Description: "Package with base classes for Buildings.HeatTransfer.Windows"

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## Buildings.HeatTransfer.Windows.BaseClasses

Package with base classes for Buildings.HeatTransfer.Windows

### Information

This package contains base classes that are used to construct the models in Buildings.HeatTransfer.Windows.

Extends from Modelica.Icons.BasesPackage (Icon for packages containing base classes).

### Package Content

Name | Description
--- | ---
AbsorbedRadiation | Absorbed radiation by window
CenterOfGlass | Model for center of glass of a window construction
ExteriorConvectionCoefficient | Model for the heat transfer coefficient at the outside of the window
GasConvection | Model for heat convection through gas in a window assembly
GlassLayer | Model for a glass layer of a window assembly
InteriorConvection | Model for a interior (room-side) convective heat transfer with variable surface area
InteriorConvectionCoefficient | Model for the heat transfer coefficient at the inside of the window
Overhang | For a window with an overhang, outputs the fraction of the area that is sun exposed
PartialRadiation | Partial model for variables and data used in radiation calculation
PartialShade_weatherBus | Partial model to implement overhang and side fins with weather bus connector
PartialWindowBoundaryCondition | Partial model for heat convection or radiation between a possibly shaded window that can be outside or inside the room
ShadeConvection | Model for convective heat balance of a layer that may or may not have a shade
ShadeInterface_weatherBus | Base class for models of window shade and overhangs
ShadeRadiation | Model for infrared radiative heat balance of a layer that may or may not have a shade
ShadingSignal | Converts the shading signal to be strictly bigger than 0 and smaller than 1
SideFins | For a window with side fins, outputs the fraction of the area that is sun exposed
ThermalConductor | Lumped thermal element with variable area, transporting heat without storing it
TransmittedRadiation | Transmitted radiation through window
WindowRadiation | Calculation radiation for window
convectionHorizontalCavity | Free convection in horizontal cavity
convectionVerticalCavity | Free convection in vertical cavity
nusseltHorizontalCavityEnhanced | Nusselt number for horizontal cavity, bottom surface warmer than top surface
nusseltHorizontalCavityReduced | Nusselt number for horizontal cavity, bottom surface colder than top surface
smoothInterpolation | Get interpolated data without triggering events
RadiationBaseData | Basic parameters for window radiation calculation
RadiationData | Radiation data of a window
Examples | Collection of models that illustrate model use and test models

## Buildings.HeatTransfer.Windows.BaseClasses.AbsorbedRadiation

Absorbed radiation by window

### Information

The model calculates absorbed solar radiation on the window. The calculations follow the description in Wetter (2004), Appendix A.4.3.

The absorbed radiation by exterior shades includes:

1. the directly absorbed exterior radiation: `AWin*uSha*(HDir+HDif)*(1-tau-rho)`
2. the indirectly absorbed exterior radiantion from reflection (angular part): `AWin*uSha*HDir*tau*rho(IncAng)*(1-tau-rho)`
3. the indirectly absorbed of exterior irradiantion from reflection (diffusive part): `AWin*uSha*HDif*tau*rho(HEM)*(1-tau-rho)`
4. the absorbed interior radiation is neglected.

The output is `absRad[2, 1]`

The absorbed radiation by interior shades includes:

1. the absorbed exterior radiation (angular part): `AWin*uSha*HDir*alpha(IncAng)`
2. the absorbed exterior radiation (diffusive part): `AWin*uSha*HDif*alpha(HEM)`
3. the absorbed interior radiation (diffusive part): `AWin*uSha*HRoo*(1-tau-rho)`

The output is `absRad[2, N+2]`

The absorbed radiation by glass includes:

1. the absorbed radiation by unshaded part (diffusive part): `AWin*(1-uSha)*(HDif*alphaEx(HEM)+HRoo*alphaIn(HEM))`
2. the absorbed radiation by unshaded part (angular part from exterior source): `AWin*(1-uSha)*HDir*alphaEx(IncAng)`
3. the absorbed radiaiton by shaded part (diffusive part): `AWin*uSha*(HDif*alphaExSha(HEM)+HRoo*alphaInSha(HEM))`
4. the absorbed radiation by shaded part (angular part from exterior source): `AWin*uSha*HDir*alphaExSha(IncAng)`

The output is `absRad[1, 2:N+1] = Part1 + Part2; absRad[2, 2:N+1] = Part3 + Part4`

#### References

- Michael Wetter.
  Simulation-based Building Energy Optimization.
  Dissertation. University of California at Berkeley. 2004.

Extends from Buildings.HeatTransfer.Windows.BaseClasses.PartialRadiation (Partial model for variables and data used in radiation calculation).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Boolean | haveExteriorShade |  | Set to true if window has an exterior shade
Boolean | haveInteriorShade |  | Set to true if window has an interior shade
Area | AWin |  | Area of window [m2]
Glass
Integer | N |  | Number of glass layers
Length | xGla[N] |  | Thickness of glass [m]
TransmissionCoefficient | tauGlaSol[N] |  | Solar transmissivity of glass [1]
ReflectionCoefficient | rhoGlaSol_a[N] |  | Solar reflectivity of glass at surface a (facing outside) [1]
ReflectionCoefficient | rhoGlaSol_b[N] |  | Solar reflectivity of glass at surface b (facing room-side) [1]
Shade
TransmissionCoefficient | tauShaSol_a |  | Solar transmissivity of shade for irradiation from air-side [1]
TransmissionCoefficient | tauShaSol_b |  | Solar transmissivity of shade for irradiation from glass-side [1]
ReflectionCoefficient | rhoShaSol_a |  | Solar reflectivity of shade for irradiation from air-side [1]
ReflectionCoefficient | rhoShaSol_b |  | Solar reflectivity of shade for irradiation from glass-side [1]

### Connectors

Type | Name | Description
--- | --- | ---
input RealInput | uSha | Control signal for shading (0: unshaded; 1: fully shaded)
input RealInput | HDif | Diffussive solar radiation [W/m2]
input RealInput | incAng | Incident angle [rad]
input RealInput | HDir | Direct solar radiation [W/m2]
input RealInput | HRoo | Diffussive radiation from room [W/m2]
output RealOutput | QAbsExtSha_flow | Absorbed interior and exterior radiation by exterior shading device [W]
output RealOutput | QAbsIntSha_flow | Absorbed interior and exterior radiation by interior shading device [W]
output RealOutput | QAbsGlaUns_flow[N] | Absorbed interior and exterior radiation by unshaded part of glass [W]
output RealOutput | QAbsGlaSha_flow[N] | Absorbed interior and exterior radiation by shaded part of glass [W]

### Modelica definition

block AbsorbedRadiation "Absorbed radiation by window" extends Buildings.HeatTransfer.Windows.BaseClasses.PartialRadiation; Modelica.Blocks.Interfaces.RealInput HRoo(quantity="RadiantEnergyFluenceRate", unit="W/m2") "Diffussive radiation from room "; Modelica.Blocks.Interfaces.RealOutput QAbsExtSha_flow(final quantity="Power", final unit="W") "Absorbed interior and exterior radiation by exterior shading device"; Modelica.Blocks.Interfaces.RealOutput QAbsIntSha_flow(final quantity="Power", final unit="W") "Absorbed interior and exterior radiation by interior shading device"; Modelica.Blocks.Interfaces.RealOutput QAbsGlaUns_flow[N](each quantity= "Power", each final unit="W") "Absorbed interior and exterior radiation by unshaded part of glass"; Modelica.Blocks.Interfaces.RealOutput QAbsGlaSha_flow[N](each quantity= "Power", each final unit="W") "Absorbed interior and exterior radiation by shaded part of glass"; output Modelica.SIunits.Power absRad[2, N + 2] "Absorbed interior and exterior radiation. (absRad[2,1]: exterior shading device, absRad[1,2 to N+1]: glass (unshaded part), absRad[2,2 to N+1]: glass (shaded part), absRad[2,N+2]: interior shading device)"; protected constant Integer k=1; Real x; final parameter Integer NDIR=radDat.NDIR; final parameter Integer HEM=radDat.HEM; constant Integer NoShade=1; constant Integer Shade=2; constant Integer Interior=1; constant Integer Exterior=2; final parameter Real coeAbsEx[2, radDat.N, radDat.HEM + 2](each fixed=false); final parameter Real coeRefExtPan1[radDat.HEM + 2](each fixed=false) "Reflectivity of pane 1"; final parameter Real coeAbsIn[2, radDat.N](each fixed=false); final parameter Real coeAbsDevExtIrrIntSha[radDat.HEM + 2](each fixed=false) "Absorptivity of interior shading device for exterior radiation"; final parameter Real coeAbsDevExtIrrExtSha=1 - radDat.traRefShaDev[1, 1] - radDat.traRefShaDev[2, 1] "Absorptivity of exterior shading device for exterior radiation"; final parameter Real coeAbsDevIntIrrIntSha=radDat.devAbsIntIrrIntSha "Absorptivity of interior shading device for interior radiation"; final parameter Real coeAbsDevIntIrrExtSha=1 - radDat.winTraRefIntIrrExtSha[1] - radDat.winTraRefIntIrrExtSha[2] "Absorptivity of exterior shading device for interior radiation"; Real tmpNoSha; Real tmpSha; Real incAng2; initial equation //************************************************************** // Assign coefficients. // Data dimension changes from Original ([1 : HEM]) to New ([2 : HEM+1]) // with 2 dummy variable for interpolation. //************************************************************** // Glass for i in 1:N loop coeAbsIn[NoShade, i] = radDat.absIntIrrNoSha[i]; // Properties for glass with shading if haveInteriorShade then coeAbsIn[Shade, i] = radDat.absIntIrrIntSha[i]; elseif haveExteriorShade then coeAbsIn[Shade, i] = radDat.absIntIrrExtSha[i]; else // No Shade coeAbsIn[Shade, i] = 0.0; end if; for j in 1:HEM loop // Properties for glass without shading coeAbsEx[NoShade, i, j + 1] = radDat.absExtIrrNoSha[i, j]; // Properties for glass with shading if haveInteriorShade then coeAbsEx[Shade, i, j + 1] = radDat.absExtIrrIntSha[i, j]; elseif haveExteriorShade then coeAbsEx[Shade, i, j + 1] = radDat.absExtIrrExtSha[i, j]; else // No Shade coeAbsEx[Shade, i, j + 1] = 0.0; end if; end for; // Dummy variables at 1 and HEM+2 for k in NoShade:Shade loop coeAbsEx[k, i, 1] = coeAbsEx[k, i, 2]; coeAbsEx[k, i, HEM + 2] = coeAbsEx[k, i, HEM + 1]; end for; end for; // Glass Pane 1: Reflectivity for j in 1:HEM loop coeRefExtPan1[j + 1] = radDat.traRef[2, 1, N, j]; end for; // Interior shades for j in 1:HEM loop coeAbsDevExtIrrIntSha[j + 1] = radDat.devAbsExtIrrIntShaDev[j]; end for; // Dummy variables at 1 and HEM+2 coeRefExtPan1[1] = coeRefExtPan1[2]; coeRefExtPan1[HEM + 2] = coeRefExtPan1[HEM + 1]; coeAbsDevExtIrrIntSha[1] = coeAbsDevExtIrrIntSha[2]; coeAbsDevExtIrrIntSha[HEM + 2] = coeAbsDevExtIrrIntSha[HEM + 1]; algorithm absRad[NoShade, 1] := 0.0; absRad[NoShade, N + 2] := 0.0; absRad[Shade, 1] := 0.0; absRad[Shade, N + 2] := 0.0; //************************************************************** // Glass: absorbed diffusive radiation from exterior and interior sources //************************************************************** for i in 1:N loop absRad[NoShade, i + 1] := AWin*(1 - uSha_internal)*(HDif*coeAbsEx[NoShade, i, HEM + 1] + HRoo*coeAbsIn[NoShade, i]); absRad[Shade, i + 1] := AWin*uSha_internal*(HDif*coeAbsEx[Shade, i, HEM + 1] + HRoo*coeAbsIn[Shade, i]); end for; //************************************************************** // Shading device: absorbed radiation from exterior source //************************************************************** // Exterior Shading Device: // direct radiation: 1. direct absorption; // diffusive radiation: 1. direct absorption 2. absorption from back reflection if haveExteriorShade then absRad[Shade, 1] := AWin*uSha_internal*coeAbsDevExtIrrExtSha*(HDif + HDir + HDif*radDat.traRefShaDev[1, 1]*radDat.traRef[2, 1, N, HEM]); // Interior Shading Device: diffusive radiation from both interior and exterior elseif haveInteriorShade then absRad[Shade, N + 2] := AWin*uSha_internal*(HDif*radDat.devAbsExtIrrIntShaDev[ HEM] + HRoo*coeAbsDevIntIrrIntSha); end if; //************************************************************** // Glass, Device: add absorbed direct radiation from exterior sources //************************************************************** // Use min() instead of if() to avoid event incAng2 := min(incAng, 0.5*Modelica.Constants.pi); x := 2*(NDIR - 1)*abs(incAng2)/Modelica.Constants.pi "x=(index-1)*incAng/(0.5pi), 0<=x<=NDIR"; x := x + 2; for i in 1:N loop // Glass without shading: Add absorbed direct radiation tmpNoSha := Buildings.HeatTransfer.Windows.BaseClasses.smoothInterpolation({ coeAbsEx[NoShade, i, k] for k in 1:(HEM + 2)}, x); absRad[NoShade, i + 1] := absRad[NoShade, i + 1] + AWin*HDir*(1 - uSha_internal)*tmpNoSha; // Glass with shading: add absorbed direct radiation tmpSha := Buildings.HeatTransfer.Windows.BaseClasses.smoothInterpolation({ coeAbsEx[Shade, i, k] for k in 1:(HEM + 2)}, x); absRad[Shade, i + 1] := absRad[Shade, i + 1] + AWin*HDir*uSha_internal* tmpSha; end for; // Interior shading device: add absorbed direct radiation if haveInteriorShade then tmpSha := Buildings.HeatTransfer.Windows.BaseClasses.smoothInterpolation({ coeAbsDevExtIrrIntSha[k] for k in 1:(HEM + 2)}, x); absRad[Shade, N + 2] := absRad[Shade, N + 2] + AWin*HDir*uSha_internal* tmpSha; end if; // Exterior shading device: add absorbed reflection of direct radiation from exterior source if haveExteriorShade then tmpNoSha := Buildings.HeatTransfer.Windows.BaseClasses.smoothInterpolation({ coeRefExtPan1[k] for k in 1:(HEM + 2)}, x); absRad[Shade, 1] := absRad[Shade, 1] + AWin*HDir*uSha_internal* coeAbsDevExtIrrExtSha*tmpNoSha; end if; // Assign quantities to output connectors QAbsExtSha_flow := absRad[2, 1]; QAbsIntSha_flow := absRad[2, N + 2]; QAbsGlaUns_flow[:] := absRad[1, 2:N + 1]; QAbsGlaSha_flow[:] := absRad[2, 2:N + 1]; end AbsorbedRadiation;

## Buildings.HeatTransfer.Windows.BaseClasses.CenterOfGlass

Model for center of glass of a window construction

### Information

This is a model for the heat transfer through the center of the glass. The properties of the glazing system is defined by the parameter `glaSys`. The model contains these main component models:

- the models `extSha` and `intSha` for the heat balance of the shade, modeled using Buildings.HeatTransfer.Windows.BaseClasses.Shade.
- an array of models `glass` for the heat conduction and the infrared radiative heat balance of the glass layers. There can be an arbitrary number of glass layers, which are all modeled using instances of Buildings.HeatTransfer.Windows.BaseClasses.GlassLayer.
- an array of models `gas` for the gas layers. There is one model of a gas layer between each window panes. The gas layers are modeled using instances of Buildings.HeatTransfer.Windows.BaseClasses.GasConvection.

Note that this model does not compute heat conduction through the frame and it does not model the convective heat transfer at the exterior and interior surface. These models are implemented in Buildings.HeatTransfer.Windows.Window, Buildings.HeatTransfer.Windows.ExteriorHeatTransfer, and Buildings.HeatTransfer.Windows.InteriorHeatTransfer

Extends from Buildings.HeatTransfer.Radiosity.BaseClasses.RadiosityTwoSurfaces (Model for the radiosity balance of a device with two surfaces).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Area | A |  | Surface area [m2]
Angle | til |  | Surface tilt (only 90 degrees=vertical is implemented) [rad]
Generic | glaSys |  | Glazing system
Boolean | linearize | false | Set to true to linearize emissive power
Advanced
Boolean | homotopyInitialization | true | = true, use homotopy method

### Connectors

Type | Name | Description
--- | --- | ---
input RadiosityInflow | JIn_a | Incoming radiosity at surface a [W]
input RadiosityInflow | JIn_b | Incoming radiosity at surface b [W]
output RadiosityOutflow | JOut_a | Outgoing radiosity at surface a [W]
output RadiosityOutflow | JOut_b | Outgoing radiosity at surface b [W]
input RealInput | u | Input connector, used to scale the surface area to take into account an operable shading device
HeatPort_a | glass_a | Heat port connected to the outside facing surface of the glass
HeatPort_b | glass_b | Heat port connected to the room-facing surface of the glass
input RealInput | QAbs_flow[nGlaLay] | Solar radiation absorbed by glass [W]

### Modelica definition

model CenterOfGlass "Model for center of glass of a window construction" extends Buildings.HeatTransfer.Radiosity.BaseClasses.RadiosityTwoSurfaces; parameter Modelica.SIunits.Area A "Heat transfer area"; parameter Modelica.SIunits.Angle til(displayUnit="deg") "Surface tilt (only 90 degrees=vertical is implemented)"; parameter Buildings.HeatTransfer.Data.GlazingSystems.Generic glaSys "Glazing system"; parameter Boolean linearize=false "Set to true to linearize emissive power"; parameter Boolean homotopyInitialization = true "= true, use homotopy method"; Modelica.Blocks.Interfaces.RealInput u "Input connector, used to scale the surface area to take into account an operable shading device"; Buildings.HeatTransfer.Windows.BaseClasses.GlassLayer[nGlaLay] glass( each final A=A, final x=glaSys.glass.x, final k=glaSys.glass.k, final absIR_a=glaSys.glass.absIR_a, final absIR_b=glaSys.glass.absIR_b, final tauIR=glaSys.glass.tauIR, each final linearize=linearize, each final homotopyInitialization=homotopyInitialization) "Window glass layer"; Buildings.HeatTransfer.Windows.BaseClasses.GasConvection gas[nGlaLay-1]( each final A=A, final gas=glaSys.gas, each final til=til, each linearize=linearize, each final homotopyInitialization=homotopyInitialization) "Window gas layer"; // Note that the interior shade is flipped horizontally. Hence, surfaces a and b are exchanged, // i.e., surface a faces the room, while surface b faces the window Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a glass_a "Heat port connected to the outside facing surface of the glass"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_b glass_b "Heat port connected to the room-facing surface of the glass"; Modelica.Blocks.Interfaces.RealInput QAbs_flow[nGlaLay]( each unit="W", each quantity = "Power") "Solar radiation absorbed by glass"; protected final parameter Integer nGlaLay = size(glaSys.glass, 1) "Number of glass layers"; equation for i in 1:nGlaLay-1 loop connect(glass[i].port_b, gas[i].port_a); connect(gas[i].port_b, glass[i+1].port_a); connect(glass[i].JOut_b, glass[i+1].JIn_a); connect(glass[i].JIn_b, glass[i+1].JOut_a); connect(u, gas[i].u); end for; for i in 1:nGlaLay loop connect(u, glass[i].u); end for; connect(glass_b, glass[nGlaLay].port_b); connect(glass_a, glass[1].port_a); connect(JIn_a, glass[1].JIn_a); connect(glass[1].JOut_a, JOut_a); connect(glass[nGlaLay].JOut_b, JOut_b); connect(JIn_b, glass[nGlaLay].JIn_b); connect(glass.QAbs_flow, QAbs_flow); end CenterOfGlass;

## Buildings.HeatTransfer.Windows.BaseClasses.ExteriorConvectionCoefficient

Model for the heat transfer coefficient at the outside of the window

### Information

Model for the convective heat transfer coefficient at the outside of a window. The computation is according to TARCOG 2006, which specifies the convection coefficient as

h = 4+4 v

where v is the wind speed in m/s and h is the convective heat transfer coefficient in W/(m2*K).

#### References

TARCOG 2006: Carli, Inc., TARCOG: Mathematical models for calculation of thermal performance of glazing systems with our without shading devices, Technical Report, Oct. 17, 2006.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Area | A |  | Heat transfer area [m2]

### Connectors

Type | Name | Description
--- | --- | ---
output RealOutput | GCon | Convective thermal conductance [W/K]
input RealInput | v | Wind speed [m/s]

### Modelica definition

model ExteriorConvectionCoefficient "Model for the heat transfer coefficient at the outside of the window" extends Modelica.Blocks.Icons.Block; parameter Modelica.SIunits.Area A "Heat transfer area"; Modelica.Blocks.Interfaces.RealOutput GCon(unit="W/K") "Convective thermal conductance"; Modelica.Blocks.Interfaces.RealInput v(unit="m/s") "Wind speed"; equation GCon = A*(4+4*Buildings.Utilities.Math.Functions.smoothMax(v, -v, 0.1)); end ExteriorConvectionCoefficient;

## Buildings.HeatTransfer.Windows.BaseClasses.GasConvection

Model for heat convection through gas in a window assembly

### Information

Model for convective heat tranfer in a single layer of window gas. Currently, the model only implements equations for vertical windows and for horizontal windows. The computation is according to TARCOG 2006, except that this implementation computes the convection coefficient as a function that is differentiable in the temperatures.

To use this model, set the parameter `til` to a value defined in Buildings.Types.Tilt.

If the parameter `linearize` is set to `true`, then all equations are linearized.

#### References

TARCOG 2006: Carli, Inc., TARCOG: Mathematical models for calculation of thermal performance of glazing systems with our without shading devices, Technical Report, Oct. 17, 2006.

Extends from Modelica.Thermal.HeatTransfer.Interfaces.Element1D (Partial heat transfer element with two HeatPort connectors that does not store energy), Buildings.BaseClasses.BaseIcon (Base icon).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Generic | gas |  | Thermophysical properties of gas fill
Area | A |  | Heat transfer area [m2]
Area | h | sqrt(A) | Height of window [m2]
Angle | til |  | Surface tilt (only 0, 90 and 180 degrees are implemented) [rad]
Boolean | linearize | false | Set to true to linearize emissive power
Temperature | T0 | 293.15 | Temperature used to compute thermophysical properties [K]
Advanced
Boolean | homotopyInitialization | true | = true, use homotopy method

### Connectors

Type | Name | Description
--- | --- | ---
input RealInput | u | Input connector, used to scale the surface area to take into account an operable shading device

### Modelica definition

model GasConvection "Model for heat convection through gas in a window assembly" extends Modelica.Thermal.HeatTransfer.Interfaces.Element1D( port_a(T(start=293.15)), port_b(T(start=293.15))); extends Buildings.BaseClasses.BaseIcon; parameter Buildings.HeatTransfer.Data.Gases.Generic gas "Thermophysical properties of gas fill"; parameter Modelica.SIunits.Area A "Heat transfer area"; parameter Modelica.SIunits.Area h(min=0) = sqrt(A) "Height of window"; parameter Modelica.SIunits.Angle til(displayUnit="deg") "Surface tilt (only 0, 90 and 180 degrees are implemented)"; parameter Boolean linearize=false "Set to true to linearize emissive power"; parameter Modelica.SIunits.Temperature T0 = 293.15 "Temperature used to compute thermophysical properties"; parameter Boolean homotopyInitialization = true "= true, use homotopy method"; Modelica.Blocks.Interfaces.RealInput u "Input connector, used to scale the surface area to take into account an operable shading device"; Modelica.SIunits.CoefficientOfHeatTransfer hCon(min=0, start=3) "Convective heat transfer coefficient"; Modelica.SIunits.HeatFlux q_flow "Convective heat flux"; Real Nu(min=0) "Nusselt number"; Real Ra(min=0) "Rayleigh number"; protected Modelica.SIunits.Temperature T_a "Temperature used for thermophysical properties at port_a"; Modelica.SIunits.Temperature T_b "Temperature used for thermophysical properties at port_b"; Modelica.SIunits.Temperature T_m "Temperature used for thermophysical properties"; Real deltaNu(min=0.01) = 0.1 "Small value for Nusselt number, used for smoothing"; Real deltaRa(min=0.01) = 100 "Small value for Rayleigh number, used for smoothing"; final parameter Real cosTil=Modelica.Math.cos(til) "Cosine of window tilt"; final parameter Real sinTil=Modelica.Math.sin(til) "Sine of window tilt"; final parameter Boolean isVertical = abs(cosTil) < 10E-10 "Flag, true if the window is in a wall"; final parameter Boolean isHorizontal = abs(sinTil) < 10E-10 "Flag, true if the window is horizontal"; // Quantities that are only used in linearized model parameter Modelica.SIunits.CoefficientOfHeatTransfer hCon0(fixed=false) "Convective heat transfer coefficient"; parameter Real Nu0(fixed=false, min=0) "Nusselt number"; parameter Real Ra0(fixed=false, min=0) "Rayleigh number"; initial equation // This assertion is required to ensure that the default value of // in Buildings.HeatTransfer.Data.Gases.Generic is overwritten. assert(gas.x > 0, "The gas thickness must be non-negative. Obtained gas.x = " + String(gas.x) + ". Check the parameter for the gas thickness of the window model."); assert(isVertical or isHorizontal, "Only vertical and horizontal windows are implemented."); // Computations that are used in the linearized model only Ra0 = Buildings.HeatTransfer.Convection.Functions.HeatFlux.rayleigh( x=gas.x, rho=Buildings.HeatTransfer.Data.Gases.density(gas=gas, T=T0), c_p=Buildings.HeatTransfer.Data.Gases.specificHeatCapacity(gas=gas, T=T0), mu=Buildings.HeatTransfer.Data.Gases.dynamicViscosity(gas=gas, T=T0), k=Buildings.HeatTransfer.Data.Gases.thermalConductivity(gas=gas, T=T0), T_a=T0-5, T_b=T0+5, Ra_min=100); (Nu0, hCon0) = Buildings.HeatTransfer.Windows.BaseClasses.convectionVerticalCavity( gas=gas, Ra=Ra0, T_m=T0, dT=10, h=h, deltaNu=deltaNu, deltaRa=deltaRa); equation T_a = port_a.T; T_b = port_b.T; T_m = (port_a.T+port_b.T)/2; if linearize then Ra=Ra0; Nu=Nu0; hCon=hCon0; q_flow = hCon0 * dT; else Ra = Buildings.HeatTransfer.Convection.Functions.HeatFlux.rayleigh( x=gas.x, rho=Buildings.HeatTransfer.Data.Gases.density(gas, T_m), c_p=Buildings.HeatTransfer.Data.Gases.specificHeatCapacity(gas, T_m), mu=Buildings.HeatTransfer.Data.Gases.dynamicViscosity(gas, T_m), k=Buildings.HeatTransfer.Data.Gases.thermalConductivity(gas, T_m), T_a=T_a, T_b=T_b, Ra_min=100); if isVertical then (Nu, hCon, q_flow) = Buildings.HeatTransfer.Windows.BaseClasses.convectionVerticalCavity( gas=gas, Ra=Ra, T_m=T_m, dT=dT, h=h, deltaNu=deltaNu, deltaRa=deltaRa); elseif isHorizontal then (Nu, hCon, q_flow) = Buildings.HeatTransfer.Windows.BaseClasses.convectionHorizontalCavity( gas=gas, Ra=Ra, T_m=T_m, dT=dT, til=til, sinTil=sinTil, cosTil=cosTil, h=h, deltaNu=deltaNu, deltaRa=deltaRa); else Nu = 0; hCon=0; q_flow=0; end if; // isVertical or isHorizontal end if; // linearize if homotopyInitialization then Q_flow = u*A*homotopy(actual=q_flow, simplified=hCon0*dT); else Q_flow = u*A*q_flow; end if; end GasConvection;

## Buildings.HeatTransfer.Windows.BaseClasses.GlassLayer

Model for a glass layer of a window assembly

### Information

Model of a single layer of window glass. The input port `QAbs_flow` needs to be connected to the solar radiation that is absorbed by the glass pane. The model computes the heat conduction between the two glass surfaces. The heat flow `QAbs_flow` is added at the center of the glass. The model also computes the infrared radiative heat balance using an instance of the model Buildings.HeatTransfer.Radiosity.WindowPane.

Extends from Buildings.HeatTransfer.Radiosity.BaseClasses.RadiosityTwoSurfaces (Model for the radiosity balance of a device with two surfaces), Buildings.HeatTransfer.Radiosity.BaseClasses.ParametersTwoSurfaces (Parameters that are used to model two surfaces with the same area).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Area | A |  | Surface area [m2]
Emissivity | absIR_a |  | Infrared absorptivity of surface a [1]
Emissivity | absIR_b |  | Infrared absorptivity of surface b [1]
ReflectionCoefficient | rhoIR_a | 1 - absIR_a - tauIR | Infrared reflectivity of surface a [1]
ReflectionCoefficient | rhoIR_b | 1 - absIR_b - tauIR | Infrared reflectivity of surface b [1]
TransmissionCoefficient | tauIR |  | Infrared transmissivity of glass pane [1]
Boolean | linearize | false | Set to true to linearize emissive power
Temperature | T0 | 293.15 | Temperature used to linearize radiative heat transfer [K]
Length | x |  | Material thickness [m]
ThermalConductivity | k |  | Thermal conductivity [W/(m.K)]
Advanced
Boolean | homotopyInitialization | true | = true, use homotopy method

### Connectors

Type | Name | Description
--- | --- | ---
input RadiosityInflow | JIn_a | Incoming radiosity at surface a [W]
input RadiosityInflow | JIn_b | Incoming radiosity at surface b [W]
output RadiosityOutflow | JOut_a | Outgoing radiosity at surface a [W]
output RadiosityOutflow | JOut_b | Outgoing radiosity at surface b [W]
input RealInput | u | Input connector, used to scale the surface area to take into account an operable shading device
HeatPort_a | port_a | Heat port at surface a
HeatPort_b | port_b | Heat port at surface b
input RealInput | QAbs_flow | Solar radiation absorbed by glass [W]

### Modelica definition

model GlassLayer "Model for a glass layer of a window assembly" extends Buildings.HeatTransfer.Radiosity.BaseClasses.RadiosityTwoSurfaces; extends Buildings.HeatTransfer.Radiosity.BaseClasses.ParametersTwoSurfaces( final rhoIR_a=1-absIR_a-tauIR, final rhoIR_b=1-absIR_b-tauIR); parameter Modelica.SIunits.Length x "Material thickness"; parameter Modelica.SIunits.ThermalConductivity k "Thermal conductivity"; parameter Modelica.SIunits.Area A "Heat transfer area"; parameter Modelica.SIunits.Emissivity absIR_a "Infrared absorptivity of surface a (usually room-facing surface)"; parameter Modelica.SIunits.Emissivity absIR_b "Infrared absorptivity of surface b (usually outside-facing surface)"; parameter Modelica.SIunits.TransmissionCoefficient tauIR "Infrared transmittance of glass"; Modelica.Blocks.Interfaces.RealInput u "Input connector, used to scale the surface area to take into account an operable shading device"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a port_a(T(start=293.15)) "Heat port at surface a"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_b port_b(T(start=293.15)) "Heat port at surface b"; Modelica.Blocks.Interfaces.RealInput QAbs_flow(unit="W", quantity="Power") "Solar radiation absorbed by glass"; parameter Boolean linearize=false "Set to true to linearize emissive power"; parameter Boolean homotopyInitialization = true "= true, use homotopy method"; protected Real T4_a(min=1E8, unit="K4", start=293.15^4, nominal=1E10) "4th power of temperature at surface a"; Real T4_b(min=1E8, unit="K4", start=293.15^4, nominal=1E10) "4th power of temperature at surface b"; Modelica.SIunits.HeatFlowRate E_a(min=0, nominal=1E2) "Emissive power of surface a"; Modelica.SIunits.HeatFlowRate E_b(min=0, nominal=1E2) "Emissive power of surface b"; final parameter Modelica.SIunits.ThermalResistance R = x/2/k/A "Thermal resistance from surface of glass to center of glass"; equation // Heat balance of surface node // These equations are from Window 6 Technical report, (2.1-14) to (2.1-17) 0 = port_a.Q_flow + port_b.Q_flow + QAbs_flow + JIn_a + JIn_b - JOut_a - JOut_b; u * (port_b.T-port_a.T) = 2*R * (-port_a.Q_flow-QAbs_flow/2-JIn_a+JOut_a + tauIR * (JIn_a - JIn_b)); // Radiosity balance if linearize then T4_a = 4*T03*port_a.T - 3*T04; T4_b = 4*T03*port_b.T - 3*T04; else if homotopyInitialization then T4_a = homotopy(actual=port_a.T^4, simplified=4*T03*port_a.T - 3*T04); T4_b = homotopy(actual=port_b.T^4, simplified=4*T03*port_b.T - 3*T04); else T4_a = port_a.T^4; T4_b = port_b.T^4; end if; end if; // Emissive power E_a = u * A * absIR_a * Modelica.Constants.sigma * T4_a; E_b = u * A * absIR_b * Modelica.Constants.sigma * T4_b; // Radiosities that are outgoing from the surface, which are // equal to the infrared absorptivity plus the reflected incoming // radiosity plus the radiosity that is transmitted from the // other surface. JOut_a = E_a + rhoIR_a * JIn_a + tauIR * JIn_b; JOut_b = E_b + rhoIR_b * JIn_b + tauIR * JIn_a; end GlassLayer;

## Buildings.HeatTransfer.Windows.BaseClasses.InteriorConvection

Model for a interior (room-side) convective heat transfer with variable surface area

### Information

This is a model for a convective heat transfer for interior, room-facing surfaces. The parameter `conMod` determines the model that is used to compute the heat transfer coefficient:

- If `conMod= Buildings.HeatTransfer.Types.InteriorConvection.Fixed`, then the convective heat transfer coefficient is set to the value specified by the parameter `hFixed`.
- If `conMod= Buildings.HeatTransfer.Types.InteriorConvection.Temperature`, then the convective heat tranfer coefficient is a function of the temperature difference. The convective heat flux is computed using
  - for floors the function Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor
  - for ceilings the function Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling
  - for walls the function Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall

This model is identical to Buildings.HeatTransfer.Convection.Interior except that it has an input `u` that is used to scale the heat transfer. This can be used if the heat transfer area is variable. An example usage is for a window with shade, in which the surface area of a shaded part of a window changes depending on the shading control signal.

Extends from Buildings.HeatTransfer.Convection.BaseClasses.PartialConvection (Partial model for heat convection).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Area | A |  | Heat transfer area [m2]
CoefficientOfHeatTransfer | hFixed | 3 | Constant convection coefficient [W/(m2.K)]
Angle | til |  | Surface tilt [rad]
InteriorConvection | conMod | Buildings.HeatTransfer.Types... | Convective heat transfer model
Initialization
TemperatureDifference | dT.start | 0 | = solid.T - fluid.T [K]
Advanced
Boolean | homotopyInitialization | true | = true, use homotopy method

### Connectors

Type | Name | Description
--- | --- | ---
HeatPort_a | solid |
HeatPort_b | fluid |
input RealInput | u | Input connector, used to scale the surface area to take into account an operable shading device

### Modelica definition

model InteriorConvection "Model for a interior (room-side) convective heat transfer with variable surface area" extends Buildings.HeatTransfer.Convection.BaseClasses.PartialConvection; parameter Buildings.HeatTransfer.Types.InteriorConvection conMod= Buildings.HeatTransfer.Types.InteriorConvection.Fixed "Convective heat transfer model"; parameter Boolean homotopyInitialization = true "= true, use homotopy method"; Modelica.Blocks.Interfaces.RealInput u "Input connector, used to scale the surface area to take into account an operable shading device"; protected constant Modelica.SIunits.Temperature dT0 = 2 "Initial temperature used in homotopy method"; equation if (conMod == Buildings.HeatTransfer.Types.InteriorConvection.Fixed) then q_flow = u*hFixed * dT; else // Even if hCon is a step function with a step at zero, // the product hCon*dT is differentiable at zero with // a continuous first derivative if homotopyInitialization then if isCeiling then q_flow = u*homotopy(actual=Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling(dT=dT), simplified=dT/dT0*Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling(dT=dT0)); elseif isFloor then q_flow = u*homotopy(actual=Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor(dT=dT), simplified=dT/dT0*Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor(dT=dT0)); else q_flow = u*homotopy(actual=Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall(dT=dT), simplified=dT/dT0*Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall(dT=dT0)); end if; else if isCeiling then q_flow = u*Buildings.HeatTransfer.Convection.Functions.HeatFlux.ceiling(dT=dT); elseif isFloor then q_flow = u*Buildings.HeatTransfer.Convection.Functions.HeatFlux.floor(dT=dT); else q_flow = u*Buildings.HeatTransfer.Convection.Functions.HeatFlux.wall(dT=dT); end if; end if; end if; end InteriorConvection;

## Buildings.HeatTransfer.Windows.BaseClasses.InteriorConvectionCoefficient

Model for the heat transfer coefficient at the inside of the window

### Information

Model for the convective heat transfer coefficient at the room-facing surface of a window. The computation is according to TARCOG 2006, which specifies the convection coefficient as

h = 4 W ⁄ (m2 K).

#### References

TARCOG 2006: Carli, Inc., TARCOG: Mathematical models for calculation of thermal performance of glazing systems with our without shading devices, Technical Report, Oct. 17, 2006.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Area | A |  | Heat transfer area [m2]

### Connectors

Type | Name | Description
--- | --- | ---
output RealOutput | GCon | Convective thermal conductance [W/K]

### Modelica definition

model InteriorConvectionCoefficient "Model for the heat transfer coefficient at the inside of the window" extends Modelica.Blocks.Icons.Block; parameter Modelica.SIunits.Area A "Heat transfer area"; Modelica.Blocks.Interfaces.RealOutput GCon(unit="W/K") "Convective thermal conductance"; equation GCon = 4*A; end InteriorConvectionCoefficient;

## Buildings.HeatTransfer.Windows.BaseClasses.Overhang

For a window with an overhang, outputs the fraction of the area that is sun exposed

### Information

For a window with an overhang, this block outputs the fraction of the area that is exposed to the sun. This models can also be used for doors with an overhang.

Input to this block are the wall solar azimuth angle and the altitude angle of the sun. These angles can be calculated using blocks from the package Buildings.BoundaryConditions.SolarGeometry.BaseClasses.

The overhang can be asymmetrical (i.e. `wR ≠ wL`) about the vertical centerline of the window. The overhang must completely cover the window (i.e., `wL ≥ 0` and `wR ≥ 0`). `wL` and `wR` are measured from the left and right edge of the window.

The surface azimuth `azi` is as defined in Buildings.Types.Azimuth.

#### Implementation

The method of super position is used to calculate the window shaded area. The area below the overhang is divided as shown in the figure.

Dimensional variables used in code for the rectangle DEGI, AEGH, CFGI and BFGH are shown in the figure below:

The rectangles DEGI, AEGH, CFGI and BFGH have the same geometric configuration with respect to the overhang. Thus, the same algorithm can be used to calculate the shaded portion in these areas. A single equation in the `for` loop improves the total calculation time, as compared to `if-then-else` conditions, considering the various shapes of the shaded portions. To find the shaded area in window ABCD, the shaded portion of AEGD and CFGI should be subtracted from that of DEGI and BFGH. This shaded area of the window is then divided by the total window area to calculate the shaded fraction of the window.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block), Buildings.Rooms.BaseClasses.Overhang (Record for window overhang).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Angle | lat |  | Latitude [rad]
Angle | azi |  | Surface azimuth; azi= -90 degree East; azi= 0 degree South [rad]
Overhang
Length | wL |  | Overhang width left to the window, measured from the window corner [m]
Length | wR |  | Overhang width right to the window, measured from the window corner [m]
Length | dep |  | Overhang depth (measured perpendicular to the wall plane) [m]
Length | gap |  | Distance between window upper edge and overhang lower edge [m]
Window
Length | hWin |  | Window height [m]
Length | wWin |  | Window width [m]

### Connectors

Type | Name | Description
--- | --- | ---
input RealInput | verAzi | Wall solar azimuth angle (angle between projection of sun's rays and normal to vertical surface) [rad]
input RealInput | alt | Altitude angle [rad]
output RealOutput | fraSun | Fraction of window area exposed to the sun [1]
Bus | weaBus |

### Modelica definition

block Overhang "For a window with an overhang, outputs the fraction of the area that is sun exposed" extends Modelica.Blocks.Icons.Block; extends Buildings.Rooms.BaseClasses.Overhang; Modelica.Blocks.Interfaces.RealInput verAzi(quantity="Angle", unit="rad", displayUnit="deg") "Wall solar azimuth angle (angle between projection of sun's rays and normal to vertical surface)"; Modelica.Blocks.Interfaces.RealInput alt( quantity="Angle", unit="rad", displayUnit="deg") "Altitude angle"; Modelica.Blocks.Interfaces.RealOutput fraSun(final min=0, final max=1, final unit="1") "Fraction of window area exposed to the sun"; parameter Modelica.SIunits.Angle lat "Latitude"; parameter Modelica.SIunits.Angle azi(displayUnit="deg") "Surface azimuth; azi= -90 degree East; azi= 0 degree South"; // Window dimensions parameter Modelica.SIunits.Length hWin "Window height"; parameter Modelica.SIunits.Length wWin "Window width"; Buildings.BoundaryConditions.WeatherData.Bus weaBus; protected constant Modelica.SIunits.Angle delSolAzi = 0.005 "Half-width of transition interval between left and right formulation for overhang"; final parameter Modelica.SIunits.Area AWin= hWin*wWin "Window area"; parameter Modelica.SIunits.Length tmpH[4](each fixed=false) "Height rectangular sections used for superposition"; Modelica.SIunits.Length w "Either wL or wR, depending on the sun relative to the wall azimuth"; Modelica.SIunits.Length tmpW[4] "Width of rectangular sections used for superpositions"; Modelica.SIunits.Length del_L = wWin/100 "Fraction of window dimension over which min-max functions are smoothened"; Modelica.SIunits.Length x1 "Horizontal distance between window side edge and shadow corner"; Modelica.SIunits.Length x2[4] "Horizontal distance between window side edge and point where shadow line and window lower edge intersects"; Modelica.SIunits.Length y1 "Vertical distance between overhang and shadow lower edge"; Modelica.SIunits.Length y2[4] "Window height (vertical distance corresponding to x2)"; Real shdwTrnglRtio "Ratio of y1 and x1"; Modelica.SIunits.Area area[4] "Shaded areas of the sections used in superposition"; Modelica.SIunits.Area shdArea "Shaded area calculated from equations"; Modelica.SIunits.Area crShdArea "Final value for shaded area"; Modelica.SIunits.Area crShdArea1 "Corrected for the sun behind the surface/wall"; Modelica.SIunits.Area crShdArea2 "Corrected for the sun below horizon"; Buildings.BoundaryConditions.SolarGeometry.BaseClasses.SolarAzimuth solAzi(lat=lat) "Solar azimuth"; initial algorithm assert(wL >= 0, "Overhang must cover complete window Received overhang width on left hand side, wL = " + String(wL)); assert(wR >= 0, "Overhang must cover complete window Received overhang width on right hand side, wR = " + String(wR)); for i in 1:4 loop tmpH[i] := gap + mod((i - 1), 2)*hWin; end for; equation // if dep=0, then the equation // y1*Modelica.Math.cos(verAzi) = dep*Modelica.Math.tan(alt); // is singular. Hence, we treat this special case with an // if-then construct. // This also increases computing efficiency in // Buildings.HeatTransfer.Windows.FixedShade in case the window has no overhang. if haveOverhang then //Temporary height and widths are for the areas below the overhang //These areas are used in superposition w = Buildings.Utilities.Math.Functions.spliceFunction( pos=wL, neg=wR, x=solAzi.solAzi-azi, deltax=delSolAzi); tmpW[1] = w + wWin; tmpW[2] = w; tmpW[3] = w; tmpW[4] = w + wWin; y1*Modelica.Math.cos(verAzi) = dep*Modelica.Math.tan(alt); x1 = dep*Modelica.Math.tan(verAzi); shdwTrnglRtio*x1 = y1; for i in 1:4 loop y2[i] = tmpH[i]; // For the equation below, Dymola generated the following code in MixedAirFreeResponse. // This led to a division by zero as y1 crosses zero. The problem occurred in an // FMU simulation. Therefore, we guard against division by zero when computing // x2[i]. // roo.bouConExtWin.sha[1].ove.x2[1] := roo.bouConExtWin.sha[1].ove.x1* // roo.bouConExtWin.sha[1].ove.tmpH[1]/roo.bouConExtWin.sha[1].ove.y1; // x2[i]*y1 = x1*tmpH[i]; x2[i] = x1*tmpH[i]/Buildings.Utilities.Math.Functions.smoothMax( x1=y1, x2=1E-8*hWin, deltaX=1E-9*hWin); area[i] = Buildings.Utilities.Math.Functions.smoothMin( x1=y1, x2=y2[i], deltaX=del_L)*tmpW[i] - (Buildings.Utilities.Math.Functions.smoothMin( y1, tmpH[i], del_L)*Buildings.Utilities.Math.Functions.smoothMin( x1=x2[i], x2=y1, deltaX=del_L)/2) + Buildings.Utilities.Math.Functions.smoothMax( x1=shdwTrnglRtio*(Buildings.Utilities.Math.Functions.smoothMin( x1=x1, x2=x2[i], deltaX=del_L) - tmpW[i]), x2=0, deltaX=del_L)*Buildings.Utilities.Math.Functions.smoothMax( x1=(Buildings.Utilities.Math.Functions.smoothMin( x1=x1, x2=x2[i], deltaX=del_L) - tmpW[i]), x2=0, deltaX=del_L)/2; end for; shdArea = area[4] + area[3] - area[2] - area[1]; // correction case: Sun not in front of the wall crShdArea1 = Buildings.Utilities.Math.Functions.spliceFunction( pos=shdArea, neg=AWin, x=(Modelica.Constants.pi/2)-verAzi, deltax=0.01); // correction case: Sun not above horizon crShdArea2 = Buildings.Utilities.Math.Functions.spliceFunction( pos=shdArea, neg=AWin, x=alt, deltax=0.01); crShdArea=Buildings.Utilities.Math.Functions.smoothMax(x1=crShdArea1, x2=crShdArea2, deltaX=0.01); fraSun = Buildings.Utilities.Math.Functions.smoothMin( x1=Buildings.Utilities.Math.Functions.smoothMax(x1=1-crShdArea/AWin,x2=0,deltaX=0.01), x2=1.0, deltaX=0.01); else w = 0; tmpW=fill(0.0, 4); y1 = 0; x1 = 0; shdwTrnglRtio = 0; for i in 1:4 loop y2[i] = 0; x2[i] = 0; area[i] = 0; end for; shdArea = 0; crShdArea1 = 0; crShdArea2 = 0; crShdArea = 0; fraSun = 0; end if; connect(weaBus.solTim, solAzi.solTim); connect(weaBus.solZen, solAzi.zen); connect(weaBus.solDec, solAzi.decAng); end Overhang;

## Buildings.HeatTransfer.Windows.BaseClasses.PartialRadiation

Partial model for variables and data used in radiation calculation

### Information

The model calculates solar absorbance on the window. The calculations follow the description in Wetter (2004), Appendix A.4.3.

#### References

- Michael Wetter.
  Simulation-based Building Energy Optimization.
  Dissertation. University of California at Berkeley. 2004.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block), Buildings.HeatTransfer.Windows.BaseClasses.RadiationBaseData (Basic parameters for window radiation calculation).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Boolean | haveExteriorShade |  | Set to true if window has an exterior shade
Boolean | haveInteriorShade |  | Set to true if window has an interior shade
Area | AWin |  | Area of window [m2]
Glass
Integer | N |  | Number of glass layers
Length | xGla[N] |  | Thickness of glass [m]
TransmissionCoefficient | tauGlaSol[N] |  | Solar transmissivity of glass [1]
ReflectionCoefficient | rhoGlaSol_a[N] |  | Solar reflectivity of glass at surface a (facing outside) [1]
ReflectionCoefficient | rhoGlaSol_b[N] |  | Solar reflectivity of glass at surface b (facing room-side) [1]
Shade
TransmissionCoefficient | tauShaSol_a |  | Solar transmissivity of shade for irradiation from air-side [1]
TransmissionCoefficient | tauShaSol_b |  | Solar transmissivity of shade for irradiation from glass-side [1]
ReflectionCoefficient | rhoShaSol_a |  | Solar reflectivity of shade for irradiation from air-side [1]
ReflectionCoefficient | rhoShaSol_b |  | Solar reflectivity of shade for irradiation from glass-side [1]

### Connectors

Type | Name | Description
--- | --- | ---
input RealInput | uSha | Control signal for shading (0: unshaded; 1: fully shaded)
input RealInput | HDif | Diffussive solar radiation [W/m2]
input RealInput | incAng | Incident angle [rad]
input RealInput | HDir | Direct solar radiation [W/m2]

### Modelica definition

partial block PartialRadiation "Partial model for variables and data used in radiation calculation" extends Modelica.Blocks.Icons.Block; extends Buildings.HeatTransfer.Windows.BaseClasses.RadiationBaseData; ////////////////// Parameters that are not used by RadiationData parameter Boolean haveExteriorShade "Set to true if window has an exterior shade"; parameter Boolean haveInteriorShade "Set to true if window has an interior shade"; parameter Modelica.SIunits.Area AWin "Area of window"; ////////////////// Derived parameters final parameter Boolean haveShade=haveExteriorShade or haveInteriorShade "Set to true if window has a shade"; final parameter Buildings.HeatTransfer.Windows.BaseClasses.RadiationData radDat( final N=N, final tauGlaSol=tauGlaSol, final rhoGlaSol_a=rhoGlaSol_a, final rhoGlaSol_b=rhoGlaSol_b, final xGla=xGla, final tauShaSol_a=tauShaSol_a, final tauShaSol_b=tauShaSol_b, final rhoShaSol_a=rhoShaSol_a, final rhoShaSol_b=rhoShaSol_b) "Optical properties of window for different irradiation angles"; Modelica.Blocks.Interfaces.RealInput uSha(min=0, max=1) if haveShade "Control signal for shading (0: unshaded; 1: fully shaded)"; Modelica.Blocks.Interfaces.RealInput HDif(quantity="RadiantEnergyFluenceRate", unit="W/m2") "Diffussive solar radiation"; Modelica.Blocks.Interfaces.RealInput incAng( final quantity="Angle", final unit="rad", displayUnit="deg") "Incident angle"; Modelica.Blocks.Interfaces.RealInput HDir(quantity="RadiantEnergyFluenceRate", unit="W/m2") "Direct solar radiation"; protected Modelica.Blocks.Interfaces.RealInput uSha_internal(min=0, max=1) "Control signal for shading (0: unshaded; 1: fully shaded)"; initial equation /* Current model assumes that the window only has either an interior or exterior shade. Warn user if it has an interior and exterior shade. Allowing both shades at the same time would require rewriting part of the model. */ assert(not (haveExteriorShade and haveInteriorShade), "Window radiation model does not support an exterior and interior shade at the same time."); equation // Connect statement for conditionally removed connector uSha connect(uSha, uSha_internal); if (not haveShade) then uSha_internal = 0; end if; end PartialRadiation;

## Buildings.HeatTransfer.Windows.BaseClasses.PartialShade_weatherBus

Partial model to implement overhang and side fins with weather bus connector

### Information

Partial model to implement overhang and side fin model with weather bus as a connector.

Extends from Buildings.HeatTransfer.Windows.BaseClasses.ShadeInterface_weatherBus (Base class for models of window shade and overhangs).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Window
Length | hWin |  | Window height [m]
Length | wWin |  | Window width [m]

### Connectors

Type | Name | Description
--- | --- | ---
Bus | weaBus | Weather data bus
input RealInput | incAng | Solar incidence angle [rad]
input RealInput | HDirTilUns | Direct solar irradiation on tilted, unshaded surface [W/m2]
output RealOutput | HDirTil | Direct solar irradiation on tilted, shaded surface [W/m2]
output RealOutput | fraSun | Fraction of the area that is unshaded [1]

### Modelica definition

partial model PartialShade_weatherBus "Partial model to implement overhang and side fins with weather bus connector" extends Buildings.HeatTransfer.Windows.BaseClasses.ShadeInterface_weatherBus; // Window dimensions parameter Modelica.SIunits.Length hWin "Window height"; parameter Modelica.SIunits.Length wWin "Window width"; protected Buildings.BoundaryConditions.SolarGeometry.BaseClasses.WallSolarAzimuth walSolAzi "Wall solar azimuth"; Modelica.Blocks.Math.Product product; equation connect(weaBus.solAlt, walSolAzi.alt); connect(walSolAzi.incAng, incAng); connect(product.y, HDirTil); connect(product.u1, HDirTilUns); end PartialShade_weatherBus;

## Buildings.HeatTransfer.Windows.BaseClasses.PartialWindowBoundaryCondition

Partial model for heat convection or radiation between a possibly shaded window that can be outside or inside the room

### Information

Partial model for boundary conditions for convection and radiation for a window surface with or without shade, that is outside or inside the room.

This allows using the model as a base class for windows with inside shade, outside shade, or no shade.

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Area | A |  | Heat transfer area of frame and window [m2]
Real | fFra |  | Fraction of window frame divided by total window area
Shading
Boolean | haveExteriorShade |  | Set to true if window has exterior shade (at surface a)
Boolean | haveInteriorShade |  | Set to true if window has interior shade (at surface b)
Boolean | thisSideHasShade |  | Set to true if this side of the model has a shade

### Connectors

Type | Name | Description
--- | --- | ---
input RealInput | uSha | Input connector, used to scale the surface area to take into account an operable shading device, 0: unshaded; 1: fully shaded
HeatPort_a | air | Port that connects to the air (room or outside)
HeatPort_b | glaUns | Heat port that connects to unshaded part of glass
HeatPort_b | glaSha | Heat port that connects to shaded part of glass
HeatPort_a | frame | Heat port at window frame

### Modelica definition

partial model PartialWindowBoundaryCondition "Partial model for heat convection or radiation between a possibly shaded window that can be outside or inside the room" parameter Modelica.SIunits.Area A "Heat transfer area of frame and window"; parameter Real fFra "Fraction of window frame divided by total window area"; final parameter Modelica.SIunits.Area AFra = fFra * A "Frame area"; final parameter Modelica.SIunits.Area AGla = A-AFra "Glass area"; parameter Boolean haveExteriorShade "Set to true if window has exterior shade (at surface a)"; parameter Boolean haveInteriorShade "Set to true if window has interior shade (at surface b)"; final parameter Boolean haveShade = haveExteriorShade or haveInteriorShade "Set to true if window system has a shade"; parameter Boolean thisSideHasShade "Set to true if this side of the model has a shade"; Modelica.Blocks.Interfaces.RealInput uSha if haveShade "Input connector, used to scale the surface area to take into account an operable shading device, 0: unshaded; 1: fully shaded"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a air "Port that connects to the air (room or outside)"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_b glaUns "Heat port that connects to unshaded part of glass"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_b glaSha if haveShade "Heat port that connects to shaded part of glass"; protected Modelica.Blocks.Math.Product proSha if haveShade "Product for shaded part of window"; ShadingSignal shaSig(final haveShade=haveShade) "Conversion for shading signal"; public Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a frame "Heat port at window frame"; initial equation assert(( thisSideHasShade and haveShade) or (not thisSideHasShade), "Parameters \"thisSideHasShade\" and \"haveShade\" are not consistent. Check parameters"); equation connect(uSha, shaSig.u); connect(proSha.u2, shaSig.y); end PartialWindowBoundaryCondition;

## Buildings.HeatTransfer.Windows.BaseClasses.ShadeConvection

Model for convective heat balance of a layer that may or may not have a shade

### Information

Model for the convective heat balance of a shade that is in the outside or the room-side of a window.

The convective heat balance is based on the model described by Wright (2008), which can be shown as a convective heat resistance model as follows:

Wright (2008) reports that if the shading layer is far enough from the window, the boundary layers associated with each surface will not interfere with each other. In this case, it is reasonable to consider each surface on an individual basis by setting the convective heat transfer coefficient shown in grey to zero, and setting the black depicted convective heat transfer coefficients to h=4 W/m2 K. In the here implemented model, the grey depicted convective heat transfer coefficient is set set to h' = k h, where 0 ≤ k ≤ 1 is a parameter.

#### References

- Jon L. Wright.
  Calculating Center-Glass Performance Indices of Glazing Systems with Shading Devices.
  ASHRAE Transactions, SL-08-020. 2008.

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Area | A |  | Heat transfer area [m2]
Boolean | thisSideHasShade |  | Set to true if this side of the window has a shade
Real | k | 1 | Coefficient used to scale convection between shade and glass

### Connectors

Type | Name | Description
--- | --- | ---
input RealInput | Gc | Signal representing the convective thermal conductance [W/K]
HeatPort_a | air | Port that connects to the air (room or outside)
HeatPort_b | glass | Heat port that connects to shaded part of glass
input RealInput | QRadAbs_flow | Total net radiation that is absorbed by the shade (positive if absorbed) [W]
output RealOutput | TSha | Shade temperature [K]

### Modelica definition

model ShadeConvection "Model for convective heat balance of a layer that may or may not have a shade" parameter Modelica.SIunits.Area A "Heat transfer area"; parameter Boolean thisSideHasShade "Set to true if this side of the window has a shade"; parameter Real k(min=0, max=1)=1 "Coefficient used to scale convection between shade and glass"; Modelica.Blocks.Interfaces.RealInput Gc(unit="W/K") "Signal representing the convective thermal conductance"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a air "Port that connects to the air (room or outside)"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_b glass "Heat port that connects to shaded part of glass"; Modelica.Blocks.Interfaces.RealInput QRadAbs_flow(unit="W") "Total net radiation that is absorbed by the shade (positive if absorbed)"; Modelica.Blocks.Interfaces.RealOutput TSha(quantity="ThermodynamicTemperature", unit="K") "Shade temperature"; equation if thisSideHasShade then // Convective heat balance of shade. // The term 2*Gc is to combine the parallel convective heat transfer resistances, // see figure in info section. // 2*(air.T-TSha) = k*(glass.T-TSha); // Convective heat flow at air node air.Q_flow = Gc*(2*(air.T-TSha) + (air.T-glass.T)); // Convective heat flow at glass node glass.Q_flow = Gc*((glass.T-air.T)+k*(glass.T-TSha)); air.Q_flow + glass.Q_flow + QRadAbs_flow = 0; else air.Q_flow = Gc*(air.T-glass.T); air.Q_flow + glass.Q_flow = 0; TSha = (air.T+glass.T)/2; end if; end ShadeConvection;

## Buildings.HeatTransfer.Windows.BaseClasses.ShadeInterface_weatherBus

Base class for models of window shade and overhangs

### Information

Partial model to implement overhang and side fin model with weather bus as a connector.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

### Connectors

Type | Name | Description
--- | --- | ---
Bus | weaBus | Weather data bus
input RealInput | incAng | Solar incidence angle [rad]
input RealInput | HDirTilUns | Direct solar irradiation on tilted, unshaded surface [W/m2]
output RealOutput | HDirTil | Direct solar irradiation on tilted, shaded surface [W/m2]
output RealOutput | fraSun | Fraction of the area that is unshaded [1]

### Modelica definition

partial model ShadeInterface_weatherBus "Base class for models of window shade and overhangs" extends Modelica.Blocks.Icons.Block; Buildings.BoundaryConditions.WeatherData.Bus weaBus "Weather data bus"; Modelica.Blocks.Interfaces.RealInput incAng(quantity="Angle", unit="rad", displayUnit="rad") "Solar incidence angle"; Modelica.Blocks.Interfaces.RealInput HDirTilUns( quantity="RadiantEnergyFluenceRate", unit="W/m2") "Direct solar irradiation on tilted, unshaded surface"; Modelica.Blocks.Interfaces.RealOutput HDirTil( quantity="RadiantEnergyFluenceRate", unit="W/m2") "Direct solar irradiation on tilted, shaded surface"; Modelica.Blocks.Interfaces.RealOutput fraSun(final min=0, final max=1, final unit="1") "Fraction of the area that is unshaded"; end ShadeInterface_weatherBus;

## Buildings.HeatTransfer.Windows.BaseClasses.ShadeRadiation

Model for infrared radiative heat balance of a layer that may or may not have a shade

### Information

Model for the infrared radiative heat balance of a shade that is at the outside or the room-side of a window. The model also includes the absorbed solar radiation.

The input port `QAbs_flow` needs to be connected to the solar radiation that is absorbed by the shade.

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Area | A |  | Heat transfer area [m2]
Emissivity | absIR_air |  | Infrared absorptivity of surface that faces air [1]
Emissivity | absIR_glass |  | Infrared absorptivity of surface that faces glass [1]
TransmissionCoefficient | tauIR_air |  | Infrared transmissivity of shade for radiation coming from the exterior or the room [1]
TransmissionCoefficient | tauIR_glass |  | Infrared transmissivity of shade for radiation coming from the glass [1]
Boolean | thisSideHasShade |  | Set to true if this side of the window has a shade
Boolean | linearize | false | Set to true to linearize emissive power
Temperature | T0 | 293.15 | Temperature used to linearize radiative heat transfer [K]
Advanced
Boolean | homotopyInitialization | true | = true, use homotopy method

### Connectors

Type | Name | Description
--- | --- | ---
input RealInput | u | Input connector, used to scale the surface area to take into account an operable shading device
input RealInput | QSolAbs_flow | Solar radiation absorbed by shade [W]
input RadiosityInflow | JIn_air | Incoming radiosity at the air-side surface of the shade [W]
input RadiosityInflow | JIn_glass | Incoming radiosity at the glass-side surface of the shade [W]
output RadiosityOutflow | JOut_air | Outgoing radiosity at the air-side surface of the shade [W]
output RadiosityOutflow | JOut_glass | Outgoing radiosity at the glass-side surface of the shade [W]
output RealOutput | QRadAbs_flow | Total net radiation that is absorbed by the shade (positive if absorbed) [W]
input RealInput | TSha | Shade temperature [K]

### Modelica definition

model ShadeRadiation "Model for infrared radiative heat balance of a layer that may or may not have a shade" parameter Modelica.SIunits.Area A "Heat transfer area"; parameter Modelica.SIunits.Emissivity absIR_air "Infrared absorptivity of surface that faces air"; parameter Modelica.SIunits.Emissivity absIR_glass "Infrared absorptivity of surface that faces glass"; parameter Modelica.SIunits.TransmissionCoefficient tauIR_air "Infrared transmissivity of shade for radiation coming from the exterior or the room"; parameter Modelica.SIunits.TransmissionCoefficient tauIR_glass "Infrared transmissivity of shade for radiation coming from the glass"; parameter Boolean thisSideHasShade "Set to true if this side of the window has a shade"; final parameter Modelica.SIunits.ReflectionCoefficient rhoIR_air=1-absIR_air-tauIR_air "Infrared reflectivity of surface that faces air"; final parameter Modelica.SIunits.ReflectionCoefficient rhoIR_glass=1-absIR_glass-tauIR_glass "Infrared reflectivity of surface that faces glass"; parameter Boolean linearize = false "Set to true to linearize emissive power"; parameter Boolean homotopyInitialization = true "= true, use homotopy method"; parameter Modelica.SIunits.Temperature T0=293.15 "Temperature used to linearize radiative heat transfer"; Modelica.Blocks.Interfaces.RealInput u "Input connector, used to scale the surface area to take into account an operable shading device"; Modelica.Blocks.Interfaces.RealInput QSolAbs_flow(unit="W", quantity="Power") "Solar radiation absorbed by shade"; Interfaces.RadiosityInflow JIn_air(start=A*0.8*Modelica.Constants.sigma*293.15^4) "Incoming radiosity at the air-side surface of the shade"; Interfaces.RadiosityInflow JIn_glass(start=A*0.8*Modelica.Constants.sigma*293.15^4) "Incoming radiosity at the glass-side surface of the shade"; Interfaces.RadiosityOutflow JOut_air "Outgoing radiosity at the air-side surface of the shade"; Interfaces.RadiosityOutflow JOut_glass "Outgoing radiosity at the glass-side surface of the shade"; Modelica.Blocks.Interfaces.RealOutput QRadAbs_flow(unit="W") "Total net radiation that is absorbed by the shade (positive if absorbed)"; Modelica.Blocks.Interfaces.RealInput TSha(quantity="ThermodynamicTemperature", unit="K", start=293.15) if thisSideHasShade "Shade temperature"; protected Modelica.Blocks.Interfaces.RealInput TSha_internal(quantity="ThermodynamicTemperature", unit="K", start=293.15) "Internal connector for shade temperature"; final parameter Real T03(min=0, final unit="K3")=T0^3 "3rd power of temperature T0"; Real T4(min=1E8, start=293.15^4, nominal=1E10, final unit="K4") "4th power of temperature"; Modelica.SIunits.RadiantPower E_air "Emissive power of surface that faces air"; Modelica.SIunits.RadiantPower E_glass "Emissive power of surface that faces glass"; equation connect(TSha_internal, TSha); if thisSideHasShade then // Radiosities that are outgoing from the surface, which are // equal to the infrared absorptivity plus the reflected incoming // radiosity plus the radiosity that is transmitted from the // other surface. if linearize then T4 = T03 * TSha_internal; else if homotopyInitialization then T4 = homotopy(actual=(TSha_internal)^4, simplified=T03 * TSha_internal); else T4 = TSha_internal^4; end if; end if; E_air = u * A * absIR_air * Modelica.Constants.sigma * T4; E_glass = u * A * absIR_glass * Modelica.Constants.sigma * T4; // Radiosity outgoing from shade towards air side and glass side JOut_air = E_air + tauIR_glass * JIn_glass + rhoIR_air*JIn_air; JOut_glass = E_glass + tauIR_air * JIn_air + rhoIR_glass*JIn_glass; // Radiative heat balance of shade. QSolAbs_flow + absIR_air*JIn_air + absIR_glass*JIn_glass = E_air+E_glass+QRadAbs_flow; else QRadAbs_flow = 0; T4 = T03 * T0; E_air = 0; E_glass = 0; JOut_air = JIn_glass; JOut_glass = JIn_air; TSha_internal = T0; end if; end ShadeRadiation;

## Buildings.HeatTransfer.Windows.BaseClasses.ShadingSignal

Converts the shading signal to be strictly bigger than 0 and smaller than 1

### Information

This model changes the shading control signal to avoid a singularity in the window model if the input signal is zero or one. Since the window heat balance multiplies the area of the window by `u` or by `1-u` (if a shade is present), the heat balance can be singular for `u=0` or for `u=1`. This model avoids this singularity by slightly changing the control signal.

Extends from Modelica.Blocks.Interfaces.SO (Single Output continuous control block).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Boolean | haveShade |  | Set to true if a shade is present

### Connectors

Type | Name | Description
--- | --- | ---
output RealOutput | y | Connector of Real output signal
input RealInput | u | Shading control signal, 0: unshaded; 1: fully shaded
output RealOutput | yCom | 1-u

### Modelica definition

block ShadingSignal "Converts the shading signal to be strictly bigger than 0 and smaller than 1" extends Modelica.Blocks.Interfaces.SO; parameter Boolean haveShade "Set to true if a shade is present"; Modelica.Blocks.Interfaces.RealInput u if haveShade "Shading control signal, 0: unshaded; 1: fully shaded"; Modelica.Blocks.Interfaces.RealOutput yCom "1-u"; protected constant Real y0 = 1E-6 "Smallest allowed value for y if a shade is present"; constant Real k = 1-2*y0 "Gain for shading signal"; Modelica.Blocks.Interfaces.RealInput u_in_internal "Needed to connect to conditional connector"; equation connect(u, u_in_internal); if not haveShade then u_in_internal = 0; end if; if haveShade then y = y0 + k * u_in_internal; yCom = 1-y; else y = 0; yCom = 1; end if; end ShadingSignal;

## Buildings.HeatTransfer.Windows.BaseClasses.SideFins

For a window with side fins, outputs the fraction of the area that is sun exposed

### Information

For a window with side fins, this block outputs the fraction of the area that is exposed to the sun. This models can also be used for doors with side fins.

Input to this block are the wall solar azimuth angle and the altitude angle of the sun. These angles can be calculated using blocks from the package Buildings.BoundaryConditions.SolarGeometry.BaseClasses.

#### Limitations

The model assumes that

- the side fins are placed symmetrically to the left and right of the window,
- the top of the side fins must be at an equal or greater height than the window, and
- the bottom of the side fins must be at an equal or lower height than the bottom of the window.

#### Implementation

The method of super position is used to calculate the shaded area of the window. The area besides the side fin is divided as shown in the figure below.

Variables used in the code for the rectangle AEGI, BEGH, DFGI and CFGH are shown in figure below.

The rectangles AEGI, BEGH, DFGI and CFGH have the same geometric configuration with respect to the side fin. Thus, the same algorithm is used to calculate the shaded portion in these areas. A single equation in the `for` loop improves the total calculation time, as compared to `if-then-else` conditions, considering the various shapes of the shaded portions. To find the shaded area in the window ABCD, the shaded portion of BEGH and DFGI is subtracted from AEGI and CFGH. This shaded area of the window is then divided by the total window area to calculate the shaded fraction of the window.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block), Buildings.Rooms.BaseClasses.SideFins (Record for window side fins).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Side fin
Length | h |  | Height of side fin that extends above window, measured from top of window [m]
Length | dep |  | Side fin depth (measured perpendicular to the wall plane) [m]
Length | gap |  | Distance between side fin and window edge [m]
Window
Length | hWin |  | Window height [m]
Length | wWin |  | Window width [m]

### Connectors

Type | Name | Description
--- | --- | ---
input RealInput | alt | Solar altitude angle (angle between sun ray and horizontal surface) [rad]
input RealInput | verAzi | Angle between projection of sun's rays and normal to vertical surface [rad]
output RealOutput | fraSun | Fraction of window area exposed to the sun [1]

### Modelica definition

block SideFins "For a window with side fins, outputs the fraction of the area that is sun exposed" extends Modelica.Blocks.Icons.Block; extends Buildings.Rooms.BaseClasses.SideFins; Modelica.Blocks.Interfaces.RealInput alt(quantity="Angle", unit="rad", displayUnit="deg") "Solar altitude angle (angle between sun ray and horizontal surface)"; Modelica.Blocks.Interfaces.RealInput verAzi(quantity="Angle", unit="rad", displayUnit="deg") "Angle between projection of sun's rays and normal to vertical surface"; Modelica.Blocks.Interfaces.RealOutput fraSun(final min=0, final max=1, final unit="1") "Fraction of window area exposed to the sun"; // Window dimensions parameter Modelica.SIunits.Length hWin "Window height"; parameter Modelica.SIunits.Length wWin "Window width"; // Other calculation variables protected final parameter Modelica.SIunits.Length tmpH[4]= {h+hWin, h, h+hWin, h} "Height of rectangular sections used for superposition"; final parameter Modelica.SIunits.Length tmpW[4]= {gap + wWin,gap + wWin,gap, gap} "Width of rectangular sections used for superpositions; c1,c2 etc"; final parameter Modelica.SIunits.Length deltaL=wWin/100 "Fraction of window dimension over which min-max functions are smoothened"; final parameter Modelica.SIunits.Area AWin=hWin*wWin "Window area"; Modelica.SIunits.Length x1[4] "Horizontal distance between side fin and point where shadow line and window lower edge intersects"; Modelica.SIunits.Length x2 "Horizontal distance between side fin and shadow corner"; Modelica.SIunits.Length x3[4] "Window width"; Modelica.SIunits.Length y1[4] "Window height"; Modelica.SIunits.Length y2 "Vertical distance between window upper edge and shadow corner"; Modelica.SIunits.Length y3[4] "Vertical distance between window upper edge and point where shadow line and window side edge intersects"; Modelica.SIunits.Area area[4] "Shaded areas of the sections used in superposition"; Modelica.SIunits.Area shdArea "Shaded area"; Modelica.SIunits.Area crShdArea "Final value of shaded area"; Modelica.SIunits.Area crShdArea1 "Shaded area, corrected for the sun behind the surface/wall"; Modelica.SIunits.Area crShdArea2 "Shaded area, corrected for the sun below horizon"; Modelica.SIunits.Length minX[4]; Modelica.SIunits.Length minY[4]; Modelica.SIunits.Length minX2X3[4]; Modelica.SIunits.Length minY2Y3[4]; Real delta=1e-6 "Small number to avoid division by zero"; Real tanLambda "Tangent of angle between horizontal and sun ray projection on vertical wall"; Real verAzi_t; Real lambda_t; Real verAzi_c; Real alt_t; initial algorithm assert(h >= 0, "Sidefin parameter 'h' must be at least zero. It is measured from the upper edge of the window to the top of the side fin. Received h = " + String(h)); equation // This if-then construct below increases computing efficiency in // Buildings.HeatTransfer.Windows.FixedShade in case the window has no overhang. if haveSideFins then //avoiding division by zero lambda_t = Buildings.Utilities.Math.Functions.smoothMax( x1=tanLambda, x2=delta, deltaX=delta/10); verAzi_t = Buildings.Utilities.Math.Functions.smoothMax( x1=Modelica.Math.tan(verAzi), x2=delta, deltaX=delta/10); verAzi_c = Buildings.Utilities.Math.Functions.smoothMax( x1=Modelica.Math.cos(verAzi), x2=delta, deltaX=delta/10); alt_t = Buildings.Utilities.Math.Functions.smoothMax( x1=Modelica.Math.tan(alt), x2=delta, deltaX=delta/10); tanLambda = alt_t / verAzi_t; y2 = dep*alt_t/verAzi_c; x2 = dep*verAzi_t; for i in 1:4 loop x1[i] = tmpH[i]/lambda_t; x3[i] = tmpW[i]; y1[i] = tmpH[i]; y3[i] = tmpW[i]*lambda_t; minX2X3[i] = Buildings.Utilities.Math.Functions.smoothMin( x1=x2, x2=x3[i], deltaX=deltaL); minX[i] = Buildings.Utilities.Math.Functions.smoothMin( x1=x1[i], x2=minX2X3[i], deltaX=deltaL); minY2Y3[i] = Buildings.Utilities.Math.Functions.smoothMin( x1=y2, x2=y3[i], deltaX=deltaL); minY[i] = Buildings.Utilities.Math.Functions.smoothMin( x1=y1[i], x2=minY2Y3[i], deltaX=deltaL); area[i] = tmpH[i]*minX[i] - minX[i]*minY[i]/2; end for; //by superposition shdArea = area[1] + area[4] - area[2] - area[3]; // The corrections below ensure that the shaded area is 1 if the // sun is below the horizon or behind the wall. // This correction is not required (because the direct solar irradiation // will be zero in this case), but it leads to more realistic time series // of this model. //correction case: Sun not in front of the wall crShdArea1 = Buildings.Utilities.Math.Functions.spliceFunction( pos=shdArea, neg=AWin, x=(Modelica.Constants.pi/2)-verAzi, deltax=0.01); //correction case: Sun below horizon crShdArea2 = Buildings.Utilities.Math.Functions.spliceFunction( pos=shdArea, neg=AWin, x=alt, deltax=0.01); crShdArea=Buildings.Utilities.Math.Functions.smoothMax( x1=crShdArea1, x2=crShdArea2, deltaX=0.0001*AWin); fraSun = 1-crShdArea/AWin; else lambda_t = 0; verAzi_t = 0; verAzi_c = 0; alt_t = 0; tanLambda = 0; y2 = 0; x2 = 0; x1 = fill(0.0, 4); x3 = fill(0.0, 4); y1 = fill(0.0, 4); y3 = fill(0.0, 4); minX2X3 = fill(0.0, 4); minX = fill(0.0, 4); minY2Y3 = fill(0.0, 4); minY = fill(0.0, 4); area = fill(0.0, 4); shdArea = 0; crShdArea1 = 0; crShdArea2 = 0; crShdArea = 0; fraSun = 0; end if; end SideFins;

## Buildings.HeatTransfer.Windows.BaseClasses.ThermalConductor

Lumped thermal element with variable area, transporting heat without storing it

### Information

This is a model for transport of heat without storing it. It is identical to the thermal conductor from the Modelica Standard Library, except that it adds an input signal `u`.

Extends from Modelica.Thermal.HeatTransfer.Interfaces.Element1D (Partial heat transfer element with two HeatPort connectors that does not store energy).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
ThermalConductance | G |  | Constant thermal conductance of material [W/K]

### Connectors

Type | Name | Description
--- | --- | ---
HeatPort_a | port_a |
HeatPort_b | port_b |
input RealInput | u | Input signal for thermal conductance

### Modelica definition

model ThermalConductor "Lumped thermal element with variable area, transporting heat without storing it" extends Modelica.Thermal.HeatTransfer.Interfaces.Element1D; parameter Modelica.SIunits.ThermalConductance G "Constant thermal conductance of material"; Modelica.Blocks.Interfaces.RealInput u(min=0) "Input signal for thermal conductance"; equation Q_flow = u*G*dT; end ThermalConductor;

## Buildings.HeatTransfer.Windows.BaseClasses.TransmittedRadiation

Transmitted radiation through window

### Information

The model calculates solar radiation through the window. The calculations follow the description in Wetter (2004), Appendix A.4.3.
The transmitted exterior radiation for window system includes:

1. the transmitted diffusive radiation on unshaded part: `AWin*(1-uSha)*HDif*tau(HEM)`
2. the transmitted direct radiation on no shade part: `AWin*(1-uSha)*HDir*tau(IncAng)`
3. the transmitted diffusive radiation on shaded part: `AWin*uSha*HDif*tauSha(HEM)`
4. the transmitted direct radiation on shaded part: `AWin*uSha*HDir*tauSha(IncAng);`

The output is `QTra_flow = Part1 + Part2 + Part3 + Part4`

#### References

- Michael Wetter.
  Simulation-based Building Energy Optimization.
  Dissertation. University of California at Berkeley. 2004.

Extends from Buildings.HeatTransfer.Windows.BaseClasses.PartialRadiation (Partial model for variables and data used in radiation calculation).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Boolean | haveExteriorShade |  | Set to true if window has an exterior shade
Boolean | haveInteriorShade |  | Set to true if window has an interior shade
Area | AWin |  | Area of window [m2]
Glass
Integer | N |  | Number of glass layers
Length | xGla[N] |  | Thickness of glass [m]
TransmissionCoefficient | tauGlaSol[N] |  | Solar transmissivity of glass [1]
ReflectionCoefficient | rhoGlaSol_a[N] |  | Solar reflectivity of glass at surface a (facing outside) [1]
ReflectionCoefficient | rhoGlaSol_b[N] |  | Solar reflectivity of glass at surface b (facing room-side) [1]
Shade
TransmissionCoefficient | tauShaSol_a |  | Solar transmissivity of shade for irradiation from air-side [1]
TransmissionCoefficient | tauShaSol_b |  | Solar transmissivity of shade for irradiation from glass-side [1]
ReflectionCoefficient | rhoShaSol_a |  | Solar reflectivity of shade for irradiation from air-side [1]
ReflectionCoefficient | rhoShaSol_b |  | Solar reflectivity of shade for irradiation from glass-side [1]

### Connectors

Type | Name | Description
--- | --- | ---
input RealInput | uSha | Control signal for shading (0: unshaded; 1: fully shaded)
input RealInput | HDif | Diffussive solar radiation [W/m2]
input RealInput | incAng | Incident angle [rad]
input RealInput | HDir | Direct solar radiation [W/m2]
output RealOutput | QTra_flow | Transmitted exterior radiation through the window. (1: no shade; 2: shade) [W]

### Modelica definition

block TransmittedRadiation "Transmitted radiation through window" extends Buildings.HeatTransfer.Windows.BaseClasses.PartialRadiation; Modelica.Blocks.Interfaces.RealOutput QTra_flow(final quantity="Power", final unit="W") "Transmitted exterior radiation through the window. (1: no shade; 2: shade)"; final parameter Real traCoeRoo(fixed=false) "Transmitivity of the window glass for interior radiation without shading"; output Modelica.SIunits.Power QTraUns_flow "Transmitted solar radiation through unshaded part of window"; output Modelica.SIunits.Power QTraSha_flow "Transmitted solar radiation through shaded part of window"; protected Real x "Intermediate variable"; final parameter Integer NDIR=radDat.NDIR; final parameter Integer HEM=radDat.HEM; constant Integer NoShade=1; constant Integer Shade=2; constant Integer Interior=1; constant Integer Exterior=2; final parameter Real coeTraWinExtIrr[2, radDat.HEM + 2](each fixed=false); Real tmpNoSha; Real tmpSha; Real incAng2; initial equation //************************************************************** // Assign coefficients. // Data dimension from Original ([1 : HEM]) to New ([2 : HEM+1]) // with 2 dummy variable for interpolation. //************************************************************** // Glass for j in 1:HEM loop // Properties for glass without shading coeTraWinExtIrr[NoShade, j + 1] = radDat.traRef[1, 1, N, j]; // Properties for glass with shading if haveInteriorShade then coeTraWinExtIrr[Shade, j + 1] = radDat.winTraExtIrrIntSha[j]; elseif haveExteriorShade then coeTraWinExtIrr[Shade, j + 1] = radDat.winTraExtIrrExtSha[j]; else // No Shade coeTraWinExtIrr[Shade, j + 1] = 0.0; end if; end for; // Dummy variables at 1 and HEM+2 for k in NoShade:Shade loop coeTraWinExtIrr[k, 1] = coeTraWinExtIrr[k, 2]; coeTraWinExtIrr[k, HEM + 2] = coeTraWinExtIrr[k, HEM + 1]; end for; //************************************************************** // Glass: transmissivity for interior irradiation //************************************************************** traCoeRoo = radDat.traRef[1, N, 1, HEM]; algorithm QTraUns_flow := AWin*HDif*(1 - uSha_internal)*coeTraWinExtIrr[NoShade, HEM + 1]; QTraSha_flow := AWin*HDif*uSha_internal*coeTraWinExtIrr[Shade, HEM + 1]; //************************************************************** // Glass, Device: add absorbed radiation (angular part) from exterior sources //************************************************************** // Use min() instead of if() to avoid event incAng2 := min(incAng, 0.5*Modelica.Constants.pi); x := 2*(NDIR - 1)*abs(incAng2)/Modelica.Constants.pi "x=(index-1)*incAng/(0.5pi), 0<=x<=NDIR-1"; x := x + 2; // Window unshaded parts: add transmitted radiation for angular radiation tmpNoSha := Buildings.HeatTransfer.Windows.BaseClasses.smoothInterpolation({ coeTraWinExtIrr[NoShade, k] for k in 1:(HEM + 2)}, x); QTraUns_flow := QTraUns_flow + AWin*HDir*(1 - uSha_internal)*tmpNoSha; // Window shaded parts: add transmitted radiation for angular radiation tmpSha := Buildings.HeatTransfer.Windows.BaseClasses.smoothInterpolation( {coeTraWinExtIrr[Shade, k] for k in 1:(HEM + 2)}, x); QTraSha_flow := QTraSha_flow + AWin*HDir*uSha_internal*tmpSha; // Assign quantities to output connectors QTra_flow := QTraUns_flow + QTraSha_flow; end TransmittedRadiation;

## Buildings.HeatTransfer.Windows.BaseClasses.WindowRadiation

Calculation radiation for window

### Information

The model calculates solar radiation through the window. The calculations follow the description in Wetter (2004), Appendix A.4.3.

The absorbed radiation by exterior shades includes:

1. the directly absorbed exterior radiation: `AWin*uSha*(HDir+HDif)*(1-tau-rho)`
2. the indirectly absorbed exterior radiantion from reflection (angular part): `AWin*uSha*HDir*tau*rho(IncAng)*(1-tau-rho)`
3. the indirectly absorbed of exterior irradiantion from reflection (diffusive part): `AWin*uSha*HDif*tau*rho(HEM)*(1-tau-rho)`
4. the absorbed interior radiation is neglected.

The output is `absRad[2, 1]`

The absorbed radiation by interior shades includes:

1. the absorbed exterior radiation (angular part): `AWin*uSha*HDir*alpha(IncAng)`
2. the absorbed exterior radiation (diffusive part): `AWin*uSha*HDif*alpha(HEM)`
3. the absorbed interior radiation (diffusive part): `AWin*uSha*HRoo*(1-tau-rho)`

The output is `absRad[2, N+2]`

The absorbed radiation by glass includes:

1. the absorbed radiation by unshaded part (diffusive part): `AWin*(1-uSha)*(HDif*alphaEx(HEM)+HRoo*alphaIn(HEM))`
2. the absorbed radiation by unshaded part (angualr part from exterior source): `AWin*(1-uSha)*HDir*alphaEx(IncAng)`
3. the absorbed radiaiton by shaded part (diffusive part): `AWin*uSha*(HDif*alphaExSha(HEM)+HRoo*alphaInSha(HEM))`
4. the absorbed radiation by shaded part (angular part from exterior source): `AWin*uSha*HDir*alphaExSha(IncAng)`

The output is `absRad[1, 2:N+1] = Part1 + Part2; absRad[2, 2:N+1] = Part3 + Part4`

The transmitted exterior radiation for window system includes:

1. the transmitted diffusive radiation on unshaded part: `AWin*(1-uSha)*HDif*tau(HEM)`
2. the transmitted direct radiation on no shade part: `AWin*(1-uSha)*HDir*tau(IncAng)`
3. the transmitted diffusive radiation on shaded part: `AWin*uSha*HDif*tauSha(HEM)`
4. the transmitted direct radiation on shaded part: `AWin*uSha*HDir*tauSha(IncAng);`

The output is `QTra_flow = Part1 + Part2 + Part3 + Part4`

#### References

- Michael Wetter.
  Simulation-based Building Energy Optimization.
  Dissertation. University of California at Berkeley. 2004.

Extends from Buildings.HeatTransfer.Windows.BaseClasses.PartialRadiation (Partial model for variables and data used in radiation calculation).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Boolean | haveExteriorShade |  | Set to true if window has an exterior shade
Boolean | haveInteriorShade |  | Set to true if window has an interior shade
Area | AWin |  | Area of window [m2]
Glass
Integer | N |  | Number of glass layers
Length | xGla[N] |  | Thickness of glass [m]
TransmissionCoefficient | tauGlaSol[N] |  | Solar transmissivity of glass [1]
ReflectionCoefficient | rhoGlaSol_a[N] |  | Solar reflectivity of glass at surface a (facing outside) [1]
ReflectionCoefficient | rhoGlaSol_b[N] |  | Solar reflectivity of glass at surface b (facing room-side) [1]
Shade
TransmissionCoefficient | tauShaSol_a |  | Solar transmissivity of shade for irradiation from air-side [1]
TransmissionCoefficient | tauShaSol_b |  | Solar transmissivity of shade for irradiation from glass-side [1]
ReflectionCoefficient | rhoShaSol_a |  | Solar reflectivity of shade for irradiation from air-side [1]
ReflectionCoefficient | rhoShaSol_b |  | Solar reflectivity of shade for irradiation from glass-side [1]

### Connectors

Type | Name | Description
--- | --- | ---
input RealInput | uSha | Control signal for shading (0: unshaded; 1: fully shaded)
input RealInput | HDif | Diffussive solar radiation [W/m2]
input RealInput | incAng | Incident angle [rad]
input RealInput | HDir | Direct solar radiation [W/m2]
input RealInput | HRoo | Diffussive radiation from room [W/m2]
output RealOutput | QTra_flow | Transmitted exterior radiation through the window. (1: no shade; 2: shade) [W]
output RealOutput | QAbsExtSha_flow | Absorbed interior and exterior radiation by exterior shading device [W]
output RealOutput | QAbsIntSha_flow | Absorbed interior and exterior radiation by interior shading device [W]
output RealOutput | QAbsGlaUns_flow[N] | Absorbed interior and exterior radiation by unshaded part of glass [W]
output RealOutput | QAbsGlaSha_flow[N] | Absorbed interior and exterior radiation by shaded part of glass [W]

### Modelica definition

block WindowRadiation "Calculation radiation for window" extends Buildings.HeatTransfer.Windows.BaseClasses.PartialRadiation; Modelica.Blocks.Interfaces.RealInput HRoo(quantity="RadiantEnergyFluenceRate", unit="W/m2") "Diffussive radiation from room "; Modelica.Blocks.Interfaces.RealOutput QTra_flow(final quantity="Power", final unit="W") "Transmitted exterior radiation through the window. (1: no shade; 2: shade)"; Modelica.Blocks.Interfaces.RealOutput QAbsExtSha_flow(final quantity="Power", final unit="W") "Absorbed interior and exterior radiation by exterior shading device"; Modelica.Blocks.Interfaces.RealOutput QAbsIntSha_flow(final quantity="Power", final unit="W") "Absorbed interior and exterior radiation by interior shading device"; Modelica.Blocks.Interfaces.RealOutput QAbsGlaUns_flow[N](each quantity= "Power", each final unit="W") "Absorbed interior and exterior radiation by unshaded part of glass"; Modelica.Blocks.Interfaces.RealOutput QAbsGlaSha_flow[N](each quantity= "Power", each final unit="W") "Absorbed interior and exterior radiation by shaded part of glass"; Buildings.HeatTransfer.Windows.BaseClasses.TransmittedRadiation tra( final N=N, final tauGlaSol=tauGlaSol, final rhoGlaSol_a=rhoGlaSol_a, final rhoGlaSol_b=rhoGlaSol_b, final xGla=xGla, final tauShaSol_a=tauShaSol_a, final rhoShaSol_a=rhoShaSol_a, final rhoShaSol_b=rhoShaSol_b, final haveExteriorShade=haveExteriorShade, final haveInteriorShade=haveInteriorShade, final AWin=AWin, final tauShaSol_b=tauShaSol_b); Buildings.HeatTransfer.Windows.BaseClasses.AbsorbedRadiation abs( final N=N, final tauGlaSol=tauGlaSol, final rhoGlaSol_a=rhoGlaSol_a, final rhoGlaSol_b=rhoGlaSol_b, final xGla=xGla, final tauShaSol_a=tauShaSol_a, final tauShaSol_b=tauShaSol_b, final rhoShaSol_a=rhoShaSol_a, final rhoShaSol_b=rhoShaSol_b, final haveExteriorShade=haveExteriorShade, final haveInteriorShade=haveInteriorShade, final AWin=AWin); protected final parameter Boolean noShade=not (haveExteriorShade or haveInteriorShade) "Flag, true if the window has a shade"; equation if noShade then assert(uSha_internal < 1E-6, "Window has no shade, but control signal is non-zero.\n" + " Received uSha_internal = " + String(uSha_internal)); end if; connect(HDif, tra.HDif); connect(HDif, abs.HDif); connect(HDir, tra.HDir); connect(HDir, abs.HDir); connect(incAng, tra.incAng); connect(incAng, abs.incAng); connect(HRoo, abs.HRoo); connect(tra.uSha, uSha); connect(abs.uSha, uSha); connect(tra.QTra_flow, QTra_flow); connect(abs.QAbsIntSha_flow, QAbsIntSha_flow); connect(abs.QAbsGlaSha_flow, QAbsGlaSha_flow); connect(abs.QAbsGlaUns_flow, QAbsGlaUns_flow); connect(abs.QAbsExtSha_flow, QAbsExtSha_flow); end WindowRadiation;

## Buildings.HeatTransfer.Windows.BaseClasses.convectionHorizontalCavity

Free convection in horizontal cavity

### Information

Function for convective heat transfer in horizontal window cavity. The computation is according to TARCOG 2006, except that this implementation computes the convection coefficient as a function that is differentiable in the temperatures.

#### References

TARCOG 2006: Carli, Inc., TARCOG: Mathematical models for calculation of thermal performance of glazing systems with our without shading devices, Technical Report, Oct. 17, 2006.

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
Generic | gas |  | Thermophysical properties of gas fill
Real | Ra |  | Rayleigh number
Temperature | T_m |  | Temperature used for thermophysical properties [K]
TemperatureDifference | dT |  | Temperature difference used to compute q_flow = h*dT [K]
Angle | til |  | Window tilt [rad]
Real | sinTil |  | Sine of window tilt
Real | cosTil |  | Cosine of the window tilt
Area | h | 1.5 | Height of window [m2]
Real | deltaNu | 0.1 | Small value for Nusselt number, used for smoothing
Real | deltaRa | 1E3 | Small value for Rayleigh number, used for smoothing

### Outputs

Type | Name | Description
--- | --- | ---
Real | Nu | Nusselt number
CoefficientOfHeatTransfer | hCon | Convective heat transfer coefficient [W/(m2.K)]
HeatFlux | q_flow | Convective heat flux [W/m2]

### Modelica definition

function convectionHorizontalCavity "Free convection in horizontal cavity" input Buildings.HeatTransfer.Data.Gases.Generic gas "Thermophysical properties of gas fill"; input Real Ra(min=0) "Rayleigh number"; input Modelica.SIunits.Temperature T_m "Temperature used for thermophysical properties"; input Modelica.SIunits.TemperatureDifference dT "Temperature difference used to compute q_flow = h*dT"; input Modelica.SIunits.Angle til "Window tilt"; input Real sinTil "Sine of window tilt"; input Real cosTil "Cosine of the window tilt"; input Modelica.SIunits.Area h(min=0) = 1.5 "Height of window"; input Real deltaNu(min=0.01) = 0.1 "Small value for Nusselt number, used for smoothing"; input Real deltaRa(min=0.01) = 1E3 "Small value for Rayleigh number, used for smoothing"; output Real Nu(min=0) "Nusselt number"; output Modelica.SIunits.CoefficientOfHeatTransfer hCon(min=0) "Convective heat transfer coefficient"; output Modelica.SIunits.HeatFlux q_flow "Convective heat flux"; protected Real Nu_1(min=0) "Nusselt number"; Real Nu_2(min=0) "Nusselt number"; constant Real dx=0.1 "Half-width of interval used for smoothing"; algorithm if cosTil > 0 then Nu :=Buildings.Utilities.Math.Functions.spliceFunction( pos= Buildings.HeatTransfer.Windows.BaseClasses.nusseltHorizontalCavityReduced( gas=gas, Ra=Ra, T_m=T_m, dT=dT, h=h, sinTil=sinTil, deltaNu=deltaNu, deltaRa=deltaRa), neg= Buildings.HeatTransfer.Windows.BaseClasses.nusseltHorizontalCavityEnhanced( gas=gas, Ra=Ra, T_m=T_m, dT=dT, til=til, cosTil=abs(cosTil)), x=dT+dx, deltax=dx); else Nu :=Buildings.Utilities.Math.Functions.spliceFunction( pos= Buildings.HeatTransfer.Windows.BaseClasses.nusseltHorizontalCavityEnhanced( gas=gas, Ra=Ra, T_m=T_m, dT=dT, til=til, cosTil=abs(cosTil)), neg= Buildings.HeatTransfer.Windows.BaseClasses.nusseltHorizontalCavityReduced( gas=gas, Ra=Ra, T_m=T_m, dT=dT, h=h, sinTil=sinTil, deltaNu=deltaNu, deltaRa=deltaRa), x=dT-dx, deltax=dx); end if; hCon :=Nu*Buildings.HeatTransfer.Data.Gases.thermalConductivity(gas, T_m)/gas.x; q_flow :=hCon*dT; end convectionHorizontalCavity;

## Buildings.HeatTransfer.Windows.BaseClasses.convectionVerticalCavity

Free convection in vertical cavity

### Information

Function for convective heat transfer in vertical window cavity. The computation is according to TARCOG 2006, except that this implementation computes the convection coefficient as a function that is differentiable in the temperatures.

#### References

TARCOG 2006: Carli, Inc., TARCOG: Mathematical models for calculation of thermal performance of glazing systems with our without shading devices, Technical Report, Oct. 17, 2006.

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
Generic | gas |  | Thermophysical properties of gas fill
Real | Ra |  | Rayleigh number
Temperature | T_m |  | Temperature used for thermophysical properties [K]
TemperatureDifference | dT |  | Temperature difference used to compute q_flow = h*dT [K]
Area | h | 1.5 | Height of window [m2]
Real | deltaNu | 0.1 | Small value for Nusselt number, used for smoothing
Real | deltaRa | 1E3 | Small value for Rayleigh number, used for smoothing

### Outputs

Type | Name | Description
--- | --- | ---
Real | Nu | Nusselt number
CoefficientOfHeatTransfer | hCon | Convective heat transfer coefficient [W/(m2.K)]
HeatFlux | q_flow | Convective heat flux [W/m2]

### Modelica definition

function convectionVerticalCavity "Free convection in vertical cavity" input Buildings.HeatTransfer.Data.Gases.Generic gas "Thermophysical properties of gas fill"; input Real Ra(min=0) "Rayleigh number"; input Modelica.SIunits.Temperature T_m "Temperature used for thermophysical properties"; input Modelica.SIunits.TemperatureDifference dT "Temperature difference used to compute q_flow = h*dT"; input Modelica.SIunits.Area h(min=0) = 1.5 "Height of window"; input Real deltaNu(min=0.01) = 0.1 "Small value for Nusselt number, used for smoothing"; input Real deltaRa(min=0.01) = 1E3 "Small value for Rayleigh number, used for smoothing"; output Real Nu(min=0) "Nusselt number"; output Modelica.SIunits.CoefficientOfHeatTransfer hCon(min=0) "Convective heat transfer coefficient"; output Modelica.SIunits.HeatFlux q_flow "Convective heat flux"; protected Real Nu_1(min=0) "Nusselt number"; Real Nu_2(min=0) "Nusselt number"; algorithm Nu_1 :=Buildings.Utilities.Math.Functions.spliceFunction( pos=0.0673838*Ra^(1/3), neg=Buildings.Utilities.Math.Functions.spliceFunction( pos=0.028154*Ra^(0.4134), neg=1 + 1.7596678E-10*Ra^(2.2984755), x=Ra - 1E4, deltax=deltaRa), x=Ra - 5E4, deltax=deltaRa); /* if ( Ra <= 1E4) then Nu_1 = 1 + 1.7596678E-10*Ra^(2.2984755); elseif ( Ra <= 5E4) then Nu_1 = 0.028154*Ra^(0.4134); else Nu_1 = 0.0673838*Ra^(1/3); end if; */ Nu_2 :=0.242*(Ra/(h/gas.x))^(0.272); Nu :=Buildings.Utilities.Math.Functions.smoothMax( x1=Nu_1, x2=Nu_2, deltaX=deltaNu); hCon :=Nu*Buildings.HeatTransfer.Data.Gases.thermalConductivity(gas=gas, T=T_m)/gas.x; q_flow :=hCon*dT; end convectionVerticalCavity;

## Buildings.HeatTransfer.Windows.BaseClasses.nusseltHorizontalCavityEnhanced

Nusselt number for horizontal cavity, bottom surface warmer than top surface

### Information

Function for Nusselt number in horizontal window cavity. The computation is according to TARCOG 2006, except that this implementation computes the Nusselt number as a function that is differentiable in the temperatures.

#### References

TARCOG 2006: Carli, Inc., TARCOG: Mathematical models for calculation of thermal performance of glazing systems with our without shading devices, Technical Report, Oct. 17, 2006.

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
Generic | gas |  | Thermophysical properties of gas fill
Real | Ra |  | Rayleigh number
Temperature | T_m |  | Temperature used for thermophysical properties [K]
TemperatureDifference | dT |  | Temperature difference used to compute q_flow = h*dT [K]
Angle | til |  | Window tilt [rad]
Real | cosTil |  | Cosine of the window tilt

### Outputs

Type | Name | Description
--- | --- | ---
Real | Nu | Nusselt number

### Modelica definition

function nusseltHorizontalCavityEnhanced "Nusselt number for horizontal cavity, bottom surface warmer than top surface" input Buildings.HeatTransfer.Data.Gases.Generic gas "Thermophysical properties of gas fill"; input Real Ra(min=0) "Rayleigh number"; input Modelica.SIunits.Temperature T_m "Temperature used for thermophysical properties"; input Modelica.SIunits.TemperatureDifference dT "Temperature difference used to compute q_flow = h*dT"; input Modelica.SIunits.Angle til "Window tilt"; input Real cosTil(min=0) "Cosine of the window tilt"; output Real Nu(min=0) "Nusselt number"; protected Real k1 "Auxiliary variable"; Real k2 "Auxiliary variable"; Real k11 "Auxiliary variable"; Real k22 "Auxiliary variable"; algorithm // Windows inclined from 0 to 60 deg (eqn. 3.1-42 to 3.1-43) k1 :=1 - 1708/Ra/cosTil; k2 :=(Ra*cosTil/5830)^(1/3) - 1; k11 :=(k1 + Buildings.Utilities.Math.Functions.smoothMax( x1=k1, x2=-k1, deltaX=1E-1))/2; k22 :=(k2 + Buildings.Utilities.Math.Functions.smoothMax( x1=k2, x2=-k2, deltaX=1E-1))/2; Nu :=1 + 1.44*k11*(1 - 1708*abs(Modelica.Math.sin(1.8*til*180/Modelica.Constants.pi)) ^(1.6)/Ra/cosTil) + k22; end nusseltHorizontalCavityEnhanced;

## Buildings.HeatTransfer.Windows.BaseClasses.nusseltHorizontalCavityReduced

Nusselt number for horizontal cavity, bottom surface colder than top surface

### Information

Function for Nusselt number in horizontal window cavity. The computation is according to TARCOG 2006, except that this implementation computes the Nusselt number as a function that is differentiable in the temperatures.

#### References

TARCOG 2006: Carli, Inc., TARCOG: Mathematical models for calculation of thermal performance of glazing systems with our without shading devices, Technical Report, Oct. 17, 2006.

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
Generic | gas |  | Thermophysical properties of gas fill
Real | Ra |  | Rayleigh number
Temperature | T_m |  | Temperature used for thermophysical properties [K]
TemperatureDifference | dT |  | Temperature difference used to compute q_flow = h*dT [K]
Area | h | 1.5 | Height of window [m2]
Real | sinTil |  | Sine of window tilt
Real | deltaNu | 0.1 | Small value for Nusselt number, used for smoothing
Real | deltaRa | 1E3 | Small value for Rayleigh number, used for smoothing

### Outputs

Type | Name | Description
--- | --- | ---
Real | Nu | Nusselt number

### Modelica definition

function nusseltHorizontalCavityReduced "Nusselt number for horizontal cavity, bottom surface colder than top surface" input Buildings.HeatTransfer.Data.Gases.Generic gas "Thermophysical properties of gas fill"; input Real Ra(min=0) "Rayleigh number"; input Modelica.SIunits.Temperature T_m "Temperature used for thermophysical properties"; input Modelica.SIunits.TemperatureDifference dT "Temperature difference used to compute q_flow = h*dT"; input Modelica.SIunits.Area h(min=0) = 1.5 "Height of window"; input Real sinTil "Sine of window tilt"; input Real deltaNu(min=0.01) = 0.1 "Small value for Nusselt number, used for smoothing"; input Real deltaRa(min=0.01) = 1E3 "Small value for Rayleigh number, used for smoothing"; output Real Nu(min=0) "Nusselt number"; protected Real NuVer(min=0) "Nusselt number for vertical window"; algorithm NuVer :=Buildings.HeatTransfer.Windows.BaseClasses.convectionVerticalCavity( gas=gas, Ra=Ra, T_m=T_m, dT=dT, h=h, deltaNu=deltaNu, deltaRa=deltaRa); Nu :=1 + (NuVer - 1)*sinTil; end nusseltHorizontalCavityReduced;

## Buildings.HeatTransfer.Windows.BaseClasses.smoothInterpolation

Get interpolated data without triggering events

### Information

Function to interpolate within a data array without triggerring events.

### Inputs

Type | Name | Default | Description
--- | --- | --- | ---
Real | y[:] |  | Data array
Real | x |  | x value

### Outputs

Type | Name | Description
--- | --- | ---
Real | val | Interpolated value

### Modelica definition

function smoothInterpolation "Get interpolated data without triggering events" input Real y[:] "Data array"; input Real x "x value"; output Real val "Interpolated value"; protected Integer k1 "Integer value of x"; Integer k2 "=k1+1"; Real y1d "Slope"; Real y2d "Slope"; algorithm k1 := integer(x); k2 := k1 + 1; y1d := (y[k2] - y[k1 - 1])/2; y2d := (y[k2 + 1] - y[k1])/2; val := Modelica.Fluid.Utilities.cubicHermite( x, k1, k2, y[k1], y[k2], y1d, y2d); end smoothInterpolation;

## Buildings.HeatTransfer.Windows.BaseClasses.RadiationBaseData

Basic parameters for window radiation calculation

### Information

Record that defines basic parameters for the window radiation calculation.

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Glass
Integer | N |  | Number of glass layers
Length | xGla[N] |  | Thickness of glass [m]
TransmissionCoefficient | tauGlaSol[N] |  | Solar transmissivity of glass [1]
ReflectionCoefficient | rhoGlaSol_a[N] |  | Solar reflectivity of glass at surface a (facing outside) [1]
ReflectionCoefficient | rhoGlaSol_b[N] |  | Solar reflectivity of glass at surface b (facing room-side) [1]
Shade
TransmissionCoefficient | tauShaSol_a |  | Solar transmissivity of shade for irradiation from air-side [1]
TransmissionCoefficient | tauShaSol_b |  | Solar transmissivity of shade for irradiation from glass-side [1]
ReflectionCoefficient | rhoShaSol_a |  | Solar reflectivity of shade for irradiation from air-side [1]
ReflectionCoefficient | rhoShaSol_b |  | Solar reflectivity of shade for irradiation from glass-side [1]

### Modelica definition

partial record RadiationBaseData "Basic parameters for window radiation calculation" parameter Integer N(min=1) "Number of glass layers"; parameter Modelica.SIunits.Length xGla[N] "Thickness of glass"; parameter Modelica.SIunits.TransmissionCoefficient tauGlaSol[N] "Solar transmissivity of glass"; parameter Modelica.SIunits.ReflectionCoefficient rhoGlaSol_a[N] "Solar reflectivity of glass at surface a (facing outside)"; parameter Modelica.SIunits.ReflectionCoefficient rhoGlaSol_b[N] "Solar reflectivity of glass at surface b (facing room-side)"; parameter Modelica.SIunits.TransmissionCoefficient tauShaSol_a "Solar transmissivity of shade for irradiation from air-side"; parameter Modelica.SIunits.TransmissionCoefficient tauShaSol_b "Solar transmissivity of shade for irradiation from glass-side"; parameter Modelica.SIunits.ReflectionCoefficient rhoShaSol_a "Solar reflectivity of shade for irradiation from air-side"; parameter Modelica.SIunits.ReflectionCoefficient rhoShaSol_b "Solar reflectivity of shade for irradiation from glass-side"; end RadiationBaseData;

## Buildings.HeatTransfer.Windows.BaseClasses.RadiationData

Radiation data of a window

### Information

Record that computes the solar radiation data for a glazing system.

Extends from Modelica.Icons.Record (Icon for records), Buildings.HeatTransfer.Windows.BaseClasses.RadiationBaseData (Basic parameters for window radiation calculation).

### Parameters

Type | Name | Default | Description
--- | --- | --- | ---
Glass
Integer | N |  | Number of glass layers
Length | xGla[N] |  | Thickness of glass [m]
TransmissionCoefficient | tauGlaSol[N] |  | Solar transmissivity of glass [1]
ReflectionCoefficient | rhoGlaSol_a[N] |  | Solar reflectivity of glass at surface a (facing outside) [1]
ReflectionCoefficient | rhoGlaSol_b[N] |  | Solar reflectivity of glass at surface b (facing room-side) [1]
Shade
TransmissionCoefficient | tauShaSol_a |  | Solar transmissivity of shade for irradiation from air-side [1]
TransmissionCoefficient | tauShaSol_b |  | Solar transmissivity of shade for irradiation from glass-side [1]
ReflectionCoefficient | rhoShaSol_a |  | Solar reflectivity of shade for irradiation from air-side [1]
ReflectionCoefficient | rhoShaSol_b |  | Solar reflectivity of shade for irradiation from glass-side [1]

### Modelica definition

record RadiationData "Radiation data of a window" extends Modelica.Icons.Record; extends Buildings.HeatTransfer.Windows.BaseClasses.RadiationBaseData; final parameter Real glass[3, N]={tauGlaSol,rhoGlaSol_a,rhoGlaSol_b} "Glass solar transmissivity, solar reflectivity at surface a and b, at normal incident angle"; final parameter Real traRefShaDev[2, 2]={{tauShaSol_a,tauShaSol_b},{ rhoShaSol_a,rhoShaSol_b}} "Shading device property"; final parameter Integer NDIR=10 "Number of incident angles"; final parameter Integer HEM=NDIR + 1 "Index of hemispherical integration"; final parameter Modelica.SIunits.Angle psi[NDIR]= Buildings.HeatTransfer.Windows.Functions.getAngle(NDIR) "Incident angles used for solar radiation calculation"; final parameter Real layer[3, N, HEM]= Buildings.HeatTransfer.Windows.Functions.glassProperty( N=N, HEM=HEM, glass=glass, xGla=xGla, psi=psi) "Angular and hemispherical transmissivity, front (outside-facing) and back (room facing) reflectivity of each glass pane"; final parameter Real traRef[3, N, N, HEM]= Buildings.HeatTransfer.Windows.Functions.getGlassTR( N=N, HEM=HEM, layer=layer) "Angular and hemispherical transmissivity, front (outside-facing) and back (room facing) reflectivity between glass panes for exterior or interior irradiation without shading"; final parameter Real absExtIrrNoSha[N, HEM]= Buildings.HeatTransfer.Windows.Functions.glassAbsExteriorIrradiationNoShading( traRef=traRef, N=N, HEM=HEM) "Angular and hemispherical absorptivity of each glass pane for exterior irradiation without shading"; final parameter Real absIntIrrNoSha[N]= Buildings.HeatTransfer.Windows.Functions.glassAbsInteriorIrradiationNoShading( traRef=traRef, N=N, HEM=HEM) "Hemispherical absorptivity of each glass pane for interior irradiation without shading"; final parameter Real winTraExtIrrExtSha[HEM]= Buildings.HeatTransfer.Windows.Functions.winTExteriorIrradiatrionExteriorShading( traRef=traRef, traRefShaDev=traRefShaDev, N=N, HEM=HEM) "Angular and hemispherical transmissivity of a window system (glass + exterior shading device) for exterior irradiation"; final parameter Real absExtIrrExtSha[N, HEM]= Buildings.HeatTransfer.Windows.Functions.glassAbsExteriorIrradiationExteriorShading( absExtIrrNoSha=absExtIrrNoSha, traRef=traRef, traRefShaDev=traRefShaDev, N=N, HEM=HEM) "Angular and hemispherical absorptivity of each glass pane for exterior irradiation with exterior shading"; final parameter Real winTraExtIrrIntSha[HEM]= Buildings.HeatTransfer.Windows.Functions.winTExteriorIrradiationInteriorShading( traRef=traRef, traRefShaDev=traRefShaDev, N=N, HEM=HEM) "Angular and hemispherical transmissivity of a window system (glass and interior shading device) for exterior irradiation"; final parameter Real absExtIrrIntSha[N, HEM]= Buildings.HeatTransfer.Windows.Functions.glassAbsExteriorIrradiationInteriorShading( absExtIrrNoSha=absExtIrrNoSha, traRef=traRef, traRefShaDev=traRefShaDev, N=N, HEM=HEM) "Angular and hemispherical absorptivity of each glass layer for exterior irradiation with interior shading"; final parameter Real devAbsExtIrrIntShaDev[HEM]= Buildings.HeatTransfer.Windows.Functions.devAbsExteriorIrradiationInteriorShading( traRef=traRef, traRefShaDev=traRefShaDev, N=N, HEM=HEM) "Angular and hemispherical absorptivity of an interior shading device for exterior irradiation"; final parameter Real winTraRefIntIrrExtSha[3]= Buildings.HeatTransfer.Windows.Functions.winTRInteriorIrradiationExteriorShading( traRef=traRef, traRefShaDev=traRefShaDev, N=N, HEM=HEM) "Hemisperical transmissivity and reflectivity of a window system (glass and exterior shadig device) for interior irradiation. traRefIntIrrExtSha[1]: transmissivity, traRefIntIrrExtSha[2]: Back reflectivity; traRefIntIrrExtSha[3]: dummy value"; final parameter Real absIntIrrExtSha[N]= Buildings.HeatTransfer.Windows.Functions.glassAbsInteriorIrradiationExteriorShading( absIntIrrNoSha=absIntIrrNoSha, traRef=traRef, traRefShaDev=traRefShaDev, N=N, HEM=HEM) "Hemispherical absorptivity of each glass pane for interior irradiation with exterior shading"; final parameter Real absIntIrrIntSha[N]= Buildings.HeatTransfer.Windows.Functions.glassAbsInteriorIrradiationInteriorShading( absIntIrrNoSha=absIntIrrNoSha, traRef=traRef, traRefShaDev=traRefShaDev, N=N, HEM=HEM) "Hemispherical absorptivity of each glass pane for interior irradiation with interior shading"; final parameter Real winTraRefIntIrrIntSha[3]= Buildings.HeatTransfer.Windows.Functions.winTRInteriorIrradiationInteriorShading( traRef=traRef, traRefShaDev=traRefShaDev, N=N, HEM=HEM) "Hemisperical transmissivity and back reflectivity of a window system (glass and interior shadig device) for interior irradiation"; final parameter Real devAbsIntIrrIntSha= Buildings.HeatTransfer.Windows.Functions.devAbsInteriorIrradiationInteriorShading( traRef=traRef, traRefShaDev=traRefShaDev, N=N, HEM=HEM) "Hemiperical absorptivity of an interior shading device for interior irradiation"; end RadiationData;