A Multigrid Method for the Solution of Ion Transport Using the Poisson Nernst Planck Equations

2007 ◽  
Author(s):  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Ion Transport ◽  
Multigrid Method ◽  
Convergence Rates ◽  
Relaxation Method ◽  
Governing Equations ◽  
Linear System Of Equations ◽  
Aspect Ratios ◽  
Synthetic Ion Channels ◽  
Poor Convergence ◽  
Volume Method

Recently there has been much interest in simulating ion transport in biological and synthetic ion channels using the Poisson-Nernst-Planck (PNP) equations. However, many published methods exhibit poor convergence rates, particularly at high driving voltages, and for long-aspect ratio channels. The paper addresses the development of a fast and efficient coupled multigrid method for the solution of the PNP equations. An unstructured cell-centered finite volume method is used to discretize the governing equations. An iterative procedure, based on a Newton-Raphson linearization accounting for the non-linear coupling between the Poisson and charge transport equations, is employed. The resulting linear system of equations is solved using an algebraic multigrid method, with coarse level systems being created by agglomerating finer-level equations based on the largest coefficients of the Poisson equation. A block Gauss-Seidel update is used as the relaxation method. The method is shown to perform well for ion transport in a synthetic channel for aspect ratios ranging from 16.67 to 1667 for a range of operating parameters.

scholarly journals Effect of thermally active zones and direction of magnetic field on hydromagnetic convection in an enclosure

2011 ◽  
Vol 15 (suppl. 2) ◽  
pp. 367-382 ◽  
Author(s):  
Sivanandam Sivasankaran ◽  
Marimuthu Bhuvaneswari
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Average Nusselt Number ◽  
Hartmann Number ◽  
Numerical Study ◽  
Governing Equations ◽  
Aspect Ratios ◽  
Active Zones ◽  
Volume Method ◽  
The Magnetic Field

The aim of the present numerical study is to investigate the effect of thermally active zones and direction of the external magnetic field on hydromagnetic convection in an enclosure. Nine different relative positions of the thermally active zones are considered. Top and bottom of the enclosure are adiabatic. The governing equations are solved by the finite volume method. The results are obtained for different directions of the external magnetic field, thermally active locations, Hartmann numbers, Grashof numbers and aspect ratios. It is observed that the heat transfer is enhanced for heating location is either at middle or at bottom of the hot wall while the cooling location is either at top or at middle of the cold wall. The flow field is altered when changing the direction of the magnetic field in the presence of strong magnetic field. The average Nusselt number decreases with an increase of the Hartmann number and increases with increase of the Grashof number and aspect ratio.

scholarly journals The Influence of Different Types of Nanofluid on Thermal and Fluid Flow Performance of Liquid Cold Plate

2018 ◽  
Vol 7 (4.35) ◽  
pp. 148 ◽  
Author(s):  
Nur Irmawati Om ◽  
Rozli Zulkifli ◽  
P. Gunnasegaran
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Steady State ◽  
Pressure Drop ◽  
Volume Fraction ◽  
Cold Plate ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Different Types ◽  
Volume Method

The influence of utilizing different nanofluids types on the liquid cold plate (LCP) is numerically investigated. The thermal and fluid flow performance of LCP is examined by using pure ethylene glycol (EG), Al2O3-EG and CuO-EG. The volume fraction of the nanoparticle for both nanofluid is 2%. The finite volume method (FVM) has been used to solved 3-D steady state, laminar flow and heat transfer governing equations. The presented results indicate that Al2O3-EG able to provide the lowest surface temperature of the heater block followed by CuO-EG and EG, respectively. It is also found that the pressure drop and friction factor are higher for Al2O3-EG and CuO-EG compared to the pure EG.

Bifurcation analysis of two-dimensional laminar flow through sudden expansion channel

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Laminar Flow ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Governing Equations ◽  
Bifurcation Phenomena ◽  
Different Types ◽  
Fluent Software ◽  
Flow Through ◽  
Volume Method

In this work, bifurcation characteristics of unsteady, viscous, Newtonian laminar flow in two-dimensional sudden expansion and sudden contraction-expansion channels have been studied for different values of expansion ratio. The governing equations have been solved using finite volume method and FLUENT software has been employed to visualize the simulation results. Three different mesh studies have been performed to calculate critical Reynolds number (Recr) for different types of bifurcation phenomena. It is found that Recr decreases with the increase in expansion ratio (ER).

scholarly journals Study on Optimizing Operation of Preheating Commissioning for Waxy Crude Oil Pipelines

2014 ◽  
Vol 6 ◽  
pp. 894256
Author(s):  
Jian Zhang ◽  
Yi Wang ◽  
Xinran Wang ◽  
Handu Dong ◽  
Jinping Huang ◽  
...  
Keyword(s):  
Crude Oil ◽  
Outlet Temperature ◽  
Fluid Temperature ◽  
Governing Equations ◽  
Waxy Crude Oil ◽  
Waxy Crude ◽  
Oil Pipeline ◽  
Single Station ◽  
Oil Pipelines ◽  
Volume Method

A mathematical model is established for the preheating commissioning process of waxy crude oil pipelines. The governing equations are solved by the finite volume method and the finite difference method. Accordingly, numerical computations are made for the Niger crude oil pipeline and the Daqing-Tieling 3rd pipeline. The computational results agree well with the field test data. On this basis, fluid temperature in the process of the preheating commissioning is studied for single station-to-station pipeline. By comparing different preheating modes, it is found that the effect of forward preheating is the best. Under different preheating commissioning conditions, the optimal combination of outlet temperature and flow rate is given.

Passive Heat Transfer in Porous Enclosures Using a Two-Energy Equation Model

2012 ◽  
Author(s):  
Marcelo J. S. deLemos ◽  
Paulo H. S. Carvalho
Keyword(s):  
Heat Transfer ◽  
Energy Equation ◽  
Equation Model ◽  
Thermal Conductivity Ratio ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Energy Models ◽  
Different Temperatures ◽  
Volume Method ◽  
Generalized Coordinate

This paper presents computations for natural convection within a porous cavity filled with a fluid saturated permeable medium. The finite volume method in a generalized coordinate system is applied. The walls are maintained at constant but different temperatures, while the horizontal walls are kept insulated. Governing equations are written in terms of primitive variables and are recast into a general form. Flow and heat transfer characteristics are investigated for two energy models and distinct solid-to-fluid thermal conductivity ratio.

scholarly journals OPTIMIZING THE VELOCITY OF RING SHAPE PARAMETER FOR DESIGNING THE NOZZLES USING CFD

2021 ◽  
pp. 1-10
Author(s):  
Obai Younis ◽  
Reem Ahmed ◽  
Ali Mohammed Hamdan ◽  
Dania Ahmed
Keyword(s):  
Shape Parameter ◽  
Maximum Velocity ◽  
Simulation Software ◽  
Governing Equations ◽  
Ansys Fluent ◽  
Ring Shape ◽  
Ring Location ◽  
Computational Fluid Dynamics Cfd ◽  
Triangular Elements ◽  
Volume Method

This study aims to optimize the velocity of ring shape parameter for designing the nozzles using computational fluid dynamics (CFD) and investigated the flow in nozzles using ANSYS, Inc. simulation software. The model geometries were defined using ANSYS FLUENT-Design Modeler platform. All nozzles were designed on unstructured triangular elements comprising of 1200000 mesh nodes. The differential governing equations were applied in ANSYS FLUENT based on a finite volume method. The distance and dimensions of ring location significantly influence the velocity of water during flow where the maximum velocity at double rings reduces the surface area at distance of 7mm and 15mm and 2x2 mm dimensions. Considering 8, 10, and 12 bar liner proportions, there was an increase in the velocity at maximum points in ring shapes.

A study on the dynamic process of fluid mud and its effect on siltation in the Yangtze Estuary Deepwater Channel

2021 ◽  
Author(s):  
Yue Li ◽  
Peng Hu ◽  
Ji Li
Keyword(s):  
Current Model ◽  
Yangtze Estuary ◽  
Fluid Mud ◽  
Governing Equations ◽  
The Yangtze Estuary ◽  
Simple Movement ◽  
Two Layer Model ◽  
Layer Flow ◽  
Deepwater Channel ◽  
Volume Method

<p>The Yangtze Estuary Deepwater Channel Project has brought great economic and social benefits since its completion, but the siltation problem is still worthy of attention. In order to investigate the mechanisms of fluid mud in the estuary and to study the influence of fluid mud on siltation in the Yangtze Estuary Deepwater Channel, a two-dimensional physically-enhanced two-layer flow model will be developed in this paper. The model includes two series of governing equations which are about environment fluid and fluid mud, respectively. The model is based on the unstructured grid, and the governing equations are discretized by the finite volume method, and the improved LTS/GMaTS technology is used to improve the computational efficiency. Firstly, an experiment that the fluid mud was flowing underwater along a gentle slope is reconstructed by the two-layer model. It shows the ability of the model to describe the simple movement of fluid mud. Secondly, the model is applied to Yangtze Estuary. Without the fluid mud layer, the model can be simplified as a tide-current model. The reliability of the tidal current and tide level is verified, and it means the model can describe the tide accurately. Based on this, the process of formation, transport, and break-down of fluid mud is simulated and its effect on the siltation in the Yangtze Estuary Deepwater Channel is estimated.</p>

Analysis and Numerical Simulation of no Reacting Swirling Flow by Using URANS Approach

2021 ◽  
Vol 57 ◽  
pp. 67-79
Author(s):  
Merouane Habib ◽  
Senouci Mohammed
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Swirling Flow ◽  
Navier Stokes ◽  
Governing Equations ◽  
Simulation Based ◽  
Classical Models ◽  
Recirculation Zones ◽  
Computational Fluid Dynamics Cfd ◽  
Volume Method

In this paper, we investigate the no-reacting swirling flow by using the numerical simulation based to the unsteady Reynolds-averaged Navier-Stokes approach. The numerical simulation was realized by using a computational fluid dynamics CFD code. The governing equations are solved by using the finite volume method with two classical models of turbulence K-epsilon and Shear Stress K-ω. The objective of this paper is therefore to evaluate the performance of the two models in predicting the recirculation zones in a swirled turbulent flow. The current models are validated by comparing the numerical results of the axial, radial and tangential velocities to the experimental data from literature.

scholarly journals A Framework and Numerical Solution of the Drying Process in Porous Media by Using a Continuous Model

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Hong Thai Vu ◽  
Evangelos Tsotsas
Keyword(s):  
Porous Media ◽  
Control Volume ◽  
Continuous Model ◽  
Control Volume Method ◽  
Drying Process ◽  
Transport Parameters ◽  
Governing Equations ◽  
Numerical Tools ◽  
Volume Method ◽  
The Continuum

The modelling and numerical simulation of the drying process in porous media are discussed in this work with the objective of presenting the drying problem as the system of governing equations, which is ready to be solved by many of the now widely available control-volume-based numerical tools. By reviewing the connection between the transport equations at the pore level and their up-scaled ones at the continuum level and then by transforming these equations into a format that can be solved by the control volume method, we would like to present an easy-to-use framework for studying the drying process in porous media. In order to take into account the microstructure of porous media in the format of pore-size distribution, the concept of bundle of capillaries is used to derive the needed transport parameters. Some numerical examples are presented to demonstrate the use of the presented formulas.

scholarly journals Mixed Convection and Entropy Generation of an Ag-Water Nanofluid in an Inclined L-Shaped Channel

Energies ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 1150 ◽  
Author(s):  
Taher Armaghani ◽  
Muneer Ismael ◽  
Ali Chamkha ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Entropy Generation ◽  
Richardson Number ◽  
Volume Fraction ◽  
Governing Equations ◽  
Nanoparticles Volume Fraction ◽  
The Mean ◽  
The Right ◽  
Volume Method

This paper investigates the mixed convection and entropy generation of an Ag-water nanofluid in an L-shaped channel fixed at an inclination angle of 30° to the horizontal axis. An isothermal heat source was positioned in the middle of the right inclined wall of the channel while the other walls were kept adiabatic. The finite volume method was used for solving the problem’s governing equations. The numerical results were obtained for a range of pertinent parameters: Reynolds number, Richardson number, aspect ratio, and the nanoparticles volume fraction. These results were Re = 50–200; Ri = 0.1, 1, 10; AR = 0.5–0.8; and φ = 0.0–0.06, respectively. The results showed that both the Reynolds and the Richardson numbers enhanced the mean Nusselt number and minimized the rate of entropy generation. It was also found that when AR. increased, the mean Nusselt number was enhanced, and the rate of entropy generation decreased. The nanoparticles volume fraction was predicted to contribute to increasing both the mean Nusselt number and the rate of entropy generation.

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