Use of Electromagnetic Effects for Flow Control

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Use of Electromagnetic Effects for Flow Control
Department of Mechanical and Materials
Engineering The University of Western Ontario

•  
• Presented by German A. Kalugin
• Supervisor Dr. J.M. Floryan

November 17, 2008
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Outline

• Introduction
• Objective
• Motivation
• Formulation of problem
• EM field configurations
• Particular case
• Current state

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What is MHD ?

• When an electrically conducting fluid flows in
  the presence of magnetic field, electric currents
  are induced. These currents
• produce the Lorentz force that modifies
• the motion of the fluid
• modify the magnetic field

MHD
Fluid Mechanics
Electrodynamics
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Faradays experiment (1832)
Crowds attend the opening of Waterloo Bridge in
1817
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Hartmann flow (1) Induced currents
y
x
z
u
Side wall
Müller, U. and Bühler, L. (2001)
Magnetohydrodynamics in Channels and Containers
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Hartmann flow (2) Velocity profile
y
Hartmann flow
Poiseuille flow
x
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Destabilizing effect of magnetic filed
http//web.mit.edu/html/ncfmf.html
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Objective

• To develop strategies for flow control
• using EM effects
• To find an optimal spatial distribution
• of EM field leading to the formation
• of streamwise vortices

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Why EM control

• Fast-acting
• Rapid on-demand deployment
• Absence of moving parts
• Remote control of industrial equipment
• Lower energy budgets

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Why streamwise vortices

• Streamwise vortices significantly improve fluid
  mixing and heat transfer
• Some examples with EM effects
• cooling systems for fusion blankets
• liquid metals are used as a coolant
• continuous casting of steel
• EM stirring is used for homogenization process
•  

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Formulation of problem
We consider a steady-state parallel flow of
incompressible, viscous, electrically
conducting fluid with constant properties
between two parallel infinite plates in the
presence of externally imposed electrical and
magnetic fields.

y
y
x
x
z
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Incompressible MHD equations
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Scales EM group

• Defined in terms of the fluid properties
• density
• kinematic viscosity
• electrical conductivity
• magnetic permeability

Magnetic field
Electric field
Electric current density
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Scales FD group
Dynamic effect (d)
EM effect (e)
Dimensionless form
where
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Dimensionless parameters
Magnetic field number
(Hartmann number)
Electric field number
Magnetic Reynolds number
Magnetic Prandtl number
( Reynolds number
)
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Characteristic values
Rudiger, G. Hollerbach, R. (2004) The
Magnetic Universe.
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(No Transcript)
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To formulation of problem
y

x
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Particular case

• Externally imposed fields are oriented
• Electric field in the streamwise direction
• Magnetic field in the spanwise direction

y
y
x
x
z
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Linear stability equations
Disturbance equations
Orr-Sommerfeld like modes
Squires like modes
Needed numerical solution
Always stable
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Why spanwise magnetic field does not effect on
2D disturbances
y
traveling disturbances
L
K
Q2
R1
R2
Q1
N
S1
A
P2
P1
S2
Bz
x
z
Hunt, J.C.R. (1966) On the stability of parallel
flows with parallel magnetic fields, Proceedings
of the Royal Society of London. Series A,
Mathematical and Physical Sciences, Vol. 293,
No. 1434 , pp. 342-358
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Numerical results
Contour lines for
Contour lines for kc
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Stability mechanism
y
is balanced by
1
is balanced by
y
2
x
z
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Acknowledgments

• Prof. J.M. Floryan
• Prof. K. Adamiak
• (Department of Electrical and Computer
  Engineering)
• PhD students Syed Zahid Husain
• Mohammad Zakir
  Hossain