Laminar Flow in a Uniformly Porous Channel

1958 ◽  
Vol 25 (4) ◽  
pp. 613-617
Author(s):  
F. M. White ◽  
B. F. Barfield ◽  
M. J. Goglia
Keyword(s):  
Free Parameter ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Wall Friction ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Laminar Channel Flow ◽  
Judicious Choice ◽  
Suction Or Injection ◽  
Uniform Fluid

Abstract The problem of laminar channel flow has been investigated for the case of uniform fluid suction or injection through the channel walls. The solution can be divided into three steps: (a) A judicious choice of stream function reduces the Navier-Stokes equations to an ordinary, fourth-order, nonlinear differential equation, which contains a free parameter R, the Reynolds number based upon fluid velocity through the wall. (b) Since general analysis of this equation is intractable, the parameter R is eliminated by a suitable transformation. (c) The transformed, nonparametric equation yields to a series solution, valid and absolutely convergent for all R. From this general solution, expressions are developed for velocity components, pressure distribution, and wall-friction coefficient.

Modeling of the Vortex-Structure in a Particle-Laden Mixing-Layer

2005 ◽  
Author(s):  
Jens A. Melheim ◽  
Stefan Horender ◽  
Martin Sommerfeld
Keyword(s):  
Vortex Structure ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Mixing Layer ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Calculated Concentration ◽  
Langevin Model ◽  
Particle Velocities

Numerical calculations of a particle-laden turbulent horizontal mixing-layer based on the Eulerian-Lagrangian approach are presented. Emphasis is given to the determination of the stochastic fluctuating fluid velocity seen by the particles in anisotropic turbulence. The stochastic process for the fluctuating velocity is a “Particle Langevin equation Model”, based on the Simplified Langevin Model. The Reynolds averaged Navier-Stokes equations are closed by the standard k-epsilon turbulence model. The calculated concentration profile and the mean, the root-mean-square (rms) and the cross-correlation terms of the particle velocities are compared with particle image velocimetry (PIV) measurements. The numerical results agree reasonably well with the PIV data for all of the mentioned quantities. The importance of the modeled vortex structure “seen” by the particles is discussed.

scholarly journals Mathematical Model for the Electrokinetic Instability of Electrolyte Flow

2019 ◽  
Vol 224 ◽  
pp. 02003
Author(s):  
Andrey Shobukhov
Keyword(s):  
Electric Potential ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Steady State Solution ◽  
Stability Loss ◽  
Navier Stokes ◽  
Ion Distribution ◽  
Navier Stokes Equations ◽  
Dilute Aqueous Solution

We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.

Simulation of Fluid Flow Through a Granular Bed

2006 ◽  
Author(s):  
Arezou Jafari ◽  
S. Mohammad Mousavi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Packed Bed ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Duct Geometry ◽  
Flow Through

Numerical study of flow through random packing of non-overlapping spheres in a cylindrical geometry is investigated. Dimensionless pressure drop has been studied for a fluid through the porous media at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), and numerical solution of Navier-Stokes equations in three dimensional porous packed bed illustrated in excellent agreement with those reported by Macdonald [1979] in the range of Reynolds number studied. The results compare to the previous work (Soleymani et al., 2002) show more accurate conclusion because the problem of channeling in a duct geometry. By injection of solute into the system, the dispersivity over a wide range of flow rate has been investigated. It is shown that the lateral fluid dispersion coefficients can be calculated by comparing the concentration profiles of solute obtained by numerical simulations and those derived analytically by solving the macroscopic dispersion equation for the present geometry.

scholarly journals Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xiaoyuan Wang ◽  
Sirui Li ◽  
Tingting Wang
Keyword(s):  
Energy Estimate ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Strong Solutions ◽  
Approximate Solutions ◽  
Dynamical Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Tensor Parameter ◽  
System Coupling

AbstractWe consider the inertial Qian–Sheng’s Q-tensor dynamical model for the nematic liquid crystal flow, which can be viewed as a system coupling the hyperbolic-type equations for the Q-tensor parameter with the incompressible Navier–Stokes equations for the fluid velocity. We prove the existence and uniqueness of local in time strong solutions to the system with the initial data near uniaxial equilibrium. The proof is mainly based on the classical Friedrich method to construct approximate solutions and the closed energy estimate.

Laminar channel flow driven by accelerating walls

1991 ◽  
Vol 2 (4) ◽  
pp. 359-385 ◽  
Author(s):  
P. Watson ◽  
W. H. H. Banks ◽  
M. B. Zaturska ◽  
P. G. Drazin
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Steady Flows ◽  
Navier Stokes Equations ◽  
Partial Differential System ◽  
Laminar Channel Flow ◽  
Two Dimensional Flow ◽  
Pitchfork Bifurcations ◽  
Route To Chaos ◽  
Physical Result

The two-dimensional flow of a viscous incompressible fluid in a channel with accelerating walls is analysed by use of Hiemenz's similarity solution. Steady flows and their instabilities are calculated, and unsteady flows are computed by solving the initial-value problem for the governing partial-differential system. Thereby, these exact solutions of the Navier–Stokes equations are found to exhibit turning points, pitchfork bifurcations, Hopf bifurcations and Takens–Bogdanov bifurcations along the route to chaos. The substantial physical result is that the chaos previously found for flows with symmetrically accelerating walls is easily destroyed by a little asymmetry.

On reduction of turbulent wall friction through spanwise wall oscillations

1999 ◽  
Vol 383 ◽  
pp. 175-195 ◽  
Author(s):  
M. R. DHANAK ◽  
C. SI
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Stokes Equations ◽  
Direct Numerical Simulations ◽  
Wall Friction ◽  
Navier Stokes ◽  
Spanwise Direction ◽  
Streamwise Vortices ◽  
Navier Stokes Equations ◽  
Turbulent Wall

A model for turbulent skin friction, proposed by Orlandi & Jimenez, involving consideration of quasi-streamwise vortices in the cross-stream plane, is used to study the effect on the skin friction of oscillating the surface beneath the boundary layer in the spanwise direction. Using an exact solution of the Navier–Stokes equations, it is shown that the interaction between evolving, axially stretched, streamwise vortices and a modified Stokes layer on the oscillating surface beneath, leads to reduction in the skin friction, the Reynolds stress and the rate of production of kinetic energy, consistent with predictions based on experiments and direct numerical simulations.

Nonsteady Stagnation-Point Flows Over Permeable Surfaces: Explicit Solutions of the Nevier-Stokes Equations

1995 ◽  
Vol 117 (1) ◽  
pp. 189-191 ◽  
Author(s):  
G. I. Burde
Keyword(s):  
Time Dependence ◽  
Stagnation Point ◽  
Stokes Equations ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Explicit Solutions ◽  
Navier Stokes Equations ◽  
New Approach ◽  
The Common ◽  
Suction Or Injection

Some new explicit solutions of the unsteady two-dimensional Navier-Stokes equations describing nonsteady stagnation-point flows with surface suction or injection are presented. The solutions have been obtained using a new approach for finding explicit similarity solutions of partial differential equations. As distinct from the common Birkhoff’s similarity transformation, which permits only one form of an unsteady potential flow field and only one form of time dependence for suction (or blowing) velocity, the transforms obtained permit consideration of a variety of special solutions differing in the forms of time dependence.

Exact vortex solutions of the Navier–Stokes equations with axisymmetric strain and suction or injection

2009 ◽  
Vol 626 ◽  
pp. 291-306 ◽  
Author(s):  
ALEX D. D. CRAIK
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Vortex Flows ◽  
Navier Stokes Equations ◽  
Axisymmetric Vortex ◽  
Vortex Solutions ◽  
Suction Or Injection

New solutions of the Navier–Stokes equations are presented for axisymmetric vortex flows subject to strain and to suction or injection. Those expressible in simple separable or similarity form are emphasized. These exhibit the competing roles of diffusion, advection and vortex stretching.

Equivalent Clearance Model for Solving Thermohydrodynamic Lubrication of Slider Bearings With Steps

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Hideki Ogata ◽  
Joichi Sugimura
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Differential Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Fluid Film Bearings ◽  
Clearance Model

This study focuses on the thermohydrodynamic lubrication (THD) analysis of fluid film bearings with steps on the bearing surface, such as Rayleigh step. In general, the Reynolds equation does not satisfy the continuity of fluid velocity components at steps. This discontinuity results in the difficulty to solve the energy equation for the lubricants by finite differential method (FDM), because the energy equation needs the velocity components explicitly. The authors have solved this issue by introducing the equivalent clearance height and the equivalent gradient of the clearance height at steps. These parameters remove the discontinuity of velocity components, and the Reynolds equations can be solved for any bearing surfaces with step regions by FDM. Moreover, this method results in pseudocontinuous velocity components, which enables the energy equation to be solved as well. This paper describes this method with one-dimensional and equal grids model. The numerical results of pressure and temperature distributions by the proposed method for an infinite width Rayleigh step bearing agree well with the results obtained by solving full Navier–Stokes equations with semi-implicit method for pressure-linked equations revised (SIMPLER) method.

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