From ba4705bc900c66b6bb6abb91415df52547fa40da Mon Sep 17 00:00:00 2001 From: iomags2211 <146826090+iomags2211@users.noreply.github.com> Date: Wed, 15 Jan 2025 15:08:03 +0000 Subject: [PATCH 1/9] Attempt to simulate Joule heating for the same mesh --- axisymmetric_coil/joule_heating.i | 110 ++++++++++++++++++++++++++++++ 1 file changed, 110 insertions(+) create mode 100644 axisymmetric_coil/joule_heating.i diff --git a/axisymmetric_coil/joule_heating.i b/axisymmetric_coil/joule_heating.i new file mode 100644 index 0000000..3bfc89f --- /dev/null +++ b/axisymmetric_coil/joule_heating.i @@ -0,0 +1,110 @@ +[Mesh] + [coil] + type = FileMeshGenerator + file = axi_coil.e + [] + [tmg] + type = TiledMeshGenerator + input = coil + left_boundary = left + right_boundary = right + top_boundary = top + bottom_boundary = bottom + x_tiles = 1 + y_tiles = 1 #change to number of turns in coil + [] + [] + + [Problem] + type = FEProblem + [] + + [Kernels] + [joule_heating] + type = ADJouleHeatingSource + block = 2 + variable = T + elec = elec + [] + [electric_potential] + type = ADHeatConduction + variable = elec + thermal_conductivity = 0.025 # air in W/(m K) + [] + [body_force] + type = ADBodyForce + variable = T + block = 2 + value = 0 + [] + [heat_conduction] + type = ADHeatConductionTimeDerivative + variable = T + block = 1 + [] + [] + + [BCs] + [edge] + type = DirichletBC + variable = T + boundary = 'top left bottom right' + value = 293.0 + [] + [elec_edge] + type = DirichletBC + boundary = 'wire_top wire_left wire_right wire_bottom' + value = 1 + variable = elec + [] + [] + + [Variables] + [T] + initial_condition = 293.0 + [] + [elec] + [] + [] + + [Materials] + [cp] + type = ADGenericConstantMaterial + prop_names = 'specific_heat' + prop_values = '1000' #air in J/(kg K) + block = 1 + [] + [rho] + type = ADGenericConstantMaterial + prop_names = 'density' + prop_values = '1.293' #air in kg/(m^3) + block = 1 + [] + [sigma] #copper is default material + type = ADElectricalConductivity + temperature = T + block = 2 + [] + [] + + [Preconditioning] + [SMP] + type = SMP + full = true + [] + [] + + [Executioner] + type = Transient + scheme = bdf2 + solve_type = NEWTON + petsc_options_iname = '-pc_type' + petsc_options_value = 'hypre' + dt = 0.2 + end_time = 1 + automatic_scaling = true + [] + + [Outputs] + exodus = true + [] \ No newline at end of file From c351746660956c73f0f81038b49839c030097a1c Mon Sep 17 00:00:00 2001 From: iomags2211 Date: Wed, 15 Jan 2025 15:20:53 +0000 Subject: [PATCH 2/9] Attempt to implement Joule heating --- Makefile | 2 +- axisymmetric_coil/axi_coil.e | Bin 94236 -> 96912 bytes axisymmetric_coil/joule_heating.i | 111 ++++++++++++++++++++++++++++++ 3 files changed, 112 insertions(+), 1 deletion(-) create mode 100644 axisymmetric_coil/joule_heating.i diff --git a/Makefile b/Makefile index 74da3bc..17f5128 100644 --- a/Makefile +++ b/Makefile @@ -34,7 +34,7 @@ FLUID_PROPERTIES := no FSI := no FUNCTIONAL_EXPANSION_TOOLS := no GEOCHEMISTRY := no -HEAT_TRANSFER := no +HEAT_TRANSFER := yes LEVEL_SET := no MISC := no NAVIER_STOKES := no diff --git a/axisymmetric_coil/axi_coil.e b/axisymmetric_coil/axi_coil.e index bf7358e58458e6a4e7217da8d80e3246e7cf9001..bf73d5d78989c855ec67fdd8c92637824e8a92d3 100644 GIT binary patch delta 1514 zcma)6O-~b16rK0_HEl6zB8UZ~4H%%MDeZ&`HcCb`nwZAK#09&S(2|gVA1z=sCT*fi zOfc637HUw`fRLym5tp-Y;lc$=5;tA?2TX`;Ja>k{)-K>Cch0+K&fIt2yf^cr>RSBm z3S7Q&RVr5a0G-bQkA?dAxkHqjZqLnROH=tmwp2>tmWuQ-m!CXf6eR$zR(GyJ$4sMc zs6od}olY|+9&QjaV+l<&_r|lu!i32=Xifa_lnTYt!2ATgk%>^e5J`s<$$?~QKuc(; zbU4Wi;qW6Pv?t^8;Ue`p;?loMV~!E&uhO!k*BfRHRKMuEW5}+WR8pN$+0;ja0R0o? z0CU5%;Jhx^4cc{%`uH7jY#4Obbwh3$Gz<7*&^JKPpk{Yewi%=Y+H*AR)?|l5E2ugv z^aBtI(;mo>K`~EMcIh<6P^BjxO?Fr4t0(H~;r=S`3mKj+*|S0cRV(-E%oe5#*fMjs z1nQGWJDeDV%|b*BpxNOV+A6ds@>8YR?Bw{w?BT{M+`k!VMOjhY7*)(lL>X)|d;nP7 z!sJ2Jn2A=v*=CN?u0UI7#yVY!!2HT7q#dH8n1;WoQ?W z%aH2rrI0sB)sKFcho9LR_Aalw?oSm9S=w3Kw@2%TqYsCpjs4Y~&3Ro>YM@)WtwJdMdKShScpEhb+9Qnm*sv1&0Dc}&(}^ Date: Wed, 15 Jan 2025 15:49:24 +0000 Subject: [PATCH 3/9] Attempted to fix Joule heating issues - failed --- axisymmetric_coil/joule_heating.i | 25 +++++++++++++++---------- 1 file changed, 15 insertions(+), 10 deletions(-) diff --git a/axisymmetric_coil/joule_heating.i b/axisymmetric_coil/joule_heating.i index b9321c5..49c6143 100644 --- a/axisymmetric_coil/joule_heating.i +++ b/axisymmetric_coil/joule_heating.i @@ -29,19 +29,12 @@ [electric_potential] type = ADHeatConduction variable = elec - thermal_conductivity = 0.025 # air in W/(m K) + thermal_conductivity = 397.48 # copper in W/(m K) block = 2 [] - [body_force] - type = ADBodyForce - variable = T - block = 2 - value = 0 - [] [heat_conduction] type = ADHeatConductionTimeDerivative variable = T - block = 1 [] [] @@ -69,18 +62,30 @@ [] [Materials] - [cp] + [cp_air] type = ADGenericConstantMaterial prop_names = 'specific_heat' prop_values = '1000' #air in J/(kg K) block = 1 [] - [rho] + [rho_air] type = ADGenericConstantMaterial prop_names = 'density' prop_values = '1.293' #air in kg/(m^3) block = 1 [] + [cp_copper] + type = ADGenericConstantMaterial + prop_names = 'specific_heat' + prop_values = '385.0' #copper in J/(kg K) + block = 2 + [] + [rho_copper] + type = ADGenericConstantMaterial + prop_names = 'density' + prop_values = '8920.0' #copper in kg/(m^3) + block = 2 + [] [sigma] #copper is default material type = ADElectricalConductivity temperature = T From f3e0a0f605590f9ae469a2001ac8e564c0bba213 Mon Sep 17 00:00:00 2001 From: iomags2211 Date: Fri, 17 Jan 2025 16:10:15 +0000 Subject: [PATCH 4/9] Implemented Joule heating solver with radiative + convective cooling - included changes to mesh --- axisymmetric_coil/AForm_axi_coil.i | 6 +- .../AForm_axi_coil_joule_heating.i | 209 ++++++++++++++++++ axisymmetric_coil/axi_coil.e | Bin 96912 -> 59656 bytes axisymmetric_coil/joule_heating.i | 81 ++++--- include/kernels/ADJouleHeating.h | 34 +++ src/kernels/ADJouleHeating.C | 41 ++++ 6 files changed, 334 insertions(+), 37 deletions(-) create mode 100644 axisymmetric_coil/AForm_axi_coil_joule_heating.i create mode 100644 include/kernels/ADJouleHeating.h create mode 100644 src/kernels/ADJouleHeating.C diff --git a/axisymmetric_coil/AForm_axi_coil.i b/axisymmetric_coil/AForm_axi_coil.i index a78d421..cc0ee6a 100644 --- a/axisymmetric_coil/AForm_axi_coil.i +++ b/axisymmetric_coil/AForm_axi_coil.i @@ -1,7 +1,7 @@ [Mesh] [coil] type = FileMeshGenerator - file = axi_coil.e + file = joule_heating.e [] [tmg] type = TiledMeshGenerator @@ -24,7 +24,7 @@ [Kernels] [laplacian_A] # d2A/dz2 = 0 type = ADDiffusion - variable = A + variable = A [] [body_force] # d2A/dz2 = J*mu_0 type = ADBodyForce @@ -105,7 +105,7 @@ type = ParsedFunction expression = 'J' symbol_names = 'J' - symbol_values = '50' + symbol_values = '1e8' [] [] diff --git a/axisymmetric_coil/AForm_axi_coil_joule_heating.i b/axisymmetric_coil/AForm_axi_coil_joule_heating.i new file mode 100644 index 0000000..c844a25 --- /dev/null +++ b/axisymmetric_coil/AForm_axi_coil_joule_heating.i @@ -0,0 +1,209 @@ +[Mesh] + [coil] + type = FileMeshGenerator + file = axi_coil.e + [] + [tmg] + type = TiledMeshGenerator + input = coil + left_boundary = left + right_boundary = right + top_boundary = top + bottom_boundary = bottom + x_tiles = 1 + y_tiles = 1 #change to number of turns in coil + [] + coord_type = rz + rz_coord_axis = y + [] + + [Problem] + type = FEProblem + [] + + [Kernels] + [laplacian_A] # d2A/dz2 = 0 + type = ADDiffusion + variable = A + [] + [body_force] # d2A/dz2 = J*mu_0 + type = ADBodyForce + variable = A + block = '2' + value = '1.257e-6' # mu_0 + function = 'J' + [] + [joule_heating] + type = ADJouleHeating #calculates Q = rho*J^2 + block = 2 #only the wire undergoes Joule heating due to presence of current density + variable = T + current_density = J + [] + [heat_conduction_tdot] + type = ADHeatConductionTimeDerivative #implements density * specific_heat * dT/dt + variable = T + [] + [heat_conduction] + type = ADHeatConduction #implements Q = -k*del(T) + variable = T + [] + [] + + [BCs] + [A_edge] + type = DirichletBC + variable = A + boundary = 'top left bottom right' + value = 0 + [] + [temp_edge] + type = DirichletBC + variable = T + boundary = 'top left bottom right' + value = 293.0 + [] + [convective_dissipation] + type = ADConvectiveHeatFluxBC + variable = T + boundary = 'wire_edge' + T_infinity = 293.0 + heat_transfer_coefficient = 10 + [] + [radiative_dissipation] + type = ADFunctionRadiativeBC + variable = T + boundary = 'wire_edge' + emissivity_function = '0.03' #approximate emissivity of copper wire + [] + [] + + [AuxKernels] + [dAdx_aux] + type = VariableGradientComponent + variable = dAdx + component = x + gradient_variable = A + [] + [dAdy_aux] + type = VariableGradientComponent + variable = dAdy + component = y + gradient_variable = A + [] + [mag_B_aux] + type = ParsedAux + variable = mag_B + coupled_variables = 'dAdx dAdy' + expression = 'sqrt(dAdx^2 + dAdy^2)' + [] + [Bx_unit_aux] + type = ParsedAux + variable = Bx_unit + coupled_variables = 'dAdy mag_B' + expression = 'dAdy / mag_B' + [] + [By_unit_aux] + type = ParsedAux + variable = By_unit + coupled_variables = 'dAdx mag_B' + expression = '-dAdx / mag_B' + [] + [] + + [AuxVariables] + [dAdx] + family = MONOMIAL + [] + [dAdy] + family = MONOMIAL + [] + [mag_B] + family = MONOMIAL + [] + [Bx_unit] + family = MONOMIAL + [] + [By_unit] + family = MONOMIAL + [] + [] + + [Variables] + [A] + [] + [T] + initial_condition = 293.0 + [] + [] + + [Materials] + [k_air] + type = ADGenericConstantMaterial + prop_names = 'thermal_conductivity' + prop_values = '0.03' #air in W/(m K) + block = 1 + [] + [cp_air] + type = ADGenericConstantMaterial + prop_names = 'specific_heat' + prop_values = '1000' #air in J/(kg K) + block = 1 + [] + [rho_air] + type = ADGenericConstantMaterial + prop_names = 'density' + prop_values = '1.293' #air in kg/(m^3) + block = 1 + [] + [k_copper] + type = ADGenericConstantMaterial + prop_names = 'thermal_conductivity' + prop_values = '397.48' #copper in W/(m K) + block = 2 + [] + [cp_copper] + type = ADGenericConstantMaterial + prop_names = 'specific_heat' + prop_values = '385.0' #copper in J/(kg K) + block = 2 + [] + [rho_copper] + type = ADGenericConstantMaterial + prop_names = 'density' + prop_values = '8920.0' #copper in kg/(m^3) + block = 2 + [] + [] + + [Functions] + [J] + type = ParsedFunction + expression = 'J' + symbol_names = 'J' + symbol_values = '1e8' + [] + [] + + [Preconditioning] + [SMP] + type = SMP + full = true + [] + [] + + [Executioner] + type = Transient + steady_state_detection = true + steady_state_tolerance = 1e-5 + scheme = bdf2 + solve_type = NEWTON + petsc_options_iname = '-pc_type' + petsc_options_value = 'hypre' + dt = 100 + end_time = 2000 + automatic_scaling = true + [] + + [Outputs] + exodus = true + [] \ No newline at end of file diff --git a/axisymmetric_coil/axi_coil.e b/axisymmetric_coil/axi_coil.e index 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COPYRIGHT for full restrictions +//* https://github.com/idaholab/moose/blob/master/COPYRIGHT +//* +//* Licensed under LGPL 2.1, please see LICENSE for details +//* https://www.gnu.org/licenses/lgpl-2.1.html + +#include "ADJouleHeating.h" +#include "Function.h" + +registerMooseObject("orpheusApp", ADJouleHeating); + +InputParameters +ADJouleHeating::validParams() +{ + InputParameters params = ADKernelValue::validParams(); + params.addParam("current_density", "1", "A function that describes the current density"); + params.addParam( + "resistivity", + 1.77e-8, + "Material property providing electrical conductivity of the material."); + params.addClassDescription("Calculates the heat source term corresponding to Joule " + "heating, with Jacobian contributions calculated using the automatic " + "differentiation system."); + return params; +} + +ADJouleHeating::ADJouleHeating(const InputParameters & parameters) + : ADKernelValue(parameters), + _current_density(getFunction("current_density")), + _resistivity(getADMaterialProperty("resistivity")) +{ +} + +ADReal +ADJouleHeating::precomputeQpResidual() +{ + return -_resistivity[_qp] * Utility::pow<2>(_current_density.value(_t, _q_point[_qp])); +} From 73718675e20094e87e2357d652b022585684baec Mon Sep 17 00:00:00 2001 From: iomags2211 Date: Fri, 17 Jan 2025 16:37:07 +0000 Subject: [PATCH 5/9] Added temperature dependence to resistivity of copper wire --- axisymmetric_coil/joule_heating.i | 5 +++ include/materials/Resistivity.h | 42 +++++++++++++++++++ src/kernels/ADJouleHeating.C | 4 +- src/materials/Resistivity.C | 68 +++++++++++++++++++++++++++++++ 4 files changed, 117 insertions(+), 2 deletions(-) create mode 100644 include/materials/Resistivity.h create mode 100644 src/materials/Resistivity.C diff --git a/axisymmetric_coil/joule_heating.i b/axisymmetric_coil/joule_heating.i index 4baebaa..68a185e 100644 --- a/axisymmetric_coil/joule_heating.i +++ b/axisymmetric_coil/joule_heating.i @@ -93,6 +93,11 @@ prop_values = '8920.0' #copper in kg/(m^3) block = 2 [] + [resistivity_copper] + type = ADResistivity + temperature = T + block = 2 + [] [] [Functions] diff --git a/include/materials/Resistivity.h b/include/materials/Resistivity.h new file mode 100644 index 0000000..dfea922 --- /dev/null +++ b/include/materials/Resistivity.h @@ -0,0 +1,42 @@ +//* This file is part of the MOOSE framework +//* https://www.mooseframework.org +//* +//* All rights reserved, see COPYRIGHT for full restrictions +//* https://github.com/idaholab/moose/blob/master/COPYRIGHT +//* +//* Licensed under LGPL 2.1, please see LICENSE for details +//* https://www.gnu.org/licenses/lgpl-2.1.html + +#pragma once + +#include "Material.h" + +/** + * Calculates resistivity as a function of temperature. + * It is assumed that resistivity varies linearly with temperature. + */ +template +class ResistivityTempl : public Material +{ +public: + static InputParameters validParams(); + + ResistivityTempl(const InputParameters & parameters); + +protected: + virtual void computeQpProperties(); + +private: + const Real _ref_resis; + const Real _temp_coeff; + const Real _ref_temp; + const bool _has_temp; + const GenericVariableValue & _T; + + const std::string _base_name; + GenericMaterialProperty & _resistivity; + MaterialProperty & _dresistivity_dT; +}; + +typedef ResistivityTempl Resistivity; +typedef ResistivityTempl ADResistivity; diff --git a/src/kernels/ADJouleHeating.C b/src/kernels/ADJouleHeating.C index 3fa7d9b..1b09b8b 100644 --- a/src/kernels/ADJouleHeating.C +++ b/src/kernels/ADJouleHeating.C @@ -20,7 +20,7 @@ ADJouleHeating::validParams() params.addParam( "resistivity", 1.77e-8, - "Material property providing electrical conductivity of the material."); + "Material property providing resistivity of the material."); params.addClassDescription("Calculates the heat source term corresponding to Joule " "heating, with Jacobian contributions calculated using the automatic " "differentiation system."); @@ -30,7 +30,7 @@ ADJouleHeating::validParams() ADJouleHeating::ADJouleHeating(const InputParameters & parameters) : ADKernelValue(parameters), _current_density(getFunction("current_density")), - _resistivity(getADMaterialProperty("resistivity")) + _resistivity(getADMaterialProperty("resistivity")) { } diff --git a/src/materials/Resistivity.C b/src/materials/Resistivity.C new file mode 100644 index 0000000..6cc805f --- /dev/null +++ b/src/materials/Resistivity.C @@ -0,0 +1,68 @@ +//* This file is part of the MOOSE framework +//* https://www.mooseframework.org +//* +//* All rights reserved, see COPYRIGHT for full restrictions +//* https://github.com/idaholab/moose/blob/master/COPYRIGHT +//* +//* Licensed under LGPL 2.1, please see LICENSE for details +//* https://www.gnu.org/licenses/lgpl-2.1.html + +#include "Resistivity.h" +#include "libmesh/quadrature.h" +#include "libmesh/utility.h" + +registerMooseObject("orpheusApp", Resistivity); +registerMooseObject("orpheusApp", ADResistivity); + +template +InputParameters +ResistivityTempl::validParams() +{ + InputParameters params = Material::validParams(); + params.addCoupledVar("temperature", 293.0, "Coupled variable for temperature."); + params.addParam("base_name", "Material property base name."); + params.addParam("reference_resistivity", + 1.68e-8, + "Electrical resistivity of the material at reference temperature " + "(default is copper resistivity in ohm-m)."); + params.addParam("temperature_coefficient", + 0.00386, + "Coefficient for calculating dependence of resistivity on temperature " + "(with copper as the default material)."); + params.addParam("reference_temperature", + 293.0, + "Reference temperature for Electrical resistivity in Kelvin."); + params.addClassDescription("Calculates resistivity as a function of " + "temperature, using copper for parameter defaults."); + return params; +} + +template +ResistivityTempl::ResistivityTempl(const InputParameters & parameters) + : Material(parameters), + _ref_resis(getParam("reference_resistivity")), + _temp_coeff(getParam("temperature_coefficient")), + _ref_temp(getParam("reference_temperature")), + _has_temp(isCoupled("temperature")), + _T(_has_temp ? coupledGenericValue("temperature") : genericZeroValue()), + _base_name(isParamValid("base_name") ? getParam("base_name") + "_" : ""), + _resistivity( + declareGenericProperty(_base_name + "resistivity")), + _dresistivity_dT(declareProperty(_base_name + "resistivity_dT")) +{ +} + +template +void +ResistivityTempl::computeQpProperties() +{ + const auto & temp_qp = _T[_qp]; + + const auto resistivity = _ref_resis * (1.0 + _temp_coeff * (temp_qp - _ref_temp)); + const Real dresistivity_dT = _ref_resis * _temp_coeff; + _resistivity[_qp] = resistivity; + _dresistivity_dT[_qp] = dresistivity_dT; +} + +template class ResistivityTempl; +template class ResistivityTempl; From e416125bd9ee80892709ba00a769fe5f9f8e0d2e Mon Sep 17 00:00:00 2001 From: iomags2211 Date: Mon, 20 Jan 2025 17:36:22 +0000 Subject: [PATCH 6/9] Added tests for Joule heating kernel --- .../joule_heating/gold/joule_heating_out.e | Bin 0 -> 286704 bytes .../kernels/joule_heating}/joule_heating.i | 2 +- .../kernels/joule_heating/joule_heating_mesh.e | Bin 0 -> 59656 bytes test/tests/kernels/joule_heating/tests | 8 ++++++++ 4 files changed, 9 insertions(+), 1 deletion(-) create mode 100644 test/tests/kernels/joule_heating/gold/joule_heating_out.e rename {axisymmetric_coil => test/tests/kernels/joule_heating}/joule_heating.i (98%) create mode 100644 test/tests/kernels/joule_heating/joule_heating_mesh.e create mode 100644 test/tests/kernels/joule_heating/tests diff --git a/test/tests/kernels/joule_heating/gold/joule_heating_out.e b/test/tests/kernels/joule_heating/gold/joule_heating_out.e new file mode 100644 index 0000000000000000000000000000000000000000..a7d9414150a4256dd22efaecd39a1f55b7c875b0 GIT binary patch literal 286704 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z3x#~ISrTJ_*62>i4pfTNB*qXtg6XB6?)Z{-QUKg`Q0RDB1~C^3b(}*N0~HU~b6yyM zB-dcKp>w9S)X78XD4>`^LN25ZI2SoQbJHJ#!GFB>+h70i=C6L)xBtoSOa*Rd-}gV} G`u_sIk_ Date: Mon, 20 Jan 2025 18:19:06 +0000 Subject: [PATCH 9/9] Incorporated temperature-dependent resistivity in relevant input files --- .../AForm_axi_coil_joule_heating.i | 9 +++++++++ .../joule_heating/gold/joule_heating_out.e | Bin 286704 -> 222060 bytes .../kernels/joule_heating/joule_heating.i | 1 + 3 files changed, 10 insertions(+) diff --git a/axisymmetric_coil/AForm_axi_coil_joule_heating.i b/axisymmetric_coil/AForm_axi_coil_joule_heating.i index c844a25..8d9e141 100644 --- a/axisymmetric_coil/AForm_axi_coil_joule_heating.i +++ b/axisymmetric_coil/AForm_axi_coil_joule_heating.i @@ -37,6 +37,7 @@ type = ADJouleHeating #calculates Q = rho*J^2 block = 2 #only the wire undergoes Joule heating due to presence of current density variable = T + resistivity = resistivity current_density = J [] [heat_conduction_tdot] @@ -173,6 +174,14 @@ prop_values = '8920.0' #copper in kg/(m^3) block = 2 [] + [resistivity_copper] + type = ADResistivity + temperature = T + reference_resistivity = 1.68e-8 + temperature_coefficient = 0.00386 + reference_temperature = 293.0 + block = 2 + [] [] [Functions] diff --git a/test/tests/kernels/joule_heating/gold/joule_heating_out.e b/test/tests/kernels/joule_heating/gold/joule_heating_out.e index a7d9414150a4256dd22efaecd39a1f55b7c875b0..b0624a44afb651e8f9adc6826ef675ea0e5e05ca 100644 GIT binary patch delta 98710 zcmagGcOcd8`#)}FS4Jdc?@cMRu6AUkB$2FSWn`R%^E~I+dmJ1qGbs(CvPFs_MM$NT zQjv;^Lelr{^?r5E>+}2P=a1)o9`|)W?{VGpc|ES%^iAQ99m{!l?%Kn_#>Te%D(@6K zyFGo5{SEsn`e%;SbRN$2?APd=%+Zhu^*#fLcdSYpQGOdx-^$Adm`POYa4qJ zJ&{WjrL05GUGy=o{p#Ci;4QO};Sn zHu|eKs`2DkuflW>2e}6Z>EhfrY&0;`4G8r2c6SR7()AAv@N^GhhT8rC!E)MOa^C(S zr`(-9-Ccsc{5*8Lo=g^28L{O z;RacHXOjWFx?Yy<)oe}waNkVWyA|DfM3LUx zvKke*n*MD>lP=P!M&I*Nhu(YBkl}ZmU4VY`rU2bxK%M^WrWQS*Rhi$*&nwu=<&@Kj zUs7IuDm?;RC^Q~r4OKqpuK5Wf?2>zAtZ-bb?Zcdd%3E?RWMHUqlz19^IE 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