Functions used in window radiation model
Information
This package contains functions that are used to compute
heat transfer in the window model.
Extends from Modelica.Icons.Package (Icon for standard packages).
Package Content
Angular and hemispherical absorptance of a shading device for exterior irradiation with interior shading
Information
This function computes the angular and hemispherical absorptance of a shading device for exterior irradiation with interior shading.
Pane 1 is facing the outside and pane N is facing the room.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).
Inputs
| Type | Name | Default | Description |
|---|
| Real | traRef[3, N, N, HEM] | | Transmittance and reflectance with exterior irradiation and no shading |
| Real | traRefShaDev[2, 2] | | Transmittance and reflectance of shading device |
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
Outputs
| Type | Name | Description |
|---|
| Real | absExtIrrIntShaDev[HEM] | Absorptance of a shading device for exterior irradiation with interior shading |
Modelica definition
function devAbsExteriorIrradiationInteriorShading
"Angular and hemispherical absorptance of a shading device for exterior irradiation with interior shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
output Real absExtIrrIntShaDev[HEM](
each min=0,
each max=1)
"Absorptance of a shading device for exterior irradiation with interior shading";
algorithm
for iD
in 1:HEM
loop
absExtIrrIntShaDev[iD] := traRef[TRA, 1, N, iD]*(1 - traIntShaDev -
refIntShaDev)/(1 - refIntShaDev*traRef[Rb, N, 1, HEM])
"Equation (A.4.91)";
end for;
end devAbsExteriorIrradiationInteriorShading;
Hemiperical absorptance of a shading device for interior irradiation with interior shading
Information
This function computes the hemiperical absorbtance of a shading device for interior irradiation with interior shading.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).
Inputs
| Type | Name | Default | Description |
|---|
| Real | traRef[3, N, N, HEM] | | Transmittance and reflectance with exterior irradiation and no shading |
| Real | traRefShaDev[2, 2] | | Transmittance and reflectance of shading device |
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
Outputs
| Type | Name | Description |
|---|
| Real | absIntIrrIntShaDev | Hemiperical absorbtance of a shading device for interior irradiation with interior shading |
Modelica definition
function devAbsInteriorIrradiationInteriorShading
"Hemiperical absorptance of a shading device for interior irradiation with interior shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
output Real absIntIrrIntShaDev(min=0, max=1)
"Hemiperical absorbtance of a shading device for interior irradiation with interior shading";
protected
constant Real rRho=traRef[3, N, 1, HEM]*refIntShaDev
"Part of equation (A.4.103)";
constant Real rTau=traRef[3, N, 1, HEM]*traIntShaDev
"Part of equation (A.4.103)";
constant Real c=traIntShaDev*(1 - rRho/(1 - rRho))
"Equation (4.99)";
algorithm
absIntIrrIntShaDev := (1 - traIntShaDev - refIntShaDev)*(1 + rTau/(1 - rRho))
"Equation (4.103)";
end devAbsInteriorIrradiationInteriorShading;
Generate incident angles
Information
This function computes discrete incident angles for the window radiation calculation. The range is from 0 to 90 degree.
Inputs
| Type | Name | Default | Description |
|---|
| Integer | NDIR | | Number of incident angles |
Outputs
| Type | Name | Description |
|---|
| Angle | psi[NDIR] | Array of incident angles [rad] |
Modelica definition
function getAngle
"Generate incident angles"
input Integer NDIR
"Number of incident angles";
output Modelica.SIunits.Angle psi[NDIR]
"Array of incident angles";
protected
constant Real deltaX=0.5*Modelica.Constants.pi/(NDIR - 1);
algorithm
for i
in 1:NDIR
loop
psi[i] := (i - 1)*deltaX;
end for;
end getAngle;
Transmittance and reflectance of glass
Information
This function computes the angular variation of the transmittance and reflectance of each glass pane.
It accounts for the transmittance and reflectance among different panes.
Pane 1 is facing outside and pane N is facing the room.
For instance, traRef[TRA, 1, N, iD] means transmittance between layer 1 to N for exterior irradiation and
traRef[TRA, N, 1, iD] means the transmittance for interior irradiation.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation (Partial function for glass radiation property).
Inputs
| Type | Name | Default | Description |
|---|
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
| Real | layer[3, N, HEM] | | Property of glass pane |
Outputs
| Type | Name | Description |
|---|
| Real | traRef[3, N, N, HEM] | Glass transmittance, front and back reflectance |
Modelica definition
function getGlassTR
"Transmittance and reflectance of glass"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation;
input Real layer[3, N, HEM]
"Property of glass pane";
output Real traRef[3, N, N, HEM](
each min=0,
each max=1)
"Glass transmittance, front and back reflectance";
protected
Real traRefIntIrr[3, N, N, HEM](
each min=0,
each max=1)
"temporary array for glass transmittance, front and back reflectance for interior irradiation";
algorithm
traRef :=
Buildings.HeatTransfer.Windows.Functions.glassTRExteriorIrradiationNoShading(
N,
HEM,
layer)
"property for exterior irradiation";
traRefIntIrr :=
Buildings.HeatTransfer.Windows.Functions.glassTRInteriorIrradiationNoShading(
N,
HEM,
layer)
"property for interior irradiation";
// Copy the property for interior irradiation to glass property
for k
in TRA:Rb
loop
for i
in 1:N - 1
loop
for j
in i + 1:N
loop
for iD
in 1:HEM
loop
traRef[k, N + 1 - i, N + 1 - j, iD] := traRefIntIrr[k, N + 1 - i, N
+ 1 - j, iD];
end for;
end for;
end for;
end for;
end getGlassTR;
Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading
Information
This function computes angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading.
Pane 1 is facing outside and pane N is facing the room.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).
Inputs
| Type | Name | Default | Description |
|---|
| Real | absExtIrrNoSha[N, HEM] | | Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading |
| Real | traRef[3, N, N, HEM] | | Transmittance and reflectance with exterior irradiation and no shading |
| Real | traRefShaDev[2, 2] | | Transmittance and reflectance of shading device |
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
Outputs
| Type | Name | Description |
|---|
| Real | absExtIrrExtSha[N, HEM] | Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading |
Modelica definition
function glassAbsExteriorIrradiationExteriorShading
"Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading"
input Real absExtIrrNoSha[N, HEM](
each min=0,
each max=1)
"Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading";
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
output Real absExtIrrExtSha[N, HEM](
each min=0,
each max=1)
"Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading";
protected
Real c
"Intermediate variable";
algorithm
for iD
in 1:HEM
loop
c := traExtShaDev*(1 + traRef[Ra, 1, N, iD]*refExtShaDev/(1 - traRef[Ra, 1,
N, HEM]*refExtShaDev));
for i
in 1:N
loop
absExtIrrExtSha[i, iD] := c*absExtIrrNoSha[i, iD];
end for;
end for;
end glassAbsExteriorIrradiationExteriorShading;
Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading
Information
This function computes angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading.
Pane 1 is facing the outside and pane N is facing the room.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).
Inputs
| Type | Name | Default | Description |
|---|
| Real | absExtIrrNoSha[N, HEM] | | Absorptance for exterior irradiation without shading |
| Real | traRef[3, N, N, HEM] | | Transmittance and reflectance with exterior irradiation and no shading |
| Real | traRefShaDev[2, 2] | | Transmittance and reflectance of shading device |
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
Outputs
| Type | Name | Description |
|---|
| Real | absExtIrrNoShaIntSha[N, HEM] | Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading |
Modelica definition
function glassAbsExteriorIrradiationInteriorShading
"Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading"
input Real absExtIrrNoSha[N, HEM](
each min=0,
each max=1)
"Absorptance for exterior irradiation without shading";
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
output Real absExtIrrNoShaIntSha[N, HEM](
each min=0,
each max=1)
"Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading";
protected
Real fac;
Real absFro
"Front (outside-facing) absorptance";
Real absBac
"Back (room-facing) absorptance";
Integer i
"Index of glass pane";
algorithm
for iD
in 1:HEM
loop
i := 1;
fac := traRef[TRA, 1, N, iD]*refIntShaDev/(1 - traRef[Rb, N, 1, HEM]*
refIntShaDev)
"Equation (A.4.90)";
absBac := 1 - traRef[TRA, i, i, iD] - traRef[Rb, i, i, iD]
"Equation (A.4.81b)";
if N >= 2
then
absExtIrrNoShaIntSha[i, iD] := absExtIrrNoSha[i, iD] + fac*traRef[TRA, N,
i + 1, HEM]*absBac
"Equation (A.4.90)";
for i
in 2:N - 1
loop
fac := traRef[TRA, 1, N, iD]*refIntShaDev/(1 - traRef[Rb, N, 1, HEM]*
refIntShaDev)
"Equation (A.4.90)";
absFro := 1 - traRef[TRA, i, i, iD] - traRef[Ra, i, i, iD]
"Equaiton (A.4.81a)";
absBac := 1 - traRef[TRA, i, i, iD] - traRef[Rb, i, i, iD]
"Equation (A.4.81b)";
absExtIrrNoShaIntSha[i, iD] := absExtIrrNoSha[i, iD] + fac*(traRef[TRA,
N, i, HEM]*traRef[Rb, i - 1, 1, HEM]*absFro + traRef[TRA, N, i + 1,
HEM]*absBac)
"Equation (A.4.90)";
end for;
i := N;
fac := traRef[TRA, 1, N, iD]*refIntShaDev/(1 - traRef[Rb, N, 1, HEM]*
refIntShaDev)
"Equation (A.4.90)";
absFro := 1 - traRef[TRA, i, i, iD] - traRef[Ra, i, i, iD]
"Equaiton (A.4.81a)";
absBac := 1 - traRef[TRA, i, i, iD] - traRef[Rb, i, i, iD]
"Equation (A.4.81b)";
absExtIrrNoShaIntSha[i, iD] := absExtIrrNoSha[i, iD] + fac*(traRef[TRA, N,
i, HEM]*traRef[Rb, i - 1, 1, HEM]*absFro + absBac)
"Equation (A.4.90)";
else
absExtIrrNoShaIntSha[i, iD] := absExtIrrNoSha[i, iD] + fac*absBac
"Equation (A.4.90)";
end if;
end for;
end glassAbsExteriorIrradiationInteriorShading;
Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading
Information
This function computes specular and hemispherical absorptance of each glass pane for exterior irradiation without shading.
It counts the transmittance and reflectance among different panes.
Pane 1 is facing the outside and pane N is facing the room.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowRadiation (Partial function for window radiation property).
Inputs
| Type | Name | Default | Description |
|---|
| Real | traRef[3, N, N, HEM] | | Transmittance and reflectance with exterior irradiation and no shading |
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
Outputs
| Type | Name | Description |
|---|
| Real | abs[N, HEM] | Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading.
Indices: abs[1 to N : ] -> pane 1 to N;
abs[ : 1 to HEM] -> angular (1:HEM-1) and hemispherical (HEM) |
Modelica definition
function glassAbsExteriorIrradiationNoShading
"Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowRadiation;
output Real[N, HEM] abs(
each min=0,
each max=1)
"Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading.
Indices: abs[1 to N : ] -> pane 1 to N;
abs[ : 1 to HEM] -> angular (1:HEM-1) and hemispherical (HEM)";
protected
Real af
"Front (outside-facing side) absorptance of a pane";
Real ab
"Back (room-facing side) absorptance of a pane";
Real deno1
"Denominantor";
Real deno2
"Denominantor";
Integer j;
constant Real SMALL=Modelica.Constants.small
"Small value";
algorithm
if N == 1
then
j := 1;
for iD
in 1:HEM
loop
abs[j, iD] := 1 - traRef[TRA, j, j, iD] - traRef[Ra, j, j, iD]
"Equation (A.4.79)";
end for;
else
for iD
in 1:HEM
loop
j := 1;
af := 1 - traRef[TRA, j, j, iD] - traRef[Ra, j, j, iD]
"Equation (A.4.81a)";
ab := 1 - traRef[TRA, j, j, iD] - traRef[Rb, j, j, iD]
"Equation (A.4.81b)";
deno2 := 1 - traRef[Rb, j, 1, iD]*traRef[Ra, j + 1, N, iD];
if deno2 < SMALL
then
abs[j, iD] := 0;
else
abs[j, iD] := af + ab*traRef[TRA, 1, j, iD]*traRef[Ra, j + 1, N, iD]/
deno2
"Equation (A.4.82) and (A.4.83b)";
end if;
for j
in 2:N - 1
loop
af := 1 - traRef[TRA, j, j, iD] - traRef[Ra, j, j, iD]
"Equation (A.4.81a)";
ab := 1 - traRef[TRA, j, j, iD] - traRef[Rb, j, j, iD]
"Equation (A.4.81b)";
deno1 := 1 - traRef[Ra, j, N, iD]*traRef[Rb, j - 1, 1, iD];
deno2 := 1 - traRef[Rb, j, 1, iD]*traRef[Ra, j + 1, N, iD];
if deno1 < SMALL
or deno2 < SMALL
then
abs[j, iD] := 0;
else
abs[j, iD] := af*traRef[TRA, 1, j - 1, iD]/deno1 + ab*traRef[TRA, 1,
j, iD]*traRef[Ra, j + 1, N, iD]/deno2
"Equation (A.4.83b)";
end if;
end for;
j := N;
af := 1 - traRef[TRA, j, j, iD] - traRef[Ra, j, j, iD]
"Equation (A.4.81a)";
deno1 := 1 - traRef[Ra, j, N, iD]*traRef[Rb, j - 1, 1, iD];
if deno1 < SMALL
then
abs[j, iD] := 0;
else
abs[j, iD] := af*traRef[TRA, 1, j - 1, iD]/deno1;
end if;
end for;
end if;
end glassAbsExteriorIrradiationNoShading;
Hemispherical absorptance of each glass pane for interior irradiation with exterior shading
Information
This function computes the hemispherical absorptance of each glass pane for interior irradiation with exterior shading.
Pane 1 is facing the outside and pane N is facing the room.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).
Inputs
| Type | Name | Default | Description |
|---|
| Real | absIntIrrNoSha[N] | | Absorptance for interior irradiation without shading |
| Real | traRef[3, N, N, HEM] | | Transmittance and reflectance with exterior irradiation and no shading |
| Real | traRefShaDev[2, 2] | | Transmittance and reflectance of shading device |
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
Outputs
| Type | Name | Description |
|---|
| Real | absIntIrrExtSha[N] | Hemispherical absorptance of each glass pane for interior irradiation with exterior shading |
Modelica definition
function glassAbsInteriorIrradiationExteriorShading
"Hemispherical absorptance of each glass pane for interior irradiation with exterior shading"
input Real absIntIrrNoSha[N]
"Absorptance for interior irradiation without shading";
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
output Real absIntIrrExtSha[N](
each min=0,
each max=1)
"Hemispherical absorptance of each glass pane for interior irradiation with exterior shading";
protected
Real fac;
Real absFro
"Front absorptance";
Real absBac
"Back absorptance";
Integer i
"Pane index";
algorithm
fac := traRef[TRA, N, 1, HEM]*refExtShaDev/(1 - traRef[Ra, 1, N, HEM]*
refExtShaDev);
i := 1;
absFro := 1 - traRef[TRA, i, i, HEM] - traRef[Ra, i, i, HEM]
"Equaiton (A.4.81a)";
absBac := 1 - traRef[TRA, i, i, HEM] - traRef[Rb, i, i, HEM]
"Equation (A.4.81b)";
if N >= 2
then
absIntIrrExtSha[i] := absIntIrrNoSha[i] + fac*absFro + fac*traRef[TRA, 1, i,
HEM]*traRef[Ra, i + 1, N, HEM]*absBac
"Equation (A.4.94)";
for i
in 2:N - 1
loop
absFro := 1 - traRef[TRA, i, i, HEM] - traRef[Ra, i, i, HEM]
"Equaiton (A.4.81a)";
absBac := 1 - traRef[TRA, i, i, HEM] - traRef[Rb, i, i, HEM]
"Equation (A.4.81b)";
absIntIrrExtSha[i] := absIntIrrNoSha[i] + fac*traRef[TRA, 1, i - 1, HEM]*
absFro + fac*traRef[TRA, 1, i, HEM]*traRef[Ra, i + 1, N, HEM]*absBac
"Equation (A.4.94)";
end for;
i := N;
absFro := 1 - traRef[TRA, i, i, HEM] - traRef[Ra, i, i, HEM]
"Equaiton (A.4.81a)";
absIntIrrExtSha[i] := absIntIrrNoSha[i] + fac*traRef[TRA, 1, i - 1, HEM]*
absFro
"Equation (A.4.94)";
else
absIntIrrExtSha[i] := absIntIrrNoSha[i] + fac*absFro
"Equation (A.4.94)";
end if;
end glassAbsInteriorIrradiationExteriorShading;
Hemispherical absorptance of each glass pane for interior irradiation with interior shading
Information
This function computes the hemispherical absorbtance of each glass pane for interior irradiation with interior shading.
Pane 1 is facing the outside and pane N is facing the room.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).
Inputs
| Type | Name | Default | Description |
|---|
| Real | absIntIrrNoSha[N] | | Hemispherical absorptance wfor interior irradiation without interior shading |
| Real | traRef[3, N, N, HEM] | | Transmittance and reflectance with exterior irradiation and no shading |
| Real | traRefShaDev[2, 2] | | Transmittance and reflectance of shading device |
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
Outputs
| Type | Name | Description |
|---|
| Real | absIntIrrIntSha[N] | Hemispherical absorbtance of each glass pane for interior irradiation with interior shading |
Modelica definition
function glassAbsInteriorIrradiationInteriorShading
"Hemispherical absorptance of each glass pane for interior irradiation with interior shading"
input Real absIntIrrNoSha[N](
each min=0,
each max=1)
"Hemispherical absorptance wfor interior irradiation without interior shading";
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
output Real absIntIrrIntSha[N](
each min=0,
each max=1)
"Hemispherical absorbtance of each glass pane for interior irradiation with interior shading";
protected
constant Real rRho=traRef[Rb, N, 1, HEM]*refIntShaDev
"Part of Equation (4.99)";
constant Real c=traIntShaDev*(1 + rRho/(1 - rRho))
"Equation (4.99)";
algorithm
for i
in 1:N
loop
absIntIrrIntSha[i] := c*absIntIrrNoSha[i]
"Equation (A4.100a)";
end for;
end glassAbsInteriorIrradiationInteriorShading;
Hemispherical absorptance of each glass pane for interior irradiation without shading
Information
This function computes the hemispherical absorptance of each glass pane for interior irradiation without no shading.
The angular irradiation is not considered since the interior irradiation (from the room) is assumed to be diffusive.
It is a reverse of the function
Buildings.HeatTransfer.Windows.Functions.glassAbsInterirorIrradiationNoShading.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowRadiation (Partial function for window radiation property).
Inputs
| Type | Name | Default | Description |
|---|
| Real | traRef[3, N, N, HEM] | | Transmittance and reflectance with exterior irradiation and no shading |
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
Outputs
| Type | Name | Description |
|---|
| Real | absIntIrrNoSha[N] | Hemispherical absorptance of each glass layer for interior irradiation without shading |
Modelica definition
function glassAbsInteriorIrradiationNoShading
"Hemispherical absorptance of each glass pane for interior irradiation without shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowRadiation;
output Real[N] absIntIrrNoSha(
each min=0,
each max=1)
"Hemispherical absorptance of each glass layer for interior irradiation without shading";
protected
Real dTraRef[3, N, N, HEM](
each min=0,
each max=1)
"Dummy transmittance and reflectance with exterior irradiation without shading";
Real dAbs[N, HEM](
each min=0,
each max=1)
"Dummy absorptance with exterior irradiation and no shading";
algorithm
// Reverse the data srtucture for exterior irradiation and no shading
for i
in 1:N
loop
for j
in 1:N
loop
for iD
in 1:HEM
loop
dTraRef[TRA, i, j, iD] := traRef[TRA, N + 1 - i, N + 1 - j, iD];
dTraRef[Ra, i, j, iD] := traRef[Rb, N + 1 - i, N + 1 - j, iD];
dTraRef[Rb, i, j, iD] := traRef[Ra, N + 1 - i, N + 1 - j, iD];
end for;
end for;
end for;
dAbs :=
Buildings.HeatTransfer.Windows.Functions.glassAbsExteriorIrradiationNoShading(
dTraRef,
N,
HEM)
"Dummmy absorptance with exterior irradiation";
// Only output hemispherical absorptance. Need to change order for interior irradiation.
for i
in 1:N
loop
absIntIrrNoSha[i] := dAbs[N + 1 - i, HEM];
end for;
end glassAbsInteriorIrradiationNoShading;
Compute angular variation and hemispherical integration of the transmittance and reflectance for each glass pane without shading
Information
This function computes the angular variation and the hemispherical integration of the transmittance and reflectance for each glass pane.
There are two schemes for the calculation. One is for coated glass and the other is for uncoated glass.
The function checks the difference between front and back reflectances.
If the difference is less than the tolerance (0.005), it uses the formula for uncoated glass.
Otherwise, the formula for coated glass will be used.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation (Partial function for glass radiation property).
Inputs
| Type | Name | Default | Description |
|---|
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
| Real | glass[3, N] | | Propertry of each glass pane |
| Real | xGla[N] | | Thickness of each glass pane |
| Angle | psi[HEM - 1] | | Incident angles [rad] |
Outputs
| Type | Name | Description |
|---|
| Real | layer[3, N, HEM] | Transmittance, front and back reflectance |
Modelica definition
function glassProperty
"Compute angular variation and hemispherical integration of the transmittance and reflectance for each glass pane without shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation;
input Real glass[3, N]
"Propertry of each glass pane";
input Real xGla[N]
"Thickness of each glass pane";
input Modelica.SIunits.Angle psi[HEM - 1]
"Incident angles";
output Real layer[3, N, HEM]
"Transmittance, front and back reflectance";
protected
parameter Real tol=0.005
"Tolerance for difference between front and back reflectance to decide a glass is uncoated or coated";
Real oneLay[3, HEM]
"Temporary storage for glass property of one pane";
Real oneGla[3];
algorithm
// Compute specular value for angle 0 to 90 degree (psi[1] to psi[N]) and panes from 1 to N
for i
in 1:N
loop
// Copy data to temporary place
for j
in 1:3
loop
oneGla[j] := glass[j, i];
end for;
//uncoated galss
if (
abs(glass[Ra, i] - glass[Rb, i]) < tol)
then
oneLay :=
Buildings.HeatTransfer.Windows.Functions.glassPropertyUncoated(
HEM,
oneGla,
xGla[i],
psi);
else
//coated glass
oneLay :=
Buildings.HeatTransfer.Windows.Functions.glassPropertyCoated(
HEM,
oneGla,
psi);
end if;
for j
in 1:3
loop
for k
in 1:HEM
loop
layer[j, i, k] := oneLay[j, k];
end for;
end for;
end for;
end glassProperty;
Compute angular variation and hemispherical integration of the transmittance and reflectance for a coated glass pane without shading
Information
This function computes the angular variation and the hemispherical integration of the transmittance and reflectance for one coated glass pane.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialSingleGlassRadiation (Partial function for single glass radiation property).
Inputs
| Type | Name | Default | Description |
|---|
| Integer | HEM | | Index of hemispherical integration |
| Real | glass[3] | | Propertry of one glass pane |
| Angle | psi[HEM - 1] | | Incident angles [rad] |
Outputs
| Type | Name | Description |
|---|
| Real | layer[3, HEM] | Transmittance, front and back reflectance |
Modelica definition
function glassPropertyCoated
"Compute angular variation and hemispherical integration of the transmittance and reflectance for a coated glass pane without shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialSingleGlassRadiation;
input Real glass[3]
"Propertry of one glass pane";
input Modelica.SIunits.Angle psi[HEM - 1]
"Incident angles";
output Real layer[3, HEM]
"Transmittance, front and back reflectance";
protected
Integer NDIR=HEM - 1
"Number of incident angles";
Real psi_c
"cos(psi), psi is incident angle";
Real psi_cs
"cos(psi)*sin(psi)";
Real angT
"Angular variation of transmittance";
Real angR
"Angular variation of reflectance";
Real f[3, NDIR]
"Temporary variables for integration in hemispherical transmittance and reflectance";
constant Real deltaX=0.5*Modelica.Constants.pi/(NDIR - 1);
constant Real a[4, 5]={{-0.0015,3.355,-3.840,1.460,0.0288},{0.999,-0.563,
2.043,-2.532,1.054},{-0.002,2.813,-2.341,-0.05725,0.599},{0.997,-1.868,
6.513,-7.862,3.225}}
"Coeffcients in Table A.2";
Integer id1
"Index of coefficients for transmittance";
Integer id2
"Index of coefficients for reflectance";
algorithm
// Compute specular value for angle 0 to 90 degree (psi[1] to psi[N])
for k
in TRA:Rb
loop
layer[k, 1] := glass[k]
"Copy the data at 0 degree (normal incidence)";
end for;
for j
in 2:NDIR - 1
loop
psi_c :=
Modelica.Math.cos(psi[j]);
if layer[TRA, 1] > 0.645
then
id1 := 1;
id2 := 2;
else
id1 := 3;
id2 := 4;
end if;
angT := a[id1, 1] + psi_c*(a[id1, 2] + psi_c*(a[id1, 3] + psi_c*(a[id1, 4]
+ psi_c*a[id1, 5])))
"Equation (A.4.68a)";
angR := a[id2, 1] + psi_c*(a[id2, 2] + psi_c*(a[id2, 3] + psi_c*(a[id2, 4]
+ psi_c*a[id2, 5]))) - angT
"Equation (A.4.68b)";
layer[TRA, j] := layer[TRA, 1]*angT
"Equation (A4.69a)";
layer[Ra, j] := layer[Ra, 1]*(1 - angR) + angR
"Equation (A4.69b)";
layer[Rb, j] := layer[Rb, 1]*(1 - angR) + angR
"Equation (A4.69b)";
end for;
layer[TRA, NDIR] := 0;
layer[Ra, NDIR] := 1.0;
layer[Rb, NDIR] := 1.0;
// Computer hemispherical value: HEM.
for j
in 1:NDIR
loop
psi_cs :=
Modelica.Math.cos(psi[j])*
Modelica.Math.sin(psi[j]);
for k
in TRA:Rb
loop
f[k, j] := 2*layer[k, j]*psi_cs;
end for;
end for;
for k
in TRA:Rb
loop
layer[k, HEM] :=
Buildings.Utilities.Math.Functions.trapezoidalIntegration(
NDIR,
f[k, :],
deltaX)
"Equation (A.4.70a) and (A.4.70b)";
end for;
end glassPropertyCoated;
Compute angular variation and hemispherical integration of the transmittance and reflectance for a uncoated glass pane without shading
Information
This function computes the angular variation and the hemispherical integration of the transmittance and reflectance for one uncoated glass pane.
The equations are mainly based on Finlayson et al. (1990) and Fuler et al. (1991) with some modifications.
Implementation
Step 1: Compute the reflectivity at normal incidence
ρ(0) = {β − sqrt[β2 − 4(2 − R(0))R(0)]}
⁄
[2(2−R(0))],
|
(1) |
where
β = T(0)2 − R(0)2 + 2R(0) + 1.
|
(2) |
Step 2: Compute the spectral absorption coefficient α and spectral index of refraction n
α = 4 π κλ ⁄ λ
= - ln[(R(0) − ρ(0)) ⁄ (ρ(0)T(0))] ⁄ d,
|
(3) |
n = (1 + sqrt(ρ(0)) ⁄
(1 − sqrt(ρ(0))).
|
(4) |
Step 3: For each angle of incidence measured in air φ (0 < φ < 90)
| a. Compute the angle of incidence measured in glass φ' |
φ' = asin(sinφ ⁄ n).
|
(5) |
| b. Compute spectral reflectivities at surface |
ρ1(φ)=[(n cosφ − cosφ') ⁄
(n cosφ + cosφ')] 2,
|
(6) |
ρ2(φ)=[(n cosφ' − cosφ) ⁄
(n cosφ' + cosφ)] 2.
|
(7) |
| c. Compute spectral tansmissivities at surface |
τ1(φ)= 1 − ρ1(φ),
|
(8) |
τ2(φ)= 1 − ρ2(φ).
|
(9) |
| d. Compute spectral tansmittance of the glass |
T1(φ)= τ1(φ)2 exp(-α d/cosφ') ⁄
(1 − ρ1(φ)2 exp(-2α d/cosφ')),
|
(10) |
T2(φ)= τ2(φ)2 exp(-α d/cosφ') ⁄
(1 − ρ2(φ)2 exp(-2α d/cosφ')),
|
(11) |
T(φ)= (T1(φ) + T2(φ)) / 2.
|
(12) |
| e. Compute spectral reflectance of the glass |
R1(φ)= ρ1(φ)(1+ T1(φ)exp(-α d/cosφ')),
|
(13) |
R2(φ)= ρ2(φ)(1+ T2(φ)exp(-α d/cosφ')),
|
(14) |
R(φ)= (R1(φ) + R2(φ)) / 2.
|
(15) |
Step 4: T(90)=0, R(90)=1. (16)
Limitations
WINDOW program calculates the angular property for each wave length based on the spectral data.
It uses different Rλ(0) and Tλ(0) for each wave length.
Then it integrates the properties over the wave length to get averaged property of R(0) and T(0).
The current window model in the Buildings library uses averaged R(0) and T(0) directly.
It can generate the same results as WINDOW for a single pane window and multi-pane window with the same glass.
However, the results may be slightly different for multi-pane window with different glasses.
The reason is that different glasses may have different angular properties for the same wave length.
To precisely calculate the angular properties of the entire window system, one has to calculate the property for each wave length and integrate them as WINDOW does.
For more details, see the paper of Nouidui et al. (2012).
References
Finlayson, E. U., D. K. Arasteh, C. Huizenga, M.D. Rubin, M.S. Reily. 1993. WINDOW 4.0: Documentation of Calcualtion Precedures. Technical Report LBL-33943. Lawrence Berkeley National Laboratory.
Fuler, Reto A., Angular dependence of optical properties of homogeneous glasses, ASHRAE Transaction, V.97 Part 2, 1991.
Thierry Stephane Nouidui, Michael Wetter, and Wangda Zuo.
Validation of the window model of the Modelica Buildings library.
Proc. of the 5th SimBuild Conference, Madison, WI, USA, August 2012.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialSingleGlassRadiation (Partial function for single glass radiation property).
Inputs
| Type | Name | Default | Description |
|---|
| Integer | HEM | | Index of hemispherical integration |
| Real | glass[3] | | Propertry of one glass pane |
| Length | x | | Thickness [m] |
| Angle | psi[HEM - 1] | | Incident angles [rad] |
Outputs
| Type | Name | Description |
|---|
| Real | layer[3, HEM] | Transmittance, front and back reflectance |
Modelica definition
function glassPropertyUncoated
"Compute angular variation and hemispherical integration of the transmittance and reflectance for a uncoated glass pane without shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialSingleGlassRadiation;
input Real glass[3]
"Propertry of one glass pane";
input Modelica.SIunits.Length x
"Thickness";
input Modelica.SIunits.Angle psi[HEM - 1]
"Incident angles";
output Real layer[3, HEM]
"Transmittance, front and back reflectance";
protected
Integer NDIR=HEM - 1
"Number of incident angles";
Real psi_c
"cos(psi), psi is incident angle in air";
Real psi1_c
"cos(psi1), psi1 is incident angle in glass";
Real angT
"Angular variation of transmittance";
Real angR
"Angular variation of reflectance";
Real f[3, NDIR]
"Temporary variables for integration in hemispherical transmittance and reflectance";
Real beta
"Temporary coefficient defined in (7.2.1i)";
Real rho0
"Spectral reflectivity at incident angle of 0 degree at the interface";
Real rho
"Spectral reflectivity at the interface";
Real rho1;
Real rho2;
Real tau
"Spectral transmissivity at the interface";
Real tau1;
Real tau2;
Real angT1;
Real angT2;
Real angR1;
Real angR2;
Real tmp;
Real alpha
"Spectral absorption coefficient defined in (7.2.1e)";
Real n
"Ratio of spectral index of refraction of glass to the index of refraction of air";
Real psi1
"The angle od incident angle in glass";
constant Real deltaX=0.5*Modelica.Constants.pi/(NDIR - 1);
algorithm
// Check the data
assert(glass[TRA] >= 0,
"Glass property is not correct with solar transmittance less than 0");
assert(glass[Ra] >= 0,
"Glass property is not correct with solar reflectance less than 0");
assert(glass[TRA] + glass[Ra] <= 1,
"Glass property is not correct since the summation of solar reflectance and transmittance is larger than 1");
// Compute specular value for angle 0 to 90 degree (psi[1] to psi[N])
for k
in TRA:Rb
loop
layer[k, 1] := glass[k]
"Copy the data at 0 degree (normal incidence)";
end for;
beta := glass[TRA]^2 - glass[Ra]^2 + 2*glass[Ra] + 1
"(2)";
tmp := beta^2 - 4*(2 - glass[Ra])*glass[Ra]
"part of (1)";
assert(tmp >= 0,
"Glass property is not correct and not possible to calculate spectral reflectivity at 0 degree for uncoated glass");
rho0 := 0.5*(beta -
sqrt(tmp))/(2 - glass[Ra])
"(1)";
assert(rho0 >= 0,
"Glass property is not correct so that the spectral reflectivity at 0 degree for uncoated glass is less than zero");
tmp := (glass[Ra] - rho0)/(rho0*glass[TRA])
"part of (3)";
assert(tmp > 0,
"Glass property is not correct and not possible to calculate spectral extinction coefficient for uncoated glass");
alpha := -
log(tmp)/x
"(3)";
tmp :=
sqrt(rho0);
assert(tmp <> 1,
"Glass property is not correct and not possible to calculate spectral index of refraction for uncoated glass");
n := (1 + tmp)/(1 - tmp)
"(4)";
for j
in 2:NDIR - 1
loop
psi1 :=
asin(
sin(psi[j])/n)
"(5)";
psi_c :=
cos(psi[j]);
psi1_c :=
cos(psi1);
rho1 := ((n*psi_c - psi1_c)/(n*psi_c + psi1_c))^2
"(6)";
rho2 := ((n*psi1_c - psi_c)/(n*psi1_c + psi_c))^2
"(7)";
tau1 := 1 - rho1
"(8)";
tau2 := 1 - rho2
"(9)";
tmp :=
exp(-alpha*x/psi1_c);
angT1 := tau1^2*tmp/(1 - rho1^2*tmp^2)
"(10)";
angR1 := rho1*(1 + angT1*tmp)
"(13)";
angT2 := tau2^2*tmp/(1 - rho2^2*tmp^2)
"(11)";
angR2 := rho2*(1 + angT2*tmp)
"(14)";
layer[TRA, j] := 0.5*(angT1 + angT2)
"Tansmittance in (12)";
layer[Ra, j] := 0.5*(angR1 + angR2)
"Front reflectance (15)";
layer[Rb, j] := layer[Ra, j]
"Back reflectance in (15)";
end for;
// When incident angle is equal to 90 degree
layer[TRA, NDIR] := 0
"(16)";
layer[Ra, NDIR] := 1.0
"(16)";
layer[Rb, NDIR] := 1.0
"(16)";
// Computer hemispherical value: HEM.
for j
in 1:NDIR
loop
for k
in TRA:Rb
loop
f[k, j] := 2*layer[k, j]*
Modelica.Math.cos(psi[j])*
Modelica.Math.sin(psi[
j]);
end for;
end for;
for k
in TRA:Rb
loop
layer[k, HEM] :=
Buildings.Utilities.Math.Functions.trapezoidalIntegration(
NDIR,
f[k, :],
deltaX)
"Equation (A.4.70a) and (A.4.70b) in M. Wetter 's Thesis or (7.3) in Finlayson 1993.";
end for;
end glassPropertyUncoated;
Transmittance and reflectance of glass panes for exterior irradiation without shading
Information
This function computes the angular variation of the transmittance and reflectance of each glass pane for exteior irradiation without shading.
It accounts for the transmittance and reflectance among different panes.
Pane 1 is facing outside and pane N is facing the room.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation (Partial function for glass radiation property).
Inputs
| Type | Name | Default | Description |
|---|
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
| Real | layer[3, N, HEM] | | Angular data of glass pane |
Outputs
| Type | Name | Description |
|---|
| Real | traRef[3, N, N, HEM] | Transmittance and reflectance of each glass pane for exterior irradiation without shading |
Modelica definition
function glassTRExteriorIrradiationNoShading
"Transmittance and reflectance of glass panes for exterior irradiation without shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation;
input Real layer[3, N, HEM]
"Angular data of glass pane";
output Real traRef[3, N, N, HEM](
each min=0,
each max=1)
"Transmittance and reflectance of each glass pane for exterior irradiation without shading";
protected
Real aij
"Temporary variable";
constant Real SMALL=Modelica.Constants.small
"Small value";
algorithm
// Property for single pane of glass or the first pane of multiple panes glass
for iD
in 1:HEM
loop
for k
in TRA:Rb
loop
traRef[k, 1, 1, iD] := layer[k, 1, iD]
"Equation (A.4.71)";
end for;
end for;
// Property for multiple panes glass
if N > 1
then
for iD
in 1:HEM
loop
for i
in 1:N - 1
loop
for j
in i + 1:N
loop
for k
in TRA:Rb
loop
traRef[k, j, j, iD] := layer[k, j, iD];
end for;
aij := 1 - traRef[Ra, j, j, iD]*traRef[Rb, j - 1, i, iD]
"Equation (A.4.77)";
assert(aij > -SMALL,
"Glass transmittance and reflectance data was not correct.\n");
if aij < SMALL
then
traRef[TRA, i, j, iD] := 0;
traRef[Ra, i, j, iD] := 1;
traRef[Rb, j, i, iD] := 1;
else
aij := 1/aij;
traRef[TRA, i, j, iD] := aij*traRef[TRA, i, j - 1, iD]*traRef[TRA,
j, j, iD]
"Equation (A.4.78a)";
traRef[Ra, i, j, iD] := traRef[Ra, i, j - 1, iD] + aij*traRef[TRA,
i, j - 1, iD]*traRef[TRA, i, j - 1, iD]*traRef[Ra, j, j, iD]
"Equation (A.4.78b)";
traRef[Rb, j, i, iD] := traRef[Rb, j, j, iD] + aij*traRef[TRA, j, j,
iD]*traRef[TRA, j, j, iD]*traRef[Rb, j - 1, i, iD]
"Equation (A.4.78c)";
end if;
end for;
end for;
end for;
end if;
end glassTRExteriorIrradiationNoShading;
Transmittance and reflectance of each glass pane for interior irradiation without shading
Information
This function computes the angular variation of the transmittance and reflectance of each glass pane for interior irradiation without shading.
It accounts for the transmittance and reflectance among different panes.
Pane 1 is facing outside and pane N is facing the room.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation (Partial function for glass radiation property).
Inputs
| Type | Name | Default | Description |
|---|
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
| Real | layer[3, N, HEM] | | Angular data of glass pane |
Outputs
| Type | Name | Description |
|---|
| Real | traRef[3, N, N, HEM] | Glass transmittance, front and back reflectance |
Modelica definition
function glassTRInteriorIrradiationNoShading
"Transmittance and reflectance of each glass pane for interior irradiation without shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation;
input Real layer[3, N, HEM]
"Angular data of glass pane";
output Real traRef[3, N, N, HEM](
each min=0,
each max=1)
"Glass transmittance, front and back reflectance";
protected
Real dLayer[3, N, HEM]
"Dummy glass property with Pane 1 facing inside and Pane N facing outside";
Real dTraRef[3, N, N, HEM]
"Dummy transmittance and reflectance for exterior irradiation";
algorithm
// Copy the dummy glass property
for iD
in 1:HEM
loop
for j
in 1:N
loop
dLayer[TRA, j, iD] := layer[TRA, N + 1 - j, iD];
dLayer[Ra, j, iD] := layer[Rb, N + 1 - j, iD]
"swap the front and back reflectance";
dLayer[Rb, j, iD] := layer[Ra, N + 1 - j, iD]
"swap the front and back reflectance";
end for;
end for;
// Calculate transmittance and reflectance of dummy glass for exterior irradiation without shading
dTraRef :=
Buildings.HeatTransfer.Windows.Functions.glassTRExteriorIrradiationNoShading(
N,
HEM,
dLayer);
// Convert the dummy data to real glass
for iD
in 1:HEM
loop
for i
in 1:N - 1
loop
for j
in i + 1:N
loop
traRef[TRA, N + 1 - i, N + 1 - j, iD] := dTraRef[TRA, i, j, iD];
traRef[Ra, N + 1 - i, N + 1 - j, iD] := dTraRef[Rb, i, j, iD]
"swap the front and back reflectance";
traRef[Rb, N + 1 - i, N + 1 - j, iD] := dTraRef[Ra, i, j, iD]
"swap the front and back reflectance";
end for;
end for;
end for;
end glassTRInteriorIrradiationNoShading;
Angular and hemispherical transmittance of a window system (glass and shading device) for exterior irradiation with interior shading
Information
This function computes the angular and hemispherical transmittance of a window system (glass and shading device) for exterior irradiation with interior shading.
Pane 1 is facing outside and pane N is facing the room.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).
Inputs
| Type | Name | Default | Description |
|---|
| Real | traRef[3, N, N, HEM] | | Transmittance and reflectance with exterior irradiation and no shading |
| Real | traRefShaDev[2, 2] | | Transmittance and reflectance of shading device |
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
Outputs
| Type | Name | Description |
|---|
| Real | traExtIrrIntSha[HEM] | Angular and hemispherical transmittance of a window system (glass and shading device) forh exterior irradiation with interior shading |
Modelica definition
function winTExteriorIrradiationInteriorShading
"Angular and hemispherical transmittance of a window system (glass and shading device) for exterior irradiation with interior shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
output Real traExtIrrIntSha[HEM](
each min=0,
each max=1)
"Angular and hemispherical transmittance of a window system (glass and shading device) forh exterior irradiation with interior shading";
algorithm
for iD
in 1:HEM
loop
traExtIrrIntSha[iD] := traRef[TRA, 1, N, iD]*traIntShaDev/(1 - refIntShaDev
*traRef[Rb, N, 1, HEM])
"Equation (A.4.92)";
end for;
end winTExteriorIrradiationInteriorShading;
Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading
Information
This function computes the angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading.
Pane 1 is facing outside and pane N is facing the room.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).
Inputs
| Type | Name | Default | Description |
|---|
| Real | traRef[3, N, N, HEM] | | Transmittance and reflectance with exterior irradiation and no shading |
| Real | traRefShaDev[2, 2] | | Transmittance and reflectance of shading device |
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
Outputs
| Type | Name | Description |
|---|
| Real | traExtIrrExtSha[HEM] | Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading |
Modelica definition
function winTExteriorIrradiatrionExteriorShading
"Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
output Real traExtIrrExtSha[HEM](
each min=0,
each max=1)
"Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading";
protected
Real c;
algorithm
for iD
in 1:HEM
loop
c := traExtShaDev*(1 + traRef[Ra, 1, N, iD]*refExtShaDev/(1 - traRef[Ra, 1,
N, HEM]*refExtShaDev))
"Equation (A.4.88a)";
traExtIrrExtSha[iD] := c*traRef[TRA, 1, N, iD]
"Equation (A.4.88c)";
end for;
end winTExteriorIrradiatrionExteriorShading;
Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading
Information
This function computes hemispherical transmittance and back reflectance of a window for interior irradiation with exterior shading.
Pane 1 is facing the outside and pane N is facing the room.
The variables are
traRefIntIrrExtSha[1]: Transmittance;
traRefIntIrrExtSha[2]: Back reflectance;
traRefIntIrrExtSha[3]: Dummy value
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).
Inputs
| Type | Name | Default | Description |
|---|
| Real | traRef[3, N, N, HEM] | | Transmittance and reflectance with exterior irradiation and no shading |
| Real | traRefShaDev[2, 2] | | Transmittance and reflectance of shading device |
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
Outputs
| Type | Name | Description |
|---|
| Real | traRefIntIrrExtSha[3] | Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading |
Modelica definition
function winTRInteriorIrradiationExteriorShading
"Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
output Real traRefIntIrrExtSha[3](
each min=0,
each max=1)
"Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading";
algorithm
traRefIntIrrExtSha[TRA] := traRef[TRA, N, 1, HEM]*traExtShaDev/(1 -
refExtShaDev*traRef[Ra, 1, N, HEM])
"Equation (A.4.95)";
traRefIntIrrExtSha[Rb] := traRef[Rb, N, 1, HEM] + traRef[TRA, N, 1, HEM]*
refExtShaDev*traRef[1, 1, N, HEM]/(1 - traRef[Ra, 1, N, HEM]*refExtShaDev)
"Equation (A.4.97)";
traRefIntIrrExtSha[Ra] := 0
"Dummy value";
end winTRInteriorIrradiationExteriorShading;
Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading
Information
This function computes the hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading.
Pane 1 is facing the outside and pane N is facing the room.
Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).
Inputs
| Type | Name | Default | Description |
|---|
| Real | traRef[3, N, N, HEM] | | Transmittance and reflectance with exterior irradiation and no shading |
| Real | traRefShaDev[2, 2] | | Transmittance and reflectance of shading device |
| Integer | N | | Number of glass layers |
| Integer | HEM | | Index of hemispherical integration |
Outputs
| Type | Name | Description |
|---|
| Real | traRefIntIrrIntSha[3] | Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading |
Modelica definition
function winTRInteriorIrradiationInteriorShading
"Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading"
extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
output Real traRefIntIrrIntSha[3](
each min=0,
each max=1)
"Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading";
protected
constant Real rRho=traRef[Rb, N, 1, HEM]*refIntShaDev
"Part of Equation (A.4.99)";
constant Real rTau=traRef[Rb, N, 1, HEM]*traIntShaDev
"Part of Equation (A.4.105)";
constant Real c=traIntShaDev*(1 + rRho/(1 - rRho))
"Equation (A.4.99)";
algorithm
traRefIntIrrIntSha[TRA] := c*traRef[TRA, N, 1, HEM]
"Equation (A.4.100b)";
traRefIntIrrIntSha[Rb] := refIntShaDev + c*rTau
"Equation (A.4.105)";
traRefIntIrrIntSha[Ra] := 0
"Dummy value";
end winTRInteriorIrradiationInteriorShading;
Automatically generated Thu Jun 19 10:57:51 2014.
devAbsExteriorIrradiationInteriorShading
BaseClasses