modelSolarRadiationExchange

Information

This model computes the distribution of the solar radiation gain to the room surfaces. Let N^w denote the number of windows, N^f the number of floor elements and Nⁿ the number of non-floor elements such as ceiling, wall and window elements. Input to the model are the diffuse and direct solar radiosities Jⁱ_dif, i ∈ {1, … , N^w} and Jⁱ_dir, i ∈ {1, … , N^w} that were transmitted through the window. The total incoming solar radiation is therefore for the diffuse irradiation

H_dif = ∑_i=1^Nw J_difⁱ

and for the direct irradiation

H_dir = ∑_i=1^Nw J_dirⁱ.

It is assumed that the diffuse irradiation is distributed to all surfaces proportionally to the product of surface emissivity plus transmissivity (which generally is zero except for windows) times the area. For the direct irradiation, it is assumed that it first hits the floor where some of it is absorbed, and some of it is diffusely reflected to all other surfaces. Only the first reflection is taken into account and the location of the floor patch relative to the window is neglected.

Hence, the diffuse radiation that is absorbed by each area is

Qⁱ_dif = H_dif   (εⁱ+τⁱ)   Aⁱ ⁄ ∑_j=1^N   A^j,

where the sum is over all areas. Hence, this calculation treats the wall that contains the window identical as any other construction, which is a simplification.

Similarly, the direct radiation that is absorbed by each floor patch i ∈ {1, …, N^f}, and may be partially transmitted in the unusual case that the floor contains a window, is

Qⁱ_dir = H_dir   (εⁱ+τⁱ)   Aⁱ ⁄ ∑_j=1^Nf   A^j.

The sum of the direct radiation that is reflected by the floor is therefore

J^f = H_dir   ∑_i=1^Nf (1-εⁱ-τⁱ)   Aⁱ ⁄ ∑_j=1^Nf   A^j.

This reflected radiosity is then distributed to all non-floor areas i ∈ {1, …, Nⁿ} using

Qⁱ_dir = J^f   Aⁱ   (εⁱ+τⁱ) ⁄ ∑_k=1^Nn A^k   (ε^k+τ^k)

The heat flow rate that is absorbed by each surface is

Qⁱ = Qⁱ_dif + Qⁱ_dir.

For opaque surfaces, the heat flow rate Qⁱ is set to be equal to the heat flow rate at the heat port. For the glass of the windows, the heat flow rate Qⁱ is set to the radiosity J_outⁱ that will strike the glass or the window shade as diffuse solar radiation.

Main assumptions

The main assumptions or simplifications are that the shaded and unshaded part of the window have the same solar absorbtance. Furthermore, if the room has electrochromic windows, the optical properties are taken from the state 1, which generally is the uncontrolled state. The error should be small as in the controlled state, there is little solar radiation entering the room, and with this simplification, the main error is that the radiation that is reflected in the room and hits the window is larger than it otherwise would be. This simplification allows lumping the solar distribution into a parameter.

The model also assumes that all radiation first hits the floor from which it is diffusely distributed to the other surfaces.

Parameters

Components

Revisions

• February 11, 2022, by Michael Wetter:
  Change parameter isFloor to is_floor, and isCeiling to is_ceiling, for consistency with naming convention.
• June 7, 2016, by Michael Wetter:
  Removed HTot as this is not needed, and refactored the model so that the diffuse irradiation is treated separately from the direct irradiation. This is for issue 451.
• August 7, 2015, by Michael Wetter:
  Revised model to allow modeling of electrochromic windows. This is for issue 445.
• March 13, 2015, by Michael Wetter:
  Changed model to avoid a translation error in OpenModelica.
• July 16, 2013, by Michael Wetter:
  Added assignment of heat port temperature instead of heat flow rate for the cases where a construction has been conditionally removed. This is required to avoid a singularity.
• November 6, 2011, by Michael Wetter:
  Fixed bug as in the old version, the absorbtance and reflectance of the infrared spectrum has been used instead of the solar spectrum.
• Dec. 1 2010, by Michael Wetter:
  First implementation.