.TransiEnt.Producer.Heat.SolarThermal.Base.Skymodel_HDKR

Information

1. Purpose of model

Anisotropic approach to calculate solar radiation on a tilted surface.

2. Level of detail, physical effects considered, and physical insight

Hay and Davies (1980) estimate the fraction of the diffuse that is circumsolar and consider it to be all from the same direction as the beam radiation; they do not treat horizon brightening. Reindl et al. (1990b) add a horizon-brightening term to the Hay and Davies model, as proposed by Klucher (1979), giving a model to be

referred to as the HDKR model (see Duffie & Beckman, 2006).

Theoretical model based on the assumption that the diffuse irradiance has a peak next to the angle of the sun so that this circumsolar irradiance can be added to direct irradiance.

3. Limits of validity

Usage for small values of angleOfSunIncidence.horizontal is not recommended because of refraction by atmosphere.

4. Interfaces

(no remarks)

5. Nomenclature

direct_tilted, diffuse_tilted and ground_tilted are the calculated irradiances of tilted surface.

6. Governing Equations

anisotropyIndex= min(1,max(Const.small,direct_horizontal/max(1,sun_horizontal)))

eff= sqrt(direct_horizontal / max(1,(direct_horizontal + diffuse_horizontal)))

direct_tilted= (direct_horizontal+diffuse_horizontal*anisotropy_index)*ratio_beam

diffuse_tilted= diffuse_horizontal*(1-anisotropy_index)*((1+cos(slope))/2)*(1+eff*(sin(slope/2))^3)

ground_tilted= (direct_horizontal+diffuse_horizontal)*reflectance_ground*(1-cos(slope))/2

7. Remarks for Usage

None.

8. Validation

Purely theoretical model

9. References

Duffie & Beckman (2006): Solar Engineering of Thermal Processes, p. 91 f.

10. Version History

Model created by Tobias Toerber (tobias.toerber@tuhh.de), Jul 2015

Edited by Sascha Guddusch (sascha.guddusch@tuhh.de), May 2016

Modified by Anne Senkel (anne.senkel@tuhh.de), Mar 2017

Modified by Lisa Andresen (andresen@tuhh.de), Apr. 2017

Model modified by Oliver Schülting (oliver.schuelting@tuhh.de), Jun 2018: no anisotropy if irradiance_extraterrestrial<=25 since this lead to unrealistic high irradiation peaks at morning and/or evening

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