Buildings.HeatTransfer.Windows.Functions

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Buildings.HeatTransfer.Windows.Functions

Functions used in window radiation model

Information

This package contains functions that are used to compute heat transfer in the window model.

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name Description

devAbsExteriorIrradiationInteriorShading Angular and hemispherical absorptance of a shading device for exterior irradiation with interior shading

devAbsInteriorIrradiationInteriorShading Hemiperical absorptance of a shading device for interior irradiation with interior shading

getAngle Generate incident angles

getGlassTR Transmittance and reflectance of glass

glassAbsExteriorIrradiationExteriorShading Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading

glassAbsExteriorIrradiationInteriorShading Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading

glassAbsExteriorIrradiationNoShading Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading

glassAbsInteriorIrradiationExteriorShading Hemispherical absorptance of each glass pane for interior irradiation with exterior shading

glassAbsInteriorIrradiationInteriorShading Hemispherical absorptance of each glass pane for interior irradiation with interior shading

glassAbsInteriorIrradiationNoShading Hemispherical absorptance of each glass pane for interior irradiation without shading

glassProperty Compute angular variation and hemispherical integration of the transmittance and reflectance for each glass pane without shading

glassPropertyCoated Compute angular variation and hemispherical integration of the transmittance and reflectance for a coated glass pane without shading

glassPropertyUncoated Compute angular variation and hemispherical integration of the transmittance and reflectance for a uncoated glass pane without shading

glassTRExteriorIrradiationNoShading Transmittance and reflectance of glass panes for exterior irradiation without shading

glassTRInteriorIrradiationNoShading Transmittance and reflectance of each glass pane for interior irradiation without shading

winTExteriorIrradiationInteriorShading Angular and hemispherical transmittance of a window system (glass and shading device) for exterior irradiation with interior shading

winTExteriorIrradiatrionExteriorShading Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading

winTRInteriorIrradiationExteriorShading Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading

winTRInteriorIrradiationInteriorShading Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading

BaseClasses Package with base classes for Buildings.HeatTransfer.Windows.Functions

Name	Description
devAbsExteriorIrradiationInteriorShading	Angular and hemispherical absorptance of a shading device for exterior irradiation with interior shading
devAbsInteriorIrradiationInteriorShading	Hemiperical absorptance of a shading device for interior irradiation with interior shading
getAngle	Generate incident angles
getGlassTR	Transmittance and reflectance of glass
glassAbsExteriorIrradiationExteriorShading	Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading
glassAbsExteriorIrradiationInteriorShading	Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading
glassAbsExteriorIrradiationNoShading	Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading
glassAbsInteriorIrradiationExteriorShading	Hemispherical absorptance of each glass pane for interior irradiation with exterior shading
glassAbsInteriorIrradiationInteriorShading	Hemispherical absorptance of each glass pane for interior irradiation with interior shading
glassAbsInteriorIrradiationNoShading	Hemispherical absorptance of each glass pane for interior irradiation without shading
glassProperty	Compute angular variation and hemispherical integration of the transmittance and reflectance for each glass pane without shading
glassPropertyCoated	Compute angular variation and hemispherical integration of the transmittance and reflectance for a coated glass pane without shading
glassPropertyUncoated	Compute angular variation and hemispherical integration of the transmittance and reflectance for a uncoated glass pane without shading
glassTRExteriorIrradiationNoShading	Transmittance and reflectance of glass panes for exterior irradiation without shading
glassTRInteriorIrradiationNoShading	Transmittance and reflectance of each glass pane for interior irradiation without shading
winTExteriorIrradiationInteriorShading	Angular and hemispherical transmittance of a window system (glass and shading device) for exterior irradiation with interior shading
winTExteriorIrradiatrionExteriorShading	Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading
winTRInteriorIrradiationExteriorShading	Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading
winTRInteriorIrradiationInteriorShading	Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading
BaseClasses	Package with base classes for Buildings.HeatTransfer.Windows.Functions

Buildings.HeatTransfer.Windows.Functions.devAbsExteriorIrradiationInteriorShading

Angular and hemispherical absorptance of a shading device for exterior irradiation with interior shading

Information

This function computes the angular and hemispherical absorptance of a shading device for exterior irradiation with interior shading. Pane 1 is facing the outside and pane N is facing the room.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).

Inputs

Type Name Default Description

Real traRef[3, N, N, HEM] Transmittance and reflectance with exterior irradiation and no shading

Real traRefShaDev[2, 2] Transmittance and reflectance of shading device

Integer N Number of glass layers

Integer HEM Index of hemispherical integration

Type	Name	Description
Real	traRef[3, N, N, HEM]	Transmittance and reflectance with exterior irradiation and no shading
Real	traRefShaDev[2, 2]	Transmittance and reflectance of shading device
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration

Outputs

Type Name Description

Real absExtIrrIntShaDev[HEM] Absorptance of a shading device for exterior irradiation with interior shading

Type	Name	Description
Real	absExtIrrIntShaDev[HEM]	Absorptance of a shading device for exterior irradiation with interior shading

Modelica definition

function devAbsExteriorIrradiationInteriorShading 
  "Angular and hemispherical absorptance of a shading device for exterior irradiation with interior shading"
  import Buildings;
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;

  output Real absExtIrrIntShaDev[HEM](each min=0, each max=1) 
    "Absorptance of a shading device for exterior irradiation with interior shading";

algorithm 
  for iD in 1:HEM loop
    absExtIrrIntShaDev[iD] := traRef[TRA, 1, N, iD]*(1 - traIntShaDev -
      refIntShaDev)/(1 - refIntShaDev*traRef[Rb, N, 1, HEM]) 
      "Equation (A.4.91)";
  end for;

end devAbsExteriorIrradiationInteriorShading;

Buildings.HeatTransfer.Windows.Functions.devAbsInteriorIrradiationInteriorShading

Hemiperical absorptance of a shading device for interior irradiation with interior shading

Information

This function computes the hemiperical absorbtance of a shading device for interior irradiation with interior shading.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).

Inputs

Type	Name	Description
Real	traRef[3, N, N, HEM]	Transmittance and reflectance with exterior irradiation and no shading
Real	traRefShaDev[2, 2]	Transmittance and reflectance of shading device
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration

Outputs

Type Name Description

Real absIntIrrIntShaDev Hemiperical absorbtance of a shading device for interior irradiation with interior shading

Type	Name	Description
Real	absIntIrrIntShaDev	Hemiperical absorbtance of a shading device for interior irradiation with interior shading

Modelica definition

function devAbsInteriorIrradiationInteriorShading 
  "Hemiperical absorptance of a shading device for interior irradiation with interior shading"
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;

  output Real absIntIrrIntShaDev(min=0, max=1) 
    "Hemiperical absorbtance of a shading device for interior irradiation with interior shading";
protected 
  constant Real rRho=traRef[3, N, 1, HEM]*refIntShaDev 
    "Part of equation (A.4.103)";
  constant Real rTau=traRef[3, N, 1, HEM]*traIntShaDev 
    "Part of equation (A.4.103)";
  constant Real c=traIntShaDev*(1 - rRho/(1 - rRho)) "Equation (4.99)";

algorithm 
  absIntIrrIntShaDev := (1 - traIntShaDev - refIntShaDev)*(1 + rTau/(1 - rRho)) 
    "Equation (4.103)";

end devAbsInteriorIrradiationInteriorShading;

Buildings.HeatTransfer.Windows.Functions.getAngle

Generate incident angles

Information

This function computes discrete incident angles for the window radiation calculation. The range is from 0 to 90 degree.

Inputs

Type Name Default Description

Integer NDIR Number of incident angles

Type	Name	Default	Description
Integer	NDIR		Number of incident angles

Outputs

Type Name Description

Angle psi[NDIR] Array of incident angles [rad]

Type	Name	Description
Angle	psi[NDIR]	Array of incident angles [rad]

Modelica definition

function getAngle "Generate incident angles"
  input Integer NDIR "Number of incident angles";
  output Modelica.SIunits.Angle psi[NDIR] "Array of incident angles";

protected 
  constant Real deltaX=0.5*Modelica.Constants.pi/(NDIR - 1);

algorithm 
  for i in 1:NDIR loop
    psi[i] := (i - 1)*deltaX;
  end for;

end getAngle;

Buildings.HeatTransfer.Windows.Functions.getGlassTR

Transmittance and reflectance of glass

Information

This function computes the angular variation of the transmittance and reflectance of each glass pane. It accounts for the transmittance and reflectance among different panes. Pane 1 is facing outside and pane N is facing the room. For instance, traRef[TRA, 1, N, iD] means transmittance between layer 1 to N for exterior irradiation and traRef[TRA, N, 1, iD] means the transmittance for interior irradiation.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation (Partial function for glass radiation property).

Inputs

Type Name Default Description

Integer N Number of glass layers

Integer HEM Index of hemispherical integration

Real layer[3, N, HEM] Property of glass pane

Type	Name	Description
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration
Real	layer[3, N, HEM]	Property of glass pane

Outputs

Type Name Description

Real traRef[3, N, N, HEM] Glass transmittance, front and back reflectance

Type	Name	Description
Real	traRef[3, N, N, HEM]	Glass transmittance, front and back reflectance

Modelica definition

function getGlassTR "Transmittance and reflectance of glass"
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation;

  input Real layer[3, N, HEM] "Property of glass pane";
  output Real traRef[3, N, N, HEM](each min=0, each max=1) 
    "Glass transmittance, front and back reflectance";

protected 
  Real traRefIntIrr[3, N, N, HEM](each min=0, each max=1) 
    "temporary array for glass transmittance, front and back reflectance for interior irradiation";

algorithm 
  traRef :=
    Buildings.HeatTransfer.Windows.Functions.glassTRExteriorIrradiationNoShading(
    N,
    HEM,
    layer) "property for exterior irradiation";
  traRefIntIrr :=
    Buildings.HeatTransfer.Windows.Functions.glassTRInteriorIrradiationNoShading(
    N,
    HEM,
    layer) "property for interior irradiation";

  // Copy the property for interior irradiation to glass property
  for k in TRA:Rb loop
    for i in 1:N - 1 loop
      for j in i + 1:N loop
        for iD in 1:HEM loop
          traRef[k, N + 1 - i, N + 1 - j, iD] := traRefIntIrr[k, N + 1 - i, N
             + 1 - j, iD];
        end for;
      end for;
    end for;
  end for;

end getGlassTR;

Buildings.HeatTransfer.Windows.Functions.glassAbsExteriorIrradiationExteriorShading

Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading

Information

This function computes angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading. Pane 1 is facing outside and pane N is facing the room.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).

Inputs

Type Name Default Description

Real absExtIrrNoSha[N, HEM] Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading

Real traRef[3, N, N, HEM] Transmittance and reflectance with exterior irradiation and no shading

Real traRefShaDev[2, 2] Transmittance and reflectance of shading device

Integer N Number of glass layers

Integer HEM Index of hemispherical integration

Type	Name	Description
Real	absExtIrrNoSha[N, HEM]	Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading
Real	traRef[3, N, N, HEM]	Transmittance and reflectance with exterior irradiation and no shading
Real	traRefShaDev[2, 2]	Transmittance and reflectance of shading device
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration

Outputs

Type Name Description

Real absExtIrrExtSha[N, HEM] Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading

Type	Name	Description
Real	absExtIrrExtSha[N, HEM]	Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading

Modelica definition

function glassAbsExteriorIrradiationExteriorShading 
  "Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading"
  input Real absExtIrrNoSha[N, HEM](each min=0, each max=1) 
    "Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading";
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;

  output Real absExtIrrExtSha[N, HEM](each min=0, each max=1) 
    "Angular and hemispherical absorptance of each glass pane for exterior irradiation with exterior shading";

protected 
  Real c "Intermediate variable";

algorithm 
  for iD in 1:HEM loop
    c := traExtShaDev*(1 + traRef[Ra, 1, N, iD]*refExtShaDev/(1 - traRef[Ra, 1,
      N, HEM]*refExtShaDev));
    for i in 1:N loop
      absExtIrrExtSha[i, iD] := c*absExtIrrNoSha[i, iD];
    end for;
  end for;

end glassAbsExteriorIrradiationExteriorShading;

Buildings.HeatTransfer.Windows.Functions.glassAbsExteriorIrradiationInteriorShading

Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading

Information

This function computes angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading. Pane 1 is facing the outside and pane N is facing the room.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).

Inputs

Type Name Default Description

Real absExtIrrNoSha[N, HEM] Absorptance for exterior irradiation without shading

Real traRef[3, N, N, HEM] Transmittance and reflectance with exterior irradiation and no shading

Real traRefShaDev[2, 2] Transmittance and reflectance of shading device

Integer N Number of glass layers

Integer HEM Index of hemispherical integration

Type	Name	Description
Real	absExtIrrNoSha[N, HEM]	Absorptance for exterior irradiation without shading
Real	traRef[3, N, N, HEM]	Transmittance and reflectance with exterior irradiation and no shading
Real	traRefShaDev[2, 2]	Transmittance and reflectance of shading device
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration

Outputs

Type Name Description

Real absExtIrrNoShaIntSha[N, HEM] Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading

Type	Name	Description
Real	absExtIrrNoShaIntSha[N, HEM]	Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading

Modelica definition

function glassAbsExteriorIrradiationInteriorShading 
  "Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading"
  input Real absExtIrrNoSha[N, HEM](each min=0, each max=1) 
    "Absorptance for exterior irradiation without shading";
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
  output Real absExtIrrNoShaIntSha[N, HEM](each min=0, each max=1) 
    "Angular and hemispherical absorptance of each glass pane for exterior irradiation with interior shading";

protected 
  Real fac;
  Real absFro "Front (outside-facing) absorptance";
  Real absBac "Back (room-facing) absorptance";
  Integer i "Index of glass pane";

algorithm 
  for iD in 1:HEM loop
    i := 1;
    fac := traRef[TRA, 1, N, iD]*refIntShaDev/(1 - traRef[Rb, N, 1, HEM]*
      refIntShaDev) "Equation (A.4.90)";
    absBac := 1 - traRef[TRA, i, i, iD] - traRef[Rb, i, i, iD] 
      "Equation (A.4.81b)";

    if N >= 2 then
      absExtIrrNoShaIntSha[i, iD] := absExtIrrNoSha[i, iD] + fac*traRef[TRA, N,
        i + 1, HEM]*absBac "Equation (A.4.90)";

      for i in 2:N - 1 loop
        fac := traRef[TRA, 1, N, iD]*refIntShaDev/(1 - traRef[Rb, N, 1, HEM]*
          refIntShaDev) "Equation (A.4.90)";
        absFro := 1 - traRef[TRA, i, i, iD] - traRef[Ra, i, i, iD] 
          "Equaiton (A.4.81a)";
        absBac := 1 - traRef[TRA, i, i, iD] - traRef[Rb, i, i, iD] 
          "Equation (A.4.81b)";
        absExtIrrNoShaIntSha[i, iD] := absExtIrrNoSha[i, iD] + fac*(traRef[TRA,
          N, i, HEM]*traRef[Rb, i - 1, 1, HEM]*absFro + traRef[TRA, N, i + 1,
          HEM]*absBac) "Equation (A.4.90)";
      end for;

      i := N;
      fac := traRef[TRA, 1, N, iD]*refIntShaDev/(1 - traRef[Rb, N, 1, HEM]*
        refIntShaDev) "Equation (A.4.90)";
      absFro := 1 - traRef[TRA, i, i, iD] - traRef[Ra, i, i, iD] 
        "Equaiton (A.4.81a)";
      absBac := 1 - traRef[TRA, i, i, iD] - traRef[Rb, i, i, iD] 
        "Equation (A.4.81b)";
      absExtIrrNoShaIntSha[i, iD] := absExtIrrNoSha[i, iD] + fac*(traRef[TRA, N,
        i, HEM]*traRef[Rb, i - 1, 1, HEM]*absFro + absBac) "Equation (A.4.90)";

    else
      absExtIrrNoShaIntSha[i, iD] := absExtIrrNoSha[i, iD] + fac*absBac 
        "Equation (A.4.90)";
    end if;
  end for;

end glassAbsExteriorIrradiationInteriorShading;

Buildings.HeatTransfer.Windows.Functions.glassAbsExteriorIrradiationNoShading

Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading

Information

This function computes specular and hemispherical absorptance of each glass pane for exterior irradiation without shading. It counts the transmittance and reflectance among different panes. Pane 1 is facing the outside and pane N is facing the room.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowRadiation (Partial function for window radiation property).

Inputs

Type Name Default Description

Real traRef[3, N, N, HEM] Transmittance and reflectance with exterior irradiation and no shading

Integer N Number of glass layers

Integer HEM Index of hemispherical integration

Type	Name	Description
Real	traRef[3, N, N, HEM]	Transmittance and reflectance with exterior irradiation and no shading
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration

Outputs

Type Name Description

Real abs[N, HEM] Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading. Indices: abs[1 to N : ] -> pane 1 to N; abs[ : 1 to HEM] -> angular (1:HEM-1) and hemispherical (HEM)

Type	Name	Description
Real	abs[N, HEM]	Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading. Indices: abs[1 to N : ] -> pane 1 to N; abs[ : 1 to HEM] -> angular (1:HEM-1) and hemispherical (HEM)

Modelica definition

function glassAbsExteriorIrradiationNoShading 
  "Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading"
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowRadiation;
  output Real[N, HEM] abs(each min=0, each max=1) "Angular and hemispherical absorptance of each glass pane for exterior irradiation without shading. 
     Indices: abs[1 to N : ] -> pane 1 to N; 
     abs[ : 1 to HEM] -> angular (1:HEM-1) and hemispherical (HEM)";

protected 
  Real af "Front (outside-facing side) absorptance of a pane";
  Real ab "Back (room-facing side) absorptance of a pane";
  Real deno1 "Denominantor";
  Real deno2 "Denominantor";
  Integer j;
  constant Real SMALL=Modelica.Constants.small "Small value";

algorithm 
  if N == 1 then
    j := 1;
    for iD in 1:HEM loop
      abs[j, iD] := 1 - traRef[TRA, j, j, iD] - traRef[Ra, j, j, iD] 
        "Equation (A.4.79)";
    end for;
  else
    for iD in 1:HEM loop
      j := 1;
      af := 1 - traRef[TRA, j, j, iD] - traRef[Ra, j, j, iD] 
        "Equation (A.4.81a)";
      ab := 1 - traRef[TRA, j, j, iD] - traRef[Rb, j, j, iD] 
        "Equation (A.4.81b)";
      deno2 := 1 - traRef[Rb, j, 1, iD]*traRef[Ra, j + 1, N, iD];
      if deno2 < SMALL then
        abs[j, iD] := 0;
      else
        abs[j, iD] := af + ab*traRef[TRA, 1, j, iD]*traRef[Ra, j + 1, N, iD]/
          deno2 "Equation (A.4.82) and (A.4.83b)";
      end if;

      for j in 2:N - 1 loop
        af := 1 - traRef[TRA, j, j, iD] - traRef[Ra, j, j, iD] 
          "Equation (A.4.81a)";
        ab := 1 - traRef[TRA, j, j, iD] - traRef[Rb, j, j, iD] 
          "Equation (A.4.81b)";
        deno1 := 1 - traRef[Ra, j, N, iD]*traRef[Rb, j - 1, 1, iD];
        deno2 := 1 - traRef[Rb, j, 1, iD]*traRef[Ra, j + 1, N, iD];
        if deno1 < SMALL or deno2 < SMALL then
          abs[j, iD] := 0;
        else
          abs[j, iD] := af*traRef[TRA, 1, j - 1, iD]/deno1 + ab*traRef[TRA, 1,
            j, iD]*traRef[Ra, j + 1, N, iD]/deno2 "Equation (A.4.83b)";
        end if;
      end for;

      j := N;
      af := 1 - traRef[TRA, j, j, iD] - traRef[Ra, j, j, iD] 
        "Equation (A.4.81a)";
      deno1 := 1 - traRef[Ra, j, N, iD]*traRef[Rb, j - 1, 1, iD];
      if deno1 < SMALL then
        abs[j, iD] := 0;
      else
        abs[j, iD] := af*traRef[TRA, 1, j - 1, iD]/deno1;
      end if;
    end for;
  end if;

end glassAbsExteriorIrradiationNoShading;

Buildings.HeatTransfer.Windows.Functions.glassAbsInteriorIrradiationExteriorShading

Hemispherical absorptance of each glass pane for interior irradiation with exterior shading

Information

This function computes the hemispherical absorptance of each glass pane for interior irradiation with exterior shading. Pane 1 is facing the outside and pane N is facing the room.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).

Inputs

Type Name Default Description

Real absIntIrrNoSha[N] Absorptance for interior irradiation without shading

Real traRef[3, N, N, HEM] Transmittance and reflectance with exterior irradiation and no shading

Real traRefShaDev[2, 2] Transmittance and reflectance of shading device

Integer N Number of glass layers

Integer HEM Index of hemispherical integration

Type	Name	Description
Real	absIntIrrNoSha[N]	Absorptance for interior irradiation without shading
Real	traRef[3, N, N, HEM]	Transmittance and reflectance with exterior irradiation and no shading
Real	traRefShaDev[2, 2]	Transmittance and reflectance of shading device
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration

Outputs

Type Name Description

Real absIntIrrExtSha[N] Hemispherical absorptance of each glass pane for interior irradiation with exterior shading

Type	Name	Description
Real	absIntIrrExtSha[N]	Hemispherical absorptance of each glass pane for interior irradiation with exterior shading

Modelica definition

function glassAbsInteriorIrradiationExteriorShading 
  "Hemispherical absorptance of each glass pane for interior irradiation with exterior shading"
  input Real absIntIrrNoSha[N] 
    "Absorptance for interior irradiation without shading";
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;

  output Real absIntIrrExtSha[N](each min=0, each max=1) 
    "Hemispherical absorptance of each glass pane for interior irradiation with exterior shading";

protected 
  Real fac;
  Real absFro "Front absorptance";
  Real absBac "Back absorptance";
  Integer i "Pane index";

algorithm 
  fac := traRef[TRA, N, 1, HEM]*refExtShaDev/(1 - traRef[Ra, 1, N, HEM]*
    refExtShaDev);

  i := 1;
  absFro := 1 - traRef[TRA, i, i, HEM] - traRef[Ra, i, i, HEM] 
    "Equaiton (A.4.81a)";
  absBac := 1 - traRef[TRA, i, i, HEM] - traRef[Rb, i, i, HEM] 
    "Equation (A.4.81b)";

  if N >= 2 then
    absIntIrrExtSha[i] := absIntIrrNoSha[i] + fac*absFro + fac*traRef[TRA, 1, i,
      HEM]*traRef[Ra, i + 1, N, HEM]*absBac "Equation (A.4.94)";

    for i in 2:N - 1 loop
      absFro := 1 - traRef[TRA, i, i, HEM] - traRef[Ra, i, i, HEM] 
        "Equaiton (A.4.81a)";
      absBac := 1 - traRef[TRA, i, i, HEM] - traRef[Rb, i, i, HEM] 
        "Equation (A.4.81b)";
      absIntIrrExtSha[i] := absIntIrrNoSha[i] + fac*traRef[TRA, 1, i - 1, HEM]*
        absFro + fac*traRef[TRA, 1, i, HEM]*traRef[Ra, i + 1, N, HEM]*absBac 
        "Equation (A.4.94)";
    end for;

    i := N;
    absFro := 1 - traRef[TRA, i, i, HEM] - traRef[Ra, i, i, HEM] 
      "Equaiton (A.4.81a)";
    absIntIrrExtSha[i] := absIntIrrNoSha[i] + fac*traRef[TRA, 1, i - 1, HEM]*
      absFro "Equation (A.4.94)";
  else
    absIntIrrExtSha[i] := absIntIrrNoSha[i] + fac*absFro "Equation (A.4.94)";
  end if;
end glassAbsInteriorIrradiationExteriorShading;

Buildings.HeatTransfer.Windows.Functions.glassAbsInteriorIrradiationInteriorShading

Hemispherical absorptance of each glass pane for interior irradiation with interior shading

Information

This function computes the hemispherical absorbtance of each glass pane for interior irradiation with interior shading. Pane 1 is facing the outside and pane N is facing the room.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).

Inputs

Type Name Default Description

Real absIntIrrNoSha[N] Hemispherical absorptance wfor interior irradiation without interior shading

Real traRef[3, N, N, HEM] Transmittance and reflectance with exterior irradiation and no shading

Real traRefShaDev[2, 2] Transmittance and reflectance of shading device

Integer N Number of glass layers

Integer HEM Index of hemispherical integration

Type	Name	Description
Real	absIntIrrNoSha[N]	Hemispherical absorptance wfor interior irradiation without interior shading
Real	traRef[3, N, N, HEM]	Transmittance and reflectance with exterior irradiation and no shading
Real	traRefShaDev[2, 2]	Transmittance and reflectance of shading device
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration

Outputs

Type Name Description

Real absIntIrrIntSha[N] Hemispherical absorbtance of each glass pane for interior irradiation with interior shading

Type	Name	Description
Real	absIntIrrIntSha[N]	Hemispherical absorbtance of each glass pane for interior irradiation with interior shading

Modelica definition

function glassAbsInteriorIrradiationInteriorShading 
  "Hemispherical absorptance of each glass pane for interior irradiation with interior shading"
  input Real absIntIrrNoSha[N](each min=0, each max=1) 
    "Hemispherical absorptance wfor interior irradiation without interior shading";
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;

  output Real absIntIrrIntSha[N](each min=0, each max=1) 
    "Hemispherical absorbtance of each glass pane for interior irradiation with interior shading";

protected 
  constant Real rRho=traRef[Rb, N, 1, HEM]*refIntShaDev 
    "Part of Equation (4.99)";
  constant Real c=traIntShaDev*(1 + rRho/(1 - rRho)) "Equation (4.99)";

algorithm 
  for i in 1:N loop
    absIntIrrIntSha[i] := c*absIntIrrNoSha[i] "Equation (A4.100a)";
  end for;

end glassAbsInteriorIrradiationInteriorShading;

Buildings.HeatTransfer.Windows.Functions.glassAbsInteriorIrradiationNoShading

Hemispherical absorptance of each glass pane for interior irradiation without shading

Information

This function computes the hemispherical absorptance of each glass pane for interior irradiation without no shading. The angular irradiation is not considered since the interior irradiation (from the room) is assumed to be diffusive. It is a reverse of the function Buildings.HeatTransfer.Windows.Functions.glassAbsInterirorIrradiationNoShading.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowRadiation (Partial function for window radiation property).

Inputs

Type	Name	Description
Real	traRef[3, N, N, HEM]	Transmittance and reflectance with exterior irradiation and no shading
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration

Outputs

Type Name Description

Real absIntIrrNoSha[N] Hemispherical absorptance of each glass layer for interior irradiation without shading

Type	Name	Description
Real	absIntIrrNoSha[N]	Hemispherical absorptance of each glass layer for interior irradiation without shading

Modelica definition

function glassAbsInteriorIrradiationNoShading 
  "Hemispherical absorptance of each glass pane for interior irradiation without shading"

  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowRadiation;

  output Real[N] absIntIrrNoSha(each min=0, each max=1) 
    "Hemispherical absorptance of each glass layer for interior irradiation without shading";

protected 
  Real dTraRef[3, N, N, HEM](each min=0, each max=1) 
    "Dummy transmittance and reflectance with exterior irradiation without shading";
  Real dAbs[N, HEM](each min=0, each max=1) 
    "Dummy absorptance with exterior irradiation and no shading";

algorithm 
  // Reverse the data srtucture for exterior irradiation and no shading
  for i in 1:N loop
    for j in 1:N loop
      for iD in 1:HEM loop
        dTraRef[TRA, i, j, iD] := traRef[TRA, N + 1 - i, N + 1 - j, iD];
        dTraRef[Ra, i, j, iD] := traRef[Rb, N + 1 - i, N + 1 - j, iD];
        dTraRef[Rb, i, j, iD] := traRef[Ra, N + 1 - i, N + 1 - j, iD];
      end for;
    end for;
  end for;

  dAbs :=
    Buildings.HeatTransfer.Windows.Functions.glassAbsExteriorIrradiationNoShading(
    dTraRef,
    N,
    HEM) "Dummmy absorptance with exterior irradiation";

  // Only output hemispherical absorptance. Need to change order for interior irradiation.
  for i in 1:N loop
    absIntIrrNoSha[i] := dAbs[N + 1 - i, HEM];
  end for;

end glassAbsInteriorIrradiationNoShading;

Buildings.HeatTransfer.Windows.Functions.glassProperty

Compute angular variation and hemispherical integration of the transmittance and reflectance for each glass pane without shading

Information

This function computes the angular variation and the hemispherical integration of the transmittance and reflectance for each glass pane. There are two schemes for the calculation. One is for coated glass and the other is for uncoated glass. The function checks the difference between front and back reflectances. If the difference is less than the tolerance (0.005), it uses the formula for uncoated glass. Otherwise, the formula for coated glass will be used.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation (Partial function for glass radiation property).

Inputs

Type Name Default Description

Integer N Number of glass layers

Integer HEM Index of hemispherical integration

Real glass[3, N] Propertry of each glass pane

Real xGla[N] Thickness of each glass pane

Angle psi[HEM - 1] Incident angles [rad]

Type	Name	Description
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration
Real	glass[3, N]	Propertry of each glass pane
Real	xGla[N]	Thickness of each glass pane
Angle	psi[HEM - 1]	Incident angles [rad]

Outputs

Type Name Description

Real layer[3, N, HEM] Transmittance, front and back reflectance

Type	Name	Description
Real	layer[3, N, HEM]	Transmittance, front and back reflectance

Modelica definition

function glassProperty 
  "Compute angular variation and hemispherical integration of the transmittance and reflectance for each glass pane without shading"
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation;
  input Real glass[3, N] "Propertry of each glass pane";
  input Real xGla[N] "Thickness of each glass pane";
  input Modelica.SIunits.Angle psi[HEM - 1] "Incident angles";

  output Real layer[3, N, HEM] "Transmittance, front and back reflectance";

protected 
  parameter Real tol=0.005 
    "Tolerance for difference between front and back reflectance to decide a glass is uncoated or coated";
  Real oneLay[3, HEM] "Temporary storage for glass property of one pane";
  Real oneGla[3];

algorithm 
  // Compute specular value for angle 0 to 90 degree (psi[1] to psi[N]) and panes from 1 to N
  for i in 1:N loop
    // Copy data to temporary place
    for j in 1:3 loop
      oneGla[j] := glass[j, i];
    end for;

    //uncoated galss
    if (abs(glass[Ra, i] - glass[Rb, i]) < tol) then
      oneLay := Buildings.HeatTransfer.Windows.Functions.glassPropertyUncoated(
        HEM,
        oneGla,
        xGla[i],
        psi);

    else
      //coated glass
      oneLay := Buildings.HeatTransfer.Windows.Functions.glassPropertyCoated(
        HEM,
        oneGla,
        psi);
    end if;

    for j in 1:3 loop
      for k in 1:HEM loop
        layer[j, i, k] := oneLay[j, k];
      end for;
    end for;
  end for;
end glassProperty;

Buildings.HeatTransfer.Windows.Functions.glassPropertyCoated

Compute angular variation and hemispherical integration of the transmittance and reflectance for a coated glass pane without shading

Information

This function computes the angular variation and the hemispherical integration of the transmittance and reflectance for one coated glass pane.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialSingleGlassRadiation (Partial function for single glass radiation property).

Inputs

Type Name Default Description

Integer HEM Index of hemispherical integration

Real glass[3] Propertry of one glass pane

Angle psi[HEM - 1] Incident angles [rad]

Type	Name	Description
Integer	HEM	Index of hemispherical integration
Real	glass[3]	Propertry of one glass pane
Angle	psi[HEM - 1]	Incident angles [rad]

Outputs

Type Name Description

Real layer[3, HEM] Transmittance, front and back reflectance

Type	Name	Description
Real	layer[3, HEM]	Transmittance, front and back reflectance

Modelica definition

function glassPropertyCoated 
  "Compute angular variation and hemispherical integration of the transmittance and reflectance for a coated glass pane without shading"
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialSingleGlassRadiation;
  input Real glass[3] "Propertry of one glass pane";
  input Modelica.SIunits.Angle psi[HEM - 1] "Incident angles";

  output Real layer[3, HEM] "Transmittance, front and back reflectance";

protected 
  Integer NDIR=HEM - 1 "Number of incident angles";

  Real psi_c "cos(psi), psi is incident angle";
  Real psi_cs "cos(psi)*sin(psi)";
  Real angT "Angular variation of transmittance";
  Real angR "Angular variation of reflectance";
  Real f[3, NDIR] 
    "Temporary variables for integration in hemispherical transmittance and reflectance";
  constant Real deltaX=0.5*Modelica.Constants.pi/(NDIR - 1);
  constant Real a[4, 5]={{-0.0015,3.355,-3.840,1.460,0.0288},{0.999,-0.563,
      2.043,-2.532,1.054},{-0.002,2.813,-2.341,-0.05725,0.599},{0.997,-1.868,
      6.513,-7.862,3.225}} "Coeffcients in Table A.2";
  Integer id1 "Index of coefficients for transmittance";
  Integer id2 "Index of coefficients for reflectance";

algorithm 
  // Compute specular value for angle 0 to 90 degree (psi[1] to psi[N])
    for k in TRA:Rb loop
      layer[k, 1] := glass[k] "Copy the data at 0 degree (normal incidence)";
    end for;

    for j in 2:NDIR - 1 loop
      psi_c := Modelica.Math.cos(psi[j]);
       if layer[TRA, 1] > 0.645 then
        id1 := 1;
        id2 := 2;
      else
        id1 := 3;
        id2 := 4;
      end if;
      angT := a[id1, 1] + psi_c*(a[id1, 2] + psi_c*(a[id1, 3] + psi_c*(a[id1, 4]
         + psi_c*a[id1, 5]))) "Equation (A.4.68a)";
      angR := a[id2, 1] + psi_c*(a[id2, 2] + psi_c*(a[id2, 3] + psi_c*(a[id2, 4]
         + psi_c*a[id2, 5]))) - angT "Equation (A.4.68b)";
      layer[TRA, j] := layer[TRA, 1]*angT "Equation (A4.69a)";
      layer[Ra, j] := layer[Ra, 1]*(1 - angR) + angR "Equation (A4.69b)";
      layer[Rb, j] := layer[Rb, 1]*(1 - angR) + angR "Equation (A4.69b)";

    end for;

    layer[TRA, NDIR] := 0;
    layer[Ra, NDIR] := 1.0;
    layer[Rb, NDIR] := 1.0;

  // Computer hemispherical value: HEM.
    for j in 1:NDIR loop
      psi_cs := Modelica.Math.cos(psi[j])*Modelica.Math.sin(psi[j]);
      for k in TRA:Rb loop
        f[k, j] := 2*layer[k, j]*psi_cs;
      end for;
    end for;

    for k in TRA:Rb loop
      layer[k, HEM] :=
        Buildings.Utilities.Math.Functions.trapezoidalIntegration(
        NDIR,
        f[k, :],
        deltaX) "Equation (A.4.70a) and (A.4.70b)";
    end for;

end glassPropertyCoated;

Buildings.HeatTransfer.Windows.Functions.glassPropertyUncoated

Compute angular variation and hemispherical integration of the transmittance and reflectance for a uncoated glass pane without shading

Information

This function computes the angular variation and the hemispherical integration of the transmittance and reflectance for one uncoated glass pane. The equations are mainly based on Finlayson et al. (1990) and Fuler et al. (1991) with some modifications.

Implementation

Step 1: Compute the reflectivity at normal incidence

ρ(0) = {β − sqrt[β² − 4(2 − R(0))R(0)]} ⁄ [2(2−R(0))],

(1)

where

β = T(0)² − R(0)² + 2R(0) + 1.

(2)

Step 2: Compute the spectral absorption coefficient α and spectral index of refraction n

α = 4 π κ_λ ⁄ λ = - ln[(R(0) − ρ(0)) ⁄ (ρ(0)T(0))] ⁄ d,	(3)
n = (1 + sqrt(ρ(0)) ⁄ (1 − sqrt(ρ(0))).	(4)

Step 3: For each angle of incidence measured in air φ (0 < φ < 90)

a. Compute the angle of incidence measured in glass φ'
φ' = asin(sinφ ⁄ n).	(5)
b. Compute spectral reflectivities at surface
ρ₁(φ)=[(n cosφ − cosφ') ⁄ (n cosφ + cosφ')] ²,	(6)
ρ₂(φ)=[(n cosφ' − cosφ) ⁄ (n cosφ' + cosφ)] ².	(7)
c. Compute spectral tansmissivities at surface
τ₁(φ)= 1 − ρ₁(φ),	(8)
τ₂(φ)= 1 − ρ₂(φ).	(9)
d. Compute spectral tansmittance of the glass
T₁(φ)= τ₁(φ)² exp(-α d/cosφ') ⁄ (1 − ρ₁(φ)² exp(-2α d/cosφ')),	(10)
T₂(φ)= τ₂(φ)² exp(-α d/cosφ') ⁄ (1 − ρ₂(φ)² exp(-2α d/cosφ')),	(11)
T(φ)= (T₁(φ) + T₂(φ)) / 2.	(12)
e. Compute spectral reflectance of the glass
R₁(φ)= ρ₁(φ)(1+ T₁(φ)exp(-α d/cosφ')),	(13)
R₂(φ)= ρ₂(φ)(1+ T₂(φ)exp(-α d/cosφ')),	(14)
R(φ)= (R₁(φ) + R₂(φ)) / 2.	(15)

Step 4: T(90)=0, R(90)=1. (16)

Limitations

WINDOW program calculates the angular property for each wave length based on the spectral data. It uses different R_λ(0) and T_λ(0) for each wave length. Then it integrates the properties over the wave length to get averaged property of R(0) and T(0).

The current window model in the Buildings library uses averaged R(0) and T(0) directly. It can generate the same results as WINDOW for a single pane window and multi-pane window with the same glass. However, the results may be slightly different for multi-pane window with different glasses. The reason is that different glasses may have different angular properties for the same wave length. To precisely calculate the angular properties of the entire window system, one has to calculate the property for each wave length and integrate them as WINDOW does. For more details, see the paper of Nouidui et al. (2012).

References

Finlayson, E. U., D. K. Arasteh, C. Huizenga, M.D. Rubin, M.S. Reily. 1993. WINDOW 4.0: Documentation of Calcualtion Precedures. Technical Report LBL-33943. Lawrence Berkeley National Laboratory.

Fuler, Reto A., Angular dependence of optical properties of homogeneous glasses, ASHRAE Transaction, V.97 Part 2, 1991.

Thierry Stephane Nouidui, Michael Wetter, and Wangda Zuo. Validation of the window model of the Modelica Buildings library. Proc. of the 5th SimBuild Conference, Madison, WI, USA, August 2012.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialSingleGlassRadiation (Partial function for single glass radiation property).

Inputs

Type Name Default Description

Integer HEM Index of hemispherical integration

Real glass[3] Propertry of one glass pane

Length x Thickness [m]

Angle psi[HEM - 1] Incident angles [rad]

Type	Name	Description
Integer	HEM	Index of hemispherical integration
Real	glass[3]	Propertry of one glass pane
Length	x	Thickness [m]
Angle	psi[HEM - 1]	Incident angles [rad]

Outputs

Type Name Description

Real layer[3, HEM] Transmittance, front and back reflectance

Type	Name	Description
Real	layer[3, HEM]	Transmittance, front and back reflectance

Modelica definition

function glassPropertyUncoated 
  "Compute angular variation and hemispherical integration of the transmittance and reflectance for a uncoated glass pane without shading"
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialSingleGlassRadiation;

  input Real glass[3] "Propertry of one glass pane";
  input Modelica.SIunits.Length x "Thickness";
  input Modelica.SIunits.Angle psi[HEM - 1] "Incident angles";
  output Real layer[3, HEM] "Transmittance, front and back reflectance";

protected 
  Integer NDIR=HEM - 1 "Number of incident angles";
  Real psi_c "cos(psi), psi is incident angle in air";
  Real psi1_c "cos(psi1), psi1 is incident angle in glass";
  Real angT "Angular variation of transmittance";
  Real angR "Angular variation of reflectance";
  Real f[3, NDIR] 
    "Temporary variables for integration in hemispherical transmittance and reflectance";
  Real beta "Temporary coefficient defined in (7.2.1i)";
  Real rho0 
    "Spectral reflectivity at incident angle of 0 degree at the interface";
  Real rho "Spectral reflectivity at the interface";
  Real rho1;
  Real rho2;
  Real tau "Spectral transmissivity at the interface";
  Real tau1;
  Real tau2;
  Real angT1;
  Real angT2;
  Real angR1;
  Real angR2;
  Real tmp;
  Real alpha "Spectral absorption coefficient defined in (7.2.1e)";
  Real n 
    "Ratio of spectral index of refraction of glass to the index of refraction of air";
  Real psi1 "The angle od incident angle in glass";
  constant Real deltaX=0.5*Modelica.Constants.pi/(NDIR - 1);

algorithm 
  // Check the data
  assert(glass[TRA] >= 0,
    "Glass property is not correct with solar transmittance less than 0");
  assert(glass[Ra] >= 0,
    "Glass property is not correct with solar reflectance less than 0");
  assert(glass[TRA] + glass[Ra] <= 1,
    "Glass property is not correct since the summation of solar reflectance and transmittance is larger than 1");

  // Compute specular value for angle 0 to 90 degree (psi[1] to psi[N])
  for k in TRA:Rb loop
    layer[k, 1] := glass[k] "Copy the data at 0 degree (normal incidence)";
  end for;

  beta := glass[TRA]^2 - glass[Ra]^2 + 2*glass[Ra] + 1 "(2)";

  tmp := beta^2 - 4*(2 - glass[Ra])*glass[Ra] "part of (1)";
  assert(tmp >= 0,
    "Glass property is not correct and not possible to calculate spectral reflectivity at 0 degree for uncoated glass");

  rho0 := 0.5*(beta - sqrt(tmp))/(2 - glass[Ra]) "(1)";
  assert(rho0 >= 0,
    "Glass property is not correct so that the spectral reflectivity at 0 degree for uncoated glass is less than zero");

  tmp := (glass[Ra] - rho0)/(rho0*glass[TRA]) "part of (3)";
  assert(tmp > 0,
    "Glass property is not correct and not possible to calculate spectral extinction coefficient for uncoated glass");

  alpha := -log(tmp)/x "(3)";
  tmp := sqrt(rho0);
  assert(tmp <> 1,
    "Glass property is not correct and not possible to calculate spectral index of refraction for uncoated glass");
  n := (1 + tmp)/(1 - tmp) "(4)";

  for j in 2:NDIR - 1 loop
    psi1 := asin(sin(psi[j])/n) "(5)";
    psi_c := cos(psi[j]);
    psi1_c := cos(psi1);

    rho1 := ((n*psi_c - psi1_c)/(n*psi_c + psi1_c))^2 "(6)";
    rho2 := ((n*psi1_c - psi_c)/(n*psi1_c + psi_c))^2 "(7)";

    tau1 := 1 - rho1 "(8)";
    tau2 := 1 - rho2 "(9)";

    tmp := exp(-alpha*x/psi1_c);

    angT1 := tau1^2*tmp/(1 - rho1^2*tmp^2) "(10)";
    angR1 := rho1*(1 + angT1*tmp) "(13)";
    angT2 := tau2^2*tmp/(1 - rho2^2*tmp^2) "(11)";
    angR2 := rho2*(1 + angT2*tmp) "(14)";

    layer[TRA, j] := 0.5*(angT1 + angT2) "Tansmittance in (12)";
    layer[Ra, j] := 0.5*(angR1 + angR2) "Front reflectance (15)";
    layer[Rb, j] := layer[Ra, j] "Back reflectance in (15)";
  end for;

  // When incident angle is equal to 90 degree
  layer[TRA, NDIR] := 0 "(16)";
  layer[Ra, NDIR] := 1.0 "(16)";
  layer[Rb, NDIR] := 1.0 "(16)";

  // Computer hemispherical value: HEM.
  for j in 1:NDIR loop
    for k in TRA:Rb loop
      f[k, j] := 2*layer[k, j]*Modelica.Math.cos(psi[j])*Modelica.Math.sin(psi[
        j]);
    end for;
  end for;

  for k in TRA:Rb loop
    layer[k, HEM] := Buildings.Utilities.Math.Functions.trapezoidalIntegration(
      NDIR,
      f[k, :],
      deltaX) 
      "Equation (A.4.70a) and (A.4.70b) in M. Wetter 's Thesis or (7.3) in Finlayson 1993.";
  end for;

end glassPropertyUncoated;

Buildings.HeatTransfer.Windows.Functions.glassTRExteriorIrradiationNoShading

Transmittance and reflectance of glass panes for exterior irradiation without shading

Information

This function computes the angular variation of the transmittance and reflectance of each glass pane for exteior irradiation without shading. It accounts for the transmittance and reflectance among different panes. Pane 1 is facing outside and pane N is facing the room.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation (Partial function for glass radiation property).

Inputs

Type Name Default Description

Integer N Number of glass layers

Integer HEM Index of hemispherical integration

Real layer[3, N, HEM] Angular data of glass pane

Type	Name	Description
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration
Real	layer[3, N, HEM]	Angular data of glass pane

Outputs

Type Name Description

Real traRef[3, N, N, HEM] Transmittance and reflectance of each glass pane for exterior irradiation without shading

Type	Name	Description
Real	traRef[3, N, N, HEM]	Transmittance and reflectance of each glass pane for exterior irradiation without shading

Modelica definition

function glassTRExteriorIrradiationNoShading 
  "Transmittance and reflectance of glass panes for exterior irradiation without shading"
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation;
  input Real layer[3, N, HEM] "Angular data of glass pane";
  output Real traRef[3, N, N, HEM](each min=0, each max=1) 
    "Transmittance and reflectance of each glass pane for exterior irradiation without shading";

protected 
  Real aij "Temporary variable";
  constant Real SMALL=Modelica.Constants.small "Small value";

algorithm 
  // Property for single pane of glass or the first pane of multiple panes glass
  for iD in 1:HEM loop
    for k in TRA:Rb loop
      traRef[k, 1, 1, iD] := layer[k, 1, iD] "Equation (A.4.71)";
    end for;
  end for;

  // Property for multiple panes glass
  if N > 1 then
    for iD in 1:HEM loop
      for i in 1:N - 1 loop
        for j in i + 1:N loop
          for k in TRA:Rb loop
            traRef[k, j, j, iD] := layer[k, j, iD];
          end for;

          aij := 1 - traRef[Ra, j, j, iD]*traRef[Rb, j - 1, i, iD] 
            "Equation (A.4.77)";
          assert(aij > -SMALL,
            "Glass transmittance and reflectance data was not correct.\n");
          if aij < SMALL then
            traRef[TRA, i, j, iD] := 0;
            traRef[Ra, i, j, iD] := 1;
            traRef[Rb, j, i, iD] := 1;
          else
            aij := 1/aij;
            traRef[TRA, i, j, iD] := aij*traRef[TRA, i, j - 1, iD]*traRef[TRA,
              j, j, iD] "Equation (A.4.78a)";
            traRef[Ra, i, j, iD] := traRef[Ra, i, j - 1, iD] + aij*traRef[TRA,
              i, j - 1, iD]*traRef[TRA, i, j - 1, iD]*traRef[Ra, j, j, iD] 
              "Equation (A.4.78b)";
            traRef[Rb, j, i, iD] := traRef[Rb, j, j, iD] + aij*traRef[TRA, j, j,
              iD]*traRef[TRA, j, j, iD]*traRef[Rb, j - 1, i, iD] 
              "Equation (A.4.78c)";
          end if;
        end for;
      end for;
    end for;
  end if;

end glassTRExteriorIrradiationNoShading;

Buildings.HeatTransfer.Windows.Functions.glassTRInteriorIrradiationNoShading

Transmittance and reflectance of each glass pane for interior irradiation without shading

Information

This function computes the angular variation of the transmittance and reflectance of each glass pane for interior irradiation without shading. It accounts for the transmittance and reflectance among different panes. Pane 1 is facing outside and pane N is facing the room.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation (Partial function for glass radiation property).

Inputs

Type Name Default Description

Integer N Number of glass layers

Integer HEM Index of hemispherical integration

Real layer[3, N, HEM] Angular data of glass pane

Type	Name	Description
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration
Real	layer[3, N, HEM]	Angular data of glass pane

Outputs

Type Name Description

Real traRef[3, N, N, HEM] Glass transmittance, front and back reflectance

Type	Name	Description
Real	traRef[3, N, N, HEM]	Glass transmittance, front and back reflectance

Modelica definition

function glassTRInteriorIrradiationNoShading 
  "Transmittance and reflectance of each glass pane for interior irradiation without shading"
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialGlassRadiation;
  input Real layer[3, N, HEM] "Angular data of glass pane";
  output Real traRef[3, N, N, HEM](each min=0, each max=1) 
    "Glass transmittance, front and back reflectance";

protected 
  Real dLayer[3, N, HEM] 
    "Dummy glass property with Pane 1 facing inside and Pane N facing outside";
  Real dTraRef[3, N, N, HEM] 
    "Dummy transmittance and reflectance for exterior irradiation";

algorithm 
  // Copy the dummy glass property
  for iD in 1:HEM loop
    for j in 1:N loop
      dLayer[TRA, j, iD] := layer[TRA, N + 1 - j, iD];
      dLayer[Ra, j, iD] := layer[Rb, N + 1 - j, iD] 
        "swap the front and back reflectance";
      dLayer[Rb, j, iD] := layer[Ra, N + 1 - j, iD] 
        "swap the front and back reflectance";
    end for;
  end for;

  // Calculate transmittance and reflectance of dummy glass for exterior irradiation without shading
  dTraRef :=
    Buildings.HeatTransfer.Windows.Functions.glassTRExteriorIrradiationNoShading(
    N,
    HEM,
    dLayer);

  // Convert the dummy data to real glass
  for iD in 1:HEM loop
    for i in 1:N - 1 loop
      for j in i + 1:N loop
        traRef[TRA, N + 1 - i, N + 1 - j, iD] := dTraRef[TRA, i, j, iD];
        traRef[Ra, N + 1 - i, N + 1 - j, iD] := dTraRef[Rb, i, j, iD] 
          "swap the front and back reflectance";
        traRef[Rb, N + 1 - i, N + 1 - j, iD] := dTraRef[Ra, i, j, iD] 
          "swap the front and back reflectance";
      end for;
    end for;
  end for;

end glassTRInteriorIrradiationNoShading;

Buildings.HeatTransfer.Windows.Functions.winTExteriorIrradiationInteriorShading

Angular and hemispherical transmittance of a window system (glass and shading device) for exterior irradiation with interior shading

Information

This function computes the angular and hemispherical transmittance of a window system (glass and shading device) for exterior irradiation with interior shading. Pane 1 is facing outside and pane N is facing the room.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).

Inputs

Type	Name	Description
Real	traRef[3, N, N, HEM]	Transmittance and reflectance with exterior irradiation and no shading
Real	traRefShaDev[2, 2]	Transmittance and reflectance of shading device
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration

Outputs

Type Name Description

Real traExtIrrIntSha[HEM] Angular and hemispherical transmittance of a window system (glass and shading device) forh exterior irradiation with interior shading

Type	Name	Description
Real	traExtIrrIntSha[HEM]	Angular and hemispherical transmittance of a window system (glass and shading device) forh exterior irradiation with interior shading

Modelica definition

function winTExteriorIrradiationInteriorShading 
  "Angular and hemispherical transmittance of a window system (glass and shading device) for exterior irradiation with interior shading"
  import Buildings;
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;

  output Real traExtIrrIntSha[HEM](each min=0, each max=1) 
    "Angular and hemispherical transmittance of a window system (glass and shading device) forh exterior irradiation with interior shading";

algorithm 
  for iD in 1:HEM loop
    traExtIrrIntSha[iD] := traRef[TRA, 1, N, iD]*traIntShaDev/(1 - refIntShaDev
      *traRef[Rb, N, 1, HEM]) "Equation (A.4.92)";
  end for;

end winTExteriorIrradiationInteriorShading;

Buildings.HeatTransfer.Windows.Functions.winTExteriorIrradiatrionExteriorShading

Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading

Information

This function computes the angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading. Pane 1 is facing outside and pane N is facing the room.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).

Inputs

Type	Name	Description
Real	traRef[3, N, N, HEM]	Transmittance and reflectance with exterior irradiation and no shading
Real	traRefShaDev[2, 2]	Transmittance and reflectance of shading device
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration

Outputs

Type Name Description

Real traExtIrrExtSha[HEM] Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading

Type	Name	Description
Real	traExtIrrExtSha[HEM]	Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading

Modelica definition

function winTExteriorIrradiatrionExteriorShading 
  "Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading"
  import Buildings;
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
  output Real traExtIrrExtSha[HEM](each min=0, each max=1) 
    "Angular and hemispherical transmittance of a window system (glass + shading device) for exterior irradiation with exterior shading";

protected 
  Real c;

algorithm 
  for iD in 1:HEM loop
    c := traExtShaDev*(1 + traRef[Ra, 1, N, iD]*refExtShaDev/(1 - traRef[Ra, 1,
      N, HEM]*refExtShaDev)) "Equation (A.4.88a)";
    traExtIrrExtSha[iD] := c*traRef[TRA, 1, N, iD] "Equation (A.4.88c)";
  end for;

end winTExteriorIrradiatrionExteriorShading;

Buildings.HeatTransfer.Windows.Functions.winTRInteriorIrradiationExteriorShading

Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading

Information

This function computes hemispherical transmittance and back reflectance of a window for interior irradiation with exterior shading. Pane 1 is facing the outside and pane N is facing the room. The variables are

traRefIntIrrExtSha[1]: Transmittance;
traRefIntIrrExtSha[2]: Back reflectance; 
traRefIntIrrExtSha[3]: Dummy value

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).

Inputs

Type	Name	Description
Real	traRef[3, N, N, HEM]	Transmittance and reflectance with exterior irradiation and no shading
Real	traRefShaDev[2, 2]	Transmittance and reflectance of shading device
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration

Outputs

Type Name Description

Real traRefIntIrrExtSha[3] Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading

Type	Name	Description
Real	traRefIntIrrExtSha[3]	Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading

Modelica definition

function winTRInteriorIrradiationExteriorShading 
  "Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading"
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;
  output Real traRefIntIrrExtSha[3](each min=0, each max=1) 
    "Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with exterior shading";
algorithm 
  traRefIntIrrExtSha[TRA] := traRef[TRA, N, 1, HEM]*traExtShaDev/(1 -
    refExtShaDev*traRef[Ra, 1, N, HEM]) "Equation (A.4.95)";
  traRefIntIrrExtSha[Rb] := traRef[Rb, N, 1, HEM] + traRef[TRA, N, 1, HEM]*
    refExtShaDev*traRef[1, 1, N, HEM]/(1 - traRef[Ra, 1, N, HEM]*refExtShaDev) 
    "Equation (A.4.97)";
  traRefIntIrrExtSha[Ra] := 0 "Dummy value";
end winTRInteriorIrradiationExteriorShading;

Buildings.HeatTransfer.Windows.Functions.winTRInteriorIrradiationInteriorShading

Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading

Information

This function computes the hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading. Pane 1 is facing the outside and pane N is facing the room.

Extends from Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation (Partial function for window radiation property with shading device).

Inputs

Type	Name	Description
Real	traRef[3, N, N, HEM]	Transmittance and reflectance with exterior irradiation and no shading
Real	traRefShaDev[2, 2]	Transmittance and reflectance of shading device
Integer	N	Number of glass layers
Integer	HEM	Index of hemispherical integration

Outputs

Type Name Description

Real traRefIntIrrIntSha[3] Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading

Type	Name	Description
Real	traRefIntIrrIntSha[3]	Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading

Modelica definition

function winTRInteriorIrradiationInteriorShading 
  "Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading"
  extends Buildings.HeatTransfer.Windows.Functions.BaseClasses.partialWindowShadingRadiation;

  output Real traRefIntIrrIntSha[3](each min=0, each max=1) 
    "Hemispherical transmittance and back reflectance of a window system (glass and shading device) for interior irradiation with interior shading";

protected 
  constant Real rRho=traRef[Rb, N, 1, HEM]*refIntShaDev 
    "Part of Equation (A.4.99)";
  constant Real rTau=traRef[Rb, N, 1, HEM]*traIntShaDev 
    "Part of Equation (A.4.105)";
  constant Real c=traIntShaDev*(1 + rRho/(1 - rRho)) "Equation (A.4.99)";

algorithm 
  traRefIntIrrIntSha[TRA] := c*traRef[TRA, N, 1, HEM] "Equation (A.4.100b)";
  traRefIntIrrIntSha[Rb] := refIntShaDev + c*rTau "Equation (A.4.105)";
  traRefIntIrrIntSha[Ra] := 0 "Dummy value";

end winTRInteriorIrradiationInteriorShading;

Automatically generated Tue Jan 8 08:31:19 2013.