Manuel Collares-Pereira

The average distribution of solar radiation-correlations between diffuse and hemispherical and between daily and hourly insolation values

Abstract The correlations of Hottel, Whillier, Liu and Jordan between diffuse and hemispherical, and between instantaneous (hourly) values and daily totals of solar radiation are recalibrated against pyrheliometer data for five stations in the U.S. The validity of the Liu and Jordan approach is confirmed, and numerical inaccuracies of the original correlations are found to arise from three factors: (i) reliance on uncorrected measurements of diffuse insolation with pyranometer plus shade ring, (ii) use of a single value of extraterrestrial insolation for a whole month, and (iii) neglect of seasonal variations in the diffuse/hemispherical ratio. The new correlation for the daily total ratio of diffuse over hemispherical insolation agrees with results reported for India, Israel and Canada which included the shade ring correction. This suggests that latitude independence is a good approximation. The new correlations imply that the diffuse component is significantly larger than that predicted by the original formulas of Liu and Jordan. Analytical expressions are presented the parameters of which are obtained by a least squares fit to the data. The resulting formulas provide a complete description of the long term average insolation incident on surfaces of arbitrary orientation; the only meteorological input is the long term average daily total of hemispherical insolation on the horizontal surface. Comparison between model and data shows an accuracy better than 3 per cent for the long term average insolation available to solar correctors, both fixed and tracking. The model provides a framework for optimal matching between solar radiation and ideal concentrators (based on the principle of phase space conservation). In addition to computing radiation availability for solar collectors, the model can be used for calculating heating and cooling loads of buildings.

Simple procedure for generating sequences of daily radiation values using a library of Markov transition matrices

This article describes how sequences of daily global radiation can be generated for any location, using as input only the average monthly radiation for that location (or the average monthly number of sunshine hours—insolation). The generated sequences are statistically indistinguishable from real ones and the method derived here is, therefore, a way of obtaining radiation sequences for locations were such sequences have not been measured, and for which many types of long-term performance calculations could not be made until now. The method is based on the observation that (1) there is a significant correlation only between radiation values for consecutive days and (2) that the probability of occurrence of radiation values is the same for months with the same Kt (clearness index). The method employs a library of Markov transition matrices, each corresponding to a specific interval in Kt. This article explains the derivation of the matrices, how they are to be used to generate radiation sequences, and compares synthetized and measured sequences.

TAG: A time-dependent, autoregressive, Gaussian model for generating synthetic hourly radiation

Abstract A model is described which generates synthetic daily sequences of hourly radiation values, on the horizontal plane, for any location, with the daily clearness index Kt as input. The model assumes that for each Kt and solar hour the probability density of the hourly clearness index kt is (simply) a truncated Gaussian function. A first-order autoregressive model is fitted for the kt variable, normalised using parametrisations for the time-dependent average and standard deviation values. Values generated by this ARMA (1,0) model can then be transformed backwards to generate synthetic sequances of kt values. Using a diffuse fraction correlation and a tilted radiation model, the horizontal global data can be transformed to any desired plane, thus providing solar system designers with the necessary hourly data for the accurate sizing of every type of solar system, including stand-alone, high solar fraction and passive ones.

The frequency distribution of daily insolation values

Abstract Frequency distributions of insolation values are needed in order to derive simple correlations for predicting the performance of solar energy systems. In this paper the frequency distribution of daily total hemispherical solar irradiation values on the horizontal surface is derived from measured data for 90 locations in the U.S. The results can be approximated by generalized distribution curves which depend only on the clearness index, defined as ratio of terrestrial over extraterrestrial insolation. The results agree well with the curves originally derived by Liu and Jordan, except for a correction at high insolation values. The deviation of individual locations from the generalized curves is examined. A breakdown according to time of year reveals some seasonal variation. The theoretical distribution corresponding to random insolation sequences is also derived; it agrees very well with the generalized frequency distribution curves.

Compound parabolic concentrator technology development to commercial solar detoxification applications

Abstract An EC-DGXII BRITE-EURAM-III-financed project called ‘Solar detoxification technology in the treatment of persistent non-biodegradable chlorinated industrial water contaminants’ is described. The objectives are to develop a simple, efficient and commercially competitive solar water treatment technology based on compound parabolic collectors (CPC) enabling design and erection of turnkey installations. A European industrial consortium, SOLARDETOX, representing industry and research in Spain, Portugal, Germany and Italy has been created through this project. Some of the most up-to-date scientific and technological results are given, including the design of the first industrial European solar detoxification treatment plant, the main project deliverable.

Simple procedure for predicting long term average performance of nonconcentrating and of concentrating solar collectors

Abstract The Liu and Jordan method of calculating long term average energy collection of flat plate collectors is simplified (by about a factor of 4), improved, and generalized to all collectors, concentrating and nonconcentrating. The only meteorological input needed are the long term average daily total hemispherical isolation H h on a horizontal surface and, for thermal collectors the average ambient temperature. The collector is characterized by optical efficiency, heat loss (or U-value), heat extraction efficiency, concentration ratio and tracking mode. An average operating temperature is assumed. If the operating temperature is not known explicitly, the model will give adequate results when combined with the Φ , f-chart of Klein and Beckman. A conversion factor is presented which multiplies the daily total horizontal insolation H h to yield the long term average useful energy Q delivered by the collector. This factor depends on a large number of variables such as collector temperature, optical efficiency, tracking mode, concentration, latitude, clearness index, diffuse insolation etc., but it can be broken up into several component factors each of which depends only on two or three variables and can be presented in convenient graphical on analytical form. In general, the seasonal variability of the weather will necessitate a separate calculation for each month of the year; however, one calculation for the central day of each month will be adequate. The method is simple enough for hand calculation. Formulas and examples are presented for five collector types: flat plate, compound parabolic concentrator, concentrator with east-west tracking axis, concentrator with polar tracking axis, and concentrator with 2-axis tracking. The examples show that even for relatively low temperature applications and cloudy climates (50°C in New York in February), concentrating collectors can outperform the flat plate. The method has been validated against hourly weather data (with measurements of hemispherical and beam insolation), and has been found to have an average accuracy better than 3 per cent for the long term average radiation available to solar collectors. For the heat delivery of thermal collectors the average error has been 5 per cent. The excellent suitability of this method for comparison studies is illustrated by comparing in a location independent manner the radiation availability for several collector types or operating conditions: 2-axis tracking versus one axis tracking; polar tracking axis versus east-west tracking axis; fixed versus tracking flat plate; effect of ground reflectance; and acceptance for diffuse radiation as function of concentration ratio.

Spectrally selective composite coatings of Cr–Cr2O3 and Mo–Al2O3 for solar energy applications

Abstract Efficient solar photothermal conversion benefits from spectrally selective absorber surfaces. In this paper, a numerical model that allows correlation of the selectivity of the absorbers produced to the collector efficiency is presented. Since magnetron sputtering is a promising method to produce thin, solar selective films, a study of cermet Cr–Cr 2 O 3 and Mo–Al 2 O 3 coatings obtained by this technique in a reactive atmosphere is presented. The multilayered cermets produced have a thickness of approximately 300 nm and were based on metallic chromium (molybdenum) in a matrix of a chromium oxide (aluminium oxide) with a gradient in oxygen composition. The selective cermet graded films were produced by a reactive DC magnetron sputtering of pure chromium (aluminium with molybdenum) target in a plasma of argon–oxygen at different sputtering pressures (ranging from 5×10 −3 to 1.2×10 −2 mbar) and substrate temperatures (150 and 250°C). The microstructure, surface roughness, crystallographic phases, composition and chemical analysis were determined by X-ray photoelectron spectroscopy, reflectivity spectra in the vis/NIR region were analysed, and thermal emissivity was measured with an emissometer. The coatings have high spectral selectivity, with solar absorption ranging from 0.88 to 0.94 and thermal emissivity ranging from 0.15 to 0.04, depending on the coating materials and sputtering conditions.

Derivation of method for predicting long term average energy delivery of solar collectors

Abstract Based on the utilizability concept of Hottel, Whillier, Liu and Jordan, an analytical model has been developed to predict the long term average energy delivery of almost any solar collector. The presentation has been split into two separate papers: a users guide (without explanation of the origin of the formulas) and the present paper (which derives these formulas and documents the validation). The model is applicable whenever the average operating temperature of the collector (receiver surface, fluid inlet, fluid outlet or mean fluid) is known. If the operating temperature is not known explicitly the model will give adequate results when combined with the Φ , f -chart of Klein and Beckman. By contrast to the alternative of hour-by-hour simulation, prediction methods such as the present model and the f -chart offer the advantages of automatically averaging over year-to-year weather fluctuations and of being sufficiently simple to permit hand calculation of long term performance. In a comparison with hourly summations of insolation data, the present model has been found to have an error of less than 3 per cent for the radiation available to a solar collector and an error of about 5 per cent for the heat delivery of solar thermal collectors.

Truncation of CPC solar collectors and its effect on energy collection

Abstract Analytic expressions are derived for the angular acceptance function of two-dimensional compound parabolic concentrator solar collectors (CPCs) of arbitrary degree of truncation. Taking into account the effect of truncation on both optical and thermal losses in real collectors, we also evaluate the increase in monthly and yearly collectible energy. Prior analyses that have ignored the correct behavior of the angular acceptance function at large angles for truncated collectors are shown to be in error by 0–2% in calculations of yearly collectible energy for stationary collectors.

Lens–mirror combinations with maximal concentration

By the addition of suitable reflectors the concentration of a lens can be increased to the thermodynamic limit, which is equivalent to an f-number of one half. Such lens-mirror combinations are useful whenever concentration rather than image formation is important, for example, in radiation detectors and solar energy collectors. The design of lens-mirror combinations with maximal concentration is described. To the approximation that the lens has sharp focal points at off-axis incidence, the solution for the reflector is readily found to be compound hyperbolic. With proper choice of the f-number of the lens the hyperbolic reflector reduces to a V-trough or cone, an arrangement which offers considerable advantages for fabrication. The 2-D case (line focus lens) suffers from aberrations due to focal length variation with nonplanar incidence. The optical performance of 2-D lens-mirror combinations at nonplanar incidence is analyzed and evaluated for its suitability in solar energy applications. A prototype Fresn l lens plus V-trough has been built, and test data are presented.