## Results and Discussion

We started our numerical analysis with a two-step optimization process of the solar collector for conditions assumed in our case study. In this respect, we estimated a range for the collector factor based on typical values of heat transfer coefficient at the receiver, typical insolation, receiver temperature, and optical properties. We concluded that Fcoll=50-100 covers the values of practical interest for our case study. Furthermore, typical values of the rim angle for paraboloidal dishes are in the range 30-75°, and typical optical error in the range 5-20 mrad; for smaller angular error, the cost of the optical system increases dramatically. For the optical factor, we assumed a constant value Q = 0.9.

The first step in the optimization is illustrated in Fig. 4.7(a) which shows the variation of the collector efficiency for a fixed collector factor and rim angle. There is always an optimum concentration ratio that maximizes the collector efficiency. This optimization has been repeated for four values of the angular optical error. One may observe that the collector efficiency is very sensitive to the optical system quality, and it is worth mentioning that this is a cost-sensitive aspect. The second step in optimization implies to compute the maximum collector efficiency (as obtained for every optimal concentration ratio) for a range of rim angles. The results are reported on the right side of Fig. 4.7(b) and demonstrate that there is an optimal rim angle that maximizes the collector's performance. This angle is quite insensitive to the optical surface properties, and moreover we observed by repeating the computations for several values of the collector factor that the efficiency is insensitive to Fcoll as well. The optimal value of the rim angle is around 62.5oC. This is an important result, meaning that the parabolic dish can be constructed with a rim angle of 60o for most of situations.

"o

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Fig. 4.7 Optimization of the solar collector geometry for maximum performance: influence of concentration ratio (a) and of rim angle (b).

The maximum values of the collector efficiency, obtained by optimization with respect to C and are computed for a range of collector factor Fcon, and the results of this process are reported in Fig. 4.8(a). As expected the collector efficiency decreases with Fcon, that is, it decreases with the increase of the receiver temperature. Larger receiver temperature means large Fcon and large heat losses. Alternatively, large Fcon means higher insolation for fixed Tab, which, in turn, also means higher

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heat losses. On the same plot from Fig. 4.8(b), we presented the variation of the heat engine efficiency with the heat source temperature (expressed also through the collector factor). Doing so, we got the opportunity to multiply the collector and heat engine efficiency and to get the system efficiency (without cogeneration) in the right side plot of the same figure.

 s = 0.004 —^^ ^ ✓ 06 / —— / —___S=0:008 / ^^^^ / / / 70 80 Fcol 70 80 Fcol 0.17 0.165 0.16 70 80 Fig. 4.8 Optimization of the system operation parameters for maximum performance: collector and power cycle efficiency (a) and system efficiency (b).