Layer Absorptance Correction before Hemispherical Integration

[Simon Weber]

Hi Everybody,

i would like to integrate the angular layer absorptance multiplied by anisotropic radiance L [W/m2/sr] over a defined hemisphere to get the absorbed irradiance LA [W/m2]. The surface integral is

LA = int_phi int_theta X(theta,phi)*L(theta,phi)*d_omega

d_omega = sin(theta) d_theta d_ph

So the question is, what correction do i have to apply on the layer absorption vector from WINDOW EnergyPlus BSDF IDF Report? Is it only X(theta,phi) = VectorData*cos(theta)? —> So VectorData are the radius of the sperical coordinates and with the cosine(theta) i get the normal part of the absorptance?

Kind regards

Simon

[Jacob C. Jonsson (LBNL)]

Not sure where to look up the EnergyPlus definition of the absorption vector so can just cheer you on in your search for answers.

Unit analysis is your friend (for once in optics where so much is unitless).

If it is unitless you just use X = VectorData. This would make the most sense to me.

If the unit of the layer absorption vector is sr^-1 then I believe you are right that you need the cos(theta). I'd

be surprised if this was the case, it would make more sense to define the absorption for each incident

angle (t,p) as A(t,p) = 1-Tdir_hem(t,p)-Rdir_hem(t,p)

Best,

Jacob

[Simon Weber]

Hi Jacob,

thanks for your reply. I think i got the data in sr^-1 unit for all klems angles, because the data plot makes more sense with cosine. Especially the zero absorption at (90°,phi) and the quasi cos(theta)-shape of it.