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.

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.

On the role of the ambient fluid on gravitational granular flow dynamics

2010 ◽  
Vol 648 ◽  
pp. 381-404 ◽  
Author(s):  
C. MERUANE ◽  
A. TAMBURRINO ◽  
O. ROCHE
Keyword(s):  
Granular Flow ◽  
Numerical Solutions ◽  
Solid Phase ◽  
Fluid Pressure ◽  
Mixture Theory ◽  
Flow Dynamics ◽  
Solid Particles ◽  
Ambient Fluid ◽  
Two Phase

The effects of the ambient fluid on granular flow dynamics are poorly understood and commonly ignored in analyses. In this article, we characterize and quantify these effects by combining theoretical and experimental analyses. Starting with the mixture theory, we derive a set of two-phase continuum equations for studying a compressible granular flow composed of homogenous solid particles and a Newtonian ambient fluid. The role of the ambient fluid is then investigated by studying the collapse and spreading of two-dimensional granular columns in air or water, for different solid particle sizes and column aspect (height to length) ratios, in which the front speed is used to describe the flow. The combined analysis of experimental measurements and numerical solutions shows that the dynamics of the solid phase cannot be explained if the hydrodynamic fluid pressure and the drag interactions are not included in the analysis. For instance, hydrodynamic fluid pressure can hold the reduced weight of the solids, thus inducing a transition from dense-compacted to dense-suspended granular flows, whereas drag forces counteract the solids movement, especially within the near-wall viscous layer. We conclude that in order to obtain a realistic representation of gravitational granular flow dynamics, the ambient fluid cannot be neglected.

scholarly journals Some Simulation Results and Parameter Analyses of a Generalized Quasi Two-Phase Bulk Mixture Model

2019 ◽  
Vol 2 (1) ◽  
pp. 45-56
Author(s):  
Khim B. Khattri ◽  
Parameshwari Kattel ◽  
Bhadra Man Tuladhar
Keyword(s):  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Maximum Velocity ◽  
Solid Particles ◽  
Physical Parameters ◽  
Two Phase ◽  
Mixture Flow ◽  
Non Linear ◽  
Mixture Viscosity ◽  
Bulk Model

Here, we consider a newly constructed generalized quasi two-phase bulk model for a rapid flow of a debris mixture consisting of viscous fluid and solid particles down a channel. The model is a set of coupled partial differential equations with new mechanical description of generalized bulk and shear viscosities, pressure, velocities and effective friction. The dynamical variables, physical parameters, inertial and dynamical coeffcients and drift factors involved in the equations contain certain important physics of mixture flow. So, we analyze the behaviour of some inertial and dynamical coeffcients involved in the model. These coeffcients strongly depend upon the initial material composition. We also simulate the evolution of the dynamical variables so as to reveal their strong non-linear behaviours. Through simulations, we also analyze the front position of the debris material, bottom-slip velocity and maximum velocity, which show fundamentally different dynamics for varied material compositions, from dilute to dense flows. Generalized mixture viscosity decreases as the ow moves downslope, and the rate at which it decreases depends upon the initial solid-volume fraction. We also compare the effective viscosity and the bulk mixture viscosity with respect to the norm of the strain rate tensors to reveal different non-linear behaviours.

Comparative Assessment of Turbulence Models for Prediction of Flow-Induced Corrosion Damages

2011 ◽  
Author(s):  
Kaushik Das ◽  
Debashis Basu ◽  
Todd Mintz
Keyword(s):  
Corrosion Rate ◽  
Cross Sections ◽  
Volume Fraction ◽  
Solid Phase ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Continuous Phase ◽  
Comparative Assessment ◽  
Solid Particles ◽  
Protective Film

The present study makes a comparative assessment of different turbulence models in simulating the flow-assisted corrosion (FAC) process for pipes with noncircular cross sections and bends, features regularly encountered in heat exchangers and other pipeline networks. The case study investigates material damage due to corrosion caused by dissolved oxygen (O2) in a stainless steel pipe carrying an aqueous solution. A discrete solid phase is also present in the solution, but the transport of the solid particles is not explicitly modeled. It is assumed that the volume fraction of the solid phase is low, so it does not affect the continuous phase. Traditional two-equation models are compared, such as isotropic eddy viscosity, standard k-ε and k-ω models, shear stress transport (SST) k-ω models, and the anisotropic Reynolds Stress Model (RSM). Computed axial and radial velocities, and turbulent kinetic energy profiles predicted by the turbulence models are compared with available experimental data. Results show that all the turbulence models provide comparable results, though the RSM model provided better predictions in certain locations. The convective and diffusive motion of dissolved O2 is calculated by solving the species transport equations. The study assumes that solid particle impingement on the pipe wall will completely remove the protective film formed by corrosion products. It is also assumed that the rate of corrosion is controlled by diffusion of O2 through the mass transfer boundary layer. Based on these assumptions, corrosion rate is calculated at the internal pipe walls. Results indicate that the predicted O2 corrosion rate along the walls varies for different turbulence models but show the same general trend and pattern.

Application of Wray-Agarwal turbulence model for numerical simulation of gas-solid flows in CFB risers

2021 ◽  
pp. 1-25
Author(s):  
Yali Shao ◽  
Ramesh K. Agarwal ◽  
Xudong Wang ◽  
Baosheng Jin
Keyword(s):  
Turbulence Model ◽  
Circulating Fluidized Bed ◽  
Volume Fraction ◽  
Solid Phase ◽  
Solid Volume Fraction ◽  
Turbulence Models ◽  
Two Phase ◽  
Efficient Simulation ◽  
Pressure Profiles ◽  
First Time

Abstract In recent decades, increasing attention has been focused on accurate modeling of circulating fluidized bed (CFB) risers to provide valuable guidance to design, optimization and operation of reactors. Turbulence model plays an important role in accurate prediction of complex gas-solid flows. Recently developed Wray-Agarwal (WA) model is a one-equation turbulence model with the advantages of high computational efficiency and competitive accuracy with two-equation models. In this paper for the first time, Eulerian-Eulerian approach coupled with different turbulence models including WA model, standard κ-ε model and shear stress transport (SST) κ-ω model is employed to simulate two-phase flows of gas phase and solid phase in two CFB risers, in order to assess accuracy and efficiency of WA model compared to other well-known two-equation models. Predicted gas-solid flow dynamic characteristics including the gas-solid volume fraction distributions in radial and axial directions, pressure profiles and solid mass flux distributions are compared with data obtained from experiment in detail. The results demonstrate WA model is very promising for accurate and efficient simulation of gas-solid multiphase flows.

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.

scholarly journals Interface-resolved simulations of particle suspensions in Newtonian, shear thinning and shear thickening carrier fluids

2018 ◽  
Vol 852 ◽  
pp. 329-357 ◽  
Author(s):  
Dhiya Alghalibi ◽  
Iman Lashgari ◽  
Luca Brandt ◽  
Sarah Hormozi
Keyword(s):  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Shear Thickening ◽  
Fluid Phase ◽  
Local Strain ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Strain Rates ◽  
Local Shear ◽  
The Mean

We present a numerical study of non-colloidal spherical and rigid particles suspended in Newtonian, shear thinning and shear thickening fluids employing an immersed boundary method. We consider a linear Couette configuration to explore a wide range of solid volume fractions ($0.1\leqslant \unicode[STIX]{x1D6F7}\leqslant 0.4$) and particle Reynolds numbers ($0.1\leqslant Re_{p}\leqslant 10$). We report the distribution of solid and fluid phase velocity and solid volume fraction and show that close to the boundaries inertial effects result in a significant slip velocity between the solid and fluid phase. The local solid volume fraction profiles indicate particle layering close to the walls, which increases with the nominal $\unicode[STIX]{x1D6F7}$. This feature is associated with the confinement effects. We calculate the probability density function of local strain rates and compare the latter’s mean value with the values estimated from the homogenisation theory of Chateau et al. (J. Rheol., vol. 52, 2008, pp. 489–506), indicating a reasonable agreement in the Stokesian regime. Both the mean value and standard deviation of the local strain rates increase primarily with the solid volume fraction and secondarily with the $Re_{p}$. The wide spectrum of the local shear rate and its dependency on $\unicode[STIX]{x1D6F7}$ and $Re_{p}$ point to the deficiencies of the mean value of the local shear rates in estimating the rheology of these non-colloidal complex suspensions. Finally, we show that in the presence of inertia, the effective viscosity of these non-colloidal suspensions deviates from that of Stokesian suspensions. We discuss how inertia affects the microstructure and provide a scaling argument to give a closure for the suspension shear stress for both Newtonian and power-law suspending fluids. The stress closure is valid for moderate particle Reynolds numbers, $O(Re_{p})\sim 10$.

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

Computational Study of Slurry Flow in Pipes to Determine Profiles Sensed in Near Infrared Slurry Measurements

2011 ◽  
Author(s):  
V. Pasangulapati ◽  
N. R. Kesana ◽  
G. Sharma ◽  
F. W. Chambers ◽  
M. E. McNally ◽  
...  
Keyword(s):  
Near Infrared ◽  
Volume Fraction ◽  
Solid Phase ◽  
Computational Study ◽  
Solid Volume Fraction ◽  
Density Ratio ◽  
Optical Measurements ◽  
Concentration Profiles ◽  
Horizontal Pipe ◽  
Volume Fractions

It is desired to perform accurate Near Infrared sensor measurements of slurries flowing in pipes leaving large batch reactors. A concern with these measurements is the degree to which the slurry sensed is representative of the material in the reactor and flowing through the pipe. Computational Fluid Dynamics (CFD) has been applied to the flow in the pipe to determine the flow fields and the concentration profiles seen by the sensors. The slurry was comprised of a xylene liquid phase and an ADP (2-amino-4, 6-dimethylpyrimidine) solid phase with a density ratio of 1.7. Computations were performed for a horizontal pipe with diameter 50.8 mm, length 2.032 m, and 1.76 m/s and 3.26 m/s mixture velocities. The corresponding pipe Reynolds numbers were 1.19E+05 and 2.21E+05. The flow through a slotted cylindrical probe inserted radially in the pipe also was considered. Spherical slurry particles with diameters from 10 μm to 1000 μm were considered with solid volume fractions of 12%, 24%, and 35%. Computations were performed with ANSYS FLUENT 12 software using the Realizable k-ε turbulence model and the enhanced wall treatment function. Comparisons of computed vertical profiles of solid volume fraction to results in the literature showed good agreement. Symmetric, nearly flat solid volume fraction profiles were observed for 38 μm particles for all three initial solid volume fractions. Asymmetric solid volume fraction profiles with greater values toward the bottom were observed for the larger particles. Changes in the profiles of turbulent kinetic energy also were observed. These changes are important for optical measurements which depend upon the mean concentration profiles as well as the turbulent motion of the slurry particles.

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