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Numerical and experimental study of a solar micro concentrating collector
Available online at www.sciencedirect.com
ScienceDirect Solar Energy 112 (2015) 20–29 www.elsevier.com/locate/solener
Numerical and experimental study of a solar micro concentrating collector Tanzeen Sultana a,⇑, Graham L. Morrison a, Robert A. Taylor a, Gary Rosengarten b a
School of Mechanical and Manufacturing Engineering, University of New South Wales, Australia School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Australia
b
Received 3 September 2014; received in revised form 11 November 2014; accepted 14 November 2014
Communicated by: Associate Editor Brian Norton
Abstract Natural convection in fluid-filled enclosures driven solely by a temperature difference represents an important phenomenon due to its numerous engineering applications. Applications span diverse fields such as passive solar heating, solar collectors and the energy efficient design of buildings. In this paper, we study convection inside a rooftop concentrating collector designed to operate at temperatures up to 200 C. The absorber is contained in a sealed enclosure to minimise convective losses. The main heat losses are due to natural convection inside the enclosure and radiation heat transfer from the absorber tube. A numerical and experimental analysis of the combined laminar natural convection and surface radiation heat transfer inside the collector receiver cavity are presented. A computational fluid dynamics model for the prototype collector has been developed using ANSYS-CFX. Radiation and convection heat loss has been investigated as a function of absorber temperatures, ranging from 70 C to 200 C. Measurements of overall heat loss and particle imaging velocimetry (PIV) were used to experimentally determine the heat and mass transport within the enclosure. Excellent qualitative and quantitative agreement between the CFD and experiments were achieved. 2014 Elsevier Ltd. All rights reserved.
Keywords: Cavity receiver; Computational fluid dynamics (CFD); Heat loss; Particle image velocimetry (PIV); Solar energy
1. Introduction Internal natural convection is a major source of heat loss in enclosed sealed solar thermal collectors (Duffie and Beckmann, 2006; Dey, 2004; Reynolds et al., 2004). A number of heat transfer studies (Balaji and Venkateshan, 1994; Ramesh and Venkateshan, 1999; Behnia et al., 1990) have been conducted in rectangular cavities with combined natural convection and radiation. However, there is limited literature available on the study
⇑ Corresponding author.
E-mail address: [email protected] (T. Sultana). http://dx.doi.org/10.1016/j.solener.2014.11.015 0038-092X/ 2014 Elsevier Ltd. All rights reserved.
of natural convection and radiation in a trapezoidal cavity enclosure, which is often used in Fresnel collectors. Reynolds et al. used flow visualisation to determine convective heat flow patterns within a trapezoidal cavity to investigate the heat losses from a large-scale linear Fresnel solar absorber experimentally (Reynolds et al., 2004). The cavity was also modelled using computational fluid dynamics (CFD) with, only reasonable agreement found between computational and experimental heat transfer rate. Heat loss predicted by CFD model (623 W/m2) was about 40% lower than that from the experimental results (1040 W/ m2) and the discrepancies could not be explained. Pye et al. studied a compact linear Fresnel reflector (CLFR) cavity receiver and developed computational fluid dynam-
T. Sultana et al. / Solar Energy 112 (2015) 20–29
ics models for the heat loss, which are a combination of convective, radiative and conductive losses (Pye et al., 2003). They also developed an analytical model for a trapezoidal cavity and found that radiation makes up approximately 90% of the heat loss from a 330 C sealed absorber. They also carried out CFD simulations for the cavity, simplifying the tubes by a plane surface. The results were presented through a correlation for natural convection (Nusselt versus Grashoff, based on the cavity depth dimension) and a correlation for radiation (view factor). These correlations assume that radiation convection interaction effects are negligible. Radiation modelling of the cavity showed that the effects of absorber tube geometry could not be neglected, leading to a radiative heat loss 25% higher than predicted by the cavity model with a plane absorber surface (Pye et al., 2003). Facao and Oliveira studied heat loss in a trapezoidal cavity of a linear Fresnel receiver using computational fluid dynamics. In their study, natural convection and radiation were examined using two geometrical parameters: receiver depth and insulation thickness. They found a cavity 45 mm deep represents the lowest global heat loss coefficient and 35 mm of rock wool insulation provides a good compromise between insulation and shading (Faca˜o and Oliveira, 2011). Singh et al. developed overall heat loss coefficient correlations for a trapezoidal cavity absorber by comparing pipe geometry (rectangular vs. round) and pipe coating (ordinary black coating vs. selective surfaces) at various absorber temperatures (up to 175 C). Selective surface coating on the absorbers reduced the overall heat loss coefficient by 20–30% relative to ordinary black paint (Singh and Sarviya, 2010). The present research, combines many aspects of outlined literature for the concentrating collector and investigates the role of radiation and natural convection heat transfer inside a trapezoidal cavity that protects the mirrors and absorber tube in a rooftop linear Fresnel collector. The objective of this work is to determine, through numerical and experimental means, the buoyancy-driven airflow generated in the collector cavity and the heat loss taking into account radiation in order to determine methods to increase collector efficiency. A CFD model representing these phenomena is developed and the results obtained for the air flow are compared with experimental results using particle imaging velocimetry (PIV). 2. Micro concentrating collector (MCT) system The geometry that we are focusing on in the work is a rooftop mounted system from Chromasun called an MCT which is shown in Fig. 1. The system module is 3.2 meters long by 1.2 meters wide and 0.3 m high. The MCT collector utilises linear Fresnel reflector optics that concentrate beam radiation to a stationary receiver. Each mirror array system consists of ten mirrors, which concentrate sunlight onto parallel absorber tubes. The mirrors are curved to generate a focus, with the inner six mirrors and
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outer four mirrors having a radius of 0.6 and 0.75 meters respectively. The receiver consists of two 16 mm diameter stainless steel absorber tubes. Each receiver has a secondary reflector that directs missed beam radiation to the absorber tube. The whole system is contained in a sealed glass envelop to minimise convective losses. The main heat losses are due to natural convection inside the enclosure and radiation heat transfer from the absorber tube. The design of the receiver is illustrated in Fig. 2. During operation, the hot absorber tube emits long-wavelength radiation into the cavity that is absorbed mainly by the glass and base surfaces which in turn heat up. These heated surfaces, along with the plume from the hot absorber tube, promote buoyancy-driven flows within the cavity resulting in convection losses to the environment and an associated reduction in thermal efficiency (Sultana et al., 2012). The generalised thermal analysis of a concentrating collector is similar to that of a flat plate collector. For a concentrating collector at steady state, the useful energy output is given by Duffie and Beckmann (2006): qu ¼ Ggo Aa Ar U L ðT r T a Þ
ð1Þ 2
where G is the solar irradiation (W/m ), go is the collector optical efficiency, Aa is aperture area (m2), Ar is the receiver area (m2), UL is the solar collector heat transfer loss coefficient related to the absorber area (W/m2 K), Tr is the temperature of the receiver (C) and Ta is the ambient temperature (C). 3. Laminar steady state flow A laminar steady state buoyancy model was developed for the MCT collector. In purely natural convection problems, the Rayleigh Number (Ra) indicates the relative strength of the buoyancy induced flow, and is given by: Ra ¼ Gr Pr
ð2Þ
where Gr is the Grashof number and Pr is the fluid Prandtl number. The laminar flow regime is generally characterised by Ra < 108, while turbulent buoyant flow is characterised by Ra > 1010 (Cengel and Ghajar, 2010; Zhou and Yang, 2009). The Rayleigh number for MCT receiver was calculated using Eq. (4); Ra ¼
gbðT abs T cover ÞL3 Pr #2
ð3Þ
where Tabs is the absorber tube temperature, Tcover is the glass cover temperature and L is the characteristic length. The Ra = 1.8 104 when the characteristic length, L = 16 mm used the diameter of the absorber tube and Ra = 2.7 107 when L = 300 mm used the height of the MCT collector. Therefore, the air flow in the MCT enclosure was modelled as laminar flow. Using Eq. (4) the Rayleigh number was found to be in the range of 1.8 104– 2.7 107 for air with absorber temperatures in the range from 50 to 200 C.
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Fig. 1. Cross-section of the MCT collector (dimensions in mm).
Fig. 2. Receiver design in the micro-concentrating collector.
4. Radiation model To calculate the surface radiative heat flux within the MCT collector, a Monte-Carlo method (Howell, 1968; Wang et al., 2010) was employed. The background of this method for radiative heat transfer calculations is based on the fact that the transfer process is divided into four subprocesses; i.e. emission, reflection, absorption, and scattering, and every sub-process has a probability of occurrence (Moffat, 1988). The object is divided into surface units and volume units. Every unit emits a certain quantity of light rays, after which every ray is tracked to determine whether it is absorbed by a medium or interface, or it escapes from
the system. Therefore, by tracking a large enough number of light rays it is possible to calculate the total radiation flux. In the present work, as there is only air in the cavity it is assumed to be non-participating so that scattering was omitted. The presence of dust in the cavity is ignored as the enclosure is nominally cleanly sealed. The surface to surface option was used for the calculations; volumetric emission, absorption and scattering are ignored regardless of the specified material properties. The absorber tube surface and all other cavity walls are assumed to have gray properties. First, the radiative heat transfer factor RDij was computed. RDij is defined as the percentage share that unit j takes of the energy radiated by unit i. In another words, RDij is the ratio of the number of light rays unit j gains from unit i to the number of light rays emitted by unit i. So it can be described as: RDij ¼
N ij Ni
ð4Þ
where Ni represents the total number of light rays emitted by unit i, and Nij represents the number of light rays emitted by unit i and ultimately absorbed by unit j. After the radiative heat transfer factor has been calculated, the full thermal simulation can be conducted. For a closed system that includes Ms surface units and Mv volume units, the energy equations of volume unit Vi and surface unit Si expressed as RDij are described as follows using algorithm by Moffat (1988):
T. Sultana et al. / Solar Energy 112 (2015) 20–29
4ji V i rT 4i ¼
Mv X
4jj V j rT 4j RDji þ
j¼1
ei S i rT 4i ¼
Ms X
ek S k rT 4k RDki þ Qi
ð5Þ
k¼1
Mv Ms X X 4jj V j rT 4j RDji þ ek S k rT 4k RDki þ Qi j¼1
ð6Þ
k¼1
where j is the absorption coefficient, V is the volume unit (m3), r is the Stefan-Boltzmann constant (W/m2 K4), T is the temperature (K), RD is the radiative heat transfer factor, Q is the heat rate (W), e is the emissivity and S is the surface unit (m2). The MCT cavity is a closed system, with no volume absorption or internal heat source so the equations can be expressed as ei S i rT 4i ¼
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Ms X ek S k rT 4k RDki þ Qi
ð7Þ
k¼1
The accuracy of the Monte-Carlo method is dependent upon the number of dispatched energy rays and the extent to which the pseudo random number generator is actually ‘random’ (Shuai and Xia, 2008). Fig. 3 illustrates the convergence of the absorber radiative heat loss with number of rays traced with the Monte Carlo method, and shows invariance of the heat loss is apparent after approximately 100,000 rays. Convergence of the heat loss from top and side glass cover were also investigated for different number of rays. Fig. 4 shows that the heat loss from top and side glass covers converged after approximately 100,000 rays. This convergence sensitivity analysis illustrates that heat loss results from the CFD simulation depends on the number of rays chosen in the radiation model, but that results are independent of the number of rays chosen when 100,000 or more ray are used. Based on this analysis, the total number of rays used was 100,000.
Fig. 4. Glass covers heat loss as a function of number of rays used in Monte Carlo simulation.
5.2. Boundary conditions The absorber tube is modelled as an isothermal surface. The convective flow and resulting temperature difference between the absorber tube, the secondary reflector and glass cover are studied for various absorber temperatures. The absorber tube is coated with a black chrome selective surface, and the thermal emissivity is taken as 0.2 (Sultana et al., 2012). The outside of the cover glass at the top and sides of the cavity are modelled as convection boundaries with external heat loss coefficients of 12 W/m2 K, exchanging heat with an ambient temperature of 23 C (Sultana et al., 2012). The glass has an internal emissivity of 0.9. The end walls and aluminium extrusion side walls were modelled as convection boundaries with external heat loss coefficients of 10 W/ m2 K, calculated using a vertical rectangular plate correlation (Cengel and Ghajar, 2010), exchanging heat with an ambient temperature of 23 C. (Note: this approximates the experimental condition). All discretization was carried out using second-order schemes and temperature dependent air properties are calculated using an ideal gas model. Minimum convergence criteria were set at 103 for continuity and velocity, and 106 for energy (Sultana et al., 2013).
5. Three-dimensional modelling 5.3. Mesh 5.1. Geometry A three-dimensional CFD simulation model for combined natural convection and surface radiation was developed using ANSYS CFX. Due to the symmetry plane, only half the geometry was simulated as shown in Fig. 5.
Fig. 3. Absorber tube radiative heat loss as a function of number of rays used in Monte Carlo simulation.
A structured mesh (Fig. 6) was used for the cavity area. The shape of the receiver area is such that the use of structured elements creates regions of high mesh skewness and these regions are typically in regions where the flow is of greater interest. This will impact on the accuracy of the solution by increasing the numerical error and could lead to false features developing in the flow. Therefore, an unstructured mesh with inflation layer was used near the absorber tube (Fig. 7). The resulting mesh size is approximately 6 mm, with 2.3 million mesh points in total. A grid dependency study was undertaken to ensure the adequacy of this mesh density using 1 million, 2 million and 4 million mesh elements. It was found that the peak temperature in the cavity receiver with different mesh sizes shows minimal differences (<0.1%) and the bottom cavity and temperatures are <2 C different between the 2 and 4 million meshes (Fig. 8). Therefore, 2 million was considered a good compromise between computational time and accuracy.
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Fig. 5. Cavity geometry for 3D CFD modelling (a) 3D entire model (b) cross-sectional view in XY plan.
Fig. 7. Inflation layer near the absorber tube and secondary reflector. Fig. 6. A section of the computational grid for the complete 3D model of the MCT.
6. CFD results and discussion Heat losses from different surfaces for a 200 C absorber tube temperature are shown in Table 1. Due to the relatively low emissivity of the absorber’s selective coating, radiation heat loss at 200 C is 40–50% of the convective
heat loss (Fig. 9). The heat loss coefficient from the absorber tube was calculated as 9 W/m2 K at absorber tube temperature 200 C using Eq. (8). U abs ¼
Qabs Aabs ðT abs T a Þ
ð8Þ
where Uabs is overall heat loss coefficient of the absorber tube (W/m2 K), Aabs is the absorber tube area (m2), Qabs
T. Sultana et al. / Solar Energy 112 (2015) 20–29
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Fig. 8. Mesh dependency check for cavity temperature over the vertical line A–A.
Table 1 Heat loss for 200 C absorber tube temperature (absorber tube emissivity, eabs = 0.2). Boundary zone
Heat loss (W/m)
Glass top cover Glass side cover Base surface Side aluminium extrusion Aluminium extrusion top corner Silicon adhesive top Total boundary loss
31 30 3 1 2 6 73
Fig. 10. Temperature contours. (a) Velocity streamlines. (b) Near the receiver section (absorber tube temperature 200 C and absorber emissivity = 0.2).
tube to the cavity. An experimental comparison of this flow structure near the receiver is obtained with the flow visualisation experiment described below. 7. Validation of CFD model Fig. 9. Absorber heat loss for different absorber temperatures (Sultana et al., 2012).
is the absorber tube heat loss (W), Tabs is the absorber tube temperature (C), Ta is the ambient temperature (C). The total heat loss at 200 C is approximately 73 W/m length of tube compared to an expected solar input of approximately 300 W/m to 400 W/m length of the absorber tube. Temperature distributions near the receiver area in the collector are shown in Fig. 10(a). For the boundary conditions specified, the results show significant thermal gradients in the cavity only around the absorber and secondary reflector. Streamlines near the receiver are shown in Fig. 10(b) which indicate the hot fluid flow is rising up near the aluminium extrusion surface and spreading mainly under the top glass cover. Fluid flow around the absorber tube is entrapped by the secondary reflector which minimises the convection flow from the absorber
Although CFD techniques are widely accepted, such numerical models need to be validated against experiments in order to gain confidence in the results. The flow in the MCT cavity is driven by natural convection and the magnitude is relatively low, therefore a non-intrusive measurement technique is required. Particle image velocimetry (PIV) is an optical technique that measures the velocity field in a plane without disturbing the flow (Sultana et al., 2013; Sookdeo and Siddiqui, 2010). 7.1. PIV Experiments Due to the fact that unfettered optical access is required in the collector for both a camera and a laser light sheet, PIV measurements were constrained to three locations with the collector in the horizontal position. An electrically heated absorber tube was constructed to allow direct measurement of losses under laboratory conditions. For each
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location, measurements were taken with the absorber tube heater set to 50 W and 100 W for absorber temperature up to 100 C. The flow in three areas was measured; near the receiver section, along the side glass and at the symmetry plane as is shown in Fig. 11. The absorber tube surface temperature is a function of the ambient temperature and thermal resistance from tube surface to the ambient environment. Under steady-state temperatures, all the electrical power applied to the heating element is either lost as conduction through the top of the cavity or convection and radiation heat into the cavity (Sultana et al., 2013). 7.2. PIV technique The basis of PIV is to seed the flow being measured with small particles and to rapidly acquire images of the particles as they are moved within the flow. Since it is the particles, not the flow itself, which are being observed, it is important to select particles which will accurately track the flow (Raffel et al., 1998). A schematic of the PIV setup and the schematic of the apparatus is shown in Fig. 12. A New Wave Gemini dual-pulsed Nd:YAG laser with 532 nm output wavelength was used to illuminate the flow field via an articulated optics arm and a cylindrical lens. Images of the flow field were captured using a PCO SensiCam camera with a 35 mm lens. Di-Ethyl-Hexyl-Sebacat (DEHS) was atomized into small droplets <2 lm in diameter and injected into the collector using a seeding machine. An ILA synchronizer was used to synch the laser pulses with the camera images. To minimise internal reflections, the Fresnel mirrors were removed from the base of the collector. Black paper was taped where necessary to further reduce glare in the images. Image quality was also improved by covering the camera lens with a 532 nm bandpass filter to reduce the effects of external lighting. Optimal image pairs were obtained by pulsing the dual lasers at 4 Hz, with a pulse separation time of 15 ms for each image pair. Post-processing of the image pairs was performed using ILA’s VidPIV software. Using an interrogation window
size of 64 64 pixels, VidPIV’s “Average Cross-Correlation” algorithm was performed to generate an average cross-correlation of 40 image pairs for each measurement. The resulting vector maps were locally filtered such that any spurious vectors, as determined by comparison with surrounding vectors, were replaced by the average of the neighboring vectors. 8. Comparison of CFD and PIV: results and discussion The velocity vectors near the receiver obtained experimentally by PIV and numerically are along the line X–X are shown in Fig. 13. Measurements and simulations indicate that the hot receiver creates a thin, relatively high velocity buoyant layer of hot fluid along the aluminium support holding the secondary reflector. The maximum velocity predicted by the numerical model for the 100 C absorber tube (absorber tube heat loss, Qabs = 100 W) is 75 mm/s, compared to velocity of 70 mm/s obtained from the PIV measurements (Fig. 14). Differences in the order of 5 mm/s occur between PIV and CFD results with the measurements consistently showing lower velocity due to the slightly larger heat loss in the experiments compared to the CFD. The uncertainly of the PIV measurements was calculated according to Moffat (1988) and Raffel et al. (1998) and the uncertainly in the velocity measurement estimated as ±0.3 mm/s. It should be noted that over the course of multiple measurements, the DEHS seeding particles collected on all internal surfaces of the collector to form an oily film. This film was removed as necessary from the glass to maintain optical access, but it was not removed from the absorber tubes because any cleaning procedure was likely to have damaged the black-chrome selective surface coating. A build-up of a DEHS film increases the emissivity of these absorber tubes and could thus be one explanation for discrepancies between modelled versus experimental results. The velocity profiles near the side glass wall along line Y–Y in Fig. 15 are compared with the simulated results. In general, there is good agreement in the flow structure,
Fig. 11. PIV measurement tested area in the MCT cavity.
T. Sultana et al. / Solar Energy 112 (2015) 20–29
Fig. 12. Schematic of the PIV experimental setup.
Fig. 13. Airflow near the absorber tube, Qabs = 100 W, Tabs = 100C, (a) CFD, (b) PIV at a plane z = 0.7 m from one end of the absorber tube.
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T. Sultana et al. / Solar Energy 112 (2015) 20–29
Fig. 14. Comparison of velocity magnitude profiles near the absorber tube along line X–X in Fig. 13 obtained from CFD simulations and PIV measurements, Qabs = 100 W and Tabs = 100 C.
Fig. 16. Comparison of velocity magnitude profiles along line Y–Y (Fig. 15) on the side glass obtained from CFD simulation and PIV measurements, Qabs = 100 W and Tabs = 100 C.
Fig. 17. Air flow at the symmetry plane (a) CFD and (b) symmetry air flow from PIV measurement. Fig. 15. Velocity vectors along the side glass, Qabs = 100 W, Tabs = 100 C, (a) CFD, (b) PIV.
from the top glass boundary at the symmetry plane after to the two flows collide.
showing a thin layer of hot fluid is formed near the receiver, and it moves upwards creating a small region of recirculation near the receiver and flow moving downwards along the side glass (Fig. 15). The maximum velocity predicted near the side glass by the numerical model with a 100 C absorber tube is 21 mm/s, compared to velocity of 18 mm/s obtained from the PIV measurement (Fig. 16). Fig. 17 shows a comparison of the CFD and experimental flow structure near the symmetry plane. The measurements show the buoyant flow creates a layer along the upper glass cover moving from the absorber to the symmetry plane, with the fluid dropping down into the cavity
9. Conclusion This paper presents experimental measurements and numerical modelling of a micro concentrating solar collector. The performance was numerically simulated using computational fluid dynamics (ANSYS CFX). A numerical simulation of convective and radiation heat loss has been carried out for steady-state laminar conditions and the absorber tube heat loss obtained for up to temperature 200 C. The two-dimensional velocity field was measured using PIV inside the MCT collector. The PIV experiments were conducted for heated conditions at various absorber
T. Sultana et al. / Solar Energy 112 (2015) 20–29
tube temperatures that ranged from 70 C to 100 C and results validated with the CFD simulation. The results have shown that the receiver heating creates a thin relatively high velocity layer of hot fluid near the receiver area and PIV measurements shown a lower peak velocity than CFD model, due to the slightly larger heat loss in the experiments compared to the CFD. The main uncertainty in the CFD boundary conditions is the long wavelength emissivity which may have been affected by the seeding particles. Further investigation is needed into the use of PIV for inclined collector to investigate the longitudinal flow. It is shown that receiver section in the existing MCT collector is the main heat loss and affects the efficiency of the collector. Further CFD simulation can be carried out to investigate the flows in the receiver area by optimising the air gap between the absorber tube and secondary reflector and the glass cover. Also, further work can be carried out investigating the use of evacuated tube receivers. References ANSYS CFX Help Manual 12.1.. Balaji, C., Venkateshan, S.P., 1994. Correlations for free convection and surface radiation in a square cavity. Int. J. Heat Fluid Flow 15 (3), 249–251. Behnia, M., Reizes, J.A., De Vahl Davis, G., 1990. Combined radiation and natural convection in a rectangular cavity with a transparent wall and containing a non-participating fluid. Int. J. Numer. Meth. Fluids 10 (3), 305–325. Cengel, Y.A., Ghajar, A.J., 2010. Heat and Mass Transfer: Fundamentals and Applications, fourth ed. McGrawHill. Dey, C.J., 2004. Heat transfer aspects of an elevated linear absorber. J. Solar Energy 76 (1–3), 243–249. Faca˜o, J., Oliveira, A.C., 2011. Numerical simulation of a trapezoidal cavity receiver for a linear Fresnel solar collector concentrator. Renewable Energy 36 (1), 90–96.
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Howell, J.R., 1968. Application of Monte Carlo to heat transfer problems. In: Hartnett, J.P., Irvine, T.F. (Eds.), . In: Advances in Heat Transfer, vol. 5. Academic Press, New York. Moffat, R.J., 1988. Describing the uncertainties in experimental results. Exp. Thermal Fluid Sci. 1 (1), 3–17. Duffie, J.A., Beckmann, W.A., 2006. Solar Engineering of Thermal Processes. John Wiley and Sons, New York. Pye, J.D., Morrison, G.L., Behnia, M., 2003. System Modelling of the Compact Linear Fresnel Reflector. ISES Solar World Congress, Goteborg, Sweden, P 5.73. Raffel, M., Willert, C., Kompenhans, J., 1998. Particle Image Velocimetry. Springer, Heidelberg. Ramesh, N., Venkateshan, S.P., 1999. Effect of surface radiation on natural convection in a square enclosure. J. Thermophys. Heat Transfer 13 (3), 299–301. Reynolds, D.J., Jance, M.J., Behnia, M., Morrison, G.L., 2004. An experimental and computational study of the heat loss characteristics of a trapezoidal cavity absorber. J. Solar Energy 76, 229–234. Shuai, Y., Xia, X.L., 2008. Radiation performance of dish solar concentrator/cavity receiver systems. Sol. Energy 82 (1), 13–21. Singh, P.L., Sarviya, R.M., 2010. Thermal performance of linear Fresnel reflecting solar concentrator with trapezoidal cavity absorbers. Appl. Energy 87 (2), 541–550. Sookdeo, S., Siddiqui, K., 2010. Investigation of the flow field inside flatplate collector tube using PIV technique. Sol. Energy 84 (6), 917–927. Sultana, T., Morrison, G.L., Rosengarten, G., 2012. Thermal performance of a novel rooftop solar micro-concentrating collector. J. Solar Energy 86 (7), 1992–2000. Sultana, T., Morrison, G.L., Hoffman, M., Rosengarten, G., 2013. Computational and experimental investigation of natural convection in a solar micro-concentrating collector. J. Trans. Phenom. 13 (3), 207– 217. Wang, Y.D., Xunwei, W., Jinjia, J.H., 2010. Numerical simulation of the heat flux distribution in a solar cavity receiver. Front. Energy Power Eng. Chin. 4 (4), 571–576. Zhou, X., Yang, J., 2009. Numerical investigation of a compressible flow through a solar chimney. Heat Transfer Eng. 30 (8), 670–676.
ScienceDirect Solar Energy 112 (2015) 20–29 www.elsevier.com/locate/solener
Numerical and experimental study of a solar micro concentrating collector Tanzeen Sultana a,⇑, Graham L. Morrison a, Robert A. Taylor a, Gary Rosengarten b a
School of Mechanical and Manufacturing Engineering, University of New South Wales, Australia School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Australia
b
Received 3 September 2014; received in revised form 11 November 2014; accepted 14 November 2014
Communicated by: Associate Editor Brian Norton
Abstract Natural convection in fluid-filled enclosures driven solely by a temperature difference represents an important phenomenon due to its numerous engineering applications. Applications span diverse fields such as passive solar heating, solar collectors and the energy efficient design of buildings. In this paper, we study convection inside a rooftop concentrating collector designed to operate at temperatures up to 200 C. The absorber is contained in a sealed enclosure to minimise convective losses. The main heat losses are due to natural convection inside the enclosure and radiation heat transfer from the absorber tube. A numerical and experimental analysis of the combined laminar natural convection and surface radiation heat transfer inside the collector receiver cavity are presented. A computational fluid dynamics model for the prototype collector has been developed using ANSYS-CFX. Radiation and convection heat loss has been investigated as a function of absorber temperatures, ranging from 70 C to 200 C. Measurements of overall heat loss and particle imaging velocimetry (PIV) were used to experimentally determine the heat and mass transport within the enclosure. Excellent qualitative and quantitative agreement between the CFD and experiments were achieved. 2014 Elsevier Ltd. All rights reserved.
Keywords: Cavity receiver; Computational fluid dynamics (CFD); Heat loss; Particle image velocimetry (PIV); Solar energy
1. Introduction Internal natural convection is a major source of heat loss in enclosed sealed solar thermal collectors (Duffie and Beckmann, 2006; Dey, 2004; Reynolds et al., 2004). A number of heat transfer studies (Balaji and Venkateshan, 1994; Ramesh and Venkateshan, 1999; Behnia et al., 1990) have been conducted in rectangular cavities with combined natural convection and radiation. However, there is limited literature available on the study
⇑ Corresponding author.
E-mail address: [email protected] (T. Sultana). http://dx.doi.org/10.1016/j.solener.2014.11.015 0038-092X/ 2014 Elsevier Ltd. All rights reserved.
of natural convection and radiation in a trapezoidal cavity enclosure, which is often used in Fresnel collectors. Reynolds et al. used flow visualisation to determine convective heat flow patterns within a trapezoidal cavity to investigate the heat losses from a large-scale linear Fresnel solar absorber experimentally (Reynolds et al., 2004). The cavity was also modelled using computational fluid dynamics (CFD) with, only reasonable agreement found between computational and experimental heat transfer rate. Heat loss predicted by CFD model (623 W/m2) was about 40% lower than that from the experimental results (1040 W/ m2) and the discrepancies could not be explained. Pye et al. studied a compact linear Fresnel reflector (CLFR) cavity receiver and developed computational fluid dynam-
T. Sultana et al. / Solar Energy 112 (2015) 20–29
ics models for the heat loss, which are a combination of convective, radiative and conductive losses (Pye et al., 2003). They also developed an analytical model for a trapezoidal cavity and found that radiation makes up approximately 90% of the heat loss from a 330 C sealed absorber. They also carried out CFD simulations for the cavity, simplifying the tubes by a plane surface. The results were presented through a correlation for natural convection (Nusselt versus Grashoff, based on the cavity depth dimension) and a correlation for radiation (view factor). These correlations assume that radiation convection interaction effects are negligible. Radiation modelling of the cavity showed that the effects of absorber tube geometry could not be neglected, leading to a radiative heat loss 25% higher than predicted by the cavity model with a plane absorber surface (Pye et al., 2003). Facao and Oliveira studied heat loss in a trapezoidal cavity of a linear Fresnel receiver using computational fluid dynamics. In their study, natural convection and radiation were examined using two geometrical parameters: receiver depth and insulation thickness. They found a cavity 45 mm deep represents the lowest global heat loss coefficient and 35 mm of rock wool insulation provides a good compromise between insulation and shading (Faca˜o and Oliveira, 2011). Singh et al. developed overall heat loss coefficient correlations for a trapezoidal cavity absorber by comparing pipe geometry (rectangular vs. round) and pipe coating (ordinary black coating vs. selective surfaces) at various absorber temperatures (up to 175 C). Selective surface coating on the absorbers reduced the overall heat loss coefficient by 20–30% relative to ordinary black paint (Singh and Sarviya, 2010). The present research, combines many aspects of outlined literature for the concentrating collector and investigates the role of radiation and natural convection heat transfer inside a trapezoidal cavity that protects the mirrors and absorber tube in a rooftop linear Fresnel collector. The objective of this work is to determine, through numerical and experimental means, the buoyancy-driven airflow generated in the collector cavity and the heat loss taking into account radiation in order to determine methods to increase collector efficiency. A CFD model representing these phenomena is developed and the results obtained for the air flow are compared with experimental results using particle imaging velocimetry (PIV). 2. Micro concentrating collector (MCT) system The geometry that we are focusing on in the work is a rooftop mounted system from Chromasun called an MCT which is shown in Fig. 1. The system module is 3.2 meters long by 1.2 meters wide and 0.3 m high. The MCT collector utilises linear Fresnel reflector optics that concentrate beam radiation to a stationary receiver. Each mirror array system consists of ten mirrors, which concentrate sunlight onto parallel absorber tubes. The mirrors are curved to generate a focus, with the inner six mirrors and
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outer four mirrors having a radius of 0.6 and 0.75 meters respectively. The receiver consists of two 16 mm diameter stainless steel absorber tubes. Each receiver has a secondary reflector that directs missed beam radiation to the absorber tube. The whole system is contained in a sealed glass envelop to minimise convective losses. The main heat losses are due to natural convection inside the enclosure and radiation heat transfer from the absorber tube. The design of the receiver is illustrated in Fig. 2. During operation, the hot absorber tube emits long-wavelength radiation into the cavity that is absorbed mainly by the glass and base surfaces which in turn heat up. These heated surfaces, along with the plume from the hot absorber tube, promote buoyancy-driven flows within the cavity resulting in convection losses to the environment and an associated reduction in thermal efficiency (Sultana et al., 2012). The generalised thermal analysis of a concentrating collector is similar to that of a flat plate collector. For a concentrating collector at steady state, the useful energy output is given by Duffie and Beckmann (2006): qu ¼ Ggo Aa Ar U L ðT r T a Þ
ð1Þ 2
where G is the solar irradiation (W/m ), go is the collector optical efficiency, Aa is aperture area (m2), Ar is the receiver area (m2), UL is the solar collector heat transfer loss coefficient related to the absorber area (W/m2 K), Tr is the temperature of the receiver (C) and Ta is the ambient temperature (C). 3. Laminar steady state flow A laminar steady state buoyancy model was developed for the MCT collector. In purely natural convection problems, the Rayleigh Number (Ra) indicates the relative strength of the buoyancy induced flow, and is given by: Ra ¼ Gr Pr
ð2Þ
where Gr is the Grashof number and Pr is the fluid Prandtl number. The laminar flow regime is generally characterised by Ra < 108, while turbulent buoyant flow is characterised by Ra > 1010 (Cengel and Ghajar, 2010; Zhou and Yang, 2009). The Rayleigh number for MCT receiver was calculated using Eq. (4); Ra ¼
gbðT abs T cover ÞL3 Pr #2
ð3Þ
where Tabs is the absorber tube temperature, Tcover is the glass cover temperature and L is the characteristic length. The Ra = 1.8 104 when the characteristic length, L = 16 mm used the diameter of the absorber tube and Ra = 2.7 107 when L = 300 mm used the height of the MCT collector. Therefore, the air flow in the MCT enclosure was modelled as laminar flow. Using Eq. (4) the Rayleigh number was found to be in the range of 1.8 104– 2.7 107 for air with absorber temperatures in the range from 50 to 200 C.
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Fig. 1. Cross-section of the MCT collector (dimensions in mm).
Fig. 2. Receiver design in the micro-concentrating collector.
4. Radiation model To calculate the surface radiative heat flux within the MCT collector, a Monte-Carlo method (Howell, 1968; Wang et al., 2010) was employed. The background of this method for radiative heat transfer calculations is based on the fact that the transfer process is divided into four subprocesses; i.e. emission, reflection, absorption, and scattering, and every sub-process has a probability of occurrence (Moffat, 1988). The object is divided into surface units and volume units. Every unit emits a certain quantity of light rays, after which every ray is tracked to determine whether it is absorbed by a medium or interface, or it escapes from
the system. Therefore, by tracking a large enough number of light rays it is possible to calculate the total radiation flux. In the present work, as there is only air in the cavity it is assumed to be non-participating so that scattering was omitted. The presence of dust in the cavity is ignored as the enclosure is nominally cleanly sealed. The surface to surface option was used for the calculations; volumetric emission, absorption and scattering are ignored regardless of the specified material properties. The absorber tube surface and all other cavity walls are assumed to have gray properties. First, the radiative heat transfer factor RDij was computed. RDij is defined as the percentage share that unit j takes of the energy radiated by unit i. In another words, RDij is the ratio of the number of light rays unit j gains from unit i to the number of light rays emitted by unit i. So it can be described as: RDij ¼
N ij Ni
ð4Þ
where Ni represents the total number of light rays emitted by unit i, and Nij represents the number of light rays emitted by unit i and ultimately absorbed by unit j. After the radiative heat transfer factor has been calculated, the full thermal simulation can be conducted. For a closed system that includes Ms surface units and Mv volume units, the energy equations of volume unit Vi and surface unit Si expressed as RDij are described as follows using algorithm by Moffat (1988):
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4ji V i rT 4i ¼
Mv X
4jj V j rT 4j RDji þ
j¼1
ei S i rT 4i ¼
Ms X
ek S k rT 4k RDki þ Qi
ð5Þ
k¼1
Mv Ms X X 4jj V j rT 4j RDji þ ek S k rT 4k RDki þ Qi j¼1
ð6Þ
k¼1
where j is the absorption coefficient, V is the volume unit (m3), r is the Stefan-Boltzmann constant (W/m2 K4), T is the temperature (K), RD is the radiative heat transfer factor, Q is the heat rate (W), e is the emissivity and S is the surface unit (m2). The MCT cavity is a closed system, with no volume absorption or internal heat source so the equations can be expressed as ei S i rT 4i ¼
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Ms X ek S k rT 4k RDki þ Qi
ð7Þ
k¼1
The accuracy of the Monte-Carlo method is dependent upon the number of dispatched energy rays and the extent to which the pseudo random number generator is actually ‘random’ (Shuai and Xia, 2008). Fig. 3 illustrates the convergence of the absorber radiative heat loss with number of rays traced with the Monte Carlo method, and shows invariance of the heat loss is apparent after approximately 100,000 rays. Convergence of the heat loss from top and side glass cover were also investigated for different number of rays. Fig. 4 shows that the heat loss from top and side glass covers converged after approximately 100,000 rays. This convergence sensitivity analysis illustrates that heat loss results from the CFD simulation depends on the number of rays chosen in the radiation model, but that results are independent of the number of rays chosen when 100,000 or more ray are used. Based on this analysis, the total number of rays used was 100,000.
Fig. 4. Glass covers heat loss as a function of number of rays used in Monte Carlo simulation.
5.2. Boundary conditions The absorber tube is modelled as an isothermal surface. The convective flow and resulting temperature difference between the absorber tube, the secondary reflector and glass cover are studied for various absorber temperatures. The absorber tube is coated with a black chrome selective surface, and the thermal emissivity is taken as 0.2 (Sultana et al., 2012). The outside of the cover glass at the top and sides of the cavity are modelled as convection boundaries with external heat loss coefficients of 12 W/m2 K, exchanging heat with an ambient temperature of 23 C (Sultana et al., 2012). The glass has an internal emissivity of 0.9. The end walls and aluminium extrusion side walls were modelled as convection boundaries with external heat loss coefficients of 10 W/ m2 K, calculated using a vertical rectangular plate correlation (Cengel and Ghajar, 2010), exchanging heat with an ambient temperature of 23 C. (Note: this approximates the experimental condition). All discretization was carried out using second-order schemes and temperature dependent air properties are calculated using an ideal gas model. Minimum convergence criteria were set at 103 for continuity and velocity, and 106 for energy (Sultana et al., 2013).
5. Three-dimensional modelling 5.3. Mesh 5.1. Geometry A three-dimensional CFD simulation model for combined natural convection and surface radiation was developed using ANSYS CFX. Due to the symmetry plane, only half the geometry was simulated as shown in Fig. 5.
Fig. 3. Absorber tube radiative heat loss as a function of number of rays used in Monte Carlo simulation.
A structured mesh (Fig. 6) was used for the cavity area. The shape of the receiver area is such that the use of structured elements creates regions of high mesh skewness and these regions are typically in regions where the flow is of greater interest. This will impact on the accuracy of the solution by increasing the numerical error and could lead to false features developing in the flow. Therefore, an unstructured mesh with inflation layer was used near the absorber tube (Fig. 7). The resulting mesh size is approximately 6 mm, with 2.3 million mesh points in total. A grid dependency study was undertaken to ensure the adequacy of this mesh density using 1 million, 2 million and 4 million mesh elements. It was found that the peak temperature in the cavity receiver with different mesh sizes shows minimal differences (<0.1%) and the bottom cavity and temperatures are <2 C different between the 2 and 4 million meshes (Fig. 8). Therefore, 2 million was considered a good compromise between computational time and accuracy.
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Fig. 5. Cavity geometry for 3D CFD modelling (a) 3D entire model (b) cross-sectional view in XY plan.
Fig. 7. Inflation layer near the absorber tube and secondary reflector. Fig. 6. A section of the computational grid for the complete 3D model of the MCT.
6. CFD results and discussion Heat losses from different surfaces for a 200 C absorber tube temperature are shown in Table 1. Due to the relatively low emissivity of the absorber’s selective coating, radiation heat loss at 200 C is 40–50% of the convective
heat loss (Fig. 9). The heat loss coefficient from the absorber tube was calculated as 9 W/m2 K at absorber tube temperature 200 C using Eq. (8). U abs ¼
Qabs Aabs ðT abs T a Þ
ð8Þ
where Uabs is overall heat loss coefficient of the absorber tube (W/m2 K), Aabs is the absorber tube area (m2), Qabs
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Fig. 8. Mesh dependency check for cavity temperature over the vertical line A–A.
Table 1 Heat loss for 200 C absorber tube temperature (absorber tube emissivity, eabs = 0.2). Boundary zone
Heat loss (W/m)
Glass top cover Glass side cover Base surface Side aluminium extrusion Aluminium extrusion top corner Silicon adhesive top Total boundary loss
31 30 3 1 2 6 73
Fig. 10. Temperature contours. (a) Velocity streamlines. (b) Near the receiver section (absorber tube temperature 200 C and absorber emissivity = 0.2).
tube to the cavity. An experimental comparison of this flow structure near the receiver is obtained with the flow visualisation experiment described below. 7. Validation of CFD model Fig. 9. Absorber heat loss for different absorber temperatures (Sultana et al., 2012).
is the absorber tube heat loss (W), Tabs is the absorber tube temperature (C), Ta is the ambient temperature (C). The total heat loss at 200 C is approximately 73 W/m length of tube compared to an expected solar input of approximately 300 W/m to 400 W/m length of the absorber tube. Temperature distributions near the receiver area in the collector are shown in Fig. 10(a). For the boundary conditions specified, the results show significant thermal gradients in the cavity only around the absorber and secondary reflector. Streamlines near the receiver are shown in Fig. 10(b) which indicate the hot fluid flow is rising up near the aluminium extrusion surface and spreading mainly under the top glass cover. Fluid flow around the absorber tube is entrapped by the secondary reflector which minimises the convection flow from the absorber
Although CFD techniques are widely accepted, such numerical models need to be validated against experiments in order to gain confidence in the results. The flow in the MCT cavity is driven by natural convection and the magnitude is relatively low, therefore a non-intrusive measurement technique is required. Particle image velocimetry (PIV) is an optical technique that measures the velocity field in a plane without disturbing the flow (Sultana et al., 2013; Sookdeo and Siddiqui, 2010). 7.1. PIV Experiments Due to the fact that unfettered optical access is required in the collector for both a camera and a laser light sheet, PIV measurements were constrained to three locations with the collector in the horizontal position. An electrically heated absorber tube was constructed to allow direct measurement of losses under laboratory conditions. For each
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location, measurements were taken with the absorber tube heater set to 50 W and 100 W for absorber temperature up to 100 C. The flow in three areas was measured; near the receiver section, along the side glass and at the symmetry plane as is shown in Fig. 11. The absorber tube surface temperature is a function of the ambient temperature and thermal resistance from tube surface to the ambient environment. Under steady-state temperatures, all the electrical power applied to the heating element is either lost as conduction through the top of the cavity or convection and radiation heat into the cavity (Sultana et al., 2013). 7.2. PIV technique The basis of PIV is to seed the flow being measured with small particles and to rapidly acquire images of the particles as they are moved within the flow. Since it is the particles, not the flow itself, which are being observed, it is important to select particles which will accurately track the flow (Raffel et al., 1998). A schematic of the PIV setup and the schematic of the apparatus is shown in Fig. 12. A New Wave Gemini dual-pulsed Nd:YAG laser with 532 nm output wavelength was used to illuminate the flow field via an articulated optics arm and a cylindrical lens. Images of the flow field were captured using a PCO SensiCam camera with a 35 mm lens. Di-Ethyl-Hexyl-Sebacat (DEHS) was atomized into small droplets <2 lm in diameter and injected into the collector using a seeding machine. An ILA synchronizer was used to synch the laser pulses with the camera images. To minimise internal reflections, the Fresnel mirrors were removed from the base of the collector. Black paper was taped where necessary to further reduce glare in the images. Image quality was also improved by covering the camera lens with a 532 nm bandpass filter to reduce the effects of external lighting. Optimal image pairs were obtained by pulsing the dual lasers at 4 Hz, with a pulse separation time of 15 ms for each image pair. Post-processing of the image pairs was performed using ILA’s VidPIV software. Using an interrogation window
size of 64 64 pixels, VidPIV’s “Average Cross-Correlation” algorithm was performed to generate an average cross-correlation of 40 image pairs for each measurement. The resulting vector maps were locally filtered such that any spurious vectors, as determined by comparison with surrounding vectors, were replaced by the average of the neighboring vectors. 8. Comparison of CFD and PIV: results and discussion The velocity vectors near the receiver obtained experimentally by PIV and numerically are along the line X–X are shown in Fig. 13. Measurements and simulations indicate that the hot receiver creates a thin, relatively high velocity buoyant layer of hot fluid along the aluminium support holding the secondary reflector. The maximum velocity predicted by the numerical model for the 100 C absorber tube (absorber tube heat loss, Qabs = 100 W) is 75 mm/s, compared to velocity of 70 mm/s obtained from the PIV measurements (Fig. 14). Differences in the order of 5 mm/s occur between PIV and CFD results with the measurements consistently showing lower velocity due to the slightly larger heat loss in the experiments compared to the CFD. The uncertainly of the PIV measurements was calculated according to Moffat (1988) and Raffel et al. (1998) and the uncertainly in the velocity measurement estimated as ±0.3 mm/s. It should be noted that over the course of multiple measurements, the DEHS seeding particles collected on all internal surfaces of the collector to form an oily film. This film was removed as necessary from the glass to maintain optical access, but it was not removed from the absorber tubes because any cleaning procedure was likely to have damaged the black-chrome selective surface coating. A build-up of a DEHS film increases the emissivity of these absorber tubes and could thus be one explanation for discrepancies between modelled versus experimental results. The velocity profiles near the side glass wall along line Y–Y in Fig. 15 are compared with the simulated results. In general, there is good agreement in the flow structure,
Fig. 11. PIV measurement tested area in the MCT cavity.
T. Sultana et al. / Solar Energy 112 (2015) 20–29
Fig. 12. Schematic of the PIV experimental setup.
Fig. 13. Airflow near the absorber tube, Qabs = 100 W, Tabs = 100C, (a) CFD, (b) PIV at a plane z = 0.7 m from one end of the absorber tube.
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T. Sultana et al. / Solar Energy 112 (2015) 20–29
Fig. 14. Comparison of velocity magnitude profiles near the absorber tube along line X–X in Fig. 13 obtained from CFD simulations and PIV measurements, Qabs = 100 W and Tabs = 100 C.
Fig. 16. Comparison of velocity magnitude profiles along line Y–Y (Fig. 15) on the side glass obtained from CFD simulation and PIV measurements, Qabs = 100 W and Tabs = 100 C.
Fig. 17. Air flow at the symmetry plane (a) CFD and (b) symmetry air flow from PIV measurement. Fig. 15. Velocity vectors along the side glass, Qabs = 100 W, Tabs = 100 C, (a) CFD, (b) PIV.
from the top glass boundary at the symmetry plane after to the two flows collide.
showing a thin layer of hot fluid is formed near the receiver, and it moves upwards creating a small region of recirculation near the receiver and flow moving downwards along the side glass (Fig. 15). The maximum velocity predicted near the side glass by the numerical model with a 100 C absorber tube is 21 mm/s, compared to velocity of 18 mm/s obtained from the PIV measurement (Fig. 16). Fig. 17 shows a comparison of the CFD and experimental flow structure near the symmetry plane. The measurements show the buoyant flow creates a layer along the upper glass cover moving from the absorber to the symmetry plane, with the fluid dropping down into the cavity
9. Conclusion This paper presents experimental measurements and numerical modelling of a micro concentrating solar collector. The performance was numerically simulated using computational fluid dynamics (ANSYS CFX). A numerical simulation of convective and radiation heat loss has been carried out for steady-state laminar conditions and the absorber tube heat loss obtained for up to temperature 200 C. The two-dimensional velocity field was measured using PIV inside the MCT collector. The PIV experiments were conducted for heated conditions at various absorber
T. Sultana et al. / Solar Energy 112 (2015) 20–29
tube temperatures that ranged from 70 C to 100 C and results validated with the CFD simulation. The results have shown that the receiver heating creates a thin relatively high velocity layer of hot fluid near the receiver area and PIV measurements shown a lower peak velocity than CFD model, due to the slightly larger heat loss in the experiments compared to the CFD. The main uncertainty in the CFD boundary conditions is the long wavelength emissivity which may have been affected by the seeding particles. Further investigation is needed into the use of PIV for inclined collector to investigate the longitudinal flow. It is shown that receiver section in the existing MCT collector is the main heat loss and affects the efficiency of the collector. Further CFD simulation can be carried out to investigate the flows in the receiver area by optimising the air gap between the absorber tube and secondary reflector and the glass cover. Also, further work can be carried out investigating the use of evacuated tube receivers. References ANSYS CFX Help Manual 12.1.
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