## Calculation of the Number of Collectors per Row

The first step in the calculation of the number of collectors per row is to estimate the mass flow rate per row. To guarantee an appropriate heat transfer coefficient inside the absorber tube a turbulent flow is necessary. Taking into account that the conditions of the pre-design are good ones in terms of available solar energy, it is chosen a Reynolds number high enough to have turbulent flow even at any other solar radiation conditions — like in winter, for example-. It means to work with a Reynolds number around 600.000, since the useful thermal power in winter can be, in the worst cases, 30% lower than the one collected in summer, inducing a reduction of the mass flow rate to a third of the value in summer.

The mean fluid velocity, v, in the absorber tubes is calculated from the expression of the Reynolds number. A first estimation of the mass flow rate per row, m0, is given by

m0 = vp At (eq.1)

where p is the fluid density and At is the inner cross section of the steel absorber tube.

The number of collectors required in every row depends on the conditions set at the inlet and outlet of the solar field and the thermal power supplied by every collector. The increase of temperature between the inlet and outlet of every row, ATrow, should consider that the fluid temperature at its outlet has to be higher (7-10°C) than the temperature of the steam generated in the heat transfer fluid to water heat exchanger, in order to compensate the thermal heat losses through the pipe lines which connect the rows in the solar field, the efficiency of the heat exchanger and the pinch point of the latest. The energy given by a collector is assumed to be the same for every collector, independently what the position of the collector in the row is, i. e., the heat capacity of the heat transfer fluid, cP, and thermal losses are assumed to be constant in the range of working temperatures in a row.

To calculate the temperature increment in every collector, AT°kc, an energy balance is done

considering that the solar thermal power absorbed by the collector minus its heat losses to ambient is the useful thermal power, Qutii, coic, used to increase the temperature of the working fluid mass flow. Mathematically,

where Ac is the aperture area of a collector and T^s and Qloss are the absorber tube temperature and thermal losses, respectively.

Thus, the number of collectors, N, is given by the rate of the temperature increase needed per row, ATrow, and the temperature increase in every collector, AT°kc,

The obtained number of collectors per row, N may not be an integer. If so, this number has to be rounded to an integer number, Npre_design from which the new temperature increment in a collector in the pre-design, ATcol, is obtained from (eq.3) considering N=Npre-design and the new pre-design mass flow rate, mr, comes from (eq.2) considering AT°lec = ATcolec.