Simulating annual autoregulation of daylight by grating smart window with angular-selective transmission

AbstractAs a basis for further development of the BPS computer software, a method for simulating the characteristics of buildings with grating smart windows is proposed. This novel smart technology provides annual autoregulation of light and solar transmission due to an optical filter with two thin-film gratings located on window surfaces to adapt to the Sun's trajectory and achieve angular-selective transmission. The previously developed methods for calculating the filter parameters are modified and on their basis new equations for the BPS software are obtained, which differ from the existing ones, unsuitable for grating smart windows due to their distinctive properties. The fundamentals of BPS for a building with such smart windows are considered in detail in order to select the individual parameters of grating windows for all rooms where they are needed. Calculation methods are validated by numerical simulation of the transmittance, sDA, ASE, DGP and by illuminance measurements.KEYWORDS: Daylightbuildingsimulationautoregulationgrating smart windowangular-selective transmission Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementAll data, models, and code generated or used during the study appear in the submitted article.NomenclatureA=solar azimuth [°]Aw=window azimuth [°]B=angle between normal to window and line from observer to source [°]C=sky factor of windowc1=width of transmissive strip of input gratings [mm]c2=width of non-transmissive strip of input gratings [mm]c3=width of transmissive strip of output gratings [mm]c4=width of non-transmissive strip of output gratings [mm]D=distance between observer and source [m]DGP=daylight glare probabilityDHI=diffuse horizontal irradiance [Wh/m2]DNI=direct normal irradiance [Wh/m2]EDHI=diffuse horizontal illuminance [lx]EDNI=direct normal illuminance [lx]EGHI=global horizontal illuminance [lx]Eh=horizontal daylight illuminance [lx]Ev=vertical illuminance at eye [lx]Fw=area of window [m2]F=total area of room surfaces [m2]GHI=global horizontal irradiance [Wh/m2]Hw=window height [m]h=solar elevation [°]kapp=angular coefficient of approximated trajectoryktan=angular coefficient of tangent to trajectoryL=zenith luminance [cd/m2]Ls=luminance of source [cd/m2]Lsky=sky element luminance [cd/m2]Lw=luminance of window [cd/m2]n=refractive index of glassP=Guth's position indexR=average reflectance of room surfacesRc=average reflectance of surfaces above horizontal through window centreRf=average reflectance of surfaces below horizontal through window centres=distance between gratings [mm]sΣ=total thickness of all panes of window [mm]tmin=time with required minimum transmittance [h]Ww=window width [m]α=difference between solar and window azimuths [°]αa=natural absorptance of glass [mm−1]γ=slope angle of filter's gratings [°]Δ=shift between traces of input gratings on output gratings surface [mm]Θ=incidence angle [°]Θav=average incidence angle [°]Θc=characteristic angle of filter [°]Θn=refractive angle corresponding to incidence angle [°]θ=projection of incidence angle to plane orthogonal to gratings orientation [°]ρ=ground albedoσ1=angle from vertical of plane containing source and sightline [°]σ2=angle between sightline and line from observer to source [°]τ=theoretical transmittanceτav=average transmittanceτcor=corrected transmittanceτchr=transmittance of chromogenic stripsτd=diffuse transmittance of windowτmax=maximum theoretical transmittanceτmin=minimum theoretical transmittanceΩ=solid angle of sky view [sr]ωs=solid angle of source [sr]Additional informationFundingThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.