Incidence Angle Modifier Research Articles

Prediction of flat-plate collector performance parameters using artificial neural networks

The objective of this work is to use Artificial Neural Networks (ANN) for the prediction of the performance parameters of flat-plate solar collectors. ANNs have been used in diverse applications and they have been shown to be particularly useful in system modeling and system identification. Six ANN models have been developed for the prediction of the standard performance collector equation coefficients, both at wind and no-wind conditions, the incidence angle modifier coefficients at longitudinal and transverse directions, the collector time constant, the collector stagnation temperature and the collector heat capacity. Different networks were used due to the different nature of the input and output required in each case. The data used for the training, testing and validation of the networks were obtained from the LTS database. The results obtained when unknown data were presented to the networks are very satisfactory and indicate that the proposed method can successfully be used for the prediction of the performance parameters of flat-plate solar collectors. The advantages of this approach compared to the conventional testing methods are speed, simplicity, and the capacity of the network to learn from examples. This is done by embedding experiential knowledge in the network.

Thermal performance of an air solar collector with an absorber plate made of recyclable aluminum cans

The present paper describes the development and testing of an efficient single-glass air solar collector with an absorber plate made of recyclable aluminum cans (RAC). This collector was designed as a proposal to use recycle recyclable materials to build absorber plates of air solar collectors at an acceptable cost. The absorber plate of the collector consisted of eight circular cross section air flow channels of 128 recyclable aluminium cans. Each channel was built with 16 recyclable cans blackened with common opaque black paint of 0.903 absorptance and 0.097 reflectance. The design parameters to determine the size of the collector were obtained by implementing a simulation model for double flow air solar collectors. Also, to determine the appropriate configuration for a uniform air flow distribution inside the eight RAC air channels, a hydrodynamic numerical study was carried out. The RAC air solar collector designed and built was tested outdoors following the ASHRAE 93-86 standard to determine the time constant, the thermal efficiency and the incidence angle modifier. Comparison between the predicted theoretical temperatures and the measured ones were in good agreement. Comparison between the thermal efficiency of the RAC air solar collector with the ones reported in the literature is presented.

Thermal advantages for solar heating systems with a glass cover with antireflection surfaces

Investigations elucidate how a glass cover with antireflection surfaces can improve the efficiency of a solar collector and the thermal performance of solar heating systems. The transmittances for two glass covers for a flat-plate solar collector were measured for different incidence angles. The two glasses are identical, except for the fact that one of them is equipped with antireflection surfaces by the company SunArc A/S. The transmittance was increased by 5–9%-points due to the antireflection surfaces. The increase depends on the incidence angle. The efficiency at incidence angles of 0° and the incidence angle modifier were measured for a flat-plate solar collector with the two cover plates. The collector efficiency was increased by 4–6%-points due to the antireflection surfaces, depending on the incidence angle. The thermal advantage with using a glass cover with antireflection surfaces was determined for different solar heating systems. Three systems were investigated: solar domestic hot water systems, solar heating systems for combined space heating demand and domestic hot water supply, and large solar heating plants. The yearly thermal performance of the systems was calculated by detailed simulation models with collectors with a normal glass cover and with a glass cover with antireflection surfaces. The calculations were carried out for different solar fractions and temperature levels of the solar heating systems. These parameters influence greatly the thermal performance associated with the antireflection surfaces.

424 散乱及び鏡面反射板を有する同心円形真空管式集熱器の有効透過吸収量の特性(新エネルギー(II))(空気調和・冷凍技術)

The characteristics of the Effective Transission-Absorptance factor for evacuated tubular collectors with three types of back reflectors are presented. The problems how to reduce the computational time, how to simplify the program and how to calculate the incidence angle modifier are discussed. The results show that the performance of evacuated tubular collectors is subject to huge variation with the position of sun and the distribution of the diffuse radiation intensity on the sky. The performance of the evacuated collector with a diffuse reflector is higher than it with mirror reflector at noon. However The both performances are almost equal when they are evaluated as the all-day performance. The danger of evaluation by short time testing was indicated. Testing throughout several days, at least a day, may be recommended.

Angular solar absorptance and incident angle modifier of selective absorbers for solar thermal collectors

The solar absorptance of absorbers for thermal solar collectors is usually characterized at near normal angle of incidence. The solar absorptance is however a function of the angle of the incident light on the absorbers. In this paper the angular solar absorptance of commercial nickel pigmented aluminum oxide and sputtered nickel/nickel oxide solar selective absorbers are reported. The solar absorptance was calculated from experimental total reflectance spectra in the wavelength range 300–2500 nm for angles of incidence between 5 and 80°. It was found that the solar absorptance at higher angles of incidence is lower for the sputtered nickel/nickel oxide than for the nickel pigmented aluminum oxide coating. This could be understood from theoretical calculations based on microstructure models of the two types of coatings. The nickel pigmented aluminum oxide with a double-layer structure of its coating has an enhanced higher angle solar absorptance due to thin film interference effects which can not be achieved from a graded-index thin film coatings as is the case for the sputtered nickel/nickel oxide absorber. When the absorbers were covered by glass, as is common for most solar collectors, a negligible difference in optical performance at the higher angles of incidence has been obtained. These results were consistent with a theoretical calculation by use of an incident angle modifier model.

97/04833 Modelling, optimisation and performance evaluation of a parabolic trough solar collector steam generation system: Kalogirou, S. et al. Solar Energy, 1997, 60, (11), 49–59

Chapter 4 deals with the methods to determine experimentally the performance of solar collectors. It outlines the various tests required to determine the thermal efficiency of solar collectors. Initially collector thermal efficiency measurement is presented and the effect of flow rate, collectors connected in series, and the standard requirements of the test are analyzed. Subsequently, the methods to determine the collector incidence angle modifier for flat-plate and concentrating collectors are presented followed by the acceptance angle for concentrating collectors and the collector time constant. The dynamic test method is also presented followed by the efficiency parameter conversion and assessment of the uncertainty in solar collector testing. This is followed by the way the collector test results can be used for the preliminary collector selection. Subsequently, the quality test methods are presented followed by a review of European standards used for this purpose as well as details of the Solar Keymark certification scheme. Finally, the chapter describes the characteristics of data acquisition systems including portable data loggers.

On the factorisation of incidence angle modifiers for CPC collectors

It has been suggested earlier that the incidence angle modifier K τα for low concentrating collectors with tubular absorbers could be factorised according to K τα ( θ t, θ l) ∝ K τα ( θ t,0) K τα (0, θ l, where θ tand θ l are the projected incidence angles in the transversal and longtitudinal projection planes, respectively. Ray-tracing calculations on low-concentrating CPC collectors with flat absorbers parallel to the cover show that a K τα factorisation overestimates the annual delivered energy from the collector by about 4–5%, when compared to calculations using the full incidence angle modifier. Data from outdoor testing has been used for characterization of incidence angle behaviour for a truncated CPC with a concentration of C = 1.56. Multiple linear regression analysis was used. This analysis technique makes feasible the determination of angular dependent incident angle modifiers and is an efficient tool to use for all collectors which cannot be characterised by standard equations of the incidence angle dependence.

An improved dynamic solar collector test method for determination of non-linear optical and thermal characteristics with multiple regression

The objective is to characterise the solar collector during a relatively short testing period with no requirement for steady state climatic conditions. This information is then used for predicting annual performance of the collector. A standard collector model that is compatible with the ISO 9806-1 test standard is used with correction terms for beam and diffuse incidence angle modifiers, thermal capacitance, wind speed and sky temperature. This results in a more complete characterisation of the collector. The collector parameters are identified by multiple linear regression, MLR. The method has been tested for characterisation of unglazed collectors, glazed flat plate collectors, evacuated tubular collectors, CPC collectors and concentrating collectors with satisfying results. Typically the correlation coefficient R 2 is better than 0.99 and the standard deviation of the difference between model and measurement is in the range 3–10 W/m 2. In the original method the angular dependence of the optical efficiency and the temperature dependence of the heat losses are supposed to be adjusted to a predetermined function. The most recent development is a routine that makes it possible to accurately identify non-linear optical and thermal performance. This extended MLR method can identify the zero loss efficiency for every angle of incidence interval and the temperature dependent heat losses for every temperature interval. This opens the application of the method to collectors with special incidence angle and heat loss effects that cannot be described easily with a combination of elementary functions. Instead a table of parameter values is determined, which is used directly in standard simulation programmes. This method will further increase the accuracy when comparing different collector designs. It has been used for comparing different glazings and for comparison with spectrophotometric measurements. It has also been used for analysing the heat loss factors for Teflon and honeycomb glazings. Since the total power output of the collector is less dependent on the heat loss coefficient than on the optical efficiency the scattering in this data is larger than for the incidence angle curves. The reflectance of booster mirrors cannot be derived with the MLR-method with acceptable accuracy. The correlation between direct irradiance and irradiance from the reflector exhibit a very strong correlation. Instead the effective reflectance of the mirror can be estimated by comparison of the measured output with calculation by the complete collector and reflector model. This effective reflectance is not compatible with the specular reflectance obtained from spectrophotometric measurements caused by large differences in acceptance angles. Standard multiple linear regression available in most spread sheet and statistical programs can be used for the parameter identification in the extended MLR-procedure. The identification takes only a few seconds. At the Älvkarleby Laboratory the test method is now used as a routine tool for the evaluation of new collector materials and designs. The Swedish National testing institute has evaluated the methods with the conclusion that they have a potential for being used in standardised collector testing.

Parabolic trough collector system for low temperature steam generation: Design and performance characteristics

The collector's performance is tested according to Ashrae Standard 93, 1986 1. The collector's efficiency and incidence-angle modifier are measured. The test slope and intercept are found to be 0.387 and 0.638 respectively. The collector's time constant is less than one minute and the collector's acceptance angle obtained from the test is ±0.5°, which in combination with the tracking mechanism maximum error (± 0.2°) implies that the system works continuously at almost maximum possible efficiency.

Design and performance characteristics of a parabolic-trough solar-collector system

A comparison of the advantages and disadvantages of concentrating collectors against conventional flat-plate collectors are presented. This is followed by the design of a parabolic-trough solar-collector system, due consideration having been given to collector-aperture and rim-angle optimisation, together with the receiver-diameter selection. The collector characteristic curve gives a test slope of 0·441 and a test intercept equal to 0·642. The value of the test slope differs considerably from the initially predicted value: this is attributed to the heat losses from the receiver support brackets. Subsequent allowance for these losses is presented: this reduces the difference from 24·9% to 5·7%. Other tests are presented, including the determination of the collector's incidence-angle modifier, time constant and acceptance angle.

Dynamic method for solar collector array testing and evaluation with standard database and simulation programs

A measurement and evaluation method is described by which standard collector performance parameters can be derived directly from measured outdoor data. Standard programs with routines for multiple regression can be used for the parameter identification. A continuous flow is applied in the collector loop during the test. Data for the whole day can then be used. A one-node capacitance correction for dynamic effects and separate incidence angle modifiers for direct and diffuse radiation are essential for the accuracy of the method. The model is set up for thermal power output (and not efficiency). This forces the parameters to values that are suitable for prediction of long-term performance. The collector model and parameters correspond closely to those used in existing detailed simulation programs such as TRNSYS, WATSUN, or MINSUN. The method can be used as an accurate bridge between short-term testing and long-term prediction by simulation.

A correlation model to compute the incidence angle modifier and to estimate its effect on collectible solar radiation

Radiation transmittance and absorptance of materials vary according to the angle of incidence of the incoming solar radiation. Therefore, the efficiency of most solar converters (thermal or photovoltaic) at a given radiation amount is a function of the sun's position through the angle of incidence. This problem is accounted for by the Incidence Angle Modifier, which is considered in this paper. An analytic expression for the incidence angle modifier, based on meteorological data or on geographic and geometric parameters, has been developed; this expression includes the effect of beam and diffuse radiation as well as the global influence. A comparison between measured data and computed from our model has given a very good correlation, the results being within a ±3% of difference for horizontal and tilted planes, and within ±17% for vertical surfaces, on average. The method also computes the collectible solar energy within a 5% error for thresholds up to 300 W m −2. The method has been validated for more than 30 locations of south and west Europe.

Solar transmittance characteristics of evacuated tubular collectors with diffuse back reflectors

The partition matrix between light sources and light sinks is introduced to evaluate the transmittance properties of optically asymmetric collectors constructed with evacuated tubes. A ray tracing model is used to compute its elements. Curve fits to the ray tracing results are provided. The effects of polarization are discussed. Comparisons with previously published results are presented in order to check the accuracy of the proposed model. The beam and diffuse transmittance of a tubular cover are calculated and their dependency on the tube orientation investigated. The biaxial incidence angle modifier product is extended to evacuated tube collector arrays with a diffuse back reflector, providing a simple interpolation process for the beam transmittance. An effective beam direction for diffuse radiation is computed so that transmittances for ground reflected radiation and sky diffuse radiation can be calculated from biaxial incidence angle modifier measurements.

Optimisation of evacuated tubular solar collector arrays with diffuse reflectors

The optical efficiencies η o of arrays of evacuated tubular collectors incorporating plane, triangular and semicircular shaped reflectors coated with flat-white and gloss white paint have been studied experimentally using a calorimetric technique and theoretically using a ray tracing computer program. The results showed that the plane reflector is the optimum design. Detailed studies have been made of the dependence of optical efficiency and incident angle modifier as a function of collector tube separation for collectors incorporating the plane reflector. Two collector panels complete with heat extraction manifold and incorporating the plane reflector, but with different tube spacings were subject to detailed outdoor testing. The results indicated that it is cost-effective to space the collector tubes two or more absorber tube diameters apart.

Orientational relationships for optically non-symmetric solar collectors

More details of collector orientations and incidence angle modifiers are required to specify the instantaneous optical efficiencies of optically non-symmetric solar collectors, such as those using nonimaging concentrators, than to specify the efficiencies of symmetric collectors such as flat plates. In this paper, expressions are presented for the projected incidence angles necessary for evaluating the instantaneous optical efficiencies of non-symmetric collectors. These projected angles are also used when a nearly biaxial incidence angle modifier is approximated by the product of two single-axis incidence angle modifiers. In addition, relationships for incidence angles onto an absorber tube are developed. These differ from the angle onto a cover glazing, and they effect the absorptance of the tube's coating and the transmittance of a cover tube as used in tubular evacuated collectors.

Monthly average optical efficiency of flat plate collectors

Monthly average optical efficiencies of flat plate collectors are expressed analytically in terms of the incidence angle modifier coefficient and geometric factors involving ratios of irradiations on plane of collector to irradiations of horizotal plane. Use of the method will reduce the calculation of the absorbed irradiation to a simple expression similar to the equation used to compute the irradiation incident on the collector. The monthly average error introduced by the approximate from of η 0( θ) is less than 1 per cent for all collector orientations and inclinations used in practice.

Incident Angle Modifiers for Flat-Plate Solar Collectors: Analysis of Measurement and Calculation Procedures

Existing test procedures for measuring and rating thermal performance require the determination of the angular response of collectors in order to account for non-normal incident beam irradiance. Angular response measurements for four different types of collectors, each type tested by three different laboratories, are presented and analyzed. Substantial differences, both within and between laboratories, are reported for the same type collectors. An analysis of the measurement procedure shows that experimentally determined angular response parameters are subject to relatively large uncertainties. The problem results to a large extent from measuring collector efficiencies at non-normal incident angles where measurement uncertainty is of the same order of magnitude as the efficiency reduction attributable to these off-normal angles. Other factors which can affect angular response measurements and the method of correlating results are also discussed. A theoretical analysis shows that shading of the absorber by the collector air space side- and end-walls for non-normal incident angles can be of the same order of importance as the decrease in the transmittance of the cover assembly. While this situation complicates an analytical approach, it is concluded that calculations are adequate to depict the angular response of conventional flat-plate tube-in-sheet collector designs. A simplified analytical procedure and nomographs are presented for rapid calculation of incident angle modifiers. The predicted seasonal performance of solar energy systems and clear-day ratings of typical flat-plate collectors are shown to be relatively insensitive to large uncertainties in incident angle modifiers. Typically, the values of these calculated quantities could be affected by approximately five percent as a result of uncertainty in the test-derived angular response parameter.

An analysis of the technical and economic performance of a parabolic trough concentrator for solar industrial process heat application

An identification of the principal design factors that influence the technical performance of a parabolic trough concentrator and which relate directly to design and manufacturing decisions is presented. These factors include spectral-directional reflectivity of the mirror system, the mirror-receiver tube intercept factor, the incident angle modifier and absorptivity-transmissivity product of the receiver tube and cover tube, the end loss factor and a factor describing the effect of tracking errors and receiver tube misalignment. Each of these factors has been quantified in terms of design and manufacturing tolerances and associated performance degradation. Other design considerations that relate to thermal loss from the receiver tube are low emissivity coatings, evacuation and anti-reflection coating. The analysis of energy costs using the parabolic trough concentrator is developed. This analysis determines both the break-even, current metered cost of energy and the annual cash flow over periods of investment ranging from 5 to 15 yr. The economic factors include investment tax credit, energy equipment tax credit, income tax bracket, cost of auxiliary system, foundations and controls, cost of collector at installation, costs of maintenance and taxes, costs of fuel, cost of capital, general inflation rate and fuel escalation rate. Economic determinations were made at three U.S. locations: Albuquerque, New Mexico; Fresno, California ; and Caribou, Maine using the thermal performance characteristics of the Sandia Advanced Trough Prototype Collector. The collector costs used were those determined by a manufacturing cost analysis for various manufacturing volumes up to 100 000 modules (each 516 ft 2 ; 48 m 2) per year. The results show that for a 10 yr period of investment, the current metered breakeven costs are less than $7.00 per 10 6 BTU at all locations for a collector having a total installed cost of $15.79 ft −2 ($170.00 m −2), which includes manufacturing and installation ($11.50), foundations and controls ($1.50) and auxiliary system ($2.79). For a 15 yr period of investment the corresponding fuel costs are less than $4.00 per 10 6 BTU at all locations. For a total installed collector cost of $22.79 ft −2 ($245 m −2), the break even metered fuel cost is less than $9.00 per 10° BTU at all locations, also for a 10 yr period of investment. Other conditions are evaluated. The analysis is general which permits other circumstances to be evaluated.

Factored approximations for biaxial incident angle modifiers

Solar collectors using various types of nonimaging concentrators have optical efficiencies which are not symmetrical about the collector normal. To fully specify the optical efficiency for a given sun angle, more details of the collector orientation and incident angle modifier are needed than for flat plate collectors. This could lead to the need for extensive collector test data. Fortunately, for reflecting concentrators, the detailed incident angle modifier, K ατ ( θ l , θ t ), can be approximated accurately by the product K ατ ( θ l , 0) K ατ (0, θ t ), where θ t and θ l are projected angles between the sun's position vector and the collector normal. Ray-trace calculations of the various optical effects which result in biaxial incident angle modifiers show the accuracy of the approximation. Since the various optical effects for reflecting concentrators can be represented separately by products of two projected angle factors, extension of the approximation to the general case of low concentration collectors is valid. Measurements and/or calculations need be made only for incident angles in two well-defined orthogonal planes to obtain information sufficient to approximate K ατ ( θ l , θ t ) for any projected angles of interest for solar collectors.

ASHRAE 93-77 Instantaneous and All-Day Tests of the Sunpak™ Evacuated-Tube Collector

The results of ASHRAE 93-77 instantaneous and all day tests for two Sunpak™ evacuated-tube collectors are presented and discussed in terms of a simple dynamic response model and a biaxial incidence angle modifier approximation. The dynamic model predicts, and experimental results confirm, a residence time type of response rather than the exponential response that is assumed to characterize most collectors. The anisotropic geometries of the two collectors require that their optical properties be described by an incidence angle modifier that depends on both solar altitude and azimuth in the tilted aperture plane. The test results support the idea that this dependence can be characterized with sufficient accuracy by a biaxial approximation which requires that incidence angle modifiers be measured in each of two mutually perpendicular symmetry planes of the collectors. The all-day measurements are compared with the results to be expected from the ASHRAE 93-77 instantaneous tests, and excellent agreement is obtained when the dynamic model is used to account for the time variations in insolation and inlet temperature. It is concluded that the two Sunpak™ evacuated-tube models can be characterized adequately within the scope of ASHRAE 93-77, but that measurements over and above those actually required by this standard are necessary for a complete characterization. In addition, it is recommended that these collectors be tested on a tracking mount because of their long response times. Such instantaneous test results, in combination with the dynamic model, can be used to predict daily and long-term performance under most conditions.