Optimizing the tilt angle of solar collectors

Solar collectors need to be tilted at the correct angle to maximize the performance of the system. In this paper, the annual solar fraction of the system (the fraction of energy that is supplied by solar energy) is used as an indicator to find the optimum inclination angles for a thermosyphon solar water heater installed in northern and southern parts of Jordan. Calculations are carried out using the powerful computer program TRNSYS (Transient System Simulation). The system is assumed to operate with a daily hot water load of 150 l at 55°C flowing during the day according to the widely used Rand consumption profile. The results show that the optimum inclination angle for the maximum solar fraction is about φ+(0→10°) for the northern region (represented by Amman) and about φ+(0→20°) for the southern region (represented by the town of Aqaba). These values are greater than those for maximum solar radiation (which is commonly used as an indicator) at the top of the collector by about 5 to 8°.     

Optimum tilt angle for solar collectors used in Cyprus

Flat-plate solar collectors are widely used in Cyprus for water heating purposes. The roofs of nearly all the residential premises on the island are fitted with such collectors. This article examines the theoretical aspects of choosing a tilt angle for the solar flat-plate collectors used in Cyprus and makes recommendations on how the collected energy can be increased by varying the tilt angle. In this paper, the collector surface is assumed to be facing South and the calculations are based upon the measured values of daily global solar radiation on a horizontal surface on the island. The beam and diffuse components of the horizontal global radiation are then estimated and the solar radiation on a tilted surface is calculated as the angle of tilt is varied from 0° to 90°. It is shown that very nearly optimal energy can be collected if the angle of tilt is varied seasonally, four times a year.     

On the calculation of solar utilizability for south oriented flat plate collectors tilted to an angle equal to the local latitude

The utilizability or -curve method is a design method for some types of solar energy systems that use flat-plate solar collectors. It can be a very useful design tool, for the preliminary design or the design of small systems, cases where methods easy to use and apply are required.

In this paper, a simple method to calculate monthly average hourly and daily flat plate collector utilizability is presented. It is based on empirical correlation of with independent variables that separate meteorological and collector parameters, making possible quick evaluations of changes in collector design and collector inlet temperature. In general, the method reduces the calculations required to determine , and gives good results compared to long-term hourly simulations as well as to existing hourly and daily utilizability calculations methods.     

On the climatic optimization of the tilt and azimuth of flat-plate solar collectors

A numerical climatic model for computing total solar irradiance on the surface of a flat-plate collector, positioned at any tilt and azimuth, is described. Owing to a small time-step (one hour), and a quasi-realistic characterization of a collector's environment, the algorithm is able to produce credible estimates of both the climatically “optimal” position and the amount of energy lost to a collector when it is non-optimally positioned. Exemplary computations for Sterling, Virginia and Sunnyvale, California are presented and they suggest that the non-optimal positioning of a collector, e.g. as a simple function of latitude and a few highly summarized climatic-environmental variables, will not, in many cases, produce significant losses of available solar irradiance. In other situations, however, where a collector's horizon is significantly obstructed and/or the climatic environment of the area creates large diurnal or seasonal asymmetries in available irradiance, non-optimal positioning may cause sizeable energy losses. It is also apparent that even moderately sized horizonal obstructions, which are “seen” by a collector, can substantially reduce the amount of available irradiance, relative to an unobstructed horizon.     

Optimum tilt angle for a flat plate solar collector

One of the important parameters that affects the performance of a flat plate solar collector is its angle of tilt with the horizontal. This is due to the fact that the variation of tilt angle changes the top loss coefficient and the amount of solar radiation reaching the absorber plate. A mathematical model has been developed for calculating the useful energy gained by a flat plate collector under various operating conditions. The model is then used to determine the optimum tilt angles for a typical collector in Basrah on a daily basis, as well as on the basis of a specified period. The optimum tilt angle is found by searching its value for which the useful energy gained by the collector is a maximum for a particular day or a specified period.From the results, it is observed that changing the tilt angle eight times in a year determines the useful energy in Basrah near its value which is found by changing the tilt angle daily to its optimum value. Furthermore, the influence of various operating parameters is studied on the daily optimum tilt angle.     

乌鲁木齐地区太阳能集热器最佳倾角计算

一引言 乌鲁木齐地区太阳能资源丰富,水平面上年太阳辐射总量达5000～6000MJ/m2,积极开发利用乌鲁木齐地区的太阳能资源是满足该地区持续增长的能源需求和节能降耗的重要途径.     

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.     

Optimum tilt angle and orientation for solar collector in Brunei Darussalam

One of the important parameters that affects the performance of a solar collector is its tilt angle with the horizontal. This is due to the fact that the variation of tilt angle changes the amount of solar radiation reaching the collector surface. A mathematical model was used for estimating the total (global) solar radiation on a tilted surface, and to determine the optimum tilt angle and orientation (surface azimuth angle) for the solar collector in Brunei Darussalam on a daily basis, as well as for a specific period. The optimum angle was computed by searching for the values for which the total radiation on the collector surface is a maximum for a particular day or a specific period. The results reveal that changing the tilt angle 12 times in a year (i.e. using the monthly-averaged optimum tilt angle) maintains approximately the total amount of solar radiation near the maximum value that is found by changing the tilt angle daily to its optimum value. This achieves a yearly gain in solar radiation of 5% more than the case of a solar collector fixed on a horizontal surface.     

Determination of the optimal tilt angle and orientation for solar photovoltaic arrays

This paper deals with the determination of optimum tilt angle and orientation for solar photovoltaic arrays in order to maximize incident solar irradiance exposed on the array, for a specific period of time. The method is extended, by introducing a second objective, i.e. minimization of variance of the produced power, in terms of hourly power generation throughout the given period of time. The proposed method uses both well-established models and data collected from the particular area where the photovoltaic panels will be installed and is built upon four steps. In the first step, the recorded data are used in order to select the most accurate, among several isotropic and anisotropic models that can be found in the literature, for predicting diffuse solar irradiance on inclined surfaces. In the second step, the recorded data and the selected model are used to construct a database that contains the averages and the variances of the hourly global solar irradiance on tilted surfaces over specific periods of time, for various tilt angles and orientations. In the third step, the database of the previous step is utilized to produce meta-models that correlate tilt angle and orientation with mean global irradiance and its variance on tilted surfaces. Finally, an optimization problem is formulated, aiming to determining the optimum values of tilt angle and orientation, taking into account the constraints and limitations of the system.     

On the optimum orientation of solar collectors

A simple model of atmospheric absorption and scattering, incorporating only three parameters, has been used to fit meteorological data for direct and diffuse radiation and hours of sunshine at latitude 55°N, longitude 6°W. Using this fit for insolation on a horizontal plane, annual and monthly figures for insolation on an inclined plane have been computed. It is found that the annual insolation is relatively insensitive to orientation for angles of tilt between zero and 60°, but that the optimum tilt is 30.5°. When ground reflection is included, the optimum tilt angle rises steadily to 65' as the ground albedo increases from zero to unity. Optimization for summer and winter operation is also considered, as is the effect of various characteristics of practical collectors.     

On the factorisation of incidence angle modifiers for CPC collectors

It has been suggested earlier that the incidence angle modifier K_τ for low concentrating collectors with tubular absorbers could be factorised according to K_τ(θ_t,θ_l) ∝ K_τ(θ_t,0)K_τ(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_τ 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.     

A theoretical study on area compensation for non-directly-south-facing solar collectors

Solar energy integrated with the building is an important approach for the synchronous development of solar energy and architecture. The energy gain of the solar collector integrated with the pitched roof has been greatly influenced by the roof azimuth and tilted angle. Investment cost of the collectors is mainly decided by the size of the collector area. Accordingly, it is significant for solar building design to economically determinate the area compensation of the solar collector at different azimuth and tilted angles. Take Kunming and Beijing as examples, area compensation for the flat-plate tube-fin solar collector used in southern regions and the evacuated tube collector with cylindrical absorbers used in northern regions in China have been theoretically calculated. The results to some extent show that the daily horizontal solar radiation, ambient temperature, the azimuth and tilted angle of the collector integrated into the roof have an influence on the area compensation. The azimuth angle and tilted angle of the roof are the main factors that influence the A/A₀, which is defined as the collector area ratio of the non-south-facing collectors to the south-facing ones with the optimal tilted angle. Comparative studies found that the range of A/A₀ for the evacuated tube collector used in the northern regions is close to that for the flat-plate tube-fin solar collector used in the southern regions. When the pitched roof tilted angle β ∈ [25°, 45°] and the azimuth angle ∣γ∣ ⩽ 30°, the collectors can intercept a lot of solar radiant-energy. Considering the economic situations of the ordinary consumers in China, the optimal area compensation A/A₀ ⩽ 1.30 is recommended in this paper.     

On the optimum tilt of a solar collector

In the literature different values are found for the best tilt of a solar collector, but these are usually given as a function of latitude only. In this investigation we formulate the problem more rigidly and obtain the optimum tilt as a function of latitude, weather data and character of the energy demand. The resulting minimum collector area is only moderately sensitive to small deviations from the best angle. For inexpensive collector construction one can therefore replace the previous rules by one single recommendation, where the best angle is always equal to the latitude. However, large scale installations or direct conversion of solar into electrical energy requires a more accurate determination of the minimum collector area for a given objective function. A general method for doing this is devised and illustrated.     

On the optimum exposure of flat-plate fixed solar collectors

With the increasing range and scale of applications of solar energy conversion systems a detailed knowledge of the available solar fluxes on surfaces of various tilt and slope aspect is required. The widely used engineering routines for siting and exposing of solar collector arrays may not always be consistent with the maximum available solar energy income. In the present study a computational algorithm is proposed suitable for the calculation of optimum tilt angles of a solar collector, receiving the maximum insolation for given values of direct beam, global and diffuse radiation, and given surface reflectivity. Formulas are derived also for the calculation of optimum tilt angles yielding maximum daily insolation for each month of the year. The dependence of the optimum tilt angle on the diffuse-to-global radiation ratio, as well as on the surface reflectivity is evaluated.     

Thermal performance of a south facing wall as solar collector storage system

This paper illustrates an analysis of the performance of a solar wall as a collector storage system. the south facing wall consists of a mass of concrete/brick whose one surface is blackened and glazed, and a network of pipes (metallic or plastic) is laid in a plane from which heat can be extracted by flow of fluid in such a manner that the temperature of the plane of heat retrieval keeps constant. the collection efficiency of the system is found to be 80·0 and 60·7 per cent for collection temperatures 20 and 25°C respectively on the surface; the maxima/minima of the rate of heat retrieval (Q(t)) occurs about 12 h after the maxima/minima of solar temperature at a depth of the plane of heat retrieval = π/α1, with a maximum efficiency of 21·47.     

Optimization of tilt angle for solar panel: Case study for Madinah,Saudi Arabia

This article analyzes the optimal choice of the tilt angle for the solar panel in order to collect the maximum solar irradiation. In this paper, the collector surface is assumed to be facing toward equator. The study is based upon the measured values of daily global and diffuse solar radiation on a horizontal surface. It is shown that the optimal angle of tilt (β_opt) for each month, allows us to collected the maximum solar energy for Madinah site. Annual optimum tilt angle is found to be approximately equal to latitude of the location. It is found that the loss in the amount of collected energy when using the yearly average fixed angle is around 8% compared with the monthly optimum tilt β_opt.     

Comparative analysis of diffused solar radiation models for optimum tilt angle determination for Indian locations

Tilt angle and orientation greatly are influenced on the performance of the solar photo voltaic panels. The tilt angle of solar photovoltaic panels is one of the important parameters for the optimum sizing of solar photovoltaic systems. This paper analyses six different isotropic and anisotropic diffused solar radiation models for optimum tilt angle determination. The predicted optimum tilt angles are compared with the experimentally measured values for summer season under outdoor conditions. The Liu and Jordan model is found to exhibit t lowest error as compared to other models for the location.     

Performance evaluation for solar collectors in Taiwan

In this paper, the global irradiation observed in Taiwan from 1990 to 1999 was used to estimate the optimal tilt angle for solar collectors. The observed data are resolved into diffusion and beam components, and transformed into instantaneous time frames using mathematical models. The energy gain on installing a single-axis tracked panel as compared to a traditional fixed panel is originally analyzed theoretically. In addition to the observation data, both types of radiation will be taken into account for comparison, i.e. both extraterrestrial radiation and global radiation predicted using empirical models. The results show that the yearly optimal angles for six selected stations are about 0.95 and 0.88 times their latitudes for extraterrestrial and predicted radiation, respectively. All of the observed irradiations are less than the predicted values for all times and stations, consequently resulting in a flatter tilt angle, with a few exceptions in summer. Since Taipei has the lowest clearness index, its yearly optimal angle calculated from observed data shows the greatest discrepancy when compared to its latitude. By employing a tracked panel, the yearly gains calculated from the observed data lie between 14.3% and 25.3%, which is significantly less than those from the extraterrestrial and predicted radiations.     

Optimisation of the micro-climate in solar collectors

Flat collectors are usually not air or water tight. Therefore, they can exchange air and moisture with the environment. Moisture can accumulate in the collector, especially when the thermal insulation material acts as a storage for moisture (for example mineral wool). The moisture can increase the corrosivity of the micro-climate in the collector. An optimised ventilation rate, which is a measure of the air exchange between the collector and the environment, with respect to the moisture absorption properties of the thermal insulation materials helps to keep the collector dry. Optimum might be a relatively high ventilation if the collector case is not designed to be completely tight.