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--- doc:user:elements:boundaries:flux [2024/12/09 10:18] – [Tm[2]HeatSource[2|3]DElement] vanhulle
+++ doc:user:elements:boundaries:flux [2024/12/09 11:40] (current) – [Tm[2]ConvectionHeatFlux[2|3]DElement] vanhulle
@@ Line 4: / Line 4: @@
 ''ElementProperty'' contains the type of element and all necessary information to compute the value of the heat flux/source at each Gauss point with a spatial distribution function. This spatial heat distribution function is expressed in a set of local coordinates {$x'$, $y'$, $z'$}, which is handled by the ''HeatInteraction''.
- {{:doc:user:elements:boundaries:heat_localcoord.png?400|}}
+{{ doc:user:elements:boundaries:heat_localcoord.png?400 |Coordonnées locales du la source de chaleur}}
 Using this set of local coordinates allows to easily define a moving/rotating heat source/flux, which is particularly useful for some applications (//e.g.// additive manufacturing).
@@ Line 126: / Line 126: @@
 ==== Tm[2]ConvectionHeatFlux[2|3]DElement ====
-<note important> Only for Metafor version > 3544 </note>
+<note important> **Metafor version >= 3545** </note>
 === Description ===
-Thermal convection heat flux element in 2/3D, first or second order (thermal field of second order), that can be created on "boundary" geometries (//i.e.// curves in 2D and sides in 3D).
+Thermal convection heat flux element in 2/3D, first or second order (thermal field of second order), that can be created on "boundary" geometries (//i.e.// curves in 2D and sides in 3D). These elements are particularly suited to model moving hot gas torches.
 These elements are similar to ''Tm[2]HeatFlux[2|3]DElement'' except that heat flux is computed as a convection boundary
 $$
-q = h(x',y')*(T_s - T_f),
+q = h(x',y')~(T_s - T_f),
 $$
 with the surface temperature $T_s$ and fluid temperature $T_f$ (''TEMP_FLUIDE''). The convection coefficient $h$ is a space-dependent quantity (in the local coordinates) which writes
 $$
-h(x',y')=A*\mathcal{f}(x',y'),
+h(x',y')=A~\mathcal{f}(x',y'),
 $$
 where $A$ is the amplitude of the convection coefficient (''CONV_COEF'') and $\mathcal{f}\in [0,~1]$ is a spatial distribution function which can be selected using the ''HEATEL_TYPE'' parameter.
 == Rectangular Distribution ==
+Convection coefficient is equal to a constant value within a rectangular surface centered in the local coordinates axes and 0 outside the surface
+$$
+h(x',y') =\begin{cases}
+ A~~\text{if}~~~ x'\in [-k_x,~k_x] ~~ \text{and} ~~ y'\in [-k_y,~k_y],\\
+~~~\text{else}.
+\end{cases}
+$$
+where $k_x$ and $k_y$ are the half lengths of the rectangle in the $x'$ and $y'$ directions respectively.
+   prp.put(HEATEL_TYPE, CONVHEATEL_RECTANGULAR)
+== Gaussian Distribution ==
+Convection coefficient is distributed with a Gaussian distribution as defined by [Zacherl //et. al.// 2023] centered on the local coordinates
+$$
+h(x',y') = A~e^{(-\left[ \frac{x'}{k_x} \right]^2 -\left[ \frac{y'}{k_y} \right]^2)},
+$$
+where $k_x$ and $k_y$ are concentration coefficients which define the slope of the curve in the $x'$ and $y'$ directions respectively.
+   prp.put(HEATEL_TYPE, CONVHEATEL_GAUSSIAN)
+== Modified Log-Normal  Distribution ==
+Convection coefficient is distributed with a modified log-normal distribution as defined by [Zacherl //et. al.// 2023] centered on the local coordinates
+$$
+h(x',y') = A~e^{(-[\text{ln}\left( \frac{|x'|}{k_x}+1 \right)]^2 -[\text{ln}\left( \frac{|y'|}{k_y}+1 \right)]^2)},
+$$
+where $k_x$ and $k_y$ are concentration coefficients which define the slope of the curve in the $x'$ and $y'$ directions respectively.
+   prp.put(HEATEL_TYPE, CONVHEATEL_LOGNORM)
+== Combined Distribution ==
+Allows to choose between a Gaussian or log-normal distribution in the front ($x' \geq 0$), rear ($x'<0$) and $y'$ directions. Convection coefficient is distributed as
+$$
+h(x',y') =\begin{cases}
+ A~\mathcal{f}_{xf}(x',k_x)~\mathcal{f}_{y}(y',k_y) ~~~~~ x' \geq 0\\
+ A~\mathcal{f}_{xr}(x',k_{xr})~\mathcal{f}_{y}(y',k_y) ~~~~ x' < 0.
+\end{cases}
+$$
+where distribution function $\mathcal{f}$ is either a Gaussian distribution (''CONVHEATEL_GAUSSIAN'')
+$$
+\mathcal{f_i} = e^{-\left[ \frac{i}{k_i} \right]^2},
+$$
+or a modified log-normal distribution (''CONVHEATEL_LOGNORM'')
+$$
+\mathcal{f_i} = e^{-[\text{ln}\left( \frac{|i|}{k_i}+1 \right)]^2}.
+$$
+Difference between these 2 distribution types is highlighted below for $k_i=1$.
+{{ doc:user:elements:boundaries:heat_GaussLogNorm.png?400 |Distribution Gaussienne v.s. Log-Normale avec k=1}}
-<note>TODO : Ajouter équations de flux </note>
+__Example:__ \\
+Modelling of an inclined hot gas torch in Automated Fiber Placement process (AFP).
+Convection heat flux element is modelled using a modified log-normal distribution at the rear and Gaussian distributions at the front and along $y'$.
+    # convection heat source (LogNorm - Gauss - Gauss)
+    prpHeat = ElementProperties(TmConvectionHeatFlux3DElement)
+    prpHeat.put(        HEATEL_TYPE,  CONVHEATEL_COMBINE)
+    prpHeat.put(        TEMP_FLUIDE,          p['T_HGT'])
+    prpHeat.put(          CONV_COEF,          p['HGT_A'])
+    prpHeat.put( CONVHEATEL_TYPE_XF,  CONVHEATEL_LOGNORM) #front
+    prpHeat.put(      CONVHEATEL_KX,         p['HGT_kf'])
+    prpHeat.put( CONVHEATEL_TYPE_XR, CONVHEATEL_GAUSSIAN) #rear
+    prpHeat.put(     CONVHEATEL_KXR,         p['HGT_kr'])
+    prpHeat.put(  CONVHEATEL_TYPE_Y, CONVHEATEL_GAUSSIAN) #y
+    prpHeat.put(      CONVHEATEL_KY,         p['HGT_ky'])
 === Parameters ===