Extended PCT capabilities to low pressure for YHx

doc/content/source/interfacekernels/ADMatInterfaceReactionYHxPCT.md

@@ -16,13 +16,20 @@ $K_b$ and $K_f$ are the backward and forward surface reaction rate in 1/s, respe
 $f_{at}(T,P)$ is the composition in atomic fraction of H in YHx given a gas temperature $T$ and gas pressure $P$,
 and $\rho$ is the yttrium atomic density in mol/m$^3$.
 
-[YHx_PCT_fit_2D] shows the data used in this interface kernel. The experimental data originates from [!cite](Lundin_1962), and the fit is from [!cite](Matthews2021SWIFT).
+[YHx_PCT_Data] shows the data used in this interface kernel. The experimental data originates from [!cite](Lundin_1962).
+The [YHx_PCT_fit_2D] shows high and low pressure fit with the high pressure fit from [!cite](Matthews2021SWIFT) and the low-pressure is a newly fitted curve.
+
+!media comparison_YHx_PCT.py
+       image_name=YHx_PCT_Data.png
+       style=width:80%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=YHx_PCT_Data
+       caption=PCT data for YHx from [!cite](Lundin_1962).
 
 !media comparison_YHx_PCT.py
        image_name=YHx_PCT_fit_2D.png
        style=width:80%;margin-bottom:2%;margin-left:auto;margin-right:auto
        id=YHx_PCT_fit_2D
-       caption=PCT data for YHx from [!cite](Lundin_1962) with fits from [!cite](Matthews2021SWIFT) implemented in TMAP8, and test results.
+       caption=PCT data for YHx from [!cite](Lundin_1962) with high pressure fits from [!cite](Matthews2021SWIFT) implemented in TMAP8, and test results.
 
 The plateau representing phase transition is captured as [!citep](Matthews2021SWIFT):
 \begin{equation} \label{eq:pressure_plateau}
@@ -37,16 +44,15 @@ This fit is shown in [YHx_PCT_plateau_pressure_fit].
        id=YHx_PCT_plateau_pressure_fit
        caption=Fit phase transition region as pressure as a function of temperature.
 
-The model currently only captures the high pressure region of the data, i.e., for pressure and temperatures above the plateau.
-In this region, the atomic fraction $f_{at}$ is determined as [!citep](Matthews2021SWIFT):
-\begin{equation} \label{eq:atomic_fraction}
+In the high pressure region, the atomic fraction $f_{at}$ is determined as [!citep](Matthews2021SWIFT):
+\begin{equation}
 f_{at}(T,P) = 2-\left[1+\exp(21.6 -0.0225 T + (-0.0445 + 7.18 \times 10^{-4} T) (\log\left(P - P_{lim}(T)\right)))\right]^{-1},
 \end{equation}
-where $P$ is the hydrogen partial pressure in Pa. This fit is plotted in [YHx_PCT_fit_2D].
+where $P$ is the hydrogen partial pressure in Pa. While in the low pressure region, the atomic fraction $f_{at}$ is determined as:
+\begin{equation}
+f_{at}(T,P) = 0.5-\left[0.001+\exp(-89.75 + 0.0975 T + (1.20 - 4.41 \times 10^{-3} T) (\log\left(P_{lim}(T) - P\right)))\right]^{-1},
+\end{equation}
 
-The [!param](/InterfaceKernels/ADMatInterfaceReactionYHxPCT/silence_warnings) option can be used to dictate how TMAP8 reacts when the pressure gets out of bounds.
-If `silence_warnings = false`, which is the default behavior, then TMAP8 will print a warning stating that the pressure and temperature are outside the bounds of the atomic fraction correlation.
-If `silence_warnings = true`, then TMAP8 will let the simulation continue without issuing any warnings.
 
 ## Test
 
@@ -59,7 +65,7 @@ To model the interface, the input file employs the [InterfaceDiffusion.md] objec
 \end{equation}
 where $\rho$ is the yttrium atomic density.
 
-The results of the test for ($T$, $P$) = (1173.15 K, $1 \times 10^{3}$ Pa), (1173.15 K, $1 \times 10^{4}$ Pa), (1173.15 K, $5 \times 10^{4}$ Pa), and(1473.15 K, $5 \times 10^{4}$ Pa) are shown in [YHx_PCT_fit_2D] and show good agreement with [eq:atomic_fraction].
+The results of the high pressure test for ($T$, $P$) = (1173.15 K, $1 \times 10^{3}$ Pa), (1173.15 K, $1 \times 10^{4}$ Pa), (1173.15 K, $5 \times 10^{4}$ Pa), and(1473.15 K, $5 \times 10^{4}$ Pa). While the low pressure test for ($T$, $P$) = (1473.15 K, $3 \times 10^{3}$ Pa), (1273.15 K, $3 \times 10^{2}$ Pa), (1573.15 K, $5 \times 10^{3}$ Pa), and(1573.15 K, $6 \times 10^{2}$ Pa).
 
 ## Example Input File Syntax
 

include/interfacekernels/ADMatInterfaceReactionYHxPCT.h

@@ -21,6 +21,7 @@
  * (1962) 838–5.
  * The fits are from Matthews et al., Metal Hydride Simulations Using SWIFT, LANL technical report
  * LA-UR-21-27538, 2021.
+
  */
 
 class ADMatInterfaceReactionYHxPCT : public ADInterfaceKernel

src/interfacekernels/ADMatInterfaceReactionYHxPCT.C

@@ -1,10 +1,10 @@
-/************************************************************/
+/*************************************************************/
 /*                DO NOT MODIFY THIS HEADER                 */
 /*   TMAP8: Tritium Migration Analysis Program, Version 8   */
 /*                                                          */
 /*   Copyright 2021 - 2025 Battelle Energy Alliance, LLC    */
 /*                   ALL RIGHTS RESERVED                    */
-/************************************************************/
+/*************************************************************/
 
 #include "ADMatInterfaceReactionYHxPCT.h"
 
@@ -53,30 +53,57 @@ ADMatInterfaceReactionYHxPCT::computeQpResidual(Moose::DGResidualType type)
   using std::pow;
   ADReal r = 0;
 
+  // tolerance for the pressure being closed to the plateau region
+  const Real tolerance = 10; // Pa
+
   // Calculate the equilibrium concentration value based on PCT curve
-  // (/2 because two atoms for a molecule) (pressure in Pa)
+  // (2 because two atoms for a molecule
   auto neighbor_pressure =
       PhysicalConstants::ideal_gas_constant * _neighbor_temperature[_qp] * _neighbor_value[_qp] / 2;
 
-  // Calculate the value of the pressures for the phase transition plateau (pressure in Pa)
+  // Plateau/limit pressure (Pa)
   auto limit_pressure = exp(-26.1 + 3.88e-2 * _neighbor_temperature[_qp] -
                             9.7e-6 * Utility::pow<2>(_neighbor_temperature[_qp]));
 
-  // return warning if the PCT curves is used out of bounds (pressure in Pa)
-  if (!_silence_warnings && ((neighbor_pressure < limit_pressure) || (neighbor_pressure > 1.e6)))
+  // define atomic fraction variable
+  ADReal atomic_fraction = 0.0;
+
+  if (!_silence_warnings && ((neighbor_pressure < 0.011) || (neighbor_pressure > 1.e6)))
     mooseDoOnce(mooseWarning("In YHxPCT: pressure ",
                              neighbor_pressure,
                              "Pa and temperature ",
                              _neighbor_temperature[_qp],
                              "K are outside the bounds of the atomic fraction correlation. See "
                              "documentation for YHxPCT material."));
 
-  // Calculate the atomic fraction based on the PCT curve
-  auto atomic_fraction =
-      2. - pow(1. + exp(21.6 - 0.0225 * _neighbor_temperature[_qp] +
-                        (-0.0445 + 7.18e-4 * _neighbor_temperature[_qp]) *
-                            (log(max(neighbor_pressure - limit_pressure, 1e-10)))),
-               -1);
+  if (neighbor_pressure > limit_pressure && abs(neighbor_pressure - limit_pressure) < tolerance)
+  {
+    // High pressure region, near limit
+    atomic_fraction = 0.5;
+  }
+  else if (neighbor_pressure > limit_pressure)
+  {
+    // High pressure region (far enough from plateau)
+    atomic_fraction = 2. - pow(1. + exp(21.6 - 0.0225 * _neighbor_temperature[_qp] +
+                                        (-0.0445 + 7.18e-4 * _neighbor_temperature[_qp]) *
+                                            log(max(neighbor_pressure - limit_pressure, 1e-10))),
+                               -1);
+  }
+  else if ((neighbor_pressure < limit_pressure) &&
+           (abs(neighbor_pressure - limit_pressure) < tolerance))
+  {
+    // Low pressure region, near limit
+    atomic_fraction = 1.0;
+  }
+  else if (neighbor_pressure < limit_pressure)
+  {
+    // Low pressure region (far enough from plateau)
+    atomic_fraction =
+        0.5 - pow(0.001 + exp(-8.97e01 + 9.75e-2 * _neighbor_temperature[_qp] +
+                              (1.20 - 4.41e-3 * _neighbor_temperature[_qp]) *
+                                  log(max(limit_pressure - neighbor_pressure, 1e-10))),
+                  -1);
+  }
 
   // Convert to concentration
   auto _surface_equilibrium_concentration = atomic_fraction * _density[_qp];

test/tests/yttrium_hydrogen_system/PCT_data/1000.csv

@@ -14,22 +14,22 @@ Atom Ratio (-),Partial Pressure (mm Hg)
 0.5003812713236798, 9.661704954868043
 0.5248298036256153, 11.417576632627881
 0.5468295520651542, 13.19528722851941
-0.5663805166422968, 14.913806704747937
-0.5980103139789005, 14.90591251598713
-0.6345062339826738, 14.896809028798605
-0.6783091992516077, 15.052940279008315
-0.7196633806581451, 14.875589174160138
-0.7513010392591545, 15.034559330727195
-0.7877969592629279, 15.025377275076085
-0.8194267565995315, 15.01742402968676
-0.8461825700045595, 14.84411833474094
-0.8778123673411633, 14.836261033487002
-0.9143161486093423, 14.993589543517993
-0.943512884612361, 14.986263468670607
-0.9775757432825496, 14.977720905469436
-1.011638601952738, 14.969183211753325
-1.0432683992893417, 14.961259711053058
-1.0481345219565115, 14.960041083256012
+0.5663805166422968, 14.836261033487002
+0.5980103139789005, 14.84411833474094
+0.6345062339826738, 14.875589174160138
+0.6783091992516077, 14.896809028798605
+0.7196633806581451, 14.90591251598713
+0.7513010392591545, 14.913806704747937
+0.7877969592629279, 14.960041083256012
+0.8194267565995315, 14.961259711053058
+0.8461825700045595, 14.969183211753325
+0.8778123673411633, 14.977720905469436
+0.9143161486093423, 14.986263468670607
+0.943512884612361, 14.993589543517993
+0.9775757432825496, 15.01742402968676
+1.011638601952738, 15.025377275076085
+1.0432683992893417, 15.034559330727195
+1.0481345219565115, 15.052940279008315
 1.0798114868795496, 15.987540632145134
 1.1212285584013335, 17.27453057131089
 1.1455906167948053, 18.05573840599329
@@ -62,7 +62,4 @@ Atom Ratio (-),Partial Pressure (mm Hg)
 1.9119538386554096, 524.2537323663885
 1.9291896608650534, 700.5286849730287
 1.9365517349810544, 765.8515855528643
-0.5712466393094666, 14.912591942103536
-0.5761127619766364, 14.911377278404247
-1.0384022766221719, 14.962478438118127
-1.0651895350848233, 15.464944999627683
+

test/tests/yttrium_hydrogen_system/PCT_data/1050.csv

@@ -26,20 +26,20 @@ Atom Ratio (-),Partial Pressure (mm Hg)
 0.5399077087558763, 22.547710391605136
 0.5594586733330189, 25.48426484330247
 0.5716790088517838, 27.54919779324486
-0.5790017766457557, 28.483627797847237
-0.5960332059808501, 28.475508433196833
-0.6325291259846234, 28.45811758738781
-0.6763242299891515, 28.437262591711786
-0.7176862726600947, 28.417580240273985
-0.761473515400217, 28.08162556388147
-0.7931111740012262, 28.38172395731534
+0.5790017766457557, 28.021074736663728
+0.5960332059808501, 28.08162556388147
+0.6325291259846234, 28.276729535554693
+0.6763242299891515, 28.282488362300167
+0.7176862726600947, 28.298619317459913
+0.761473515400217, 28.317065960779317
+0.7931111740012262, 28.351685833131302
 0.82474097133783, 28.366700919219717
-0.8563707686744337, 28.351685833131302
-0.8904257660802164, 28.021074736663728
-0.9293626086819804, 28.317065960779317
-0.9682915900193385, 28.298619317459913
-1.0023544486895273, 28.282488362300167
-1.0145197553574516, 28.276729535554693
+0.8563707686744337, 28.38172395731534
+0.8904257660802164, 28.417580240273985
+0.9293626086819804, 28.437262591711786
+0.9682915900193385, 28.45811758738781
+1.0023544486895273, 28.475508433196833
+1.0145197553574516, 28.483627797847237
 1.0388975362797352, 30.222550814781602
 1.068133578604783, 31.9411986552508
 1.102243604861406, 34.13362375347649
@@ -72,7 +72,3 @@ Atom Ratio (-),Partial Pressure (mm Hg)
 1.8658671760766001, 641.3779884427049
 1.878111095388583, 716.9523738731084
 1.8854653082401773, 775.1085545978324
-0.5741277927141802, 28.169828844760538
-0.5838678993129256, 28.4813077431683
-1.0096536326902819, 28.279032925527343
-1.0267086458185937, 29.233455068878477

test/tests/yttrium_hydrogen_system/PCT_data/1100.csv

@@ -30,16 +30,16 @@ Atom Ratio (-),Partial Pressure (mm Hg)
 0.5427259720453438, 38.954870591321125
 0.5573950914265051, 43.05998403229226
 0.5769460560036477, 48.668003010889905
-0.5916151753848089, 53.796698608449915
-0.635410279389337, 53.75727471073713
-0.684071506061035, 53.71350426360323
-0.7278666100655631, 53.67414133329971
-0.7619294687357515, 53.643545665102174
-0.8154568180746191, 53.59550199070021
-0.8714172287470716, 53.54532051887158
-0.91034621008443, 53.510439382866785
-0.9444090687546185, 53.479937029074186
-0.976038866091222, 53.45162898363805
+0.5916151753848089, 53.45162898363805
+0.635410279389337, 53.479937029074186
+0.684071506061035, 53.510439382866785
+0.7278666100655631, 53.54532051887158
+0.7619294687357515, 53.59550199070021
+0.8154568180746191, 53.643545665102174
+0.8714172287470716, 53.67414133329971
+0.91034621008443, 53.71350426360323
+0.9444090687546185, 53.75727471073713
+0.976038866091222, 53.796698608449915
 1.002841847082685, 56.49353181939432
 1.0345188120057232, 60.373673467170235
 1.0661957769287613, 64.52031463660713
@@ -71,8 +71,3 @@ Atom Ratio (-),Partial Pressure (mm Hg)
 1.7757810166187131, 587.4849499543402
 1.7977729037938461, 671.4214149099407
 1.8173395908998007, 775.9929751479735
-0.5867254689244219, 52.029732360862724
-0.5964812980519788, 53.792316747993
-0.6013474207191485, 53.787935244448335
-0.9711727434240522, 53.45598309206024
-0.9882277565523638, 55.260131561070004

test/tests/yttrium_hydrogen_system/PCT_data/1150.csv

@@ -30,17 +30,17 @@ Atom Ratio (-),Partial Pressure (mm Hg)
 0.5455442353348113, 67.30093284112601
 0.5699770451079351, 77.77648448455122
 0.5870870870870871, 86.93390519466453
-0.6041892678018332, 96.0911962129842
-0.6504174331399463, 96.01686695668666
-0.6917794758108895, 95.9504105699897
-0.7307084571482477, 95.88790540075408
-0.7672043771520212, 95.82934378519286
-0.8037081584202002, 96.8455491378044
-0.837763155825983, 95.71622605709229
-0.8791251984969264, 95.64997775370932
-0.9229203025014545, 95.57988246837148
+0.6041892678018332, 95.57988246837148
+0.6504174331399463, 95.64997775370932
+0.6917794758108895, 95.71622605709229
+0.7307084571482477, 95.82934378519286
+0.7672043771520212, 95.88790540075408
+0.8037081584202002, 95.9504105699897
+0.837763155825983, 96.01686695668666
+0.8791251984969264, 96.0911962129842
+0.9229203025014545, 96.60524527949393
 0.9423926544345393, 96.62098462559449
-0.9521248997688787, 96.60524527949393
+0.9521248997688787, 96.8455491378044
 0.9813688033583321, 103.24458202382107
 1.0106127069477855, 110.34021689437361
 1.0398644718016445, 119.2468362939784
@@ -62,9 +62,3 @@ Atom Ratio (-),Partial Pressure (mm Hg)
 1.5738054808735438, 563.7401394031765
 1.6006477681870352, 630.0123853764603
 1.6323640394321024, 711.9185511096462
-1.6470095750200464, 761.0321426711316
-0.5968665000078613, 92.9388415495683
-0.611488451802588, 96.0794561903707
-0.6236537584705124, 96.05989267336636
-0.9472587771017089, 96.61311463202999
-0.9667468515636057, 99.86975603349624