Bengt Perers

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 R2 is better than 0.99 and the standard deviation of the difference between model and measurement is in the range 3–10 W/m2. 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 Alvkarleby 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.

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.

The influence of climate and location on collector performance

The influence of annual climate variations on the performance of solar thermal collectors in the northern part of Europe has been investigated. The annual solar collector energy output has been calculated with the MINSUN simulation program using hourly, measured climatic data for the years 1983–98 for three cities situated in the south (Lund), central (Stockholm) and north (Lulea) of Sweden. A synthetic year created with the Meteonorm weather simulation program was also used in the simulations. Two solar thermal collectors were modelled: a flat plate solar collector and a tubular vacuum collector, both of commercial standard.

Construction and testing of a large-area CPC-collector and comparison with a flat plate collector

Construction and testing of a large area CPC-collector and comparison with a flat plate collector

On the factorisation of incidence angle modifiers for CPC collectors

Abstract It has been suggested earlier that the incidence angle modifier Kτα for low concentrating collectors with tubular absorbers could be factorised according to Kτα(θt,θl) ∝ Kτα(θt,0)Kτα(0,θl, where θtand θl 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 Kτα 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.

Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations

Abstract While testing different reflector materials for external reflectors for solar collector arrays, it was found that standard rolled aluminium and corrugated aluminium materials could perform almost as well as mirror-like materials. A ray tracing model was developed to calculate the intensity in the collector plane for solar radiation from reflector materials with grooves or corrugations. Laboratory measurements, for reflector samples, with a specially designed spectral scatterometer were used to determine the angular intensity distribution of the reflected radiation. Calculations with the model using measured intensity distributions show that the scatter from aluminium materials with rolling grooves will be directed close to the specular direction and along an almost circular arc in the collector plane. The intensity in the collector plane will be redistributed slightly upward or downward depending on the season and time of day; therefore, both an increase and decrease in average intensity can occur during the year relative to a mirror-like material with the same total reflectance. For rolled aluminium, a small performance improvement can be achieved compared to a mirror reflector with equal total reflectance. Corrugated surfaces will yield a significant increase in average intensity onto the collector aperture at times when the radiation from a mirror-like reflector would otherwise be lost above the collector.

Optical properties of nonimaging concentrators with corrugated reflectors

A ray tracing study has been performed on the optical properties of cylindrical nonimaging concentrators with linear corrugated reflectors. The corrugations are assumed to be V-formed and to have an extension parallel to the meridian plane of the concentrators. It is shown that the acceptance angle for radiation incident in the meridian plane can be increased for moderate corrugations. This increased acceptance is balanced by a decreased acceptance of radiation from other directions. Calculations of angular acceptance for a 2X compound parabolic concentrator is presented. It is shown that the annual irradiation on a solar collector with booster reflector can be increased if corrugated reflectors are used instead of smooth reflectors.

Analytical Model for the Input/Output Energy Relationship

The purpose of the work is to analyse the relationship between daily energy collected and daily total solar insolation in the plane of the collector observed in so called input/output diagrams. As a first approximation linear regression lines are used to present this relationship.

TX model: a quantitative heat-loss analysis of district heating pipes by means of IR surface-temperature measurements

The aim of this study is to investigate the possibility of analyzing the temperature profile at the ground surface above buried district heating pipes in such a way that enables the quantitative determination of heat loss from the pair of pipes. In practical applications, it is supposed that this temperature profile is generated by means of thermography. For this purpose, the principle of the TX-model has been developed, implementing that the heat losses from pipes buried in the ground has a temperature signature on the ground surface. A qualitative analysis of this temperature signature is very well known and in practical use for detecting leaks from pipes. These techniques mostly makes use of relative changes of the temperature pattern along the pipe. In the quantitative heat loss analysis, however, it is presumed that the temperature profile across the pipes is related to the pipe heat loss in Watt/m. The basic idea is that the integral of the temperature variation across the pipe, called TX, is a function of the heat loss, but affected by some other parameters such as depth, heat diffusivity and so on. In order to analyze the parameters influencing the TX-factor, a simulation model for the energy balance at the ground surface has been developed. This model includes the heat flow from the pipe to the surface and the heat exchange at the surface with the environment due to convection, latent heat change, solar and long wave radiation. The simulation gives the surprising result that the TX factor is relatively unaffected during the course of a day even when the sun is shining, as long as other climate conditions are relatively stable (low wind, no rain, no shadows). The results from the simulations were verified at a testfield in Studsvik, Sweden, with electrically controlled pipe heat losses and long term monitoring of the surface temperature profile and TX factor with temperature sensors at the ground surface. The quantitative TX model for heat loss determination was also tested with IR thermography in a district heating network in Vasteras. The work was performed under the IEA District Heating Programme, Task III, and is continued under Task IV.

AN ANNUAL UTILIZABILTTY METHOD FOR SOLAR COLLECTORS IN THE SWEDISH CLIMATE

ABSTRACT An annual utilizability method is presented that gives a very accurate estimation (within a few percent) of the yearly performance of a solar collector directly from instantaneous collector parameters . The model has been validated against long term outdoor measurements and detailed simulation as presented in this paper.