Download simulation of liquid metal mhd flows in complex geometries

SIMULATION OF LIQUID METAL MHD
FLOWS IN COMPLEX GEOMETRIES
Vinayak Eswaran
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
(with V.Naveen , R. Paniharan,
Profs M.K.Verma and K.Muralidhar)
Main features of a CFD software being
developed at IITK (2004- )
The aim is to develop a general-purpose CFD code which will
 allow the numerical solutions of a wide variety of problems
with flow and heat-transfer, chemical reaction, combustion,
turbulence, and many other specialized applications,
 run on a parallel cluster,
 allow used-defined modules,
 and be capable of enhancement and a life of 20 years
Brief Overview of Solver Features.
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A multi-block Finite-volume solver for nonorthogonal hexahedral grids, that can read grids
and write solutions in CGNS format.
Solves Navier Stokes, Continuity, Temperature
and Species transport equations, for constant
density and variable density flows .
Solves 2-D, 2-D axi-symmetric and 3-D problems in
complex geometries.
Time Stepping Schemes:
First order (Implicit) and Second order (Crank
Nicolson) schemes.
Physics incorporated in the Solver
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Conduction in solids
Laminar and turbulent (6 models) forced, natural and
mixed convection
Conjugate Heat transfer with laminar and turbulent
flows
Melting and solidification problems
Variable density laminar and turbulent flows
Reactive laminar and turbulent flows with variable
density
Combustion with fast chemistry
Physics…
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Flow of ionised gasses in electric fields
Flow and contaminant transport through ground-water
and porous media
Thermal radiation in enclosures
Combined flow and thermal radiation in participative
media
Homogeneous equilibrium model for two-phase flow
Two-fluid model for gas-liquid two-phase flow (with
turbulence model)
Two-fluid model for particle-gas two-phase flow (with
turbulence model)
A typical application :Temperature Distribution in a Heat Exchanger :
This is a conjugate heat transfer problem. Here the velocity and temperature
distribution through out the Heat Exchanger vessel is to be simulated
numerically using turbulence models, and the temperature distribution in the
vessel walls is to be found.
NUMERICAL SIMULATION OF LIQUID METAL
MHD FLOWS WITH IMPOSED AND INDUCED
MAGNETIC FIELD
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Magneto Hydro Dynamics deals with flows of
electrically conducting and non-magnetic
fluids which are subjected to a magnetic field.
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Typical industrial applications of liquid metal
MHD flows include electromagnetic flow
meter, conduction pump, liquid metal blankets
in fusion reactor etc.
Governing Equations (for induction-less
approach)
Derived from Maxwell’s equations and Navier-Stokes
and continuity equation
Governing Equations (including
induced magnetic field)
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In addition we also solve the induction equation:
where
is the magnetic diffusivity.
Important Parameters
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Hartmann number:
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Interaction parameter or Stuart number:
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Magnetic Reynolds number:
Solution methodology
 Structured, non-uniform, non-orthogonal and
collocated grid.
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FVM Discretization.
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Semi-coupled method.
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BTCS with blending of QUICK/upwind for
convection terms.
Results
Hartmann Flow
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The steady flow of liquid metal between infinitely
broad parallel plates in presence of magnetic field.
Analytical solution given by Chang et. al. (1961)
where c is the wall conductance ratio
Insulating walls
Variation of velocity for Rem=10
Perfectly conducting walls
Variation of velocity for Rem=1
Arbitrary conducting walls
Variation of velocity for Rem=10
Buoyancy driven convection in a rectangular cavity
in presence of magnetic field (induction-less):
Schematic of the problem
Stream lines of the flow
a) Ha = 0; b) Ha = 5; c) Ha = 50; d) Ha = 100
Comparison of horizontal velocity with the analytical solution given by
Garandet et. al. (1992)
Variation of normalized vertical velocity along the horizontal direction
at the mid length of the cavity
Isotherms
Isotherms giving the temperature distribution in the cavity
a) Ha = 0; b) Ha = 5; c) Ha = 50; d) Ha = 100
Variation of applied magnetic field along the length of the channel
Variation of axial velocity for Ha=10 and Rem=1
Flow in 3D channel (Induction-less approach)
Ha=0
Insulated walls
Ha=5
Contd.
Ha=10
Ha=20
Induction less approach (M-profile)
M-Profile for Ha=50
M-Profile for Ha=600
Conclusions
 An algorithm is developed for solving velocity and
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magnetic field to simulate MHD flows.
The present algorithm works well for capturing flow
and magnetic fields accurately for several cases of
channel flows.
The induction less algorithm works well for 3-D
geometries and captures the familiar M-profile.
Scope for the future work
 Code should be thoroughly tested on complex
geometries.
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In case of high Hartmann numbers grids need to be
finer especially near the wall due to Hartmann layer
and side layer. This can be eliminated by core flow
approximation.
THANK YOU
Boundary conditions for Φ
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The boundary conditions at the inlet and the exit are
chosen such that no electric currents leave or enter the
domain.
for insulating walls
for perfectly conducting walls
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Boundary conditions for Arbitrary conducting
walls:
Boundary conditions for B
The boundary conditions for the total magnetic field :
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At the inlet a homogeneous Dirichlet condition is
specified and at outlet homogeneous Neumann
condition is given.
for perfectly conducting walls
for insulating walls depending on the direction in
which magnetic field is applied
or
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