A User's Manual for DELSOL3 - prod.sandia.gov - Sandia National ...
A User's Manual for DELSOL3 - prod.sandia.gov - Sandia National ...
A User's Manual for DELSOL3 - prod.sandia.gov - Sandia National ...
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1II.F. Flux Density and SDillane<br />
The details of the theoretical method <strong>for</strong> calculating the flux in DELSOL is<br />
given in References 3 and 5. The flux distribution from a heliostat, normalized<br />
to unit power, is represented analytically by a truncated expansion in Hermite<br />
polynomials:<br />
(1II.F - 1)<br />
where ax, cyy, and Aij are calculated from the projection of the heliostat on the<br />
receiver, the sunshape, and the heliostat per<strong>for</strong>mance error distribution, and<br />
where x and y are the coordinates in the plane of the reflected image (Table II-<br />
1). The H’s are Hermite polynomials, the first three of which are:<br />
H~(x) = 1<br />
Hl(x) = x<br />
H~(x) = x2-I<br />
(1113 - 2)<br />
Reference 5 shows that the Aij and a’s have a simple power law dependence on<br />
the tower height THT. There<strong>for</strong>e, once the flux is found <strong>for</strong> one tower height, it is<br />
straight<strong>for</strong>ward to calculate the dependence <strong>for</strong> other tower heights. Furthermore,<br />
since Equation (1II.F-1) describes the flux over the entire image plane, the flux<br />
can be projected onto any receiver as long as the receiver dimensions are small<br />
compared to the slant range.<br />
The code assumes that total energy in the flux distribution is reduced by<br />
shadowing and blocking, but that the spatial distribution of the flux is taken as<br />
proportional to that of an unshaded and unblocked heliostat. This is generally<br />
justified because shadowing and blocking losses are usually small and the con-<br />
volution of the mirror shape with the sunshape and errors reduces the effect of<br />
shadowing and blocking on the flux profile.<br />
The ability to use one flux calculation to predict the flux from a<br />
given heliostat design on any tower or receiver is the main strength of<br />
DELSOL. With this ability, DELSOL can scale the results of one detailed initial<br />
per<strong>for</strong>mance run during system optimization calculations and quickly calculate<br />
per<strong>for</strong>mances <strong>for</strong> comparison between different systems. However, note that the<br />
per<strong>for</strong>mance which is scaled is an annual average per<strong>for</strong>mance (flux map). Thus,<br />
if the design point per<strong>for</strong>mance is different than the annual average then the pre-<br />
dicted per<strong>for</strong>mance during the optimization (scaled per<strong>for</strong>mance) will not match<br />
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