Use of Immersed Boundary Method for the Analysis of Electro-Osmotic Flow Generated by a Pair of Cylindrical Electrodes in a Micro-Cavity

2008 ◽  
Author(s):  
Dolfred V. Fernandes ◽  
Sangmo Kang ◽  
Yong K. Suh
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Ionic Concentration ◽  
Ion Concentration ◽  
Dimensional Case ◽  
Immersed Boundary ◽  
Bench Mark ◽  
Step Method ◽  
Fractional Step Method ◽  
Micro Cavity

The bulk motion of an aqueous solution induced by the application of DC electric field is studied numerically. The physical model consists of a micro-cavity with two completely polarizable cylindrical electrodes. The electric double layer (EDL) model coupled with Navier-Stokes equations governing the electroosmotic flow has been described. The Nernst-Planck model uses two extra equations for the prediction of ion concentration. We employed IB (immersed boundary) technique for the implementation of boundary conditions and semi-implicit fractional-step method for solving the governing equations. A new method is described for implementing concentration boundary conditions on the electrodes. The bench mark problems, driven cavity flow and flow over a cylnder were used for the validation of our present code. The numerical results are compared with the analytical results obtained using Gouy-Chapman-Stern model for the one dimensional case. For the two dimensional case the flow field and the ionic concentration distributions obtained shows that the electoosmotic effect is predominant in the thin region around the electrode.

Numerical Analysis of Electroosmosis in a Micro-Cavity

2008 ◽  
Author(s):  
Dolfred V. Fernandes ◽  
Sangmo Kang ◽  
Yong K. Suh
Keyword(s):  
Electric Fields ◽  
Stokes Equations ◽  
Ionic Species ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Bench Mark ◽  
Step Method ◽  
Fractional Step Method ◽  
Navier Stokes Equations ◽  
Micro Cavity

The bulk motion of an aqueous solution induced by the application of DC and AC electric fields is studied numerically. The physical model consists of a rectangular micro-cavity filled with dilute, symmetric, binary electrolyte and two completely polarizable cylindrical electrodes. The electric double layer (EDL) model coupled with Navier-Stokes equations governing the electroosmotic flow has been described. The ion-transport in the domain is obtained by solving Poisson-Nernst-Plank equations. We employed IB (immersed boundary) technique for the implementation of boundary conditions and semi-implicit fractional-step method for solving the momentum equations. The Poisson equation for potential distribution is coupled with Nernst-Plank equations for ionic species distribution and solved using CGSTAB iteration solver. Numerical codes are validated using bench-mark problems; driven-cavity-flow and flow over a cylinder. The electric field is almost completely balanced by the accumulation of the counter-ions at the electrodes, at steady state the potential in the most part of domain is zero. The flow field is found predominant in the region near the electrodes.

Numerical Investigation of Vortex Shedding Modes of Flow past Two Circular Cylinders in Side-by-Side Using Immersed Boundary Method

2013 ◽  
Vol 275-277 ◽  
pp. 482-485
Author(s):  
Li Wei Song ◽  
Song Ping Wu
Keyword(s):  
Vortex Shedding ◽  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Circular Cylinders ◽  
Immersed Boundary ◽  
Step Method ◽  
Fractional Step Method ◽  
Flow Past ◽  
Boundary Method ◽  
Vortex Shedding Modes

The vortex shedding modes of flow past two circular cylinders in side-by-side arrangement are investigated numerically in this paper. The simulations are carried out using a ghost cell immersed boundary method which imposes the boundary condition through reconstruction of the local velocity field near the immersed boundary. The two-dimensional unsteady incompressible Navier-Stokes equations are solved using an implicit fractional step method based on cell-center, collocated arrangement of the primary variables. Vorticity contours of the flow around the cylinders and force time histories are presented. Anti-phase and in-phase vortex shedding modes were found to exist in the flow simulation. These results of simulations were in agreement with phenomena observed in experiment and numerical results of previous researchers.

Ghost Cell Immersed Boundary Method for Simulating Flow over Two Circular Cylinders in Tandem Arrangement

2013 ◽  
Vol 275-277 ◽  
pp. 478-481
Author(s):  
Li Wei Song ◽  
Song Ping Wu
Keyword(s):  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Ghost Cell ◽  
Step Method ◽  
Fractional Step Method ◽  
Tandem Arrangement ◽  
Boundary Method

In this work, a ghost cell immersed boundary method is applied to the numerical simulation of a uniform flows over a circular cylinder and two circular cylinders in tandem arrangement. The Navier-Stokes equations are solved using an implicit fractional step method employed on collocated arrangement variables. Immersed boundary method permit the use of structured Cartesian meshes to simulate flows involving complex boundaries. The shedding of vortices and flow interference between two circular cylinders in tandem arrangement are investigated numerically. The calculations are validated against the experimental and numerical results obtained by other researchers to prove the accuracy and effectiveness.

scholarly journals Immersed Boundary Method Application as a Way to Deal with the Three-Dimensional Sudden Contraction

Computation ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 50
Author(s):  
Jonatas Borges ◽  
Marcos Lourenço ◽  
Elie Padilla ◽  
Christopher Micallef
Keyword(s):  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Immersed Boundary ◽  
Fractional Step Method ◽  
Central Difference ◽  
Boundary Method ◽  
Contraction Ratio ◽  
Sudden Contraction

The immersed boundary method has attracted considerable interest in the last few years. The method is a computational cheap alternative to represent the boundaries of a geometrically complex body, while using a cartesian mesh, by adding a force term in the momentum equation. The advantage of this is that bodies of any arbitrary shape can be added without grid restructuring, a procedure which is often time-consuming. Furthermore, multiple bodies may be simulated, and relative motion of those bodies may be accomplished at reasonable computational cost. The numerical platform in development has a parallel distributed-memory implementation to solve the Navier-Stokes equations. The Finite Volume Method is used in the spatial discretization where the diffusive terms are approximated by the central difference method. The temporal discretization is accomplished using the Adams-Bashforth method. Both temporal and spatial discretizations are second-order accurate. The Velocity-pressure coupling is done using the fractional-step method of two steps. The present work applies the immersed boundary method to simulate a Newtonian laminar flow through a three-dimensional sudden contraction. Results are compared to published literature. Flow patterns upstream and downstream of the contraction region are analysed at various Reynolds number in the range 44 ≤ R e D ≤ 993 for the large tube and 87 ≤ R e D ≤ 1956 for the small tube, considerating a contraction ratio of β = 1 . 97 . Comparison between numerical and experimental velocity profiles has shown good agreement.

An Aid to Learn Computational Fluid Dynamics: Immersed-Boundary-Based Simulation of 2D Flow

Volume 1 ◽  
2004 ◽  
Author(s):  
Sungsu Lee ◽  
Kyung-Soo Yang ◽  
Jong-Yeon Hwang
Keyword(s):  
Complex Geometry ◽  
Mass Conservation ◽  
Computational Method ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Step Method ◽  
Fractional Step Method ◽  
Navier Stokes Equation ◽  
Finite Volume Approach

Development of geometry-independent computational method and educational codes for simulation of 2D flows around objects of complex geometry is presented. Referred as immersed boundary method, it introduces virtual forcing to governing equations to represent the effect of physical boundaries. The present method is based on a finite-volume approach on a staggered grid with a fractional-step method to solve Navier-Stokes equation and continuity equation. Both momentum and mass forcings are introduced on and inside the object to satisfy no-slip condition and mass conservation. Since Cartesian grid lines in general do not coincide with the immersed boundaries, several interpolation schemes are employed. Several examples are simulated using the method presented in this study and the results agree well with other results. Both user-friendly preprocessor with GUI and FORTRAN-based solver are open to the public for educational purposes.

Numerical Simulation of Solitary Wave Using the Fully Lagrangian Method of Moving Particle Semi Implicit

2014 ◽  
Author(s):  
Mohammad Amin Nabian ◽  
Leila Farhadi
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Solitary Wave ◽  
Stokes Equations ◽  
Rock Avalanche ◽  
Water Tank ◽  
Step Method ◽  
Fractional Step Method ◽  
Time Step ◽  
Moving Particle

A mesh-less numerical approach, called the moving particle semi implicit method (MPS), is presented to solve inviscid Navier-Stokes equations in a fully Lagrangian form using a fractional step method. This method consists of splitting each time step in two steps. The fluid is represented with particles and the motion of each particle is calculated through interactions with neighboring particles by means of a kernel function. In this paper, the MPS method is used to simulate a dynamic system consisting of a heavy box sinking vertically into a water tank, known as Scott Russell’s wave generator problem. This problem is an example of a falling rock avalanche into natural or artificial reservoirs. The box sinks into water tank and as a result the water is heaved up to form a solitary wave and a reverse plunging wave which forms a vortex. This vortex follows the solitary wave down the water tank. The good agreement between the numerical simulation and the analytical solution confirms the accuracy of the model. This proves the applicability of the present model in simulating complex free surface problems. The number of particles on free surface is presented as an indicator of stability of the model.

scholarly journals A divergence free fractional step method for the Navier-Stokes equations on non-staggered grids

2010 ◽  
Vol 51 ◽  
pp. 654 ◽  
Author(s):  
Steven William Armfield ◽  
Nicholas Williamson ◽  
Michael Kirkpatrick ◽  
Robert Street
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Fractional Step ◽  
Step Method ◽  
Fractional Step Method ◽  
Navier Stokes Equations ◽  
Staggered Grids ◽  
Divergence Free
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