A User's Manual for DELSOL3 - prod.sandia.gov - Sandia National ...

1II.F. Flux Density and SDillane
The details of the theoretical method for calculating the flux in DELSOL is
given in References 3 and 5. The flux distribution from a heliostat, normalized
to unit power, is represented analytically by a truncated expansion in Hermite
polynomials:
(1II.F - 1)
where ax, cyy, and Aij are calculated from the projection of the heliostat on the
receiver, the sunshape, and the heliostat performance error distribution, and
where x and y are the coordinates in the plane of the reflected image (Table II-
1). The H’s are Hermite polynomials, the first three of which are:
H~(x) = 1
Hl(x) = x
H~(x) = x2-I
(1113 - 2)
Reference 5 shows that the Aij and a’s have a simple power law dependence on
the tower height THT. Therefore, once the flux is found for one tower height, it is
straightforward to calculate the dependence for other tower heights. Furthermore,
since Equation (1II.F-1) describes the flux over the entire image plane, the flux
can be projected onto any receiver as long as the receiver dimensions are small
compared to the slant range.
The code assumes that total energy in the flux distribution is reduced by
shadowing and blocking, but that the spatial distribution of the flux is taken as
proportional to that of an unshaded and unblocked heliostat. This is generally
justified because shadowing and blocking losses are usually small and the con-
volution of the mirror shape with the sunshape and errors reduces the effect of
shadowing and blocking on the flux profile.
The ability to use one flux calculation to predict the flux from a
given heliostat design on any tower or receiver is the main strength of
DELSOL. With this ability, DELSOL can scale the results of one detailed initial
performance run during system optimization calculations and quickly calculate
performances for comparison between different systems. However, note that the
performance which is scaled is an annual average performance (flux map). Thus,
if the design point performance is different than the annual average then the pre-
dicted performance during the optimization (scaled performance) will not match
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