Procedure for thermal performance evaluation of steam generating point-focus solar concentrators

Solar energy can be used for substitution of the depleting fossil fuels in thermal applications and electricity generation through thermal route. For medium and high temperature applications, solar concentrators are required. Proper sizing and selection of concentrator for any thermal application calls for characterization of the concentrator at the required operating temperature. There are few procedures reported in literature for testing and evaluating solar concentrator performance which are based on sensible heating of the working fluid. One of the limitations of these procedures is requirement of precise operating conditions during testing. A test procedure for characterization of point-focus steam generating solar concentrators based on latent heating at different operating temperatures is proposed. The proposed procedure uses the phase change characteristic of water at constant temperature to measure the thermal performance. This procedure can be used to estimate thermal efficiency of solar concentrator at different operating temperatures above 100 °C. This procedure was used to estimate the efficiency of a point-focus solar concentrator having 25 m² aperture area at 161 °C (equivalent to 5.4 bar (g)). The efficiency was estimated as 47 ± 3.5%. The test procedure can be used for field evaluation of existing systems also with minimum amount of instrumentation and controls.     

Parametric performance and cost models for solar concentrators

The development of parametric performance and cost models for various solar concentrators is discussed. The equations are derived in the context of an optimization scheme which can be applied to many different problems which arise when heat is generated by means of solar concentrators. Thus, while the results presented were developed for finding a minimum cost solar electric energy power plant, the method employed has been found to have general applicability. Sensitivity analysis of the subsytems is also discussed. Finally, numerous illustrative examples are presented.     

Theoretical performance of cylindrical parabolic solar concentrators

This is a theoretical study of the performance of cylindrical parabolic solar concentrators under ideal conditions. Particular attention is given to the application of this type of concentrator in the intermediate temperature range, where wide targets are used.Suitable indices that describe the performance are defined and calculated, and the effects of the different parameters are studied. In particular, the energy available at the focal plane and the distribution of its intensity are determined. All ranges of rim angles are studied: less than 90°, more than 90°, and the whole range of 0–180°.The performances obtained are the best possible and can, therfore, be used as a standard of reference for the appraisal of actual concentrators of the type studied.     

Mathematical analysis of the performance of cylindrical-parabolic solar concentrators

Attention is devoted to the application of cylindrical-parabolic solar concentrators in the intermediate temperature range for which wide receivers are used. Suitable indices that describe the performance of the concentrator are defined and evaluated. The effect of each individual parameter on total concentrator performance is investigated. The results of the analysis are presented as a set of graphs which can be used easily when designing parabolic concentrators.     

Performance model for two-stage optical concentrators for solar thermal applications

A performance model has been developed for evaluating benefits associated with the addition of a nonimaging secondary concentrator to a conventional paraboloidal solar dish. The model uses a Monte Carlo ray-trace procedure to determine the focal plane distribution as a function of optical parameters and, by evaluating the trade-off between thermal losses and optical gain, calculates the corresponding optimized concentration and thermal efficiency as a function of temperature, both with and without the secondary. These comparative optimizations, carried out over a wide range of design parameters, show that the efficiency of a two-stage concentrator is always greater than that of a single stage if all other design parameters are the same. For example, for a reference design corresponding to a dish with a focal length to diameter ratio of 0.6 and a characteristic slope error of 5 milliradians operated at a receiver temperature of 1000°C, the optimized efficiency with a secondary is 0.70 compared to 0.59 for the primary alone. At fixed focal ratio, the relative performance advantage with a secondary increases, if either the temperature or the primary slope error or both, are increased, whereas it decreases if they are decreased. However, the advantage remains significant at temperatures above 400°C, even in the “high performance limit” of slope errors <2 milliradians.     

Thermal performance of linear solar concentrators with tubular absorbers

The outlet temperature, corresponding thermal efficiency and the stagnation temperature available with a linear solar concentrator using a tubular absorber have been calculated, taking into account the temperature dependence of the heat-loss coefficient. The results of some typical numerical calculations are presented graphically and discussed.     

Upper bounds for the yearly energy delivery of stationary solar concentrators and the implications for concentrator optical design

Compound parabolic concentrator (CPC) type collectors have been viewed as the optimal design for totally stationary concentrators. However the CPC is ideal only for uniform incident solar flux averaged over the energy collection period. The actual yearly-averaged incident flux map turns out to be highly non-uniform, as a function of projected incidence angle, which implies that concentration can be increased markedly if optical collection efficiency is compromised. The question then becomes: what concentrator angular acceptance function is best matched to nature's radiation flux input, and how much energy can such a concentrator deliver? The recently-invented tailored edge-ray concentrator (TERC) approach could be used to determine optimal reflector contours, given the optimal acceptance angle function. We demonstrate that totally stationary TERCs can have around three times the geometric concentration of corresponding optimized stationary CPCs, with greater energy delivery per absorber area, in particular for applications that are currently being considered for stationary evacuated concentrators with the latest low-emissivity selective coatings, e.g. solar-driven double-stage absorption chillers (at around 170°C) and solar thermal power generation (at around 250°C).     

On the performance of cylindrical parabolic solar concentrators with flat absorbers

An integral relationship is developed for evaluating the intensity distribution on flat absorbers used with cylindrical parabolic solar concentrators. Calculations are presented for perfect cross-section concentrators using various models, rim angles, off-axis angles and defocusing amounts. Peak concentration ratios are shown to vary as the sine of the rim angle. Off-axis and defocused operations are shown to result in considerable reduced intensities. The effect of surface slope errors is also investigated. Normally distributed surface slop errors with a standard deviation of 0.25 degree are shown to reduce peak intensities by more than a factor of 3.     

The design and performance of liquid filled stationary concentrators for use with photovoltaic cells

This paper discusses the design and practical application of dielectric filled stationary concentrators. The design adopted is a 3 × liquid filled lens-V trough concentrator fabricated as a thin walled plastic shell with total internal reflecting sides. The measured performance of both oil and water filled prototypes is in agreement with predicted performance. It is concluded that the dielectric filled LVT concentrator performs as well as the dielectric filled CPC in the stationary mode of operation and has advantages in relation to economy and ease of fabrication.     

Comparison of solar concentrators

Even though most variations of solar concentrators have been studied or built at some time or other, an important class of concentrators has been overlooked until very recently. These novel concentrators have been called ideal because of their optical properties, and an example, the compound parabolic concentrator, is being tested at Argonne National Laboratory. Ideal concentrators differ radically from conventional instruments such as focussing parabolas. They act as radiation funnel and do not have a focus. For a given acceptance angle their concentration surpasses that of other solar concentrators by a factor of two to four, but a rather large reflector area is required. The number of reflections varies with angle of incidence, with an average value around one in most cases of interest. In order to help provide a rational basis for deciding which concentrator type is best suited for a particular application, we have compared a variety of solar concentrators in terms of their most important general characteristics, namely concentration, acceptance angle, sensitivity to mirror errors, size of reflector area and average number of reflections.The connection between concentration, acceptance angle and operating temperature of a solar collector is analysed in simple intuitive terms, leading to a straightforward recipe for designing collectors with maximal concentration (no radiation emitted by the absorber must be allowed to leave the concentrator outside its acceptance angle). We propose some new concentrators, including the use of compound parabolic concentrators as second stage concentrators for conventional parabolic or Fresnel mirrors. Such a combination approaches the performance of an ideal concentrator without demanding a large reflector; it may offer significant advantages for high temperature solar systems.     

Planar concentrators for flat-plate solar collectors

A systematic study has been made of the effectiveness of planar specular reflectors for solar energy collectors. Two daily averaged indices of performance were used. One, the area ratio, indicates the amount by which the reflector extends the effective receiver area. The other is the enhancement factor, which is used to compare the energy received by an augmented collector with that by a reference collector at optimum tilt.

A reflector can be mounted either above or below a flat-plate collector. Both combinations are evaluated fully, by varying separately the angular position and dimensions of the reflector and of the collector. The principal parameters are identified and the main characteristics summarised as a series of performance curves. These curves provide an easy method for determining optimum reflector geometries.

Use of the performance curves may be extended to obtain the configuration of the two reflectors in a trough concentrator. This also allows the single-reflector system to be compared directly with the trough concentrator. Evidence is presented which shows the advantages of an asymmetrical trough configuration over a symmetrical concentrator.     

Ray trace evaluation of solar concentrators including limb darkening effects

The different correlations used to calculate intensity distribution over the sun's disc are compared. A new correlation is suggested which predicts the values to within ± 1.5 per cent of the experimental values. The distribution of local concentration ratio over a flat absorber placed in the focal plane of a cylindrical parabolic trough and that of a polygonal trough is determined using a ray-tracing technique.     

Econometric analysis of concentrators for solar cells

When concentrating collectors are used with photovoltaic solar cells, the cost of the generated electricity is controlled by the concentrator cost. This enables the use of highly efficient cells and collectors of high concentration ratios, thereby reducing both the cell and the non-cell cost components per unit generated electricity. Cost analyses indicate the significance of distinguishing between the cell-cost and the non-cell cost-components. A generalized model is formulated for correlating the electricity cost to the system parameters: the annualized cost of the collector and other non-cell components , the cell annualized cost , the concentration ratio (R), the orientation parameter (G), the insolation [I_h(kWh)m⁻²yr⁻¹], the optical efficiency (η₀), and the cell efficiency (η_c): η_aη_oGI_hC = C_o + C_c/R.The model enables the economic assessment of various concentrator-cell systems and the evaluation of the sensitivity of the cost of the produced electrical energy to various possible technological improvements. Optimization and the setting of a spectrum of target goals for cells and collectors are thus made possible. An example is included showing projected minima of generated electricity at concentration ratios between 4 and 400.     

Self absorption treatment for the luminescent solar concentrators

The effect of self absorption accompanying most dyes used as a luminescent solar concentrator in the form of rigid sheets was reduced, allowing for more efficient solar concentrators and hence high photovoltaic solar conversion. The treatment involved mixing dopant molecules of specific properties with the dyes before forming the rigid final shape. Dyes including Rhodamine 6G, Rhodamine B, Ruthenium bi byridyl and crystal violet were used while thionin molecules were utilized as the dopant. The study shows that the efficiency enhancement is a function of dopant concentration and sample thickness.     

Static concentrators for two-sided photovoltaic solar cells

The use of cylindrical mirrors to concentrate radiant energy onto a two-sided photovoltaic absorber has been studied. Both theoretical and experimental results for the illumination intensity at the exit aperture were obtained for such a concentrator. A mathematical approach was devised to obtain the theoretical intensity distribution. Experimental intensity distribution was measured for a set of different mirrors. The mirrors all had the same profile but were made of different materials and had different reflecting surfaces.The main conclusion was that the intensity distribution at the exit aperture is very inhomogeneous. The concentration was very low (less than 3) for a certain zone of the absorber, regardless of the light rays incidence angle. Another important conclusion was the effect of truncating the mirror, which was found to be a reduction in the average number of reflections of the incident light.Finally, an arrangement, different from the theoreticalone, is presented for the placement of the absorber in the concentrator.     

Two axis tracking system for solar concentrators

A two axis tracking system is described for the focussing of sunlight in paraboloid-type solar reflectors used in solar thermal devices like solar cookers. This system consists of wormgear drives and four bar type kinematic linkages for effortless and accurate focussing of reflectors at low cost.     

Impact of heliostat curvature on optical performance of Linear Fresnel solar concentrators

The present paper gives a numerical investigation of the effect of mirror curvature on optical performance of a Linear Fresnel Reflector solar field installed recently in Morocco. The objective is to highlight and discuss the effect of mirror curvature on the flux density distribution over the receiver and the system optical efficiency. For this purpose, a Monte Carlo-ray tracing simulation tool is developed and used to optimize the optical design taking into account the curvature degree of the heliostat field. In order to assess the accuracy of the numerical code developed and the validity of simulation results, a set of verification tests were developed and detailed within this article. Then, the optical performance of the system is evaluated as a function of mirror curvature and receiver height. The major challenge of this study is to find a trade-off between heliostat curvature and receiver height since lower and smaller receivers may reduce the system cost. It has been found that the flux distribution over the receiver and the optical efficiency of the system are relatively sensitive to the mirror curvature. We have demonstrated quantitatively how the use of curved mirrors can enhance the optical performance and reduce the required receiver size.     

Design and optical performance analysis of seasonally adjusted discrete mirror solar concentrators

Mirror profiles composed of small plane mirror elements have been developed for four different linear absorbers—flat horizontal, flat vertical, triangular cross-section and tubular—on lines similar to those outlined by Winston and Hinterberger. The concentration characteristics of such systems have been studied. The local concentration ratio distributions over these absorber surfaces have been investigated using the ray-tracing procedure.     

The design and performance of ideal solar concentrators based on the prism-assisted cylindrical reflector

The optical design of an ideal concentrator based on the combination of a cylindrical reflector and refracting prism is discussed and shown to have a number of advantages over other reflector type concentrators. A 20 × photovoltaic concentrator is shown to have an optical efficiency of over 70 per cent within the ideal acceptance angle in good agreement with experimental results.