scholarly journals THEORETICAL AND NUMERICAL INVESTIGATIONS OF FREQUENCY ANALYSIS OF TWO CIRCULAR CYLINDERS OSCILLATING IN A INCOMPRESSIBLE VISCOUS FLUID

2014 ◽  
Vol 06 (05) ◽  
pp. 1450049 ◽  
Author(s):  
ADIL EL BAROUDI ◽  
FULGENCE RAZAFIMAHERY
Keyword(s):  
Stokes Equation ◽  
Numerical Solutions ◽  
Human Head ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Element Analysis ◽  
Fluid Field ◽  
Skull Model ◽  
Good Agreement

A potential flow is presented in this paper for the analysis of the fluid-structure interaction systems including, but not limited to, the idealized human head. The model considers a cerebro-spinal fluid (CSF) medium interacting with two solid domain. The fluid field is governed by the linearized Navier–Stokes equation. A potential technique is used to obtain a general solution for a problem. The method consists in solving analytically partial differential equations obtained from the linearized Navier–Stokes equation. From the solution, modal shapes and stokes cells are shown. In the analysis, the elastic skull model and the rigid skull model are presented. A finite element analysis is also used to check the validity of the present method. The results from the proposed method are in good agreement with numerical solutions. The effects of the fluid thickness is also investigated.

scholarly journals Three-Dimensional Investigation of the Stokes Eigenmodes in Hollow Circular Cylinder

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Adil El Baroudi ◽  
Fulgence Razafimahery
Keyword(s):  
Present Method ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Finite Depth ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Element Analysis ◽  
Fluid Medium ◽  
Stokes Eigenmodes ◽  
Good Agreement

This paper studies the influence of boundary conditions on a fluid medium of finite depth. We determine the frequencies and the modal shapes of the fluid. The fluid is assumed to be incompressible and viscous. A potential technique is used to obtain in three-dimensional cylindrical coordinates a general solution for a problem. The method consists in solving analytically partial differential equations obtained from the linearized Navier-Stokes equation. A finite element analysis is also used to check the validity of the present method. The results from the proposed method are in good agreement with numerical solutions. The effect of the fluid thickness on the Stokes eigenmodes is also investigated. It is found that frequencies are strongly influenced.

A two-dimensional vortex condensate at high Reynolds number

2013 ◽  
Vol 715 ◽  
pp. 359-388 ◽  
Author(s):  
Basile Gallet ◽  
William R. Young
Keyword(s):  
Stokes Equation ◽  
Numerical Solutions ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Finite Limit ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Quasilinear Theory ◽  
Zero Integral ◽  
High Reynolds

AbstractWe investigate solutions of the two-dimensional Navier–Stokes equation in a $\lrm{\pi} \ensuremath{\times} \lrm{\pi} $ square box with stress-free boundary conditions. The flow is steadily forced by the addition of a source $\sin nx\sin ny$ to the vorticity equation; attention is restricted to even $n$ so that the forcing has zero integral. Numerical solutions with $n= 2$ and $6$ show that at high Reynolds numbers the solution is a domain-scale vortex condensate with a strong projection on the gravest mode, $\sin x\sin y$. The sign of the vortex condensate is selected by a symmetry-breaking instability. We show that the amplitude of the vortex condensate has a finite limit as $\nu \ensuremath{\rightarrow} 0$. Using a quasilinear approximation we make an analytic prediction of the amplitude of the condensate and show that the amplitude is determined by viscous selection of a particular solution from a family of solutions to the forced two-dimensional Euler equation. This theory indicates that the condensate amplitude will depend sensitively on the form of the dissipation, even in the undamped limit. This prediction is verified by considering the addition of a drag term to the Navier–Stokes equation and comparing the quasilinear theory with numerical solution.

One Method of Fluid-Solid Coupled Interaction Simulation

2008 ◽  
Vol 33-37 ◽  
pp. 1095-1100
Author(s):  
Yong Wen Lin ◽  
Xiao Chuan You ◽  
Zhuo Zhuang
Keyword(s):  
Stokes Equation ◽  
Elastic System ◽  
Coupling Method ◽  
Navier Stokes ◽  
Coupled Simulation ◽  
Navier Stokes Equation ◽  
Fluid Field ◽  
Elasticity Problems ◽  
Fluent Software ◽  
Interaction Simulation

In this article we presented a method of Fluid-Solid coupled simulation via FLUNET and ABAQUS in problems such as Aero/Hydro-Elasticity problems. UDF (user define function) script file in the Fluent software was utilized as the ‘Connecting File’ between FLUENT and ABAQUS for Aero-Elastic computations. Firstly, the fluid field was computed by Navier-Stokes Equation and the structure movement was directly integrated by the dynamics Equation, respectively. Then, the ‘Connecting File’ exchanged the computed data through the fluid and structure’s interface. The next analysis step continued. Analysis of the computed results showed that this coupling method designed for aero-elastic system was feasible and can be also used for other Fluid-Structure Coupling problems.

History forces and the unsteady wake of a cylinder

1999 ◽  
Vol 393 ◽  
pp. 99-121 ◽  
Author(s):  
J. R. CHAPLIN
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Stokes Equation ◽  
Oscillatory Flow ◽  
Numerical Solutions ◽  
Asymptotic Properties ◽  
Quantitative Agreement ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Unsteady Wake

History forces on a stationary cylinder in arbitrary unsteady rectilinear flow are calculated by means of a model based on the asymptotic properties of the steady-state wake. The results capture many features found in numerical solutions of the Navier–Stokes equation for the same flows, though quantitative agreement deteriorates as the Reynolds number increases over the range 2 to 40. The cases studied are the impulsive start, stop, and reverse, and oscillatory flow.

Numerical Modeling of a Static Cavitation Module

2016 ◽  
Vol 817 ◽  
pp. 64-69
Author(s):  
Tatiana Vitenko ◽  
Paweł Droździel ◽  
Nazar Horodysky
Keyword(s):  
Experimental Data ◽  
Numerical Modeling ◽  
Numerical Modelling ◽  
Stokes Equation ◽  
Liquid State ◽  
Software Package ◽  
Navier Stokes ◽  
State Equations ◽  
Navier Stokes Equation ◽  
Good Agreement

This paper presents the results of numerical modelling of cavitation flows in a hydrodynamic module. The simulation was performed using the SolidWorks software package. The computations were made based on the Navier-Stokes equation combined with liquid state equations and empirical dependencies which define liquid parameters. The numerical results are in good agreement with experimental data.

An Actively Controlled Micromixer

1999 ◽  
Author(s):  
Marion Volpert ◽  
Carl D. Meinhart ◽  
Igor Mezic ◽  
Mohammed Dahleh
Keyword(s):  
Stokes Equation ◽  
Analytical Model ◽  
Numerical Solutions ◽  
Navier Stokes ◽  
Mixing Efficiency ◽  
Navier Stokes Equation ◽  
Two Fluids ◽  
Flow Through ◽  
Flow Configurations ◽  
Active Mixing

Abstract An active mixing strategy has been developed to enhance mixing of two fluids through a microchannel. Mixing is enhanced when the flow through the main channel of the mixer is perturbed by three sets of secondary flow channels. Numerical solutions of the flow through the mixer are calculated by simulating the full Navier-Stokes equation, the Stokes equation, and a simple analytical model based upon the superposition of elementary velocity profiles. The analytical model agrees qualitatively with Navier-Stokes and Stokes solutions for Reynolds numbers, Re = 5. A mixing coefficient is developed to quantitatively evaluate mixing efficiency for various flow configurations. The results indicate enhanced mixing for two possible flow configurations.

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