The design of a solar field is one of the crucial aspects when a solar tower system is realized. In general, shading and blocking effects, which are the main causes of solar power losses, are minimized displacing the heliostats each other quite distant, with typical land coverage less than 20%, and thus, strongly limiting the construction of these plants to low value lands. A new method is proposed here to improve the collected energy for solar tower systems with high land coverage (greater than 30%), based on the chance for each heliostat to rotate about the normal passing through the center of its surface. Then, shading and blocking are minimized by optimization of the relative orientations. To this aim, a small solar field composed of 150 rectangular flat heliostats has been considered, and its performances with and without the proposed optimization have been computed and compared for a wide variety of cases. In particular, a systematic analysis is presented to study the effect of the shape of the heliostats on the solar field performance: in a series of simulations, maintaining constant the area of each heliostat, the ratio between its two sides has been varied in a range between 1 (squared heliostats) and 3 (very stretched heliostats), and optimized and nonoptimized systems have been compared. Also, the total energy collected by the solar field has been calculated for optimized and nonoptimized heliostats' orientations, considering towers of different heights. Finally, the real PS10 solar plant has been considered, demonstrating that also for an optimized, very low coverage plant (about 14%), heliostats rotation can still improve the energy collection efficiency by a non-negligible amount.
||), where the fourth-order vector refers to element-by-element exponentiation and the denominator normalizes the vector describing the radii of the circles so that the maximum is at kr = 1 cm -1 . A global search was performed for all values of ci from 0 to 1 in steps of 0.1. The maximum sidelobe height for each trajectory was recorded, and the polynomial coefficients yielding the minimum value over all trajectories was used in designing the pulse. The polynomial search was limited to fourth order to avoid lengthy computation times; the improvement in going from third order to fourth order was small, and a fifth- order term did not seem likely to provide further improvement. In order to test the accuracy of the approximation, the forward SLR transform was performed for each of the corresponding spiral trajectories, and the maximum sidelobe height was recorded and compared to the value obtained from the approximation. Results Search speed for the approximation exceeded that of the SLR transform by a factor of 16 (25 minutes vs. 6.75 hrs using MATLAB 6.5 and an Intel Pentium 4 2.26 GHz processor). The set of coefficients ci was found to be (1 0 0 .4). Figure 1 depicts the slice profile for the corresponding circle trajectory (blue) and spiral trajectory (red). The sidelobes do not completely coincide for the two trajectories because of the anti-symmetric nature of sampling for the spiral trajectory. However, the peak sidelobe height is comparable. Figure 2 depicts a scatterplot of peak sidelobe height for the spiral trajectory versus the circular trajectory for all of the trajectories sampled. Although the approximation does not precisely correspond to the spiral approximation, there is a close correlation. Furthermore, the optimal trajectory is also optimal for the spiral trajectory. Figure 3 depicts a cut through the two-dimensional inversion profile (computed using a numerical solution of the Bloch equation) for the uniform density (blue) and optimized variable density (red) spiral. For the uniform density spiral, the peak sidelobe height is 5% of the mainlobe height; the variable density spiral, the peak sidelobe is only 1% of the mainlobe height. Figure 4 depicts the trajectory in excitation k- space (4a) and the shapes of the rf waveforms (4b) for the uniform density (blue) and variable density (red) spirals. Figure 1 Figure 2 Figure 3
In this paper we deal with soliton solutions of Lorentz invariant equations. Roughly speaking, a soliton is a solution of a field equation whose energy travels as a localized packet and which preserves its form under perturbations. In this respect soliton solutions have a particle-like behaviour and they occur in many questions of mathematical physics, such as classical and quantum field theory, nonlinear optics, fluid mechanics and plasma physics (see [7], [8], [11], [13]). In general the solitonic behaviour arises when one of the following circumstances occurs:
A novel methodology for the design of heliostat fields is presented, based on the selection of heliostats from an oversized field by means of a polygon. To obtain the ideal field shape, the polygon vertices are optimized with an evolutionary algorithm. The objective function calculates a weighted tradeoff between annual optical efficiency and ground usage and is applied to the entire field instead of individual heliostats. Various other figures of merit could be readily integrated. To be able to deal with complex shaped land available for the Solar Tower plant, area boundaries are taken into account during the optimization phase. The application of the methodology is demonstrated by means of a reference scenario and multiple variations of parameters and area boundaries. The polygon selection creates smooth, coherent heliostat fields with high performance regarding the objectives, while solving several practical issues in the heliostat field design phase at the same time.
This work presents the development of an analytical model for the simulation of solid oxide fuel cells (SOFCs). The unique features of the analytical code include Stefan–Maxwell–Knudsen diffusion of five-component gas mixtures (, CO, , , and ) as fuel and of air as comburent, microdiffusion to the reaction sites, reaction kinetics described accurately beyond the linear limit, internal reforming reaction, shift reaction equilibrium, thermal sources evaluation. This results in a fast and accurate computer code, which can be used both as a stand-alone tool for one-dimensional simulations and as a user-supplied source term in the framework of fluid-dynamics three-dimensional platforms. The one-dimensional simulation model is validated against literature experimental data of SOFCs operating with hydrogen-carbon monoxide mixtures. A performance analysis on the effect of SOFC geometry variation has been reported. Analysis of the results indicates that the analytical model is an effective tool for SOFC design and optimization.
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