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Parameter
In this subsection, we will review the configuration of all parameters used to calculate the view factors and solve the heat equation through radiative transfer
1. Triangular cavity
Parameters used in the first geometry: Case : Triangular Cavity:
{
"Name": "Triangular cavity 2D RHT",
"ShortName": "triangle2d",
"Models": {
"heat": {
"name": "heat",
"materials": [
"Rectangle1",
"Rectangle2",
"Rectangle3",
"Insulation1",
"Insulation2",
"Insulation3",
"Insulation11",
"Insulation21",
"Insulation31"
]
}
},
"Parameters": {
"sigma": 5.67e-8, // W⋅m-2⋅K−4
"Tinit_C":350,
"Tref_C":0
},
"Meshes": {
"heat": {
"Import": {
"filename": "$cfgdir/triangular_cavity.geo"
}
}
},
"Materials": {
"Rectangle1": {
"k": "400", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Rectangle2": {
"k": "400", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Rectangle3": {
"k": "400", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation1": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation2": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation3": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation11": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation21": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation31": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
}
},
"Coating":{
"Rectangle1": {
"markers": [
"RadiativeSurface1"
],
"epsilon": "0.4" // 0.4
},
"Rectangle2": {
"markers": [
"RadiativeSurface2"
],
"epsilon": "0.6" // 0.6
},
"Rectangle3": {
"markers": [
"RadiativeSurface3"
],
"epsilon": "0.8" // 0.8
}
},
"InitialConditions": {
"heat": {
"temperature": {
"Expression": {
"Tini": {
"markers":["Rectangle1",
"Rectangle2",
"Rectangle3",
"Insulation1",
"Insulation2",
"Insulation3",
"Insulation11",
"Insulation21",
"Insulation31"],
"expr":"Tinit_C:Tinit_C"
}
}
}
}
},
"BoundaryConditions": {
"heat": {
"flux": {
"FixedQ3": {
"expr": "-1000"
},
"FixedQ2": {
"expr": "-2000"
}
},
"temperature":
{
"Fixed_T":{
"expr":"+300"
}
},
"radiative_enclosure_heat_flux": {
"Cavity_1": {
"enclosure": "closed",
"markers": ["RadiativeSurface1", "RadiativeSurface2","RadiativeSurface3"],
"sigma": "sigma:sigma",
"viewfactors": {
"status": "compute",
"filename":"$cfgdir/triangular_cavity_vf.json"
}
}
}
}
},
"Checker":
{
"RadiativeSurface1_q":
{
"type":"average",
"markers":["RadiativeSurface1"],
"quantity":"flux-from-temperature",
"exact_value":-2750,// 11000/L1 = 11000/4 = 2750,
"rel_tolerance":0.1
},
"RadiativeSurface2_T":
{
"type":"average",
"markers":["RadiativeSurface2"],
"quantity":"temperature",
"exact_value":641,
"rel_tolerance":0.1
},
"RadiativeSurface3_q":
{
"type":"average",
"markers":["RadiativeSurface3"],
"quantity":"temperature",
"exact_value":600,
"rel_tolerance":0.1
}
}
}
2. Rectangular cavity
Parameters used in the second geometry: Case : Rectangular Cavity:
{
"Name": "Rectangular cavity 2D RHT",
"ShortName": "rectangle2d",
"Models": {
"heat": {
"name": "heat",
"materials": [
"Rectangle1",
"Rectangle2",
"Rectangle3",
"Rectangle4",
"Insulation1",
"Insulation2",
"Insulation3",
"Insulation4",
"Insulation5",
"Insulation6",
"Insulation7",
"Insulation8"
]
}
},
"Parameters": {
"sigma": 5.67e-8, // W⋅m-2⋅K−4
"Tinit_C":1700
},
"Meshes": {
"heat": {
"Import": {
"filename": "$cfgdir/rectangular_cavity.geo"
}
}
},
"Materials": {
"Rectangle1": {
"k": "1400", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Rectangle2": {
"k": "1400", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Rectangle3": {
"k": "1400", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Rectangle4": {
"k": "1400", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation1": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation2": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation3": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation4": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation5": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation6": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation7": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"Insulation8": {
"k": "0.01", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
}
},
"Coating":{
"Top": {
"markers": [
"RadiativeSurface3"
],
"epsilon": "0.5"
},
"Bottom": {
"markers": [
"RadiativeSurface1"
],
"epsilon": "0.5"
},
"LeftRight": {
"markers": [
"RadiativeSurface2","RadiativeSurface4"
],
"epsilon": "0.5"
}
},
"InitialConditions": {
"heat": {
"temperature": {
"Expression": {
"Tini": {
"markers":["Rectangle1",
"Rectangle2",
"Rectangle3",
"Rectangle4",
"Insulation1",
"Insulation2",
"Insulation3",
"Insulation4",
"Insulation5",
"Insulation6",
"Insulation7",
"Insulation8"],
"expr":"Tinit_C:Tinit_C"
}
}
}
}
},
"BoundaryConditions": {
"heat": {
"temperature":
{
"ExternalSurface3":{
"expr":"1400"
},
"ExternalSurface1":{
"expr":"600"
},
"ExternalSurface4":{
"expr":"1700"
},
"ExternalSurface2":{
"expr":"1700"
}
},
"radiative_enclosure_heat_flux": {
"Cavity_1": {
"enclosure": "closed",
"markers": ["RadiativeSurface1", "RadiativeSurface2","RadiativeSurface3","RadiativeSurface4"],
"sigma": "sigma:sigma",
"viewfactors": {
// "status":"load",
// "filename":"$cfgdir/VF_Matrix_Cavity_1.csv"
"status":"compute",
"filename":"$cfgdir/rectangular_cavity_vf.json"
}
}
}
}
},
"Checker":
{
"RadiativeSurface3_q":
{
"type":"average",
"markers":["RadiativeSurface3"],
"quantity":"flux-from-temperature",
"exact_value":-35767,
"rel_tolerance":0.1
},
"RadiativeSurface1_q":
{
"type":"average",
"markers":["RadiativeSurface1"],
"quantity":"flux-from-temperature",
"exact_value":-159040,
"rel_tolerance":0.1
},
"RadiativeSurface4_q":
{
"type":"average",
"markers":["RadiativeSurface4"],
"quantity":"flux-from-temperature",
"exact_value":97403,
"rel_tolerance":0.1
},
"RadiativeSurface2_q":
{
"type":"average",
"markers":["RadiativeSurface2"],
"quantity":"flux-from-temperature",
"exact_value":97403,
"rel_tolerance":0.1
}
}
}
3. Cylindrical cavity
Parameters used in the third geometry: Case : Cylindrical Cavity:
{
"Name": "Cylindrical cavity 3D RHT",
"ShortName": "cylinder3d",
"Models": {
"heat": {
"name": "heat",
"materials": [
"LateralVolume","MaterialTop","MaterialBottom","InsulationBottom","InsulationTop","InsulationL1","InsulationL2"
]
}
},
"Parameters": {
"sigma": 5.67e-8, // W⋅m-2⋅K−4
"Tinit_C":500
},
"Meshes": {
"heat": {
"Import": {
"filename": "$cfgdir/cylindrical_cavity.geo"
}
}
},
"Materials": {
"LateralVolume": {
"k": "1400", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"MaterialTop": {
"k": "1400", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"MaterialBottom": {
"k": "1400", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"InsulationBottom": {
"k": "0.001", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"InsulationTop": {
"k": "0.001", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"InsulationL2": {
"k": "0.001", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
},
"InsulationL1": {
"k": "0.001", // W/(m⋅K)
"Cp": "0", // J/(kg⋅K)
"rho": "8700" // kg/m3
}
},
"Coating":{
"Top": {
"markers": ["CavityTop"],
"epsilon": "0.5"
},
"Bottom": {
"markers": ["CavityBottom"],
"epsilon": "0.5"
},
"Side": {
"markers": ["CavitySide"],
"epsilon": "0.5"
}
},
"InitialConditions": {
"heat": {
"temperature": {
"Expression": {
"Tini": {
"markers":["MaterialTop","LateralVolume","MaterialBottom","InsulationBottom","InsulationTop","InsulationL1","InsulationL2"],
"expr":"Tinit_C:Tinit_C"
}
}
}
}
},
"BoundaryConditions": {
"heat": {
"temperature":{
"ExternalBoundaryBottom":{
"expr":"500"
},
"ExternalBoundaryLateral":{
"expr":"500"
},
"ExternalBoundaryTop":{
"expr":"500"
}
},
"radiative_enclosure_heat_flux": {
"Cavity": {
"enclosure": "closed",// the cavity is treated as closed since there is no black body exchanges in this test
"markers": ["CavityTop", "CavityBottom","CavitySide"],
"sigma": "sigma:sigma",
"viewfactors": {
// "status":"compute",
// "filename":"$cfgdir/cylindrical_cavity_vf.json"
"status":"load",
"filename":"$cfgdir/VF_Matrix_Cavity.csv"
}
}
}
}
},
"Checker":
{
"RadiativeSurface1_q":
{
"type":"average",
"markers": ["CavityTop","CavitySide","CavityBottom"],
"quantity":"flux-from-temperature",
"exact_value":88.5937, // 1/40 * sigma * Tini^4
"rel_tolerance":0.1
}
}
}