scholarly journals A Closed-Form Full-State Feedback Controller for Stabilization of 3D Magnetohydrodynamic Channel Flow

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Rafael Vazquez ◽  
Eugenio Schuster ◽  
Miroslav Krstic
Keyword(s):  
Channel Flow ◽  
Electric Potential ◽  
Stokes Equations ◽  
Transverse Magnetic ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Navier Stokes Equations ◽  
Mhd Channel

We present a boundary feedback law that stabilizes the velocity, pressure, and electromagnetic fields in a magnetohydrodynamic (MHD) channel flow. The MHD channel flow, also known as Hartmann flow, is a benchmark for applications such as cooling, hypersonic flight, and propulsion. It involves an electrically conducting fluid moving between parallel plates in the presence of an externally imposed transverse magnetic field. The system is described by the inductionless MHD equations, a combination of the Navier–Stokes equations and a Poisson equation for the electric potential under the MHD approximation in a low magnetic Reynolds number regime. This model is unstable for large Reynolds numbers and is stabilized by actuation of velocity and the electric potential at only one of the walls. The backstepping method for stabilization of parabolic partial differential equations (PDEs) is applied to the velocity field system written in appropriate coordinates. Control gains are computed by solving a set of linear hyperbolic PDEs. Stabilization of nondiscretized 3D MHD channel flow has so far been an open problem.

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

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.

scholarly journals CENTRIFUGAL DESTABILIZATION AND RESTABILIZATION OF PLANE SHEAR FLOWS

1996 ◽  
Vol 06 (02) ◽  
pp. 409-413
Author(s):  
A. J. CONLEY
Keyword(s):  
Viscous Fluid ◽  
Linear Stability ◽  
Stokes Equations ◽  
Path Following ◽  
Incompressible Viscous Fluid ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Plane Shear ◽  
Navier Stokes Equations ◽  
Spectral Techniques

The flow of an incompressible viscous fluid between parallel plates becomes unstable when the plates are tumbled. As the tumbling rate increases, the flow restabilizes. This phenomenon is elucidated by path-following techniques. The solution of the Navier-Stokes equations is approximated by spectral techniques. The linear stability of these solutions is studied.

scholarly journals An Axisymmetric Squeezing Fluid Flow between the Two Infinite Parallel Plates in a Porous Medium Channel

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
S. Islam ◽  
Hamid Khan ◽  
Inayat Ali Shah ◽  
Gul Zaman
Keyword(s):  
Differential Equation ◽  
Porous Medium ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Differential Transform ◽  
Fluid Parameters

The flow between two large parallel plates approaching each other symmetrically in a porous medium is studied. The Navier-Stokes equations have been transformed into an ordinary nonlinear differential equation using a transformationψ(r,z)=r2F(z). Solution to the problem is obtained by using differential transform method (DTM) by varying different Newtonian fluid parameters and permeability of the porous medium. Result for the stream function is presented. Validity of the solutions is confirmed by evaluating the residual in each case, and the proposed scheme gives excellent and reliable results. The influence of different parameters on the flow has been discussed and presented through graphs.

scholarly journals Instability of Rayleigh-Bernard Convection Affected by Upper Wall Temperature Variation

2020 ◽  
Author(s):  
Sadoon Ayed ◽  
Keyword(s):  
Energy Equation ◽  
Stokes Equations ◽  
Time Discretization ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Chebyshev Collocation Method ◽  
Step Method ◽  
Navier Stokes Equations ◽  
Numeric Simulation ◽  
Pseudo Spectral

This paper represents the analysis of Rayleigh-Bernard convection between two parallel plates. Lower wall is being cooled while upper is heated according to periodic spatial distribution. This process has been modeled using Navier-Stokes equations, equation of continuity and energy equation. Solution of the differential equations has been obtained using pseudo spectral numeric method. For discretization in homogeneous direction, Fourier-Galerkin model has been used, while for discretization in inhomogeneous direction Chebyshev collocation method is applied. Time discretization has been performed using Adams-Bashworth two step method of second order. The results of numeric simulation have been presented by figures where vorticity fields, stream-function and velocity are shown for six different time steps.

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