Stokes Flow Through a Row of Cylinders Between Parallel Walls: Model for the Glomerular Slit Diaphragm

1994 ◽  
Vol 116 (2) ◽  
pp. 184-189 ◽  
Author(s):  
M. Claudia Drumond ◽  
William M. Deen
Keyword(s):  
Stokes Flow ◽  
Stokes Equations ◽  
Slit Diaphragm ◽  
Hydraulic Permeability ◽  
Shear Stresses ◽  
Two Factors ◽  
Additional Resistance ◽  
Flow Through ◽  
Experimental Values ◽  
Glomerular Capillaries

As a model for flow through the slit diaphragms which connect the epithelial foot processes of renal glomerular capillaries, finite element solutions of Stokes equations were obtained for flow perpendicular to a row of cylinders confined between parallel walls. A dimensionless “additional resistance” (f), defined as the increment in resistance above the Poiseuille flow value, was computed for L/W≤4 and 0.1≤ R/L≤0.9, where L is half the distance between cylinder centers, W is half the distance between walls and R is the cylinder radius. Two factors contributed to f: the drag on the cylinders, and the incremental shear stresses on the walls of the channel. Of these two factors, the drag on the cylinders tended to be dominant. A more complex representation of the slit diaphragm, suggested in the literature, was also considered. The predicted hydraulic permeability of the slit diaphragm was compared with experimental values of the overall hydraulic permeability of the glomerular capillary wall.

Prediction of Local Losses of Low Re Flows in Elastic Porous Media

2017 ◽  
Author(s):  
Sid M. Becker ◽  
Stefan Gasow
Keyword(s):  
Porous Media ◽  
Flow Field ◽  
Stokes Equations ◽  
Applied Pressure ◽  
Porous Matrix ◽  
Pore Geometry ◽  
Test Case ◽  
Hydraulic Permeability ◽  
Local Pressure ◽  
Flow Through

An isotropic elastic porous structure whose pore geometry is regular (periodically uniform) will experience non-uniform deformation when a viscous fluid flows through the matrix under the influence of an externally applied pressure difference. In such a case, the flow field will experience a non-uniform pressure gradient whose magnitude increases in the direction of bulk flow. In this study, a method is presented that predicts local losses of the flow through a porous matrix whose geometry varies in the direction of flow. Employing an asymptotic expansion about the variation in geometry provides an expression relating local hydraulic permeability to local pore geometry. In this way the pressure field is able to be determined without requiring the explicit solution of the flow field. In this study a test case is presented showing that the local pressure losses are predicted to be within 0.5% of the losses determined from the solution to the Navier-Stokes Equations. The approach can be used to simplify the coupled fluid-solid problem of flow through elastic porous media by replacing the need to explicitly solve the flow field.

Analysis of Blood flow Through Artery with Mild Stenosis

2020 ◽  
Vol 25 (2) ◽  
pp. 33-38
Author(s):  
Puskar R. Pokhrel ◽  
Jeevan Kafle ◽  
Parameshwari Kattel ◽  
Hari Prasad Gaire
Keyword(s):  
Blood Flow ◽  
Pressure Drop ◽  
Stokes Equations ◽  
Arterial Stenosis ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Navier Stokes Equations ◽  
Other Substances ◽  
Blood Flow Dynamics ◽  
Flow Through

Arterial stenosis is an abnormal condition in arteries due to the deposition of fats and other substances, called atherosclerosis.  As it restricts the blood flow, it may induce a heart attack. Employing the Navier-Stokes equations, we consider the blood flow in an artery with the presence of a stenosis in an axisymmetric shape. We analyze the blood flow dynamics in cylindrical form by evaluating pressure, pressure drop against the wall, shear stress on the wall. We also analyze the dynamics by evaluating the ratio of pressure drop with stenosis to the pressure drop without stenosis against the wall, and the ratio of maximum to minimum shear stresses with the ratios of various thicknesses of stenosis to radius of the artery.

scholarly journals Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 27
Author(s):  
Nattakarn Numpanviwat ◽  
Pearanat Chuchard
Keyword(s):  
Laplace Transform ◽  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mathieu Functions ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Elliptic Cross ◽  
Flow Through ◽  
Relative Errors

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

scholarly journals Development of Permeability Models for Saturated Fluid Flow across Arrays of Fibre Clusters

2002 ◽  
Vol 11 (3) ◽  
pp. 096369350201100
Author(s):  
E.M. Gravel ◽  
T.D. Papathanasiou
Keyword(s):  
Analytical Models ◽  
Dual Porosity ◽  
Hydraulic Permeability ◽  
Fibrous Media ◽  
Fibre Bundles ◽  
Hexagonal Packing ◽  
Composites Manufacturing ◽  
Starting Point ◽  
Wide Range ◽  
Flow Through

Dual porosity fibrous media are important in a number of applications, ranging from bioreactor design and transport in living systems to composites manufacturing. In the present study we are concerned with the development of predictive models for the hydraulic permeability ( Kp) of various arrays of fibre bundles. For this we carry out extensive computations for viscous flow through arrays of fibre bundles using the Boundary Element Method (BEM) implemented on a multi-processor computer. Up to 350 individual filaments, arranged in square or hexagonal packing within bundles, which are also arranged in square of hexagonal packing, are included in each simulation. These are simple but not trivial models for fibrous preforms used in composites manufacturing – dual porosity systems characterised by different inter- and intra-tow porosities. The way these porosities affect the hydraulic permeability of such media is currently unknown and is elucidated through our simulations. Following numerical solution of the governing equations, ( Kp) is calculated from the computed flowrate through Darcy's law and is expressed as function of the inter- and intra-tow porosities (φ, φt) and of the filament radius ( Rf). Numerical results are also compared to analytical models. The latter form the starting point in the development of a dimensionless correlation for the permeability of such dual porosity media. It is found that the numerically computed permeabilities follow that correlation for a wide range of φ i, φt and Rf.

Quantitative Analysis of Reynolds and Navier–Stokes Based Modeling Approaches for Isothermal Newtonian Elastohydrodynamic Lubrication

2021 ◽  
Vol 143 (12) ◽  
Author(s):  
Leoluca Scurria ◽  
Tommaso Tamarozzi ◽  
Oleg Voronkov ◽  
Dieter Fauconnier
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Thickness Distribution ◽  
Elastohydrodynamic Lubrication ◽  
Lubricant Film ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Low Viscosity ◽  
Fluid Film Thickness

Abstract When simulating elastohydrodynamic lubrication, two main approaches are usually followed to predict the pressure and fluid film thickness distribution throughout the contact. The conventional approach relies on the Reynolds equation to describe the thin lubricant film, which is coupled to a Boussinesq description of the linear elastic deformation of the solids. A more accurate, yet a time-consuming method is the use of computational fluid dynamics in which the Navier–Stokes equations describe the flow of the thin lubricant film, coupled to a finite element solver for the description of the local contact deformation. This investigation aims at assessing both methods for different lubrication conditions in different elastohydrodynamic lubrication (EHL) regimes and quantify their differences to understand advantages and limitations of both methods. This investigation shows how the results from both approaches deviate for three scenarios: (1) inertial contributions (Re > 1), i.e., thick films, high speed, and low viscosity; (2) high shear stresses leading to secondary flows; and (3) large deformations of the solids leading to inaccuracies of the Boussinesq equation.

scholarly journals Off-Design Performance Prediction for Radial-Flow Impellers

1988 ◽  
Author(s):  
Shen C. Lee ◽  
Daying Chen
Keyword(s):  
Stokes Equations ◽  
Mechanical Energy ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Pump Impeller ◽  
Navier Stokes Equations ◽  
Measured Velocity ◽  
Production Water ◽  
Performance Predictions ◽  
Stream Functions

A numerical method was developed to consider the two-dimensional flowfield between impeller blades of a given geometry. Solution of the laminar Navier-Stokes equations in geometry-oriented coordinates was obtained for stream functions and vorticities. Velocities and pressures were calculated to determine the output fluid-energy head. The circumferential components of the normal and shear stresses along the blade were evaluated to give the input mechanical-energy head. Performance predictions were obtained for different load conditions. Comparisons were made with the measured velocity vectors of the flowfield of an air-pump impeller and with the measured performance of a production water pump, good agreements were reached.

scholarly journals Evaluation of LNAPL Behavior in Water Table Inter-Fluctuate Zone under Groundwater Drawdown Condition

Water ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2337
Author(s):  
Reza Azimi ◽  
Abdorreza Vaezihir ◽  
Robert Lenhard ◽  
S. Hassanizadeh
Keyword(s):  
Numerical Models ◽  
Water Levels ◽  
Injection Point ◽  
Monitoring Wells ◽  
Water Pumping ◽  
Two Factors ◽  
Injection Water ◽  
Phase Liquid ◽  
Flow Through ◽  
Material Grain Size

We investigate the movement of LNAPL (light non-aqueous phase liquid) into and out of monitoring wells in an immediate-scale experimental cell. Aquifer material grain size and LNAPL viscosity are two factors that are varied in three experiments involving lowering and rising water levels. There are six monitoring wells at varying distances from a LNAPL injection point and a water pumping well. We established steady water flow through the aquifer materials prior to LNAPL injection. Water pumping lowered the water levels in the aquifer materials. Terminating water pumping raised the water levels in the aquifer materials. Our focus was to record the LNAPL thickness in the monitoring wells under transient conditions. Throughout the experiments, we measured the elevations of the air-LNAPL and LNAPL-water interfaces in the monitoring wells to obtain the LNAPL thicknesses in the wells. We analyze the results and give plausible explanations. The data presented can be employed to test multiphase flow numerical models.

scholarly journals Direct numerical simulation of conical shock wave–turbulent boundary layer interaction

2019 ◽  
Vol 877 ◽  
pp. 167-195 ◽  
Author(s):  
Feng-Yuan Zuo ◽  
Antonio Memmolo ◽  
Guo-ping Huang ◽  
Sergio Pirozzoli
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Direct Numerical Simulation ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Shear Stresses ◽  
Mean Flow ◽  
Conical Shock

Direct numerical simulation of the Navier–Stokes equations is carried out to investigate the interaction of a conical shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number $M_{\infty }=2.05$ and Reynolds number $Re_{\unicode[STIX]{x1D703}}\approx 630$, based on the upstream boundary layer momentum thickness. The shock is generated by a circular cone with half opening angle $\unicode[STIX]{x1D703}_{c}=25^{\circ }$. As found in experiments, the wall pressure exhibits a distinctive N-wave signature, with a sharp peak right past the precursor shock generated at the cone apex, followed by an extended zone with favourable pressure gradient, and terminated by the trailing shock associated with recompression in the wake of the cone. The boundary layer behaviour is strongly affected by the imposed pressure gradient. Streaks are suppressed in adverse pressure gradient (APG) zones, but re-form rapidly in downstream favourable pressure gradient (FPG) zones. Three-dimensional mean flow separation is only observed in the first APG region associated with the formation of a horseshoe vortex, whereas the second APG region features an incipient detachment state, with scattered spots of instantaneous reversed flow. As found in canonical geometrically two-dimensional wedge-generated shock–boundary layer interactions, different amplification of the turbulent stress components is observed through the interacting shock system, with approach to an isotropic state in APG regions, and to a two-component anisotropic state in FPG. The general adequacy of the Boussinesq hypothesis is found to predict the spatial organization of the turbulent shear stresses, although different eddy viscosities should be used for each component, as in tensor eddy-viscosity models, or in full Reynolds stress closures.

Computational Fluid Dynamics Analysis of Two Parallel Rectangular Jets Using OpenFOAM

2016 ◽  
Author(s):  
Han Li ◽  
Huhu Wang ◽  
Yassin A. Hassan ◽  
N. K. Anand
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Laser Doppler Anemometry ◽  
Physical Models ◽  
Shear Stresses ◽  
Turbulence Characteristic ◽  
Computational Fluid Dynamics Analysis ◽  
Simulation Results

Two or multiple parallel jets are an important shear flow that widely existing in many industrial applications. The interaction between turbulence jets enables fast and thorough mixing of two fluids. The mixing feature of parallel jets has many engineering applications, such as, in Generation IV conceptual nuclear reactors, the coolants merge in upper or lower plenum after passing through the reactor core. While study of parallel jets mixing phenomenon, numerical experiments such as Computational Fluid Dynamics (CFD) simulations are extensively incorporated. Validation of varied turbulent models is of importance to make sure that the numerical results could be trusted and served as a guideline further design purpose. Many commercial CFD packages in the market such as FLUENT and Star CCM+ can provide the ability to simulate turbulent flow with predefined turbulence model, however, such commercial solvers may lack the flexibility that allow users build their own models for R&D purpose. The existing solvers in OpenFOAM are developed to fulfill both academic and industrial needs by achieving large-scale computational capability with a variety of physical models. Moreover, as an open source CFD toolbox, OpenFOAM grants users full control of the source code with complete freedom of customization. The purpose of this study is to perform CFD simulation using OpenFOAM for two submerged parallel jets issuing from two rectangular channels. Fully hexahedron multi-density mesh is generated using blockMesh utility to ensure velocity gradients are properly evaluated. A generalized-multi-grid solver is used to enhance convergence. Based on Reynolds-Averaged Navier-Stokes Equations (RANS), the realizable k-ε and k-ε shear stress transport (SST) are selected to model turbulent flow. Steady state Finite Volume solver simpleFoam is used to perform the simulation. In addition, data from experiments run in Thermal-Hydraulic Lab at Texas A&M University using particle image velocity (PIV) and Laser Doppler Anemometry (LDA) methods are considered in order to compare and validate simulation results. A number of turbulence characteristic such as mean velocities, turbulent intensities, z-component vorticity were compared with experiments. It was found that for stream-wise mean velocity profile as well as shear stresses, the realizable k-ε model exhibits a good agreement with experimental data. However, velocity fluctuation and turbulence intensities, simulation results showed a certain discrepancy.

scholarly journals Numerical Simulation of Dispersed Particle-Blood Flow in the Stenosed Coronary Arteries

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Mongkol Kaewbumrung ◽  
Somsak Orankitjaroen ◽  
Pichit Boonkrong ◽  
Buraskorn Nuntadilok ◽  
Benchawan Wiwatanapataphee
Keyword(s):  
Numerical Simulation ◽  
Blood Flow ◽  
Shear Stress ◽  
Coronary Artery ◽  
Pressure Drop ◽  
Wall Shear Stress ◽  
Stokes Equations ◽  
Spherical Shape ◽  
Shear Stresses ◽  
Wall Shear

A mathematical model of dispersed bioparticle-blood flow through the stenosed coronary artery under the pulsatile boundary conditions is proposed. Blood is assumed to be an incompressible non-Newtonian fluid and its flow is considered as turbulence described by the Reynolds-averaged Navier-Stokes equations. Bioparticles are assumed to be spherical shape with the same density as blood, and their translation and rotational motions are governed by Newtonian equations. Impact of particle movement on the blood velocity, the pressure distribution, and the wall shear stress distribution in three different severity degrees of stenosis including 25%, 50%, and 75% are investigated through the numerical simulation using ANSYS 18.2. Increasing degree of stenosis severity results in higher values of the pressure drop and wall shear stresses. The higher level of bioparticle motion directly varies with the pressure drop and wall shear stress. The area of coronary artery with higher density of bioparticles also presents the higher wall shear stress.

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