
I. Hashim
Keyword(s):  
Heat Transfer ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Heat Transfer ◽  
Staggered Grid ◽  
Governing Equations ◽  
Nanoparticles Concentration ◽  
Quantity Of Heat ◽  
Velocity Pressure

Natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this paper. The rotating enclosure is filled with water-Ag, water-Cu, water-Al2O3, or water-TiO2nanofluids. The governing equations are in velocity, pressure, and temperature formulation and solved using the staggered grid arrangement together with MAC method. The governing parameters considered are the solid volume fraction,0.0 ≤ ϕ ≤ 0.05, and the rotational speeds,3.5≤ Ω ≤ 17.5 rpm, and the centrifugal force is smaller than the Coriolis force and both forces were kept below the buoyancy force. It is found that the angular locations of the local maximums heat transfer were sensitive to rotational speeds and nanoparticles concentration. The global quantity of heat transfer rate increases about 1.5%, 1.1%, 0.8%, and 0.6% by increasing 1%ϕof the nanoparticles Ag, Cu, Al2O3, and TiO2, respectively, for the considered rotational speeds.

The Effect of the Microstructure of Semisolid Al Alloy on its Rheology

2014 ◽  
Vol 490-491 ◽  
pp. 109-112
Author(s):  
De Wen Cao ◽  
Jia Huan Wang ◽  
Yu Qing Sun ◽  
Ke Hua Chen ◽  
Cheng Ming Yu ◽  
...  
Keyword(s):  
Particle Size ◽  
Rheological Behavior ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Alloy System ◽  
The State ◽  
Solid Particles ◽  
Al Alloy ◽  
Agglomerate Size ◽  
The One

In the present work, the effect of the microstructure of AlSi6Mg2 alloy on its macro-rheological behavior of the steady AlSi6Mg2 alloy is investigated. Specifically, the effect of particle size, packing mode and degree of the agglomeration of particles are analyzed. It can be seen that the apparent viscosity decreases with increasing the particle size (d) ifdis between a few μm and 200 μm, while the solid particle size does not affect viscosity except this region. This theoretical prediction is in qualitatively agreement with the experimental data. The trend of the variation of the average agglomerate size with the particle size is the same as the one of viscosity. The packing mode of solid particles in agglomerate is closely related to the solid volume fraction and the characteristics of the alloy system. Subsequently, the state of agglomeration of solid particles which determines the rheology of semisolid AlSi6Mg2 alloy, while the external flow conditions (such as shear rate) influence the viscosity by changing the state of agglomeration. Consequently, the particle size, the packing mode and the average agglomerate size have different effect on the rheological behavior of SSMS.

Numerical Simulation of Modified Trailing Edge of Francis Turbine Stay Vane Based on Solid-Liquid Two-Phase Flow

2014 ◽  
Vol 700 ◽  
pp. 643-646
Author(s):  
Dong Wang ◽  
Si Qing Zhang ◽  
Yun Long Zhang
Keyword(s):  
Numerical Simulation ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Francis Turbine ◽  
Phase Flow ◽  
Oblique Angle ◽  
Trailing Edge ◽  
Two Phase ◽  
High Solid ◽  
Solid Liquid

In order to investigate the silt abrasion of modified trailing edge of stay vane in Francis turbine, the numerical simulation of trailing edge with different geometries were carried out based on the solid-liquid two-phase flow by means of Computation Fluid Dynamics. The results show that low solid volume fraction distributes on the chamfered surface of trailing edge, and high solid volume fraction distributes on the end of oblique surface. The smaller the modified angle is, the larger the distribution area of high solid volume fraction is, which show the trailing edge with smaller oblique angle may suffer from silt abrasion. Therefore, in order to solve the vibration caused by Karman vortex the trailing edge has to be sharpened, the oblique angle of trailing edge should not be too small. At end of trailing edge needs to ensure a certain thickness, especially the trailing edge near the lower ring can be thicker, which can meet the anti-abrasion requirements.

scholarly journals Computational investigation of liquid-solid slurry flow through an expansion in a rectangular duct

2014 ◽  
Vol 62 (3) ◽  
pp. 234-240 ◽  
Author(s):  
Gianandrea Vittorio Messa ◽  
Stefano Malavasi
Keyword(s):  
Volume Fraction ◽  
Particle Density ◽  
Fluid Model ◽  
Solid Volume Fraction ◽  
Solid Particles ◽  
Rectangular Duct ◽  
Two Phase ◽  
Horizontal Pipe ◽  
Two Fluid Model ◽  
Two Fluid

Abstract The flow of a mixture of liquid and solid particles at medium and high volume fraction through an expansion in a rectangular duct is considered. In order to improve the modelling of the phenomenon with respect to a previous investigation (Messa and Malavasi, 2013), use is made of a two-fluid model specifically derived for dense flows that we developed and implemented in the PHOENICS code via user-defined subroutines. Due to the lack of experimental data, the two-fluid model was validated in the horizontal pipe case, reporting good agreement with measurements from different authors for fully-suspended flows. A 3D system is simulated in order to account for the effect of side walls. A wider range of the parameters characterizing the mixture (particle size, particle density, and delivered solid volume fraction) is considered. A parametric analysis is performed to investigate the role played by the key physical mechanisms on the development of the two-phase flow for different compositions of the mixture. The main focuses are the distribution of the particles in the system and the pressure recovery

Thermohydrodynamic Analysis of Solid-Liquid Lubricated Journal Bearings

1988 ◽  
Vol 110 (2) ◽  
pp. 367-374 ◽  
Author(s):  
M. M. Khonsari ◽  
V. Esfahanian
Keyword(s):  
Journal Bearing ◽  
Journal Bearings ◽  
Solid Particles ◽  
Governing Equations ◽  
Transfer Processes ◽  
Flow And Heat Transfer ◽  
Experimental Findings ◽  
Solid Liquid ◽  
General Computer Program ◽  
Good Agreement

Thermohydrodynamic theory is extended to include the effect of solid particles in hydrodynamically lubricated journal bearings. Appropriate governing equations and boundary conditions are derived for the fluid flow and heat transfer processes taking place in a finite journal bearing. A general computer program is developed to numerically solve the governing equations. Results are provided for biphase lubricants containing oil with molybdenum disulfide and polytetrafluoroethylene particles. The computational results are in good agreement with experimental findings. The results indicate that the bearing temperature field is affected significantly by the presence of particles in oil. Moreover, it is found that inclusion of particles in the lubricant results in a higher coefficient of friction in the mid-range of the Sommerfeld number compared to that of the clean oil.

On the granular lubrication theory

2005 ◽  
Vol 461 (2062) ◽  
pp. 3255-3278 ◽  
Author(s):  
J.Y Jang ◽  
M.M Khonsari
Keyword(s):  
Granular Material ◽  
Reynolds Equation ◽  
Three Dimensional ◽  
Lubrication Theory ◽  
Slider Bearing ◽  
Governing Equations ◽  
Three Dimensional Flow ◽  
Generation Capacity ◽  
Side Flow ◽  
Generalized Reynolds Equation

The governing equations for the flow of a granular material within the context of the lubrication theory are derived. The resulting analysis gives a generalized Reynolds equation that predicts the pressure generation capacity in a bearing with consideration of side flow. A series of simulations are presented that characterize the three-dimensional flow behaviour of powder in a slider bearing.

The Steady State Rheological Behavior of Semisolid AlSi6Mg2 Alloy

2011 ◽  
Vol 339 ◽  
pp. 257-260 ◽  
Author(s):  
Hong Chao Luo ◽  
Shi Pu Chen ◽  
Qin Nie ◽  
En Sheng Xu ◽  
Li Ping Ju
Keyword(s):  
Steady State ◽  
Shear Rate ◽  
Rheological Behavior ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Solid Particles ◽  
Experimental Results ◽  
Present System ◽  
Flow Conditions ◽  
Good Agreement

In the present work, basing on the rheological model of Chen and Fan (CF) [1] of semisolid metal slurries (SSMS), the rheological behavior at steady state of AlSi6Mg2 alloy is investigated. Experimental results on steady state viscosity of the present system in the literature are used to determine the parameters of the CF model by fitting. It has been shown that the steady state viscosity and the average agglomerate size increase with increasing the solid volume fraction and decreasing the shear rate. The theoretical prediction of the CF model is in good agreement with the experimental results in the literatures quantitatively. The importance of the effective solid volume fraction is shown by explaining the strong coupling between the viscosity and the microstructure. Specifically, the external flow conditions such as shear rate influences the viscosity by changing the agglomeration degree of the solid particles, that is, the effective solid volume fraction and then changing the viscosity.

Behavior of Finite Journal Bearings Under Dynamic Loading Conditions

1980 ◽  
Vol 102 (3) ◽  
pp. 333-338 ◽  
Author(s):  
G. S. A. Shawki ◽  
M. O. A. Mokhtar ◽  
Z. S. Safar
Keyword(s):  
Boundary Conditions ◽  
Computer Program ◽  
Variational Methods ◽  
Axial Length ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
The Third ◽  
Dynamic Loading Conditions ◽  
Generalized Reynolds Equation

Performance characteristics for a complete journal bearing of finite axial length are obtained analytically using a new set of boundary conditions. The generalized Reynolds equation is transformed, in the present analysis, into three ordinary differential equations, two of which being readily integrable while the third is solved by variational methods. By the aid of a specially devised computer program, the validity of the analysis has been assured when applied to prescribed journal loci including stationary, circular, elliptical, and linear harmonic journal oscillation.

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