Renewable Energy 36 (2011) 90e96 Contents lists available at ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene Numerical simulation of a trapezoidal cavity receiver for a linear Fresnel solar collector concentrator Jorge Facão*, Armando C. Oliveira New Energy Technologies Unit, Faculty of Engineering, Department of Mechanical Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal a r t i c l e i n f o a b s t r a c t Article history: Received 5 August 2009 Accepted 3 June 2010 A new trapezoidal cavity receiver for a linear Fresnel solar collector is analysed and optimized via raytrace and CFD simulations. The number of receiver absorber tubes and the inclination of lateral walls in the cavity are checked with simplified ray-trace simulation. The CFD simulation makes possible to optimize cavity depth and rock wool insulation thickness. The simulated global heat transfer coefficient, based on primary mirror area, is correlated with a power-law fit instead of a parabolic fit. The correlation results are compared with heat transfer coefficients available for linear Fresnel collector prototypes. Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved. Keywords: Linear Fresnel collector Trapezoidal cavity receiver CFD simulations Overall heat transfer coefficient 1. Introduction When looking at reducing CO2 emissions, the greatest task in creating viable solar energy conversion systems is that of reducing system cost. The solution to this problem does not necessarily lie on creating the most efficient system, but more on the development of a system that has the lowest lifetime cost per unit of electricity converted from solar energy. A linear Fresnel solar collector concentrator may have a lower efficiency than other concentrating geometries, but the likely reduced cost may well compensate that, providing a solution for cost-effective solar energy collection on a large scale [1]. The linear Fresnel collector concept uses a number of rows of relatively small one-axis tracking mirrors that concentrate the radiation on a linear receiver. The advantages of linear concentrating Fresnel collectors include their relatively simple construction, low wind loads, a stationary receiver and high ground usage [2]. Some applications allow the use of the shaded area underneath the collector (e.g. for parking lots) and supply basic needs to rural remote communities. Baum et al. [3] in 1957 were the first to develop the idea of using a tracking reflector field to concentrate solar energy onto a single fixed absorber. However, the first person to apply this principle in a large-scale system was Francia [4] in 1961. In 1991 the PAZ company built a large-scale linear Fresnel reflector at the Ben- * Corresponding author. Tel.: þ351 217127190; fax: þ351 217163688. E-mail address: jorge.facao@ineti.pt (J. Facão). Gurion Solar Electricity Technologies Test Center [5]. The system had optical problems due to the construction tolerance of the mirror field, resulting in a very low solar thermal efficiency. Mills and Morrison [6] proposed in 2000 the compact linear Fresnel reflector, using multiple stationary absorbers evenly spaced between the reflector rows. Dey [7] presented a preliminary design methodology and heat transfer calculations for an absorber based on Mills and Morrison [6] concept. The design constraint was the maximum temperature difference between an absorbing surface and fluid inside the tubes. He used a finite element analysis and obtained a temperature difference of less than 20  C. Ausra [8] commercialize a compact linear Fresnel reflector based on Mills and Morrison [6] tecnologie. The system uses flat mirrors and several absorber tubes. The Belgian company Solarmundo installed in Liege, in 2001, a 2500 m2 linear Fresnel collector prototype for steam generation. This company was integrated in 2004 in the Solar Power Group GmbH [9], Germany, which installed a demonstrator of a linear Fresnel collector in Almeria, Spain, in 2007. The PSE AG, a spin-off company of the Fraunhofer Institute, Germany, manufactures and commercializes linear Fresnel collectors, with several units installed in Europe and Tunisia [10]. Novatec Biosol [11] have installed recently in south of Spain a Fresnel collector solar plant of 1.4 MW. The system uses flat glass mirrors and a CPC cavity with one absorber tube. In this paper we analyse the optical and thermal performance of a new trapezoidal cavity for a small linear Fresnel receiver, using simplified ray-tracing and computational fluid dynamics. Natural convection inside the cavity, thermal radiation between surfaces 0960-1481/$ e see front matter Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.06.003 91 J. Facão, A.C. Oliveira / Renewable Energy 36 (2011) 90e96 Nomenclature D f r T Ta tinsulation Ttubes U u receiver depth, mm focal length, m radius of curvature, m temperature, C ambient air temperature, C insulation thickness, mm absorber tubes temperature, C global heat transfer coefficient, W/(m2 K) global heat transfer coefficient, based to the receiver length, W/(mK) Greek symbols a external heat transfer convection coefficient, W/m2K 4 angle between optical axis and line from reflector focus, deg q sun incidence angle relative to aperture normal, deg j tracking angle, deg and conduction through the walls are simulated, and the overall heat loss coefficient is evaluated. The system uses 10 rows of 4 reflector mirrors with a northesouth tracking axis e see Fig. 1. The primary mirrors are cylindrical with different small curvatures. The mirror width is 0.4 m, the length is 3 m, and mirror spacing is 0.15 m. The total mirror area is approximately 48 m2. The linear receiver is composed of 6 pipes with an inside diameter of ½ inches, placed 2.5 m above the mirrors, inside an insulated trapezoidal cavity, as shown in Fig. 2. The maximum temperature achieved in the receiver tubes was fixed through the operating temperature of an organic Rankine cycle (power cycle) driven by the linear Fresnel collectors, designed to operate at 230  C. Fig. 1. Schematic representation of the installed collector system e view from above. 2. Simplified ray-trace simulation Ray-trace was used for optical efficiency simulations of the concentrating collector. The process consists in following the paths of a large number of rays of incident radiation throughout the system. For reflecting surfaces, the direction and point of intersection of an incident ray with the reflecting surface are determined. The normal to the surface in each point is also determined, and the reflected ray follows the principle that the angle of reflection equals the angle of incidence. Exhaustive raytrace simulation enables to study the sensitivity of delivered energy to height and width of the receiver, collector tracking orientation, climate, and design modifications. We concentrated our attention in design optimization and behaviour of the receiver cavity, which means that a simplified ray-trace analysis was carried out. The tracking angle ji of the ith reflector was calculated according to Rabl [12]: ji ¼ ðfi qÞ 2 However, the manufacture of a parabolic reflector is too expensive. In this system, we adopted cylindrical mirrors with different curvature. The mirror radius of curvature ri depends on the focal length f of the mirror, and the tracking angle: ri ¼ 2f cosðjÞ (2) i (1) where 4i is the angle between optical axis and the line from the focus to reflector, q is the incident angle of the sun relative to the aperture normal. It is known that the parabolic concentrator is the unique reflector shape that focuses beam radiation into a single point. i Fig. 2. Schematic representation of the installed collector system e EasteWest plane view. 92 J. Facão, A.C. Oliveira / Renewable Energy 36 (2011) 90e96 Table 1 Radius of curvature for the different mirrors. mirror 4 [deg] j [deg] f [m] r [m] 1 2 3 4 5 6.28 18.26 28.81 37.60 44.71 3.14 9.13 14.41 18.80 22.36 2.52 2.63 2.85 3.16 3.52 5.04 5.33 5.89 6.67 7.61 For radius of curvature calculation (equation (2)), we adopted the tracking angle for perpendicular incident radiation (q ¼ 0), and for focal length the distance from mirror centre to absorber centre. Table 1 presents the calculated radius of curvature for the mirrors (numbered from centre to extremity). Figs. 3 and 4 present ray-trace simulation for perpendicular incident radiation, e.g. at the equator at solar noon on the 21st of March. The inclination of the lateral absorber walls’ cavity was fixed at 50 , which is about the complementary angle of 45Figs. 5 and 6 present the same analysis, but for an incidence angle of 30 . Here the radiation is more or less evenly distributed in the absorber tubes. Some rays are intersected by the absorber shade and by adjacent mirror shade before reaching the mirrors. The geometry of the cavity, with 6 tubes and an inclination of 50 , optically fulfils the requirements of the Fresnel collector. 3. Heat loss coefficient The efficiency parameters usually used in solar collector analyses are: the optical efficiency, the incidence angle modifier and the heat loss coefficient. To calculate the heat losses from the absorber tubes, CFD simulations were carried out, taking into account all heat transfer mechanisms: radiation, convection and conduction. To calculate the other two parameters, radiation proprieties of the reflectors, absorbers and cover are needed. A three-dimensional exhaustive ray-trace analysis must also be carried out, which is out of the scope of this work. 3.1. Review of published work Feurmann and Gordon [13] made a simulation of a linear Fresnel reflector. The heat loss coefficient for a CPC-type secondary concentrator used was 0.3 W/K-m2 (of primary mirror aperture area). The aperture area of the Fresnel collector is defined as the Fig. 3. Ray-trace simulation for perpendicular incident radiation (cross section). Fig. 4. Ray-trace simulation for perpendicular incident radiation (absorber zoom). glazed area of the primary reflectors. According to the authors, evacuation of the receiver would reduce the U-value to 0.075 W/Km2. Simulations indicate that this could increase yearly delivered energy by 10 percent, although with an increase in cost. Häberle et al., 2002 [14] evaluated the heat loss coefficient of the Solarmundo Fresnel collector by CFD simulation. The collector had one unique large tube absorber (diameter of 200 mm) with special coating, placed in a non-evacuated CPC cavity. They have used an absorber thermal emittance of 5%, an exterior thermal convection coefficient of 10 W/(m2K) and heat conductivity of backside insulation of 0.05 W/(mK) They correlated the coefficient with temperature difference and based it in the aperture area: U ¼ 3:8  10 4 ðTtubes Ta Þ (3) Reynolds et al. [15] simulated the thermal loss of a Fresnel receiver using Fluent [15] software. They have compared the simulated streamlines with experimental results and a good agreement was found. However, the heat loss predicted by the CFD model under-predicted the value measured through an infrared camera. Uncertainties in emissivity measurements, and convection and conduction coefficients could explain the deviation. The work was focused only in the cavity, and the result was expressed as a heat flux, but they didn’t present the aperture area of the Fresnel collector. The heat loss coefficient of the PSE collector was measured in 2005 and published by Häberle et al., 2006 [2] The absorber consisted of a 70 mm diameter commercial vacuum tube and a secondary non-evacuated CPC concentrator made with Fig. 5. Ray-trace simulation for an incidence angle of 30 (cross section). J. Facão, A.C. Oliveira / Renewable Energy 36 (2011) 90e96 93 Fig. 8. Modified geometry below the tubes for CFD simulation. Fig. 6. Ray-trace simulation for an incidence angle of 30 (absorber zoom). aluminium reflectors The correlation achieved for the heat loss coefficient was U ¼ 4:3  10 4 ðTtubes Ta Þ (4) Recently, Pye [17] developed a study on absorber cavity modelling. He applied an analytical model for a trapezoidal cavity and found that radiation makes up for approximately 90% of the heat loss from the top surface. He also carried out a CFD simulation of the cavity, simplifying the tubes by a plane surface. The results were presented through one correlation for natural convection (NusselteGrashoff, based on the cavity depth dimension) and one correlation for radiation (view factor), assuming that radiationeconvection interaction effects are negligible. Radiation modelling of the cavity showed that the effects of absorber tube geometry should not be neglected, leading to a radiative heat loss 25% higher than predicted by the cavity model with plane absorber surface. 3.2. CFD simulation The cavity receiver heat loss processes involve radiation, conductive and convective heat transfer, and the interaction of these makes it impossible to develop a purely analytical model. Computational Fluid Dynamics (CFD) has been greatly developed over recent years, mostly due to the rapid advance of computer technology. It is now possible to solve scientific problems in complex geometries. Natural convection inside the cavity, thermal Fig. 7. Trapezoidal geometry of the Fresnel receiver cavity. radiation between surfaces and conduction through the walls were simulated in this work using Fluent [16] software. Several simplifying assumptions were used: steady state; laminar flow; equal temperature of all receiver pipes; symmetry across the vertical mid-plane; the cavity cover has negligible thermal mass; it was modelled as having a uniform temperature, considering radiation (emissivity) on both sides and a fixed external convection coefficient;  the cavity cover is opaque to long-wave radiation;  the effect of cavity window heating, due to absorptance of the glass, was neglected;  the pipe temperatures were fixed and resulting heat losses calculated.      The cavity geometry is presented in Fig. 7. To simulate the actual cavity is complicated. The methodology was first to separate the simulated geometry in two parts: the geometry of Fig. 8, which is situated below the pipes, and the geometry of Fig. 9, which is repeated 10 times in the receiver. The circular pipes were approximated by regular hexadecagons, to avoid elements with high skewness, which lead to convergence difficulties and inaccuracies in the numerical solution. Fig. 9. Modified geometry above the tubes for CFD simulation. 94 J. Facão, A.C. Oliveira / Renewable Energy 36 (2011) 90e96 Table 2 Influence of receiver depth; tinsulation ¼ 35 mm, Ttubes ¼ 230  C, Ta ¼ 20  C and a ¼ 5 W/(m2K). D [mm] U [W/(m2K)] Loss by radiation [%] 25 0.2431 65 45 0.2383 74 65 0.2437 76 The grid has been set up with Fluent’s grid generation package, Gambit. A hybrid grid was adopted, with an elementary volume size of 0.2 mm for the geometry of Fig. 8, and a triangular one with an interval size of 0.05 mm for the geometry of Fig. 9. To check grid independence, a model with a resolution increased by a factor of 2, in all directions, was tested. This represents an increase in the number of cells of 4 times, and also an increase in computation time of approximately 4 times [18]. The heat loss coefficients with both grid sizes had a relative difference of 0.0091%, which means that the solution can be considered independent of the grid size. The density of air was approximated by the Bousinesq model. This model treats the density as a constant value in all equations, except for the buoyancy term in the momentum equation. The air temperature considered in the Bousinesq model was 350 K, and the thermal expansion coefficient was 0.002857 K 1. The model used to simulate thermal radiation was the Discrete Transfer Radiation Model (DTRM) [19,20]. The main assumption is that the radiation leaving the surface element in a certain range of solid angles can be approximated by a single ray. The polar (theta) divisions and azimuthal (Phi) divisions control the number of rays being created from each surface cluster. The number of theta divisions was set to 4 and the number of phi divisions was set to 16. These values were changed from the default values, until the total heat transfer rate from the tubes was equal to the total heat transfer rate in walls and cover. The air properties were correlated by polynomials with 3 coefficients, as a function of temperature. 3.3. Boundary conditions Three temperatures of the tubes were simulated: 110  C, 170  C and 230  C. The tube emissivity was fixed at 0.49, similar to the value used by Pye [17]. External convection was simulated with 2 different values of the heat transfer coefficient: 5 and 10 W/(m2K), considered representative of two different wind speeds. External air temperatures considered were 15, 25 and 35  C. The wall internal emissivity was taken as 0.1 [17]. In the cover, a mixed thermal boundary condition was considered, with external and internal emissivities of 0.9 [17], an external heat transfer coefficients of 5 and 10 W/(m2K); the same three values of external air temperature were considered, with a surrounding temperature 5  C lower than air temperature. Fig. 10. Contours of stream function inside the cavity for a receiver depth of 25 mm. Tube temperature of 230  C, external air temperature of 20  C and external heat transfer coefficient of 5 W/(m2K). Fig. 11. Contours of stream function inside the cavity for a receiver depth of 45 mm. Tube temperature of 230  C, external air temperature of 20  C and external heat transfer coefficient of 5 W/(m2K). 4. Heat loss simulated results In the CFD simulations, the solution was considered as converged when residuals were lower than 10 8 for the energy equation and 10 5 for the other equations. Two geometrical parameters were changed and analysed, in order to choose the best geometry: the rock wool insulation thickness and the receiver depth D. Table 2 presents the global heat transfer coefficient for three receiver depths: 25, 45 and 60 mm. The receiver with 45 mm presents the lowest heat transfer coefficient, although the differences are very small. Radiation losses dominate heat transfer, compared to convection losses, as shown in Table 2. Radiation losses increase with receiver depth, because cover and lateral wall surface are increased. The flow patterns in the cavity are presented in Figs. 10e12. Thermal stratification is observed in the cavity, confirming the small convection losses. Table 3 shows the influence of rock wool insulation thickness in overall heat transfer coefficient and the increasing width cavity by using insulation face to the cavity dimensions without insulation. As expected, the heat transfer coefficient decreases with insulation thickness. The change from 20 mm to 35 mm represents a 6.8% reduction in the heat transfer coefficient, while from 35 mm to 50 mm it represents a 3.5% reduction; 35 mm should be chosen, taking into account the heat transfer coefficient value and that the increase in insulation thickness leads to more significant shading in the Fresnel collector . Eighteen combinations were simulated and the heat loss coefficient based on primary mirror aperture area was calculated as a function of the difference between average tube temperature and ambient air temperature, as presented in Fig. 13. A power-law Fig. 12. Contours of stream function inside the cavity for a receiver depth of 65 mm. Tube temperature of 230  C, external air temperature of 20  C and external heat transfer coefficient of 5 W/(m2K). 95 J. Facão, A.C. Oliveira / Renewable Energy 36 (2011) 90e96 Table 3 Influence of insulation thickness; D ¼ 45 mm, Ttubes ¼ 230  C, Ta ¼ 20  C and a ¼ 5 W/(m2K). 2.5 Feuermann [13] CFD Feuermann evacuated [13] 2 20 0.2545 30 35 0.2383 53 50 0.2301 76 PSE [2] Solarmundo [14] u [W/mK ] tinsulation [mm] U [W/(m2K)] Increasing width cavity [%] 1.5 1 0.3 y = 0.0309x 0.389 R2 = 0.8511 0.25 0.5 0 U [W/m 2K ] 0.2 0 50 100 150 200 250 (Ttubes-T a) [K] U 0.15 Power (U) 0.1 0.05 Fig. 15. Simulated (CFD) heat transfer coefficient, based to the receiver length, compared with values available in the literature. 5. Conclusions 0 0 50 100 150 200 250 (Ttubes-Ta) [K] Fig. 13. Simulated heat loss coefficient on Fresnel receiver, as a function of temperature difference; tinsulation ¼ 35 mm and D ¼ 45 mm. trendline was chosen to fit to the results. The correlation coefficient was equal to 0.85. The correlation obtained for the Fresnel receiver cavity in analysis was compared with available literature correlations, for this type of collectors. The new cavity presents a simulated heat transfer coefficient which is smaller than for the non-evacuated receiver used by Feuermann and Gordon [13], but larger than the others available in literature correlations e see Fig. 14. Two causes for this difference are: the cavity in this analysis is non-evacuated compared with the other two that are evacuated (Feuermann and Gordon [13] and PSE [2]) and the total primary mirror area taken for the new system. The heat transfer coefficient varies inversely with total primary mirror area. Here, an aperture width of 4 m was considered, equal to the aperture of Feurmann and Gordon [13]. The prototype of PSE [2] had 5.5 m and the prototype of Solarmundo [14] had 24 m. Calculating the global heat transfer coefficient based to the receiver length e Fig. 15, the new cavity presents a better performance when compared with the non-evacuated cavities studied in literature. 0.35 A trapezoidal cavity receiver for a linear Fresnel solar collector concentrator was designed and numerically simulated. Fixing the geometry of the collector and regarding only the cavity, simplified ray-trace simulations concluded that the cavity with 6 absorber tubes of 1/2” internal diameter (5/8” outside diameter) collects all the concentrated beam radiation. The 50 inclination of the lateral cavity walls was also found to be optically acceptable. To evaluate the overall heat transfer coefficient of the Fresnel collector, CFD simulations were done. Natural convection inside the cavity, thermal radiation between surfaces and conduction through the walls were simulated. Two geometrical parameters were analysed: receiver depth and insulation thickness. It was concluded that the cavity with a 45 mm depth presents the lowest global heat transfer coefficient. Regarding insulation thickness, 35 mm of rock wool presented a good compromise between insulation and shading. Correlating the simulated heat transfer coefficient (based on primary mirror area) with the temperature difference between tubes and ambient air, a power-law fit was obtained. The simulated heat loss coefficient for the new cavity showed larger values, when compared to values presented in the existing literature for linear Fresnel collectors. Two causes for this difference are that the new cavity is not evacuated and the smaller aperture width of the system when compared to available prototypes. Calculating the global heat transfer coefficient based to the receiver length the new cavity presents a heat transfer coefficients smaller than the nonevacuated cavities studied in open literature. 0.3 Acknowledgements U [W/m K ] 0.25 Feuermann [13] 0.2 CFD Feuermann evacuated [13] 0.15 PSE [2] Solarmundo [14] 0.1 The authors wish to thank Fundação para a Ciência e a Tecnologia for the post-doc scholarship of the first author. They also wish to express their gratitude to the European Commission under Powersol research project (Contract No. FP6-INCO2004-MPC3032344). The other partners of the project are also acknowledged. 0.05 References 0 0 50 100 150 200 250 (Ttubes-Ta) [K] Fig. 14. Simulated (CFD) heat transfer coefficient compared with values available in the literature. [1] Damien Buie, Christopher Dey and David Mills. Optical considerations in line focus Fresnel concentrators. In: 11th International solar paces conference, Zurich, Switzerland; 2002. 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