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Annex60.ThermalZones.ReducedOrder.SolarGain

Package with models for solar gain corrections according to VDI 6007 Part 3

Information

This package contains models to compute solar heat gains.

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

Name Description
Annex60.ThermalZones.ReducedOrder.SolarGain.CorrectionGDoublePane CorrectionGDoublePane Double pane window solar correction
Annex60.ThermalZones.ReducedOrder.SolarGain.BaseClasses BaseClasses Package with base classes for SolarGain

Annex60.ThermalZones.ReducedOrder.SolarGain.CorrectionGDoublePane Annex60.ThermalZones.ReducedOrder.SolarGain.CorrectionGDoublePane

Double pane window solar correction

Annex60.ThermalZones.ReducedOrder.SolarGain.CorrectionGDoublePane

Information

This model computes short-wave radiation through transparent elements with any orientation and inclination by means of solar transmission correction factors. Transmission properties of transparent elements are in general dependent on the solar incidence angle. To take this dependency into account, correction factors can be multiplied with the solar radiation. These factors should not be mistaken as calculation of solar radiation on tilted surfaces, calculation of g-values or consideration of sunblinds, as it is an additional step. The implemented calculations are defined in the German Guideline VDI 6007 Part 3 (VDI, 2015). The given model is only valid for double pane windows. The guideline describes also calculations for single pane and triple pane windows.

References

VDI. German Association of Engineers Guideline VDI 6007-3 June 2015. Calculation of transient thermal response of rooms and buildings - modelling of solar radiation.

Extends from BaseClasses.PartialCorrectionG (Partial model for correction of the solar gain factor).

Parameters

TypeNameDefaultDescription
Integern Vector size for input and output
CoefficientOfHeatTransferUWin Thermal transmission coefficient of whole window [W/(m2.K)]

Connectors

TypeNameDescription
input RealInputHSkyDifTil[n]Hemispherical diffuse solar irradiation on a tilted surfce from the sky [W/m2]
input RealInputHDirTil[n]Direct solar radiation on a tilted surface per unit area [W/m2]
input RealInputHGroDifTil[n]Hemispherical diffuse solar irradiation on a tilted surfce from the ground [W/m2]
input RealInputinc[n]Incidence angles [rad]
output RealOutputsolarRadWinTrans[n]transmitted solar radiation through windows [W/m2]

Modelica definition

model CorrectionGDoublePane "Double pane window solar correction" extends BaseClasses.PartialCorrectionG; import con = Modelica.SIunits.Conversions; // Parameters for the transmission correction factor based on VDI 6007 Part 3 // A0 to A6 are experimental constants VDI 6007 Part 3 page 20 protected parameter Real A0=0.918 "Constant 0 to calculate reference transmission"; parameter Real A1=2.21*10^(-4) "Constant 1 to calculate reference transmission"; parameter Real A2=-2.75*10^(-5) "Constant 2 to calculate reference transmission"; parameter Real A3=-3.82*10^(-7) "Constant 3 to calculate reference transmission"; parameter Real A4=5.83*10^(-8) "Constant 4 to calculate reference transmission"; parameter Real A5=-1.15*10^(-9) "Constant 5 to calculate reference transmission"; parameter Real A6=4.74*10^(-12) "Constant 6 to calculate reference transmission"; parameter Modelica.SIunits.TransmissionCoefficient g_dir0=0.7537 "Reference vertical parallel transmission coefficient for direct radiation for double pane window"; parameter Modelica.SIunits.TransmissionCoefficient Ta_diff = 0.84 "Energetic degree of transmission for diffuse radiation for uniformly overcast sky"; parameter Modelica.SIunits.TransmissionCoefficient Tai_diff=0.903 "Pure degree of transmission for diffuse radiation"; parameter Modelica.SIunits.TransmissionCoefficient Ta1_diff= Ta_diff*Tai_diff "Degreee of transmission for single pane window"; parameter Modelica.SIunits.ReflectionCoefficient rho_T1_diff=1-(Ta_diff) "Part of degree of transmission for single pane window related to Ta1_diff"; parameter Modelica.SIunits.ReflectionCoefficient rho_11_diff=rho_T1_diff/ (2-(rho_T1_diff)) "Part of degree of transmission for single pane window related to rho_T1_diff"; parameter Modelica.SIunits.ReflectionCoefficient rho_1_diff= rho_11_diff+ (((1-rho_11_diff)*Tai_diff)^2*rho_11_diff)/(1-(rho_11_diff*Tai_diff)^2) "Degree of reflection for single pane window"; parameter Modelica.SIunits.ReflectionCoefficient XN2_diff=1-rho_1_diff^2 "Calculation factor to simplify equations"; parameter Modelica.SIunits.TransmissionCoefficient Ta2_diff=(Ta1_diff^2)/ XN2_diff "Energetic dregree of transmission for second pane"; parameter Modelica.SIunits.Emissivity a1_diff=1-Ta1_diff-rho_1_diff "Degree of absorption for single pane window"; parameter Modelica.SIunits.CoefficientOfHeatTransfer Q21_diff= a1_diff*(1+(Ta1_diff*rho_1_diff/XN2_diff))*UWin/25 "Coefficient of heat transfer for exterior pane of double pane window"; parameter Modelica.SIunits.CoefficientOfHeatTransfer Q22_diff= a1_diff*(Ta1_diff/XN2_diff)*(1-(UWin/7.7)) "Coefficient of heat transfer for interior pane of double pane window"; parameter Modelica.SIunits.CoefficientOfHeatTransfer Qsek2_diff= Q21_diff+Q22_diff "Overall coefficient of heat transfer for double pane window"; parameter Modelica.SIunits.TransmissionCoefficient CorG_diff= (Ta2_diff+Qsek2_diff)/g_dir0 "Transmission coefficient correction factor for diffuse radiation"; parameter Modelica.SIunits.TransmissionCoefficient CorG_gr= (Ta2_diff+Qsek2_diff)/g_dir0 "Transmission coefficient correction factor for irradiations from ground"; //Calculating the correction factor for direct solar radiation Modelica.SIunits.TransmissionCoefficient[n] Ta_dir "Energetic degree of transmission for direct radiation"; Modelica.SIunits.TransmissionCoefficient[n] Tai_dir "Pure degree of transmission for direct radiation"; Modelica.SIunits.TransmissionCoefficient[n] Ta1_dir "Pure degree of transmission for single pane window"; Modelica.SIunits.ReflectionCoefficient[n] rho_T1_dir "Part of degree of transmission for single pane window related to Ta1_dir"; Modelica.SIunits.ReflectionCoefficient[n] rho_11_dir "Part of degree of transmission for single pane window related to T1_dir"; Modelica.SIunits.ReflectionCoefficient[n] rho_1_dir "Degree of reflection for single pane window"; Modelica.SIunits.ReflectionCoefficient[n] XN2_dir "Calculation factor to simplify equations"; Modelica.SIunits.TransmissionCoefficient[n] Ta2_dir "Energetic dregree of transmission for second pane"; Modelica.SIunits.Emissivity[n] a1_dir "Degree of absorption for single pane window"; Real[n] Q21_dir "Coefficient of heat transfer for exterior pane of double pane window"; Real[n] Q22_dir "Coefficient of heat transfer for interior pane of double pane window"; Real[n] Qsek2_dir "Overall coefficient of heat transfer for double pane window"; Modelica.SIunits.TransmissionCoefficient[n] CorG_dir "Transmission coefficient correction factor for direct radiation"; equation for i in 1:n loop Ta_dir[i]= (((((A6*con.to_deg(inc[i])+A5)*con.to_deg(inc[i])+A4)*con.to_deg(inc[i])+A3)* con.to_deg(inc[i])+A2)*con.to_deg(inc[i])+A1)*con.to_deg(inc[i])+A0; Tai_dir[i]= 0.907^(1/sqrt(1-(sin(inc[i])/1.515)^2)); Ta1_dir[i]= Ta_dir[i]*Tai_dir[i]; rho_T1_dir[i]= 1-Ta_dir[i]; rho_11_dir[i]= rho_T1_dir[i]/(2-rho_T1_dir[i]); rho_1_dir[i]=rho_11_dir[i]+(((1-rho_11_dir[i])*Tai_dir[i])^2*rho_11_dir[i])/ (1-(rho_11_dir[i]*Tai_dir[i])^2); a1_dir[i]= 1-Ta1_dir[i]-rho_1_dir[i]; XN2_dir[i]= 1+10^(-20)-rho_1_dir[i]^2; Q21_dir[i]=a1_dir[i]*(1+(Ta1_dir[i]*rho_1_dir[i]/XN2_dir[i]))*UWin/25; Q22_dir[i]= a1_dir[i]*(Ta1_dir[i]/XN2_dir[i])*(1-(UWin/7.7)); Qsek2_dir[i]=Q21_dir[i]+Q22_dir[i]; Ta2_dir[i]= Ta1_dir[i]^2/XN2_dir[i]; CorG_dir[i]= (Ta2_dir[i]+Qsek2_dir[i])/g_dir0; //Calculating the input thermal energy due to solar radiation solarRadWinTrans[i] = ((HDirTil[i]*CorG_dir[i])+(HSkyDifTil[i]*CorG_diff)+ (HGroDifTil[i]*CorG_gr)); end for; end CorrectionGDoublePane;
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