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Commit 23d738b2 authored by François Henrotte's avatar François Henrotte
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tutorial Thermics

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};
Thermics/Qsource.opt 0 → 100644
+ 11
− 0
View file @ 23d738b2
Plugin(NewView).View=-1;
Plugin(NewView).Dimension=1;
Plugin(NewView).Run;
Plugin(MathEval).Expression0="1e7*Exp(-1e4*((x-0.03)^2+(y-0.02)^2))";
Plugin(MathEval).PhysicalRegion=111;
Plugin(MathEval).Run;
View[1].NormalRaise = 4e-05;
Save View[1] "Q.pos";
Thermics/brick.geo 0 → 100644
+ 111
− 0
View file @ 23d738b2
/* -------------------------------------------------------------------
File "brick.geo"
This file is the geometrical description used by GMSH to produce
the file "brick.msh".
------------------------------------------------------------------- */
/* Gmsh options can be set directly in the .geo file.
Setting "Solver.AutoMesh" to 2 ensures that GMSH systematically
regenerates the mesh at each model execution, and does not reuse
the mesh on disk if it exists (which is the default option).
This option is needed in this model, because the interactive
model parameters "Flag_Regularization" has an effect
on the definition of the regions, which makes remeshing mandatory. */
Solver.AutoMesh = 2;
Include "brick_common.pro";
/* The (very) simple geometry of this thermal model only contains
rectangles. It is the opportunity to illustrate
the function definition capabilities of Gmsh. */
Function Def_Rectangle
p1=newp; Point(newp)={xc_, yc_, 0, lc_};
p2=newp; Point(newp)={xc_+dx_, yc_, 0, lc_};
p3=newp; Point(newp)={xc_+dx_, yc_+dy_, 0, lc_};
p4=newp; Point(newp)={xc_, yc_+dy_, 0, lc_};
l1=newl; Line(newl)={p1,p2};
l2=newl; Line(newl)={p2,p3};
l3=newl; Line(newl)={p3,p4};
l4=newl; Line(newl)={p4,p1};
lines_[] = {l1, l2, l3, l4};
ll1 = newll; Line Loop(ll1) = {lines_[]};
s_ = news; Plane Surface(news) = {ll1, ll_Holes_[]};
Return // end of Function Def_Rectangle
/* Note that the code above is not parsed before it is called.
Good practice for readability (but by no means mandatory)
is to distinguish function variables from other variables.
This is done here with a trailing "_" in the variable name. */
// Window 1 (with optional layer of thickness "e_layer")
dx_ = dx_Win1;
dy_ = dy_Win1;
lc_ = lc_Win1;
xc_ = xc_Win1-dx_/2; yc_=yc_Win1-dy_/2;
ll_Holes_[]={};
Call Def_Rectangle;
s_Win1 = s_;
l_Win1[] = lines_[];
If( !Flag_Regularization )
ll_HolesForBrick[] += ll1;
Else
ll_HolesForLayer[] += ll1;
dx_ = dx_Win1+2*e_layer;
dy_ = dy_Win1+2*e_layer;
lc_ = lc_Win1;
xc_ = xc_Win1-dx_/2; yc_=yc_Win1-dy_/2;
ll_Holes_[] = {ll_HolesForLayer[]};
Call Def_Rectangle;
s_Win1_Layer = s_;
l_Win1_Layer[] = lines_[];
ll_HolesForBrick[] += ll1;
EndIf
// Window 2
dx_ = dx_Win2;
dy_ = dy_Win2;
lc_ = lc_Win2;
xc_ = xc_Win2-dx_/2; yc_=yc_Win2-dy_/2;
ll_Holes_[]={};
Call Def_Rectangle;
s_Win2 = s_;
l_Win2[] = lines_[];
ll_HolesForBrick[] += ll1;
// Brick
dx_ = dx_Brick; dy_ = dy_Brick;
lc_ = lc_Brick;
xc_ = 0; yc_ = 0;
ll_Holes_[] = {ll_HolesForBrick[]};
Call Def_Rectangle;
s_Brick = s_;
l_Brick[] = lines_[];
//Printf("l_Brick", l_Brick[]);
// Physical regions
Physical Surface("Brick", 100) = {s_Brick};
Physical Surface("Window1", 111) = {s_Win1};
Physical Surface("Window2", 112) = {s_Win2};
If( Flag_Regularization )
Physical Surface("LayerWindow1", 115) = {s_Win1_Layer};
EndIf
Physical Line("Surface1", 201) = { l_Brick[{3}] };
Physical Line("Surface2", 202) = { l_Brick[{1}] };
Physical Line("Surface3", 203) = { l_Brick[{0}], l_Brick[{2}] };
Physical Line("SurfWindow1", 211) = {l_Win1[]};
Physical Line("SurfWindow2", 212) = {l_Win2[]};
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/* -------------------------------------------------------------------
Tutorial 5 : thermal problem with contact resistances
Features:
- Contact resistances: scalar FunctionSpace with a surface discontinuity
- Region with a uniform temperature (infinite thermal conductivity)
- Computation of the heat flux through surfaces
- Import a source field from a file
To compute the solution in a terminal:
getdp brick.pro -solve Thermal_T -pos Map_T
To compute the solution interactively from the Gmsh GUI:
File > Open > brick.pro
Run (button at the bottom of the left panel)
------------------------------------------------------------------- */
/* This model is a rectangular brick with two windows,
where various kinds of thermal constraints can be set.
Dirichlet, Neumann and convection boundary conditions are imposed
on different parts of the surface of the brick.
The model is rather academic but it
demonstrates some useful high-level GetDP features.
Governing eqations are
div ( -lambda[] grad T ) = Q in Vol_Lambda_The
-lambda[] grad T . n = qn = 0 on Sur_Neumann_The
Contact thermal resistance:
First, it is shown how to implement contact thermal resistances
with surface elements. The surface elements are associated with a
thickness and a thermal conductivity (typically much lower than that
of surrounding regions). The implementation takes advantage
of the powerful FunctionSpace definition in GetDP.
With the flag "Flag_Regularization", the contact surface
can be, for the sake of comparison, replaced
by a thin volume conducting region.
Thermal "electrode":
The floating potential idea (introduced in tutorial 4)
is reconsidered here in a thermal context to represent a region
with a very large thermal conductivity where, consequently,
the temperature field is uniform (exactly like the electric potential
is uniform on an electrode).
The dual quantity of this uniform temperature "T_electrode" [K]
(which is the "associated global quantity" in GetDP language)
is the heat flux "Q_electrode" [W] injected in the electrode
by the agent that maintains the temperature equal
to the prescribed value.
The value of Q_electrode is a by-product of the system resolution
provided the term
GlobalTerm { [-Dof{Q_electrode} , {T_electrode} ] ; In Tfloating_The ; }
is present in the "Resolution" section. This term triggers the writing
in the linear system of a supplementary equation associated
with the global basis function BF{T_electrode}.
All integrations are automatically done by getDP,
and the value of Q_electrode is obtained in postprocessing
with the PostOperation
Print[ Q_electrode, OnRegion Tfloating_The, ... ]
Heat flux through surfaces:
The purpose of a thermal simulation usually goes beyond
the mere calculation of a temperature distribution.
One is in general also interested in evaluating
the heat flux q(S) through some specific surface S:
q(S) = ( -lambda[] grad T . n )_S
This quantity cannot be computed from the temperature
distribution available on the surface S only.
As heat flux is related with the gradient of temperature
in the direction normal to the surface, its computation relies on
the temperature distribution in a neighborhood of the surface.
This means that volume elements in contact with the considered surface
need be involved in the computation.
To achieve this with getDP, a good method proceeds
by the definition a smooth auxiliary function g(S),
with g(S)=1 on S, and g(S)=0 outside a finite neighborhood of S.
Typically, g(S) is the sum of the shape functions of the nodes on S.
Let w(S) be the support of g(S),
and let dw(S) denote the boundary of w(S).
We then have, just adding and substracting dw(S)
to the surface of integration S
q(S) = ( -lambda[] grad T . n g(S) )_{ dw(S) - ( dw(S)-S ) }.
dw(S) being a boundary, Stokes theorem can be invoked and,
after an integration by part one ends up with
q(S) = ( -lambda[] grad T . grad g(S) )_w(S)
- ( -lambda[] grad T . n g(S) )_{dw(S)-S}.
+ ( Q g(S) )_w(S)
Now, g(S) is zero on {dw(S)-S}, except maybe at some surface elements
adjacents to dS, but not in dS.
The second terme vanishes then if either S is closed,
or adjacent to a homogeneous Neumann boundary condition.
The third term also vanishes, except if a region
with a nonzero heatsource Q is in contact with the surface S.
So we have nearly always the following practical formula
to evaluate the heat flux across a surface S,
in terms of a well-chosen auxiliary scalar function g(S).
q(S) = ( -lambda[] grad T . grad g(S) )_{support of g(S)}
Particular cases:
For the heat flux through the boundary of a thermal electrode,
one uses g(S) = BF(T_electrode).
Note that this heat flux is equal to Q_electrode
in the stationary case.
This is the case for the heat flux through the boundary of Window2
Auxiliary functions g(S) are also generated
for the surfaces named "Surface_i", i=1,2,3 in the model.
Note that the flux computed through Surface_3 is incorrect
because this surface is not adjacent to surfaces
with homogeneous Neumann boundary conditions.
*/
Include "brick_common.pro";
QWindow1 =
DefineNumber[1e3, Name "Window1/Heat source [W]"];
/* The user is given the choice of setting either the global temperature
or the global heat flux in Window2.
Check how the variable "Flag_ConstraintWin2" is used at different
places to alter the model according to that choice
and to manage the visibility of related input and output data.*/
QWindow2 =
DefineNumber[1e3, Name "Window2/Heat source [W]",
Visible Flag_ConstraintWin2];
TWindow2 =
DefineNumber[50, Name "Window2/Temperature [degC]",
Visible !Flag_ConstraintWin2];
outQWindow2 =
DefineNumber[0, Name "Output/Q window 2 [degC]",
Visible !Flag_ConstraintWin2, Highlight "Ivory"];
outTWindow2 =
DefineNumber[0, Name "Output/T window 2 [degC]",
Visible Flag_ConstraintWin2, Highlight "Ivory"];
ConvectionCoef =
DefineNumber[1000, Name"Surface2/hconv",
Label "Convection coefficient [W/(m^2K)]"];
T_Ambiance =
DefineNumber[20, Name"Surface2/Ambiance temperature [degC]"];
T_Dirichlet =
DefineNumber[20, Name"Surface1/Imposed temperature [degC]"];
Group {
/* Geometrical regions: */
Brick = Region[100];
LayerWindow1 = Region[115];
Window1 = Region[111];
Window2 = Region[112];
SurfWindow1 = Region[211];
SurfWindow2 = Region[212];
Surface_1 = Region[201];
Surface_2 = Region[202];
Surface_3 = Region[203];
NbSurface = 3;
/* Abstract regions:
Vol_Lambda_Ele : volume regions with a thermal conductivity lambda[]
Sur_Dirichlet_The : Dirichlet bondary condition surface
Sur_Neu_Ele : Neumann bondary condition surface
Sur_Convection_The : convective surface q.n = h ( T-Tinf )
Vol_Qsource_The : volume heat source regions
Tfloating_The : thermal electrodes
*/
Vol_Lambda_The = Region[ {Brick, Window1, Window2, LayerWindow1} ];
Sur_Dirichlet_The = Region[ Surface_1 ];
Sur_Neumann_The = Region[ Surface_3 ];
Sur_Convection_The = Region[ Surface_2 ];
Vol_Qsource_The = Region[ Window1 ];
Tfloating_The = Region[ Window2 ];
If( !Flag_Regularization )
Vol_OneSide_The = Region[ Brick ];
Sur_Tdisc_The = Region[ SurfWindow1 ];
Else
Vol_OneSide_The = Region[ {} ];
Sur_Tdisc_The = Region[ {} ];
EndIf
}
Function {
lambda_Brick = 50.; // steel
lambda[ Brick ] = lambda_Brick;
lambda[ Region[ {Window1, Window2} ] ] = lambda_Brick ; // comment
lambda_Layer = 1.0; // 50 time smaller than surrounding regions
If( Flag_Regularization )
lambda[ LayerWindow1 ] = lambda_Layer;
EndIf
lambda[ Sur_Tdisc_The ] = lambda_Layer;
thickness[ Sur_Tdisc_The ] = e_layer;
h[ Surface_2 ] = ConvectionCoef;
Tinf[ Surface_2 ] = T_Ambiance;
If( Flag_QFromFile )
Qsource[ Window1 ] = ScalarField[XYZ[],0,1]{1};
Else
Qsource[ Window1 ] = 0*QWindow1/SurfaceArea[];
EndIf
}
Constraint {
{ Name Dirichlet_The ;
Case {
{ Region Sur_Dirichlet_The ; Value T_Dirichlet ; }
}
}
{ Name T_Discontinuity ;
Case {
{ Region SurfWindow1 ; Value 20 ; }
}
}
{ Name T_electrode;
Case {
If( !Flag_ConstraintWin2 )
{ Region Window2 ; Value TWindow2 ; }
EndIf
}
}
{ Name Q_electrode;
Case {
If( Flag_ConstraintWin2 )
{ Region Window2 ; Value QWindow2 ; }
EndIf
}
}
For i In {1:NbSurface}
{ Name FluxLayer~{i} ;
Case {
{ Region Surface~{i} ; Value 1. ; }
}
}
EndFor
}
Integration {
{ Name Int ;
Case {
{
Type Gauss ;
Case {
{ GeoElement Triangle ; NumberOfPoints 4 ; }
{ GeoElement Quadrangle ; NumberOfPoints 4 ; }
{ GeoElement Line ; NumberOfPoints 4 ; }
}
}
}
}
}
Jacobian {
{ Name Vol ;
Case {
{ Region All ; Jacobian Vol ; }
}
}
{ Name Sur ;
Case {
{ Region All ; Jacobian Sur ; }
}
}
}
Group {
Dom_Hgrad_T = Region[ {Vol_Lambda_The,
Sur_Convection_The,
Sur_Tdisc_The} ];
DomainWithSurf_TL_The =
ElementsOf[ {Vol_OneSide_The, Sur_Tdisc_The},
OnOneSideOf Sur_Tdisc_The ];
}
FunctionSpace {
{ Name Hgrad_T; Type Form0 ;
BasisFunction {
{ Name sn ; NameOfCoef Tn ; Function BF_Node ;
Support Dom_Hgrad_T ;
Entity NodesOf[All, Not Tfloating_The] ; }
{ Name sf ; NameOfCoef Tf ; Function BF_GroupOfNodes ;
Support Dom_Hgrad_T ; Entity GroupsOfNodesOf[ Tfloating_The ] ; }
{ Name sdn ; NameOfCoef Tdn ; Function BF_Node ;
Support DomainWithSurf_TL_The ; Entity NodesOf[ Sur_Tdisc_The ] ; }
}
SubSpace {
{ Name Tcont ; NameOfBasisFunction { sn, sf } ; }
{ Name Tdisc ; NameOfBasisFunction { sdn } ; }
}
GlobalQuantity {
{ Name T_electrode ; Type AliasOf ; NameOfCoef Tf ; }
{ Name Q_electrode ; Type AssociatedWith ; NameOfCoef Tf ; }
}
Constraint {
{ NameOfCoef Tn ; EntityType NodesOf ;
NameOfConstraint Dirichlet_The ; }
// { NameOfCoef Tdn ; EntityType NodesOf ; //
// NameOfConstraint T_Discontinuity ; } //
{ NameOfCoef T_electrode ; EntityType GroupsOfNodesOf ;
NameOfConstraint T_electrode ; }
{ NameOfCoef Q_electrode ; EntityType GroupsOfNodesOf ;
NameOfConstraint Q_electrode ; }
}
}
For i In {1:NbSurface}
{ Name FluxLayer~{i} ; Type Form0 ;
BasisFunction {
{ Name gn ; NameOfCoef un ; Function BF_GroupOfNodes;
Support Dom_Hgrad_T ; Entity GroupsOfNodesOf[ Surface~{i} ] ; }
}
Constraint {
{ NameOfCoef un ; EntityType GroupsOfNodesOf ;
NameOfConstraint FluxLayer~{i} ; }
}
}
EndFor
}
Formulation {
{ Name Thermal_T ; Type FemEquation ;
Quantity {
{ Name T ; Type Local ; NameOfSpace Hgrad_T ; }
{ Name Tcont ; Type Local ; NameOfSpace Hgrad_T[Tcont] ; }
{ Name Tdisc ; Type Local ; NameOfSpace Hgrad_T[Tdisc] ; }
{ Name Tglob ; Type Global ; NameOfSpace Hgrad_T[T_electrode] ; }
{ Name Qglob ; Type Global ; NameOfSpace Hgrad_T[Q_electrode] ; }
For i In {1:NbSurface}
{ Name un~{i} ; Type Local ; NameOfSpace FluxLayer~{i} ; }
EndFor
}
Equation {
Galerkin { [ lambda[] * Dof{d T} , {d T} ] ;
In Vol_Lambda_The; Integration Int ; Jacobian Vol ; }
Galerkin { [ ( lambda[]/thickness[] ) * Dof{Tdisc} , {Tdisc} ] ;
In Sur_Tdisc_The; Integration Int ; Jacobian Sur ; }
Galerkin { [ -Qsource[] , {T} ] ;
In Vol_Qsource_The ; Integration Int ; Jacobian Vol ; }
Galerkin { [ h[] * Dof{T} , {T} ] ;
In Sur_Convection_The ; Integration Int ; Jacobian Sur ; }
Galerkin { [ -h[] * Tinf[] , {T} ] ;
In Sur_Convection_The ; Integration Int ; Jacobian Sur ; }
GlobalTerm { [-Dof{Qglob} , {Tglob} ] ; In Tfloating_The ; }
For i In {1:NbSurface}
Galerkin { [ 0 * Dof{un~{i}} , {un~{i}} ] ;
In Vol_Lambda_The ; Integration Int ; Jacobian Vol ; }
EndFor
}
}
}
Resolution {
{ Name Thermal_T ;
System {
{ Name Sys_The ; NameOfFormulation Thermal_T ; }
}
Operation {
If( Flag_QFromFile )
GmshRead[ "Q.pos", 1];
EndIf
DeleteFile["output.txt"];
Generate Sys_The ; Solve Sys_The ; SaveSolution Sys_The ;
}
}
}
PostProcessing {
{ Name Thermal_T ; NameOfFormulation Thermal_T ;
PostQuantity {
{ Name T ; Value { Term { [ {T} ] ;
In Dom_Hgrad_T ; Jacobian Vol ; } } }
{ Name q ; Value { Term { [ -lambda[] * {d T} ] ;
In Dom_Hgrad_T ; Jacobian Vol ; } } }
{ Name Tcont ; Value { Term { [ {Tcont} ] ;
In Dom_Hgrad_T ; Jacobian Vol ; } } }
{ Name Tdisc ; Value { Term { [ {Tdisc} ] ;
In Dom_Hgrad_T ; Jacobian Vol ; } } }
{ Name Qglob; Value { Term { [ {Qglob} ]; In Tfloating_The; } } }
{ Name Tglob; Value { Term { [ {Tglob} ]; In Tfloating_The; } } }
For i In {1:NbSurface}
{ Name un~{i} ; Value { Local { [ {un~{i}} ] ;
In Vol_Lambda_The ; Jacobian Vol ; } } }
{ Name IFlux~{i} ; Value { Integral { [ -lambda[]*{d T} * {d un~{i}} ];
In Vol_Lambda_The ; Jacobian Vol ; Integration Int ; } } }
EndFor
}
}
}
PostOperation Map_T UsingPost Thermal_T {
If( !Flag_Regularization )
Print[ Tcont, OnElementsOf Vol_Lambda_The, File "Tcont.pos"] ;
Print[ Tdisc, OnElementsOf Vol_Lambda_The, File "Tdisc.pos"] ;
EndIf
If(Flag_ConstraintWin2)
Print[ Tglob, OnRegion Tfloating_The, File > "output.txt", Color "Ivory",
Format Table, SendToServer "Output/T window 2 [degC]" ];
Else
Print[ Qglob, OnRegion Tfloating_The, File > "output.txt", Color "Ivory",
Format Table, SendToServer "Output/Q window 2 [degC]" ];
EndIf
For i In {1:NbSurface}
Print[un~{i}, OnElementsOf Vol_Lambda_The,
File Sprintf("FluxLayer_%g.pos",i)];
Print[ IFlux~{i}[Vol_Lambda_The], OnGlobal,
Format TimeTable, File > "Fluxes.dat", Color "Ivory",
SendToServer Sprintf("Output/Heat flux surface %g [W]", i)];
EndFor
Print[ T, OnElementsOf Vol_Lambda_The, File "T.pos" ] ;
Echo[ StrCat["l=PostProcessing.NbViews-1;",
"View[l].IntervalsType = 3;",
"View[l].NbIso = 30;",
"View[l].NormalRaise = 0.0005;"],
File "tmp.geo", LastTimeStepOnly] ;
Print [ q, OnLine {{0.02,0.0001,0}{0.02,0.05,0}} {200},
Format SimpleTable, File "Cut.txt" ];
}
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// Onelab parameters
Flag_Regularization =
DefineNumber[0, Name "Options/Regularize field", Choices {0,1} ];
Flag_QFromFile =
DefineNumber[0, Name "Options/Heat source from file", Choices {0,1} ];
Flag_ConstraintWin2 =
DefineNumber[0, Name "Options/Constraint in Window2",
Choices {0="Fixed temperature", 1="Fixed heat flux"} ];
MeshRefinement =
DefineNumber[1, Name "Options/0Mesh refinement",
Help "Choose 1 for a coarse mesh and 0.1 for a fine mesh."];
// Geometrical dimensions
mm=1e-3; // mm to m conversion factor
dx_Brick=100*mm; dy_Brick= 50*mm;
e_layer = 1*mm;
dx_Win1 = 20*mm; dy_Win1 = 20*mm;
If( Flag_Regularization )
dx_Win1 += e_layer;
dy_Win1 += e_layer;
EndIf
dx_Win2 = 20*mm; dy_Win2 = 20*mm;
xc_Win1 = 25*mm; yc_Win1 = dy_Brick/2;
xc_Win2 = 75*mm; yc_Win2 = dy_Brick/2;
// Element sizes
s=1;
lc_Brick = dy_Brick/20 *s;
lc_Win1 = dx_Win1/10 *s;
lc_Win2 = dx_Win2/10 *s;
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