Functions used in window radiation model
This package contains functions that are used to compute heat transfer in the window model.
Extends from Modelica.Icons.Package (Icon for standard packages).
Name | Description |
---|---|
devAbsExteriorIrradiationInteriorShading | Angular and hemispherical absorptance of a shading device for exterior irradiation with interior shading |
devAbsInteriorIrradiationInteriorShading | Hemiperical absorptance of a shading device for interior irradiation with interior shading |
getAngle | Generate incident angles |
getGlassTR | Transmittance and reflectance of glass |
glassAbsExteriorIrradiationExteriorShading | Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading |
glassAbsExteriorIrradiationInteriorShading | Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading |
glassAbsExteriorIrradiationNoShading | Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading |
glassAbsInteriorIrradiationExteriorShading | Hemispherical absorptance of each glass pane for interior irradiation with exterior shading |
glassAbsInteriorIrradiationInteriorShading | Hemispherical absorptance of each glass pane for interior irradiation with interior shading |
glassAbsInteriorIrradiationNoShading | Hemispherical absorptance of each glass pane for interior irradiation without shading |
glassProperty | Compute angular variation and hemispherical integration of the transmittance and reflectance for each glass pane without shading |
glassPropertyCoated | Compute angular variation and hemispherical integration of the transmittance and reflectance for a coated glass pane without shading |
glassPropertyUncoated | Compute angular variation and hemispherical integration of the transmittance and reflectance for a uncoated glass pane without shading |
glassTRExteriorIrradiationNoShading | Transmittance and reflectance of glass panes for exterior irradiation without shading |
glassTRInteriorIrradiationNoShading | Transmittance and reflectance of each glass pane for interior irradiation without shading |
winTExteriorIrradiationInteriorShading | Angular and hemispherical transmittance of a window system (glass and shading device) for exterior irradiation with interior shading |
winTExteriorIrradiatrionExteriorShading | Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading |
winTRInteriorIrradiationExteriorShading | Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading |
winTRInteriorIrradiationInteriorShading | Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading |
BaseClasses | Package with base classes for Buildings.HeatTransfer.Windows.Functions |
Angular and hemispherical absorptance of a shading device for exterior irradiation with interior shading
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).
Type | Name | Default | Description |
---|---|---|---|
Real | traRef[3, N, N, HEM, NSta] | 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 | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration |
Type | Name | Description |
---|---|---|
Real | absExtIrrIntShaDev[HEM, NSta] | Absorptance of a shading device for exterior irradiation with interior shading |
Hemiperical absorptance of a shading device for interior irradiation with interior shading
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).
Type | Name | Default | Description |
---|---|---|---|
Real | traRef[3, N, N, HEM, NSta] | 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 | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration |
Type | Name | Description |
---|---|---|
Real | absIntIrrIntShaDev[NSta] | Hemiperical absorbtance of a shading device for interior irradiation with interior shading |
Generate incident angles
This function computes discrete incident angles for the window radiation calculation. The range is from 0 to 90 degree.
Type | Name | Default | Description |
---|---|---|---|
Integer | NDIR | Number of incident angles |
Type | Name | Description |
---|---|---|
Angle | psi[NDIR] | Array of incident angles [rad] |
Transmittance and reflectance of glass
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).
Type | Name | Default | Description |
---|---|---|---|
Integer | N | Number of glass layers | |
Integer | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration | |
Real | layer[3, N, HEM, NSta] | Property of glass pane |
Type | Name | Description |
---|---|---|
Real | traRef[3, N, N, HEM, NSta] | Glass transmittance, front and back reflectance |
Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading
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).
Type | Name | Default | Description |
---|---|---|---|
Real | absExtIrrNoSha[N, HEM, NSta] | Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading | |
Real | traRef[3, N, N, HEM, NSta] | 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 | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration |
Type | Name | Description |
---|---|---|
Real | absExtIrrExtSha[N, HEM, NSta] | Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading |
Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading
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).
Type | Name | Default | Description |
---|---|---|---|
Real | absExtIrrNoSha[N, HEM, NSta] | Absorptance for exterior irradiation without shading | |
Real | traRef[3, N, N, HEM, NSta] | 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 | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration |
Type | Name | Description |
---|---|---|
Real | absExtIrrNoShaIntSha[N, HEM, NSta] | Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading |
Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading
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).
Type | Name | Default | Description |
---|---|---|---|
Real | traRef[3, N, N, HEM, NSta] | Transmittance and reflectance with exterior irradiation and no shading | |
Integer | N | Number of glass layers | |
Integer | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration |
Type | Name | Description |
---|---|---|
Real | abs[N, HEM, NSta] | 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) |
Hemispherical absorptance of each glass pane for interior irradiation with exterior shading
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).
Type | Name | Default | Description |
---|---|---|---|
Real | absIntIrrNoSha[N, NSta] | Absorptance for interior irradiation without shading | |
Real | traRef[3, N, N, HEM, NSta] | 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 | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration |
Type | Name | Description |
---|---|---|
Real | absIntIrrExtSha[N, NSta] | Hemispherical absorptance of each glass pane for interior irradiation with exterior shading |
Hemispherical absorptance of each glass pane for interior irradiation with interior shading
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).
Type | Name | Default | Description |
---|---|---|---|
Real | absIntIrrNoSha[N, NSta] | Hemispherical absorptance wfor interior irradiation without interior shading | |
Real | traRef[3, N, N, HEM, NSta] | 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 | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration |
Type | Name | Description |
---|---|---|
Real | absIntIrrIntSha[N, NSta] | Hemispherical absorbtance of each glass pane for interior irradiation with interior shading |
Hemispherical absorptance of each glass pane for interior irradiation without shading
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).
Type | Name | Default | Description |
---|---|---|---|
Real | traRef[3, N, N, HEM, NSta] | Transmittance and reflectance with exterior irradiation and no shading | |
Integer | N | Number of glass layers | |
Integer | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration |
Type | Name | Description |
---|---|---|
Real | absIntIrrNoSha[N, NSta] | Hemispherical absorptance of each glass layer for interior irradiation without shading |
Compute angular variation and hemispherical integration of the transmittance and reflectance for each glass pane without shading
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).
Type | Name | Default | Description |
---|---|---|---|
Integer | N | Number of glass layers | |
Integer | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration | |
Real | glass[3, N, NSta] | Propertry of each glass pane | |
Real | xGla[N] | Thickness of each glass pane | |
Angle | psi[HEM - 1] | Incident angles [rad] |
Type | Name | Description |
---|---|---|
Real | layer[3, N, HEM, NSta] | Transmittance, front and back reflectance |
Compute angular variation and hemispherical integration of the transmittance and reflectance for a coated glass pane without shading
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).
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] |
Type | Name | Description |
---|---|---|
Real | layer[3, HEM] | Transmittance, front and back reflectance |
Compute angular variation and hemispherical integration of the transmittance and reflectance for a uncoated glass pane without shading
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.
Step 1: Compute the reflectivity at normal incidence
ρ(0) = {β − sqrt[β2 − 4(2 − R(0))R(0)]} ⁄ [2(2−R(0))], |
(1) |
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)
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).
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).
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] |
Type | Name | Description |
---|---|---|
Real | layer[3, HEM] | Transmittance, front and back reflectance |
Transmittance and reflectance of glass panes for exterior irradiation without shading
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).
Type | Name | Default | Description |
---|---|---|---|
Integer | N | Number of glass layers | |
Integer | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration | |
Real | layer[3, N, HEM, NSta] | Angular data of glass pane |
Type | Name | Description |
---|---|---|
Real | traRef[3, N, N, HEM, NSta] | Transmittance and reflectance of each glass pane for exterior irradiation without shading |
Transmittance and reflectance of each glass pane for interior irradiation without shading
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).
Type | Name | Default | Description |
---|---|---|---|
Integer | N | Number of glass layers | |
Integer | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration | |
Real | layer[3, N, HEM, NSta] | Angular data of glass pane |
Type | Name | Description |
---|---|---|
Real | traRef[3, N, N, HEM, NSta] | Glass transmittance, front and back reflectance |
Angular and hemispherical transmittance of a window system (glass and shading device) for exterior irradiation with interior shading
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).
Type | Name | Default | Description |
---|---|---|---|
Real | traRef[3, N, N, HEM, NSta] | 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 | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration |
Type | Name | Description |
---|---|---|
Real | traExtIrrIntSha[HEM, NSta] | Angular and hemispherical transmittance of a window system (glass and shading device) forh exterior irradiation with interior shading |
Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading
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).
Type | Name | Default | Description |
---|---|---|---|
Real | traRef[3, N, N, HEM, NSta] | 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 | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration |
Type | Name | Description |
---|---|---|
Real | traExtIrrExtSha[HEM, NSta] | Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading |
Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading
1
is facing the outside and pane N
is facing the room.
The variables aretraRefIntIrrExtSha[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).
Type | Name | Default | Description |
---|---|---|---|
Real | traRef[3, N, N, HEM, NSta] | 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 | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration |
Type | Name | Description |
---|---|---|
Real | traRefIntIrrExtSha[3, NSta] | Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading |
Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading
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).
Type | Name | Default | Description |
---|---|---|---|
Real | traRef[3, N, N, HEM, NSta] | 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 | NSta | Number of window states for electrochromic windows (set to 1 for regular windows) | |
Integer | HEM | Index of hemispherical integration |
Type | Name | Description |
---|---|---|
Real | traRefIntIrrIntSha[3, NSta] | Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading |