Normal feedback stabilization for linearized periodic MHD channel flow, at low magnetic Reynolds number

2013 ◽  
Vol 62 (1) ◽  
pp. 55-62 ◽  
Author(s):  
Ionuţ Munteanu
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Magnetic Reynolds Number ◽  
Feedback Stabilization ◽  
Mhd Channel

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.

scholarly journals Movement of a finite body in channel flow

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160164 ◽  
Author(s):  
Frank T. Smith ◽  
Edward R. Johnson
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Flow Instability ◽  
Flow Direction ◽  
Finite Size ◽  
The Body ◽  
Thin Body ◽  
Shear Stresses ◽  
Unsteady Interaction ◽  
High Reynolds

A body of finite size is moving freely inside, and interacting with, a channel flow. The description of this unsteady interaction for a comparatively dense thin body moving slowly relative to flow at medium-to-high Reynolds number shows that an inviscid core problem with vorticity determines much, but not all, of the dominant response. It is found that the lift induced on a body of length comparable to the channel width leads to differences in flow direction upstream and downstream on the body scale which are smoothed out axially over a longer viscous length scale; the latter directly affects the change in flow directions. The change is such that in any symmetric incident flow the ratio of slopes is found to be cos ⁡ ( π / 7 ) , i.e. approximately 0.900969, independently of Reynolds number, wall shear stresses and velocity profile. The two axial scales determine the evolution of the body and the flow, always yielding instability. This unusual evolution and linear or nonlinear instability mechanism arise outside the conventional range of flow instability and are influenced substantially by the lateral positioning, length and axial velocity of the body.

scholarly journals Noise Reduction Effect of Superhydrophobic Surfaces with Streamwise Strip of Channel Flow

2021 ◽  
Vol 11 (9) ◽  
pp. 3869
Author(s):  
Chen Niu ◽  
Yongwei Liu ◽  
Dejiang Shang ◽  
Chao Zhang
Keyword(s):  
Reynolds Number ◽  
Drag Reduction ◽  
Noise Reduction ◽  
Channel Flow ◽  
Superhydrophobic Surface ◽  
Sound Field ◽  
Flow Noise ◽  
Slip Boundary ◽  
Eddy Simulation ◽  
Reduction Effect

Superhydrophobic surface is a promising technology, but the effect of superhydrophobic surface on flow noise is still unclear. Therefore, we used alternating free-slip and no-slip boundary conditions to study the flow noise of superhydrophobic channel flows with streamwise strips. The numerical calculations of the flow and the sound field have been carried out by the methods of large eddy simulation (LES) and Lighthill analogy, respectively. Under a constant pressure gradient (CPG) condition, the average Reynolds number and the friction Reynolds number are approximately set to 4200 and 180, respectively. The influence on noise of different gas fractions (GF) and strip number in a spanwise period on channel flow have been studied. Our results show that the superhydrophobic surface has noise reduction effect in some cases. Under CPG conditions, the increase in GF increases the bulk velocity and weakens the noise reduction effect. Otherwise, the increase in strip number enhances the lateral energy exchange of the superhydrophobic surface, and results in more transverse vortices and attenuates the noise reduction effect. In our results, the best noise reduction effect is obtained as 10.7 dB under the scenario of the strip number is 4 and GF is 0.5. The best drag reduction effect is 32%, and the result is obtained under the scenario of GF is 0.8 and strip number is 1. In summary, the choice of GF and the number of strips is comprehensively considered to guarantee the performance of drag reduction and noise reduction in this work.

Turbulent dynamo action at low magnetic Reynolds number

1970 ◽  
Vol 41 (2) ◽  
pp. 435-452 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
Magnetic Energy Density ◽  
Magnetic Diffusivity

The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

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