Calculation of tubular absorber heat loss factor

Although several empirical equations exist for heat loss factor in flat-plate collectors, no similar relation is available for the heat loss factor of a tubular absorber with a concentric glass cover, employed as the target of a linear solar concentrator. A semi-empirical equation for the heat loss factor as a function of the various variables involved is developed. A relatively simple equation for the factor f has also been proposed. The present equation predicts the overall heat loss factor, U_L, to within ±5% of the value obtained by exact solution of the simultaneous equations, in the range of variables—absorber temperature, 60°C to 220°C, emittance of the black coating, 0.1 to 0.95, and wind velocity, 1.5 m/s to 10 m/s. The proposed correlation also takes into account the effect of property variations.     

A seasonally adjusted concentrator with modifications of absorber shape

The heat losses from concentrating solar collectors can be reduced by thermally isolating the absorber with an optimal air gap between the absorber and the glass cover. However, in reflectors attempting to attain maximum optical concentration, some of the reflected rays will escape through this gap, resulting in increased losses. A concentrator was fabricated and tested with a plane tubular absorber, the results having been reported earlier. The present paper describes a design procedure for an absorber which avoids the ‘optical’ losses through the air gap. The results for the modified absorber are compared with those for the plane tubular one. The intercept factor is improved from 0·8 to 0·92. The surface area of the modified absorber is about 9 % larger than that of the plane tubular one, but the shape is such that the overall heat loss factor is much lower. As a result, the total heat loss for the modified absorber at a temperature 100° C above ambient is only 0·2 % higher than that of the plane tubular one. The improved performance curves are shown. The absorber design is also acceptable from the point of view of strengths of the components involved.     

Suitable selective absorbers for all-glass, evacuated, tubular, solar-energy collectors

Solar technologists working on all-glass evacuated tubular collectors are handicapped because the use of selective obsorbers is inherent in the design but most of the selective absorber coatings have been investigated and tested on metallic substrates. This study reviews methods to produce solar selective absorber surfaces which have been developed and tested on glass substrates to be used in evacuated collectors for the photo-chemical conversion of solar energy. It is also aimed to examine selective surfaces which are prospective candidates to be applied on glass tubes. This may provide an impetus to the scientists working in the area of solar energy materials to develop and test selective absorbers not only on metallic substrates but on glass tubes as well.     

Experimental investigation of heat losses from low-concentrating non-imaging concentrators

Heat loss measurements have been performed on a V-trough collector model with concentration ratio 1.56 and with flat absorbers consisting of five parallel reflector troughs aligned east-west. The collector was tilted 45°. Depending on the similarity in geometry between V-troughs and compound parabolic concentrators, the results should in general be valid also for low-concentrating CPCs. The absorbers were heated electrically and the heat losses were calculated from the input power to the absorber surface. Several geometrical and material properties that affect the heat losses from the collector were investigated. It is concluded that the use of transparent insulation, such as Teflon® films, in low-concentrating solar collectors can reduce the heat losses substantially. The reflector emittance in the infrared has an impact on the heat losses. Use of highly emitting reflectors instead of low-emitting reflectors increases the overall heat losses by about 5–8%. The conversion of experimentally measured heat losses into heat losses for real collectors and practical material considerations is discussed.     

水在玻璃管真空管太阳集热器热性能计算与分析

在水在玻璃管式全玻璃真空管集热器能量平衡分析的基础上，推导了集热器热损系数、效率因子等性能参数计算公式，理论计算结果与实验数据吻合良好。计算分析表明，真空管热损系数与吸热管温和环境温度之差是非线性关系，将两者的计算关系式按环境温度分段整理将使计算结果更接近实际；随着吸热管内对流换热系数的增大，其对效率因子和效率的影响逐渐减小，这说明对于水在玻璃管连接方式而言，为得到较大的管内对流换热系数而将流速过度提高是没有必要的；涂层发射率对集热器的热损系数和效率影响较大，降低涂层发射率是提高集热器效率的有效途径。     

Vertical evacuated tubular-collectors utilizing solar radiation from all directions

A prototype collector with parallel-connected evacuated double glass tubes is investigated theoretically and experimentally. The collector has a tubular absorber and can utilize solar radiation coming from all directions. The collector performance is measured in an outdoor test facility. Further, a theoretical model for calculating the thermal performance is developed. In the model, flat-plate collector's performance equations are integrated over the whole absorber circumference and the model determines the shading on the tubes as a function of the solar azimuth. Results from calculations with the model are compared with measured results and there is a good degree of similarity between the measured and calculated results. The model is used for theoretical investigations on vertically-placed pipes at a location in Denmark (Copenhagen, lat. 56°N) and at a location in Greenland (Uummannaq, lat. 71°N). For both locations, the results show that to achieve the highest thermal performance, the tube centre distance must be about 0.2 m and the collector azimuth must be about 45–60° towards the west. Further, the thermal performance of the evacuated solar-collector is compared to the thermal performance of the Arcon HT flat-plate solar-collector with an optimum tilt and orientation. The Arcon collector is the best performing collector under Copenhagen conditions, whereas the performance of the evacuated tubular collector is highest under the Uummannaq conditions. The reason is that the tubular collector is not optimally tilted in Copenhagen but also that there is much more solar radiation “from all directions” in Uummannaq and this radiation can be utilized with the tubular collector. It is concluded that the collector design is very promising—especially for high latitudes.     

Cover systems for high temperature flat-plate solar collectors

A simulation study has been conducted of the influence of cover design on the thermal performance of flat-plate solar collectors for use at temperatures of 150°C. Detailed results are presented of the effects of changes in cover materials, cover surface treatments, cover system configuration and absorber plate surface treatments on both the instantaneous efficiency and the long term solar contribution of flat-plate collectors. For the simulation conditions, it is shown that flat-plate collectors consisting of a single high transmittance cover, a convection suppressing device such as a honeycomb and a selective absorber surface yield long term solar contributions comparable to those of evacuated tubular collectors, whereas other configurations simulated (single and multiple cover systems) are significantly inferior.     

Chemical vapour deposited SnO2:Sb heat mirror coatings for cylindrical solar collectors

A chemical vapour deposition technique for growth of SnO₂:Sb heat mirror coatings on the inner walls of long cover glass tubes for cylidrical solar collectors is reported. The best performance of the tin-oxide film is obtained for those films grown from a source of SnCl₂ + 1 mol% Sb on Corning glass tubes at 520°C. These films, supported on 2 mm glass substrates, have a solar transmittance of 0.85 and an infrared reflectance of 0.8. The heat mirror coatings are observed to increase the stagnation temperature of the absorber in anevacuated tubular collector from 142 to 161°C under incident optical flux of 1150 W/m²     

High concentration two-stage optics for parabolic trough solar collectors with tubular absorber and large rim angle

A new two-stage optical design is proposed for parabolic trough solar collectors with tubular absorbers. It can boost the concentration ratio by a factor of 2.5 relative to the conventional design, while maintaining the large rim angles (i.e., low nominal ƒ-numbers) that are desirable for practical and economical reasons. The second stage involves asymmetric nonimaging concentrators of the CPC type, facing segments of the parabolic first stage. The second stage can be accommodated inside an evacuated receiver, allowing the use of first-surface silvered reflectors. The low heat loss of this design opens the possibility of producing steam at temperatures and pressures of conventional power plants, using only one-axis tracking. The improvement in conversion efficiency would be substantial.     

Calorimetric measurement of absorptance and emittance of the Sydney University evacuated collector

Simple calorimetric techniques have been developed for determining the absorptance and emittance of individual evacuated tubular collectors incorporating a selective surface, and the efficiency, η_o, of evacuated collectors in various mirror systems. The absorptance and efficiency measurements are made in natural sunlight without the use of a solarimeter by establishing an absorptance standard based on Nextel black paint. Calibration of solarimeters using the established absorptance standard is discussed. Emittance measurements are made by measuring radiative heat losses from the absorber tube of a collector.Absorptance and emittance measurements for a number of Sydney University evacuated collectors gave values of absorptance α = (0.92 ± 0.01) and emittance = 0.05 at 120°C for the selective surface utilized. Efficiency (η_o) measurements for Sydney University collectors in two simple mirror systems are also reported.     

A comparison of optical performance between evacuated collector tubes with flat and semicylindric absorbers

In this article, concepts of solar irradiance ratio and absorbed energy factor on the surface of the evacuated collector tube absorbers were presented respectively. For evacuated collector tubes with flat and semicylindric absorbers, we used a solar simulator as a light source, measured separately distribution of the solar irradiance ratio that varies with incident angles on various points on the absorber surface in a glass-covered tube, and gave their three-dimensional regressive equations correspondingly. Experimental measurement of solar irradiance ratio and solar absorptance of coatings on absorber surfaces was carried out. On this basis, rules of absorbed energy factors on absorbers in two shapes that vary with incident angles were analyzed and studied. According to clear-day model, the daily absorbed energy and its annual changes of single evacuated collector tubes with absorbers in two shapes placed under 40° northern latitude, 40° inclined angle and south orientation were calculated and compared. The results show that the annual absorbed energy of evacuated collector tube with a semicylindric absorber is 15.9% higher than that with a flat absorber. In addition, optimized incident angles for the absorber in two shapes of evacuated collector tubes operated in a whole year were tentatively investigated.     

Design and test of non-evacuated solar collectors with compound parabolic concentrators

The intermediate range of concentration ratios (1.5X–10X) which can be achieved with CPCs without diurnal tracking provides both economic and thermal advantages for solar collector design even when used with non-evacuated absorbers. The present paper summarizes more than 3 yr of research on non-evacuated CPCs and reviews measured performance data and critical design considerations. Concentrations in the upper portions of the practical range (e.g. 6X) can provide good efficiency (40–50 per cent) in the 100–160°C temperature range with relatively frequent tilt adjustments (12–20 times per year). At lower concentrations (e.g. 3X) performance will still be substantially better than that for a double glazed flat plate collector above about 70°C and competitive below, while requiring only semi-annual adjustments for year round operation. In both cases the cost savings associated with inexpensive reflectors, and the optimal coupling to smaller, simple inexpensive absorbers (e.g. tubes, fins, etc.) can be as important an advantage as the improved thermal performance.The design problems for non-evacuated CPC collectors are entirely different from those for CPC collectors with evacuated receivers. For example, heat loss through the reflector can become critical, since ideal CPC optics demands that the reflector extend all the way to the absorber. Recent improvements in reflector surfaces and low cost antireflection coatings have made practical a double-glazed non-evacuated CPC design. It is calculated that a 1.5X version of such a collector would have an optical efficiency η_o = 0.71, a heat loss coefficient U = 2.2 W/m²°C and a heat extraction effciency factor F′ ≥ 0.98, while requiring no tilt adjustments.     

Consistent heat transfer analysis for performance evaluation of multichannel solar absorbers

The numerical evaluation of solar absorber performance must be based on the coupling between solar flux modeling and heat transfer modeling. We have developed a ray-tracing method to model the solar flux distribution absorbed at SiSiC multichannel absorber surfaces under a solar furnace, and solved one-dimensional heat transfer governing equations that import the solar flux modeling results. By consistently dealing with changes in properties or dimensions of absorbers for the two modeling processes, we are able to evaluate absorber performance with the balance of radiation loss. It turns out that the diffuse irradiation assumption is applicable for performance evaluation on multichannel absorbers although it may differ from a real solar flux distribution. A sensitivity analysis demonstrates that the increase of absorptivity is most effective to performance enhancement because the increase of reflection loss dominates the decrease of emission loss. The proposed consistent approach provides a better understanding of heat transfer in volumetric solar absorbers and thus helps the improvement of their performance.     

Analytic modeling of a solar power plant with parabolic linear collectors

An analytic model for a solar thermal electric generating system with parabolic trough collectors was developed. The energy conversion of solar radiation into thermal power along the absorber tube of the parabolic collector is studied, taking into consideration the non-linearity of heat losses and its dependence on the local temperature. The coupling between the collector and the thermodynamic cycle is made up of three heat exchangers, yielding the characteristic temperatures of the cycle. The conventional Rankine cycle is treated as an endo-reversible Carnot cycle, whereby the mechanical and electric power is calculated. For comparison, we refer to the Solar Electric Generating System VI (SEGS VI), installed in the Mojave desert-CA, whose solar field is composed by LS2 parabolic trough collectors. We simulated the efficiency curves of collectors LS2 with evacuated and non-evacuated absorbers and compared with experimental results. A second simulation was carried out to estimate the optimum quantity of non-evacuated LS2 collectors in series in a collectors’ row, when friction losses along the absorber tubes are considered. Also, the performance of a 30 (MWe) power plant, composed of 50 rows with 16 LS2 collectors in series (total 800 collectors) was simulated. Three fields of different collectors were considered, the first field with evacuated absorbers, the second with non-evacuated absorbers and the third with bare absorbers. Finally, the output power of the plant is analyzed as a function of the evaporation temperature of the water-vapor fluid. A large maximum of the overall cycle efficiency is found for evaporation temperatures around 320 °C. Good agreement is obtained when comparing the results of this model with experimental data belonging to the Solar Electric Generating Systems (SEGS) installed in the Mojave desert. The analytic model developed combines simplicity, precision and flexibility, making it an attractive tool for simulation and design of solar power stations.     

Advanced procedure for the assessment of the lifetime of solar absorber coatings

New solar absorber coatings are developed and used in advanced collector designs with improved efficiency. The operation temperature and stagnation temperature as the main durability load for the absorbers were increasing during the past due to these innovations. Especially the highly selective new coatings have to suffer by these stronger loads. The service life estimation procedures developed in the framework of research activities of the IEA Solar Heating and Cooling Programme (Task 10 and Working Group Materials in Solar–Thermal Collectors) were based on load profiles for less-advanced absorbers and collectors and did not take into account the impact of the optical properties of the absorber coatings on the stagnation temperature of the collectors, which is the main reason for temperature degradation. A new procedure was developed, which allows testing depending on the optical properties (Solar absorptance and thermal emittance) of the absorbers.     

Angular dependence of optical efficiency of evacuated tubular collectors with antireflection coatings and stationary specular reflectors

The efficiencies of η₀ of arrays of evacuated tubular collectors with non-imaging specular reflectors have been determined experimentally using a calorimetric technique and theoretically using a Monte-Carlo ray tracing technique. Results have been obtained for collectors incorporating reflectors of two concentrations, and efficiencies are compared with and without antireflection coatings on the glass envelopes for sunlight incident at angles 0–70°. The reflective properties of all optical components have been modelled in detail for the ray tracing calculations. Experimental and theoretical efficiencies agree within 0.02 for a wide range of angles of incidence. Antireflection coatings which increase the normal transmittance through a glass envelope by 5% result in an increase of 0.025 (about 4%) in collector efficiency. A theoretical study of the dependence of collector efficiency on absorptance of the absorber tube and specular reflectance of the reflectors is also discussed. Experimental and theoretical results have also been obtained for a collector incorporating a specular reflector with an accumulated dust cover. In this system, the reflector exhibits both specular and diffuse components of reflectance.     

Heat transfer in inclined rectangular receivers for concentrated solar radiation

We study heat transfer in inclined rectangular cavities, which may be used as receivers of concentrated solar radiation. One of the active walls is subject to concentrated solar radiation and the other is kept at constant temperature. Continuity, momentum and energy equations are solved by finite difference — control volume numerical method. The relevant governing parameters are: the Rayleigh numbers from 10³ to10¹², the cavity aspect ratio, A = L/H from 0.5 to 2, the inclination angle, from 30 to 90°.We found that the Nusselt number is an increasing function of the Rayleigh number, the aspect ratio and the inclination angle. Based on the computed data a correlation is derived in the form of Nu = f(Ra, A, ).     

Investigation of evacuated tube heated by solar trough concentrating system

Two types of solar evacuated tube have been used to measure their heating efficiency and temperature with fluids of water and N₂ respectively with a parabolic trough concentrator. Experiments demonstrate that both evacuated tubes present a good heat transfer with the fluid of water, the heating efficiency is about 70–80%, and the water is easy to boil when liquid rate is less than 0.0046 kg/s. However, the efficiency of solar concentrating system with evacuated tube for heating N₂ gas is less than 40% when the temperature of N₂ gas reaches 320–460 °C. A model for evacuated tube heated by solar trough concentrating system has been built in order to further analyze the characteristics of fluid which flow evacuated tube. It is found that the model agrees with the experiments to within 5.2% accuracy. The characteristics of fluid via evacuated tube heated by solar concentrated system are analyzed under the varying conditions of solar radiation and trough aperture area. This study supports research work on using a solar trough concentrating system to perform ammonia thermo-chemical energy storage for 24 h power generation. The current research work also has application to solar refrigeration.     

Heat loss coefficients for box-type solar cookers

The top and overall heat loss coefficients for the entire feasible operating range of box-type solar cookers are evaluated experimentally and presented in a graphical form as a function of the difference between mean plate temperature and ambient temperature with wind velocity and number of glass covers as parameters.

The range of plate temperatures considered is from 50°C to 180°C. While the wind velocity is varied from 0 to 3.33 m/s, and the number of glass covers considered are from 1 to 4.

Based on these experimental results, a correlation for the determination of top loss coefficient in terms of optical properties of cooker, the spacing between glass cover and absorber plate, wind velocity and number of glass covers, is derived and presented in the paper.     

Water-in-glass manifolds for heat extraction from evacuated solar collector tubes

Measurements are reported on three novel manifolds of the water-in-glass type for evacuated all-glasssingle-ended tubular collectors. The manifolds provide for series connection of tubes, but because there is virtually no partitioning of the inner volume of the collector tubes, the manifolds are extremely simple and exhibit low impedance to fluid flow. The efficiency of heat extraction from the tubes has been determined by measuring temperatures at various points on the surface of glass tubes in a panel of area 1.2 m² while heating the tubes electrically to simulate solar energy input. Measurements have been made for a range of tube inclinations (0–80°), water flow rates (0.5–5 lmin⁻¹, water inlet temperatures (13–70°C), and effective solar fluxes (100–1000 W/m²) for two absorber tube diameters. The results show that for a wide range of operating conditions buoyancy effects alone result in efficient heat transfer to the tops of the tubes. The manifold designs described offer a possible low cost solution to the problem of manifolding evacuated collectors for sub-100°C heat extraction for domestic and industrial applications.