2af8d38827
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
|
|
#------------------------------------------------------------------------------
|
|
# ========= |
|
|
# \\ / F ield | OpenFOAM: The Open Source CFD Toolbox
|
|
# \\ / O peration |
|
|
# \\ / A nd | Copyright (C) 2017 OpenCFD Ltd.
|
|
# \\/ M anipulation |
|
|
#-------------------------------------------------------------------------------
|
|
# License
|
|
# This file is part of OpenFOAM.
|
|
#
|
|
# OpenFOAM is free software: you can redistribute it and/or modify it
|
|
# under the terms of the GNU General Public License as published by
|
|
# the Free Software Foundation, either version 3 of the License, or
|
|
# (at your option) any later version.
|
|
#
|
|
# OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
|
|
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
|
|
# FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
|
# for more details.
|
|
#
|
|
# You should have received a copy of the GNU General Public License
|
|
# along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
|
|
#
|
|
# Script
|
|
# createGraphs
|
|
#
|
|
# Description
|
|
# Creates .eps graph of OpenFOAM results vs analytical solution for the
|
|
# Joule heating case
|
|
#
|
|
#------------------------------------------------------------------------------
|
|
|
|
cd ${0%/*} || exit 1 # Run from this directory
|
|
|
|
# Stop on first error
|
|
set -e
|
|
|
|
# test if gnuplot exists on the system
|
|
if ! which gnuplot > /dev/null 2>&1
|
|
then
|
|
echo "FOAM FATAL ERROR: gnuplot not found - skipping graph creation" >&2
|
|
exit 1
|
|
fi
|
|
|
|
|
|
echo "Creating graph"
|
|
OFDATA='postProcessing/sample1/solid/20000/centreLine_T_jouleHeatingSource:V_jouleHeatingSource:sigma.xy'
|
|
|
|
if [ ! -f "$OFDATA" ]
|
|
then
|
|
echo "FOAM FATAL ERROR: OpenFOAM results not available in $OFDATA" >&2
|
|
exit 1
|
|
fi
|
|
|
|
gnuplot<<EOF
|
|
set terminal postscript eps color enhanced
|
|
set output "OF_vs_ANALYTICAL.eps"
|
|
set xlabel "Length, x / [m]"
|
|
set ylabel "Temperature / [K]"
|
|
set grid
|
|
set key left top
|
|
rho = 7.837e-6
|
|
sigma = 1/rho
|
|
kappa = 200
|
|
L = 2.5
|
|
D = 0.1
|
|
H = 0.1
|
|
vol = 2.0*L*D*H
|
|
V = 1.5
|
|
R = rho*2*L/(D*H)
|
|
I = V/R
|
|
P = I*V
|
|
Q = P/vol
|
|
Ts = 500
|
|
T(x) = Q*L*L/(2*kappa)*(1-(x/L)*(x/L)) + Ts
|
|
|
|
|
|
plot \
|
|
"$OFDATA" u 1:2 w lines title "OpenFOAM", \
|
|
T(x) w linespoints lt 0 pt 6 pi 15 title "Analytical"
|
|
EOF
|
|
|
|
|
|
echo "End"
|
|
|
|
#------------------------------------------------------------------------------
|