Real
GapConductance::h_conduction()
{
_gap_thermal_conductivity[_qp] = gapK();
return _gap_thermal_conductivity[_qp] /
gapLength(_gap_geometry_type, _radius, _r1, _r2, _min_gap, _max_gap);
}
Real
GapHeatTransfer::computeQpOffDiagJacobian(unsigned jvar)
{
computeGapValues();
if (!_has_info)
return 0.0;
unsigned int coupled_component;
bool active = false;
for (coupled_component = 0; coupled_component < _disp_vars.size(); ++coupled_component)
if (jvar == _disp_vars[coupled_component])
{
active = true;
break;
}
Real dRdx = 0.0;
if (active)
{
// Compute dR/du_[xyz]
// Residual is based on
// h_gap = h_conduction() + h_contact() + h_radiation();
// grad_t = (_u[_qp] - _gap_temp) * h_gap;
// So we need
// (_u[_qp] - _gap_temp) * (dh_gap/du_[xyz]);
// Assuming dh_contact/du_[xyz] = dh_radiation/du_[xyz] = 0,
// we need dh_conduction/du_[xyz]
// Given
// h_conduction = gapK / gapLength, then
// dh_conduction/du_[xyz] = -gapK/gapLength^2 * dgapLength/du_[xyz]
// Given
// gapLength = ((u_x-m_x)^2+(u_y-m_y)^2+(u_z-m_z)^2)^1/2
// where m_[xyz] is the master coordinate, then
// dGapLength/du_[xyz] = 1/2*((u_x-m_x)^2+(u_y-m_y)^2+(u_z-m_z)^2)^(-1/2)*2*(u_[xyz]-m_[xyz])
// = (u_[xyz]-m_[xyz])/gapLength
// This is the normal vector.
const Real gapL = gapLength();
// THIS IS NOT THE NORMAL WE NEED.
// WE NEED THE NORMAL FROM THE CONSTRAINT, THE NORMAL FROM THE
// MASTER SURFACE. HOWEVER, THIS IS TRICKY SINCE THE NORMAL
// FROM THE MASTER SURFACE WAS COMPUTED FOR A POINT ASSOCIATED
// WITH A SLAVE NODE. NOW WE ARE AT A SLAVE INTEGRATION POINT.
//
// HOW DO WE GET THE NORMAL WE NEED?
//
// Until we have the normal we need,
// we'll hope that the one we have is close to the negative of the one we need.
const Point & normal(_normals[_qp]);
const Real dgap = dgapLength(-normal(coupled_component));
dRdx = -(_u[_qp] - _gap_temp) * _edge_multiplier * _gap_conductance[_qp] / gapL * dgap;
}
return _test[_i][_qp] * dRdx * _phi[_j][_qp];
}
Real
GapHeatTransfer::dgapLength(Real normalComponent) const
{
const Real gap_L = gapLength();
Real dgap = 0.0;
if (_min_gap <= gap_L && gap_L <= _max_gap)
dgap = normalComponent;
return dgap;
}
Real
GapConductance::h_conduction()
{
return gapK() / gapLength(_gap_geometry_type, _radius, _r1, _r2, _min_gap, _max_gap);
}
Real
GapConductance::h_conduction()
{
return gapK()/gapLength(-(_gap_distance), _min_gap, _max_gap);
}
