External LW-radiation heat transfer

[SchildCode]

Issue overview

Chapter 3.5.2 "External Longwave radiation" of the version 8.9.0 Engineering Reference (March 23, 2018) should be updated in line with changes in the code:

i) A new view factor (F_obs-sky) has been implemented in the code to account for nearby objects (e.g. buildings) that are assumed to be at the same temperature as the surface. This should be added to the equations in Chapter 3.5.2. These equations can be copied directly from [ref1].

ii) Another suggestion I have is that a sentence or two should be added to Chapter 3.5.2 explaining why the sky view factor (Fsky) is split into two parts (Beta) and (1-Beta), with radiative temperatures (Tsky) and (Tair) respectively. This is an empirical way of handling the fact that angle-dependent air mass causes clear skies to have highly anisotropic emissivity, being lowest (i.e. coldest) at the zenith, and approaching unity (i.e. air temperature). This phenomenon was researched in the 1980s (e.g. paper by Martin & Berdahl in 1984), and the TARP model for external radiation exchange used in EnergyPlus was documentet in 1983 [ref.2, page 73]. The effective sky temperature is a hemispherical value that is correct only for horizontal surfaces, whilst tilted surfaces' view a warm part of the sky, which can be calculated by a weighted average of the hemispherical value (Tsky) and the horizon value (Tair). The correct value of weighting factor (Beta) should be a topic of future research. Unfortunately, most energy software and supporting standards (e.g. ISO 13790/13792) still assume that the sky emissivity is isotropic (i.e. Beta=1 always), which leads to overprediction of heat loss from tilted surfaces. Text about this can be taken from [ref4, pages 123-125].

iii) Lastly, the swiss paper [ref1] claims that "A better estimate of the ground surface temperature has been implemented in EnergyPlus", i.e. ground radiative temperature with an annual sinusoidal function derived from the met data. Whenever this code becomes part of the standard E+ code, then Chapter 3.5.2 should be updated in line with this fact.

[ref1]: Ralph Evins, Viktor Dorer, Jan Carmeliet, "Simulating external longwave radiation exchange for buildings", Energy and Buildings 75 (2014) 472–482. See section 4.1. "Existing formulation in EnergyPlus" and 4.2 "Improved ground temperature". http://dx.doi.org/10.1016/j.enbuild.2014.02.030

[ref2]: Walton, George N. "Thermal analysis research program reference manual." National Bureau of Standards, March (1983).

[ref3]: P.G. Schild, "Accurate prediction of indoor climate in glazed enclosures", PhD thesis. NTNU. 1997. https://www.researchgate.net/publication/35697726_Accurate_prediction_of_indoor_climate_in_glazed_enclosures

Details

Version 8.9.0 Engineering Reference (March 23, 2018) E+ version 8.9.0-40101eaafd

Checklist

[mjwitte]

@SchildCode I'm not following where there is an error here. The revised equation assumes Tg = Ta. The current equation allows for Tg to be different. While EnergyPlus currently uses the Tg=Ta as the default assumption, there are optional inputs available to set Tg to something different, see SurfaceProperty:SurroundingSurfaces.

[SchildCode]

I see now that the fault was in fact the equations in ISO 13790 / 13792, which assume isotropic sky emissivity, whilst E+ correctly treats sky emissivity as anisotropic. However, there remain 3 issues with the documentation of external radiation exchange in the Engineering Reference, which I have edited in above.

[mjwitte]

Thanks. It has been suggested that the Martin-Berdahl model be added as an option (#4999). This is also related to #4116.