The steady state salt gradient solar pond

The three-zone salt gradient solar pond is analyzed as a steady-state flat-plate solar energy collector. The resultant efficiency equation is of the Hottel-Whillier-Bliss type commonly used for flat-plate collectors. The quantities that occur in this equation—the effective absorptivity-transmissivity product ατ, the loss factor U_L, the heat removal factor F_R, and the incident angle modifier θ(i)—are related to the physical properties and dimensions of the pond. For a given ΔT/H [(fluid inlet temperature—surface temperature)/insolation], the thickness of the nonconvective zone can be adjusted for maximum efficiency. U_L and ατ are smaller than the equivalent quantities for flat-plate collectors, while θ(i) and F_R are close to unity. As a consequence, steady-state salt-gradient solar ponds are less efficient than common flat-plate collectors at low ΔT/H, but they are more efficient at high ΔT/H.     

Thermal analysis of a flat-plate boiling collector having sub-cooled inlet and saturated exit states

The analysis of the thermal performance of a boiling flat-plate solar collector is presented. A generalized heat removal factor and a new formulation for the overall thermal loss coefficient are developed. It is demonstrated that the conventional heat removal factor for non-boiling collectors is a limiting case of a more generalized result. The new formulation for the overall thermal loss coefficient is shown to be a function of the fractional non-boiling length of the flow channel. The influence of the inlet sub-cooling is evaluated and the operating limits of solar flat-plate collectors are determined. A comparison is made between the thermal model for boiling collectors having sub-cooled inlet states and experimental results. Favorable agreement is obtained.     

Evaluation of a transient test procedure for solar flat-plate collectors

A dynamic method for testing solar flat-plate collectors under unsteady weather conditions has been validated through detailed experiments and compared with two established standards: the ASHRAE 93–86 standard for steady state testing and the British standard BS 6757 for transient testing. The new method is based on a lumped capacity model derived from a general energy balance of the collector under actual conditions. The characteristic parameters are estimated using the standard methods for unconditional non-linear optimisation. Extensive experiments have been carried out under a wide range of operating and environmental conditions. Four different collectors commercially available in the market have been tested at the same location and using the same experimental rig. The results on the basis of the new method are very close to those obtained from the ASHRAE standard. The average values of F_R(τα)_e and F_RU_L by the new method are within ±3% of the steady state values. The results of the BS 6757 method are within ±2% for F_R(τα)_e but those of F_RU_L are about 12% lower than the ASHRAE values. On average, the difference between the theoretical predictions for the outlet temperature by the new method and the corresponding experimental measurements are about ±0.3°C, while the predictions by the British standard under the same conditions are about 2°C lower than measured values. The percentage deviations of predictions for the temperature rise based on the two methods, averaged over a day, are about ±8% and ±36% respectively. The new dynamic method requires less time for experimentation, one day's test is enough to give accurate estimation of the collector parameters. The method does not impose any restriction on the variation of weather or operating parameters and, therefore, has a quite general applicability.     

Thermal performance testing of flat-plate collectors

Existing standards for testing the performance of flat-plate solar collectors are documented in ASHRAE 93 [ANSI/ASHRAE Standard 93-2003, 2003. Methods of Testing to Determine Thermal Performance of Solar Collectors, ISSN: 1041-2336, ASHRAE, Inc., 1791 Tullie Circle, Ne, Atlanta, GA30329], ISO 9806-1 [ISO Standard 9806-1:1994(E), 1994. Test Methods for Solar Collectors – Part 1: Thermal Performance of Glazed Liquid Heating Collectors Including Pressure Drop, ISO, Case Postale 56, CH-1211 Geneve 20, Switzerland] and EN12975-2 [European Standard EN12975-2:2001, 2001. Thermal Solar Systems and Components – Solar Collectors – Part 2: Test Methods, CEN, Rue de Stasart, 36, B-1050, Brussels]. The ASHRAE 93 standard requires an experimental determination of the steady-state collector efficiency under prescribed environmental conditions for a range of collector fluid temperatures. Each test requires a minimum of 20 min and 22 tests are required to fully characterize a collector’s thermal performance. The ASHRAE 93 testing procedure is further complicated by the fact that the prescribed weather conditions do not often occur in some locations, which prolongs the time required to conduct the performance tests for a given collector. The EN12975-2 collector test procedure provides an alternative transient test method that can be conducted over a larger range of environmental conditions. This paper compares the results obtained by applying the EN12975-2 standard with results obtained from the ASHRAE 93 steady-state tests for a well-designed single-glazed selective surface flat-plate collector. The collector thermal parameters, F_R(τα)_e and F_RU_L obtained by the two test methods show good agreement. The incident angle modifier coefficient determined in the ASHRAE method, which uses a separate test for this purpose, was found to be more accurate than that determined in the transient method according to the EN12975-2 standard, which obtains this value and all other collector parameters in the same step. This transient method, however, uses a refined collector model that includes specific terms for the wind speed dependence and the collector thermal capacitance, which are absent in the ASHRAE model. The long-term collector thermal performance as a part of a water heating system was simulated using the efficiency curves derived from each of the test methods. The solar fractions obtained by simulation are within 7% for both cases.     

On the correlations between collector efficiency factor and material content of parallel flow flat-plate solar collectors

The collector efficiency factor F^′, besides the collector heat loss coefficient U_L, characterizes the thermal quality of a solar collector. As F^′ is strongly influenced by the tube distance w and the absorber plate thickness δ, F^′ is also correlated with the material content of absorber plus tubing. Due to the future mass production of collectors and to the restricted copper resources (in the literature, a range until 2026 is given), the role of material savings can be expected to become more and more important. This paper focuses on the correlations between F^′ and the material content of absorber and tubing for flat-plate collectors with the fin-and-tube geometry. The correlations between w, δ, F^′ and material content are presented in a new type of nomograph. This nomograph indicates the values of w and δ that minimize the material content (for a given F^′). For a typical absorber with F^′=0.90, material savings of 25% can theoretically be achieved without any deterioration of F^′, by reducing the absorber plate thickness and the tube distance. The resulting plate thickness is below 0.1 mm; the respective tube distance will be about 7 cm. Practical restrictions are discussed. In a sensitivity analysis, the influence of different parameters on F^′ is investigated. The most important parameters are w, U_L,δ and the Reynolds number. The technique chosen for contacting tube and absorber has only a minor influence on F^′.     

A new look at long term collector performance and utilizability

A simple technique has been developed to calculate monthly collection efficiency or monthly utilizability for solar thermal flat-plate collectors. It is applicable to south facing tilted collectors operating with a fixed fluid inlet temperature although extensions to other more generalized uses of utilizability are discussed. The heart of the technique is an empirically determined performance map that makes possible quick evaluations of changes in collector design, geographic location and collector inlet temperature. The collector input variables are those that are commonly measured in most thermal test procedures; geographic input variables are the mean monthly temperature and K_T (the Liu and Jordan clearness factor). The procedure was developed for monthly optimum fixed tilts but a simple correction can be made to incorporate arbitrary monthly fixed tilts. The method, in general, gives good results compared to long term hourly simulation. The technique also allows one to determine under what operating conditions collector performance begins to depend on site-to-site solar radiation/weather variability and what uncertainties can be expected from its use.     

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

A 13.6 m² east-west aligned CPC-collector (compound parabolic concentrator) with flat absorbers, proposed for use in large-area applications, has been built and tested and compared with a flat plate collector. The performance of the CPC at a working temperature of 50°C over ambient can be described by F′η_O = 0.75 and F′U_L = 2.5 W m⁻² K⁻¹ while the flat plate collector is described by F′η_O = 0.80, and F′U_L = 3.3 W m⁻² K⁻¹. The large difference in heat loss coefficient is to a large degree explained by absorption of solar radiation in the reflectors in the CPC-collector. The incidence angle dependence of the optical performance of the two collectors showed a similar appearance. Both collector constructions are based on the LGB (long ground based) technology, which allows them to be built in large modules up to 170 m².     

Economic appraisal of small-scale solar organic Rankine cycle operating under different electric tariffs and geographical conditions

In the present paper, the economic feasibility of small-scale solar organic Rankine cycle power applications which are assisted with auxiliary gas heaters is investigated. The system is analyzed using three different capacities of ORC system with R-245fa (35, 65, and 110 kWe) in combination with solar water heating system (SWHS) using three models. Flat plate, compound parabolic and evacuated tube solar collectors were used to generate heat with overall heat transfer coefficient (F_RU_L) of 4.35, 1.57, and 2.23 W/m². K respectively. System Advisor Model (SAM) is used to simulate the solar water heater system and optimize the tilt angle, collector area, volume of storage tank and capacity of auxiliary heater under the climatic conditions of Abu Dhabi, New Delhi, Larnaca, Madrid and Munich. The simulation results revealed that the evacuated tube and the compound parabolic collectors performed better than the flat plate collectors. The economic analysis showed that Solar ORC Power Plant is economically and technically feasible with all types of the thermal collectors in Famagusta/Larnaca, Munich and Madrid where the electricity tariff is higher than other cities. Levelized cost of energy (LCOE) is calculated using mathematical model and it ranges between 0.07 and 0.2 USD/kWh based on the plant capacity and type of thermal collectors. Moreover, the profit increase as the plant capacity increase where SIR is 1.05, 1.71, and 2.10 for 35, 65, and 110 kW plant capacity SORC with CPC. A sensitivity analysis is also performed to investigate the effect of operating hours, electricity tariff, ORC unit cost and ORC unit type on the feasibility of the system. According to the results, the electricity tariff and operating hours are the most important parameters because they have a large effect and Play important role on the economic feasibility of the system.     

Performance study of a novel solar air collector

A novel solar air collector of pin-fin integrated absorber was designed to increase the thermal efficiency. According to experimental results, the average thermal efficiency of twenty-five kinds of pin-fin arrays collector reach 0.5–0.74 compared to the solar transmittance of 0.83 for the glazing. A correlation equation can be put forward to reflect the maximum thermal efficiency (η_max) of twenty-five kinds of pin-fin arrays collectors as function of dimensionless pin-fin span (s/d) and dimensionless pin-fin height (h/d). By theoretical calculation, the mathematic models of thermal efficiency of twenty-six collectors including flat-plate collector are obtained representing the influences of solar irradiation and inlet conditions of air stream on thermal efficiency. In the performance analysis of varying flow rate on PZ7-11.25 pin-fin arrays collector, the correlation equation on heat transfer coefficient is obtained and the efficiency variation vs. air flow rate is determined in this work.     

Analysis of flat-plate collectors charged with phase-changing fluids

The steady-state performance of flat-plate collectors, charged with phase-changing working fluids, has been studied analytically. The collector is divided into three distinct regions of heat transfer—(i) that in which the fluid is sensibly heated, (ii) that in which boiling occurs and (iii) that in which the vapour is superheated. The results are then combined to express the collector efficiency as a function of the saturation temperature and liquid level.Numerical calculations of the collector efficiencies were carried out for double-glazed flat-plate collectors employing R-11 as the working fluid.     

Design application of the Hottel-Whillier-Bliss equation

A method is presented for experimentally determining the three factors that determine collector efficiency in the Hottel-Whillier-Bliss equation, Q_u = F_RA_c[(τα)_cI - U_L(T_f,i - T_a)]. These factors are: the collector heat removal factor, F_R; the effective transmittance-absorptance product, (τα)_e; and the overall heat loss coefficient, U_L. The method of testing requires: computation of (τα)_e from measurements of cover transmittance and collector reflectance; computation of F_R from a test in which the heat loss term equals zero; and computation of U_L from a test in which insolation equals zero. This method was applied to collectors used on Solar House I at Colorado State University, with experimental and theoretical results being in close agreement. The method can be used to experimentally evaluate collector performance and for optimization of collector design.     

Heat removal factor for a flat-plate solar collector with a serpentine tube

The performance of a flat-plate solar collector is investigated. The collector is of the sheet-and tube design and the tube is bonded to the absorbing plate in a serpentine fashion. Equations describing the variation of the fluid temperature in the different segments of the serpentine are derived. These equations are then used to determine the heat removal factor F_R for the collector.It is shown that for the general case of an N-bend serpentine, the heat removal factor depends on three non-dimensional groups containing the different operational and design variables of the collector. A generalized chart for estimating F_R for collectors with serpentines of arbitrary geometry and number of bends is presented.     

Optimum performance of thermal trap collectors

The “thermal trap effect” in semitransparent material and the trapping system in the conventional flat-plate collectors with two, three or four glass or plastic covers with air-gaps in between are analysed under a common heading of “thermal trap collectors”. In general, a thermal trap collector consists of one or many slabs of semitransparent material of finite thickness with air-gaps in between, and an ideal withdrawal mechanism at the base of the trapping system to withdraw all available energy. This approach makes a comparative study of the two types of collectors possible, and provides data to design the appropriate withdrawal mechanism and operating conditions. A steady state analysis which neglects internal reflections and body radiation shows the existance of an optimum performance in single-layer thermal trap collectors and its dependence on thickness. A model which includes internal reflections is then analysed and the existance of the optimum performance and its dependence on thickness is demonstrated by taking the example of a single slab of methylmethacrylate plastic. The model is extended to multilayer thermal trap collectors and two examples are considered; a multilayer methylmethacrylate thermal trap collector and a multilayer “glass” thermal trap collector. The results show that the two-layer methyl methacrylate thermal trap collector has, in general, a better performance than the corresponding single or three and four-layer systems. But at high withdrawal efficiencies of about 60 per cent, the single layer methyl methacrylate shows its uniqueness and becomes competitive with the two-layer system. But the three and four-layer “glass” thermal trap collectors perform better than the corresponding single and two-layer ones, with the three-layer system having an overall better performance. These results show that the number of slabs in addition to thickness are important parameters in the study of the performance of thermal trap collectors.     

Thermal performance of artificially roughened solar air heaters

Artificially roughened solar air heaters have been analysed (Prasad and Saini, 1988) for fully developed turbulent flow and found to perform better both quantitatively and qualitatively compared to the smooth ones under the same operating conditions. Optimal thermo-hydraulic performance of such solar air heaters has been analysed (Prasad and Saini, 1991) and investigated (Prasad and Verma, 2000) for the maximum heat transfer and minimum pressure drop.This paper represents the experimental results on heat transfer and thereby thermal performance of artificially roughened solar air heaters for fully developed turbulent flow data collected under actual outdoor conditions. Such solar air heaters have been found to give considerably high value of collector heat removal factor (F_R), collector efficiency factor (F′) and thermal efficiency (η_th) as compared to the corresponding values of those of smooth collectors. In the range of the operating parameters investigated, the ratio of the respective values of the parameters F_R, F′ and η_th for the roughened collectors to the smooth collectors have been found to be 1.786, 1.806 and 1.842 respectively.     

Design, construction, performance evaluation and economic analysis of an integrated collector storage system

The design and construction of an Integrated Collector Storage (ICS) system is presented in this paper. The main advantage that such a collector system presents, with respect to conventional flat-plate collectors, is the fact that it is of a very low profile. The main disadvantage of these collectors comes from the design of the system, i.e. with the receiver of the collector being also the storage vessel, it is not possible to insulate it properly and there are significant heat losses during the night. System modelling and optimisation is carried out by the use of a computer code written for the purpose. Performance results presented are in good agreement with the predicted results, especially for the end-of-day storage temperature which is predicted to within 5.1%. The initial cost of the system presented here is 13% cheaper than the corresponding flat-plate (FP) collector of the same aperture area and storage volume. Additionally, the economic analysis of the two systems, performed with the F-Chart program, showed a yearly F-value of 0.85 for the ICS system compared to 0.83 for the FP system, a pay-back period of nine years for the ICS system, compared to 11 years for the FP system and a life cycle saving of C£330 for the ICS system compared to C£201 for the FP system.     

HIGH EFFICIENCY EVACUATED FLAT-PLATE SOLAR COLLECTOR FOR PROCESS STEAM PRODUCTION

A flat-plate solar collector for process steam production was developed. The operating temperatures are in the range between 100 and 150°C. The boiling collector can be used for process heat supply in the industry and for solar cooling applications as well. It operates as a system with controlled influx of liquid. Instabilities of the two-phase flow in the internal evaporator have been successfully suppressed and the design of the system has been investigated. We constructed a prototype collector based on a commercially available evacuated flat-plate collector. To realise high thermal efficiencies at temperatures up to 150°C, the thermal losses of the absorber have been drastically reduced using an ultra low emissive selective absorber, a low pressure krypton filling (50 hPa) in the collector casing, and a highly reflecting aluminium foil between absorber and rear side. The prototype collector was dynamically tested at our outdoor test facility and showed very high efficiencies of more than 60% at 100°C steam temperature and of 45% at 150°C steam temperature (T_amb=15°C). The operation behaviour of the prototype was always stable and the steam mass quality showed excellent values of nearly 100%.     

Approximate method for computation of glass cover temperature and top heat-loss coefficient of solar collectors with single glazing

An improved equation form for computing the glass cover temperature of flat-plate solar collectors with single glazing is developed. A semi-analytical correlation for the factor f—the ratio of inner to outer heat-transfer coefficients—as a function of collector parameters and atmospheric variables is obtained by regression analysis. This relation readily provides the glass cover temperature (T_g). The results are compared with those obtained by numerical solution of heat balance equations. Computational errors in T_g and hence in the top heat loss coefficient (U_t) are reduced by a factor of five or more. With such low errors in computation of T_g and U_t, a numerical solution of heat balance equations is not required. The method is applicable over an extensive range of variables: the error in the computation of U_t is within 2% with the range of air gap spacing 8 mm to 90 mm and the range of ambient temperature 0°C to 45°C. In this extended range of variables the errors due to simplified method based on empirical relations for U_t are substantially higher.     

Performance of a “black” liquid flat-plate solar collector

A cost-effect, “black” liquid, flat-plate solar collector has been designed, and prototypes have been built and tested. In these collectors a highly absorbent “black” liquid flows in transparent channels and directly absorbs solar energy. The liquid is the hottest substance in the collector, and no metals are required anywhere in the design. The collector differs in the following ways from conventional flat-plate collectors:

1. 1. Solar radiation is absorbed directly by the black liquid without the need to heat any other structures within the collector.

2. 2. Lower heat losses are possible since energy is absorbed directly by the working fluid, and the flow pattern can be arranged so that the hottest spot is in the center of the collector away from all edges. As the fluid moves progressively inward toward the exit, which is located at the center of the collector, it will pick up some of the heat loss along the radial direction.

3. 3. Lower cost may be possible since no metal is required in construction and only glass and/or plastic need be used in addition to the insulation and frame. The absence of metal should eliminate all corrosion problems.

4. 4. New avenues of research are opened up by the use of black liquids: an entirely new class of materials are available which may aid in finding inexpensive, durable absorbers.

5. 5. New configurational arrangements are possible with the absence of metal absorbers.

Experimental performance data for the black liquid collector is presented which compares favorably with other conventional flat-plate collectors.     

Computation of glass-cover temperatures and top heat loss coefficient of flat-plate solar collectors with double glazing

A set of correlations for computing the glass-cover temperatures of flat-plate solar collectors with double glazing is developed. A semi-analytical correlation for the factor f₂—the ratio of outer to inner thermal resistance of a double-glazed collector—as a function of collector parameters and atmospheric variables is obtained by regression analysis. This relation readily provides the temperature of the second (outer) glass cover (T₂). For estimating the temperature of first (inner) glass cover (T₁), another relation for the factor f₁—the ratio of thermal resistance between the two glass covers to the thermal resistance between the absorber plate and first glass cover—is developed. A wide range of variables is covered in the present analysis. The results are compared with those obtained by numerical solutions of heat-balance equations. Using the proposed relations of glass-cover temperatures, the values of top heat loss coefficient (U_t) can be computed and are found to be very close to those obtained by numerical solutions of heat-balance equations. The maximum absolute error in the calculation of U_t by the proposed method is only 1.0%, so numerical solutions of heat-balance equations for the computation of U_t are not required.     

The Influence of Collector Fluid Inlet Temperature on the Performance of a Solar-Assisted Absorption System Using Step-Finned Flat-Plate Collector

In the present work, an extensive analysis is developed for an evaluation of the thermal performance of a solar-powered H₂O/LiBr absorption cooling system using a step-fin flat-plate collector (SFC). The performance parameters, namely, collector efficiency factor, heat removal factor, and collector efficiency, for the SFC is derived. A system simulation model has been developed to analyze the system performance—that is, to identify an operating criterion as a function of the collector fluid inlet temperature (T _FI). It has been observed from the results that the performance of the system depends strongly on T _FI. Simulation results show that the system operates optimally (maximum coefficient of performance) at an optimal T _FI. When the system runs at this optimal value of T _FI, minimum collector material is required. Thus, when using SFC in place of a rectangular-fin flat-collector, thirty-five percent or more collector material can be saved. However, it has been observed that the effect of thermal conductivity on the plate volume of SFC has a marginal effect.