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Evolves an electrical potential equation
\f[
\grad \left( \sigma \grad V \right)
\f]
where \f$ V \f$ is electrical potential and \f$\sigma\f$ is the
electrical current
To provide a Joule heating contribution according to:
Differential form of Joule heating - power per unit volume:
\f[
\frac{d(P)}{d(V)} = J \cdot E
\f]
where \f$ J \f$ is the current density and \f$ E \f$ the electric
field.
If no magnetic field is present:
\f[
J = \sigma E
\f]
The electric field given by
\f[
E = \grad V
\f]
Therefore:
\f[
\frac{d(P)}{d(V)} = J \cdot E
= (sigma E) \cdot E
= (sigma \grad V) \cdot \grad V
\f]
Usage
Isotropic (scalar) electrical conductivity
\verbatim
jouleHeatingSourceCoeffs
{
anisotropicElectricalConductivity no;
// Optionally specify the conductivity as a function of
// temperature
// Note: if not supplied, this will be read from the time
// directory
sigma table
(
(273 1e5)
(1000 1e5)
);
}
\endverbatim
Anisotropic (vectorial) electrical conductivity
jouleHeatingSourceCoeffs
{
anisotropicElectricalConductivity yes;
coordinateSystem
{
type cartesian;
origin (0 0 0);
coordinateRotation
{
type axesRotation;
e1 (1 0 0);
e3 (0 0 1);
}
}
// Optionally specify sigma as a function of temperature
//sigma (31900 63800 127600);
//
//sigma table
//(
// (0 (0 0 0))
// (1000 (127600 127600 127600))
//);
}
Where:
\table
Property | Description | Required | Default
value
T | Name of temperature field | no | T
sigma | Electrical conductivity as a function of
temperature |no|
anisotropicElectricalConductivity | Anisotropic flag | yes |
\endtable
The electrical conductivity can be specified using either:
- If the \c sigma entry is present the electrical conductivity is
specified
as a function of temperature using a Function1 type
- If not present the sigma field will be read from file
- If the anisotropicElectricalConductivity flag is set to 'true',
sigma
should be specified as a vector quantity
88 lines
2.4 KiB
Bash
Executable File
88 lines
2.4 KiB
Bash
Executable File
#!/bin/sh
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#------------------------------------------------------------------------------
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# ========= |
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# \\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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# \\ / O peration |
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# \\ / A nd | Copyright (C) 2017 OpenCFD Ltd.
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# \\/ M anipulation |
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#-------------------------------------------------------------------------------
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# License
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# This file is part of OpenFOAM.
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#
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# OpenFOAM is free software: you can redistribute it and/or modify it
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# under the terms of the GNU General Public License as published by
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# the Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
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# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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# FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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# for more details.
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#
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# You should have received a copy of the GNU General Public License
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# along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
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#
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# Script
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# createGraphs
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#
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# Description
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# Creates .eps graph of OpenFOAM results vs analytical solution for the
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# Joule heating case
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#
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#------------------------------------------------------------------------------
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cd ${0%/*} || exit 1 # Run from this directory
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# Stop on first error
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set -e
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# test if gnuplot exists on the system
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if ! which gnuplot > /dev/null 2>&1
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then
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echo "FOAM FATAL ERROR: gnuplot not found - skipping graph creation" >&2
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exit 1
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fi
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echo "Creating graph"
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OFDATA='postProcessing/sample1/solid/20000/centreLine_T_jouleHeatingSource:V_jouleHeatingSource:sigma.xy'
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if [ ! -f "$OFDATA" ]
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then
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echo "FOAM FATAL ERROR: OpenFOAM results not available in $OFDATA" >&2
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exit 1
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fi
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gnuplot<<EOF
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set terminal postscript eps color enhanced
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set output "OF_vs_ANALYTICAL.eps"
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set xlabel "Length, x / [m]"
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set ylabel "Temperature / [K]"
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set grid
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set key left top
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rho = 7.837e-6
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sigma = 1/rho
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kappa = 200
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L = 2.5
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D = 0.1
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H = 0.1
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vol = 2.0*L*D*H
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V = 1.5
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R = rho*2*L/(D*H)
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I = V/R
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P = I*V
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Q = P/vol
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Ts = 500
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T(x) = Q*L*L/(2*kappa)*(1-(x/L)*(x/L)) + Ts
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plot \
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"$OFDATA" u 1:2 w lines title "OpenFOAM", \
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T(x) w linespoints lt 0 pt 6 pi 15 title "Analytical"
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EOF
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echo "End"
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#------------------------------------------------------------------------------
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