Radiation Converter
by Ann Barrett, 1987
This subroutine "untilts" radiation data measured on the tilted
surface to the horizontal surface value needed for input into the TRNSYS
radiation processor.
The TRNSYS subroutine, called the solar radiation processor, calculates
the diffuse solar radiation, needed angles describing the position of the sun
and can estimate insolation on as many as four surfaces of either fixed or
variable orientation. The subroutine can also interpolate radiation data
if needed, using a non-linear interpolation. One of the inputs required by
the subroutine is the value for horizontal surface radiation which was not
measured at the sites studied. This problem was overcome by writing a new
TRNSYS component to calculate the horizontal surface radiation from the tilted
surface value.
NOTE: This component uses the Isotropic Sky Model for a radiation model.
If you use this with the Solar Radiation processor, make sure that the
processor mode that you select also uses the Isotropic Sky Model.
The horizontal surface radiation is calculated using the following
relationships. First, the extraterrestrial radiation value is calculated in
Btu/ft^2 time step:
1.067 Gsc 360 n
Io = ----------- [ 1+.033cos(------)]
Pi 365
2Pi
x [ cos(del)cos(phi)cos(om2-om1)+ ----(om2-om1)sin(tht)sin(del)]
360
where:
Gsc = solar constant
n = day of the year
phi = latitude
del = solar declination angle
om1 = hour angle at beginning of time step
om2 = hour angle at end of time step
The radiation value is calculated per 5 1/3 minute time step throughout
this calculation procedure, the customary hourly value is not used. Next, an
estimate is made for the ratio of tilted surface radiation to the horizontal
surface radiation.
It cos(Tht)
R = ---- = Rb = ------
I cos(Thtz)
where:
It = total radiation incident on the tilted surface
I = total radiation incident on the horizontal surface
Rb = ratio of beam radiation on the tilted surface to the horizontal
beam radiation
Tht = angle of incidence of beam radiation on tilted surface
Thtz = angle of incidence on the horizontal surface
The angle of incidence is defined as:
Tht = sin(del)sin(phi))cos(beta) - sin(del)cos(phi)cos(gamma)
+ cos(del)cos(phi)cos(beta)cos(om)
+ cos(del)sin(phi)sin(beta)cos(gamma)cos(om)
+ cos(del)sin(beta)sin(gamma)sin(om)
where:
gamma = surface azimuth angle
beta = slope of tilted surface
The assumption that R is approximated by Rb is best on clear days
because it assumes that the diffuse radiation is concentrated from an
apparent origin near the sun. The full relationship for R is:
Ib Id
R = ---Rb + ---Rd
I I
where:
Id = diffuse component of radiation
Ib = beam component of radiation
Rd = ratio of diffuse radiation of tilted surface to the
horizontal diffuse radiation
but equation III.3.2 is useful as a first approximation. With this estimate,
Ih and the corresponding clearness index, Kt, are calculated as
I = It/Rb
Kt = I/Io
From the value of Kt, the estimate of Ih is distributed into its beam and
diffuse components using the Erbs correlation:
Id/I = 1.0-.09Kt Kt < 0.22
Id/I = .951-0.160Kt+4.38Kt^2 0.22 0.80
and
Ib = I - Id
With these values, a resulting It is calculated using the relation:
cos(beta) cos(beta)
It = IbRb + Id(1 + ---------) + (It+Ib)rho(1 - ---------)
2 2
where:
rho = ground reflectance, assumed to be 0.2
This equation assumes that the diffuse and ground reflectance radiation
are isentropic. The calculated value of It is compared to the actual values to
begin an iteration process. Kt is then adjusted by an amount weighted to the
error and the calculations are repeated until the new It agrees with the
actual values within a tolerance of 5 Btu/ft^2 hr. this tolerance was chosen
because it is the approximate error range of the radiation measurement. The
code for the "radiation converter" subroutine is listed in Appendix A.
The Ih value which results in the correct new It is then used as input
into the radiation processor. It should be noted that this is used only to
calculate the diffuse component. The It calculated by the radiation processor
is compared to the data as a check, but for precaution and simplicity, the
actual value is used as input to the collector.
PARAMETERS 5
1. day number for beginning of simulation
2. latitude
3. collector slope
4. ground reflectance
5. time shift
INPUTS 2
1. measured tilted surface radiation value
2. extraterrestrial radiation value radiation processor
OUTPUT 1
1. horizontal surface total radiation
REF: Barrett, A.L. "Thermal Modeling of Evacuated Tubular Solar Collectors"
Masters' Thesis University of Wisconsin - Madison 1987