Geometry optimization of a nanofluid-based direct absorption solar collector using response surface methodology
Introduction
Solar thermal collectors are widely used to harness solar renewable energy for thermal energy applications. The most common of these are the conventional flat-plate surface collectors, which absorb solar energy through a black or spectrally selective solid surface. The absorber transfers heat via conduction to collector tubes and this energy is then transferred via convection to the circulating fluid inside the tube. However, thermal performance of these types of solar collectors is limited by the black surface absorption capacity and how effectively the heat is transferred to the working fluid. Many methods have been proposed to overcome the drawbacks associated with conventional solid surface collectors. One proposed approach is a collector in which the solar radiation is absorbed directly by the working fluid rather than in a very thin layer at the surface. Hence, in the so-called direct absorption solar collectors (DASC) thermal resistance in converting solar energy into heat is reduced. The concept of direct absorption was originated in the 1980s to simplify the flat-plate surface absorber design and to potentially enhance the thermal performance by direct radiation absorption within the fluid volume (Arai et al., 1984, Bohn and Green, 1989). Typical heat carrier fluids such as water, ethylene glycol, propylene glycol, and heat transfer oils used in solar collectors have been shown to have poor thermo-physical properties and very low absorptive properties over the solar spectrum. Among the four mentioned liquids, water is shown to be the best absorber of solar energy, but it is still a weak absorber, only absorbing 13% of the energy (Otanicar et al., 2009). Thus, seeding the base fluid with small particles that can absorb solar energy can enhance the thermal performance of the DASC system. The idea of seeding a liquid with black particles to absorb solar radiation was initially proposed by Minardi and Chuang (1975) where the black liquid was formed by dispersing Indian ink into ethylene glycol–water mixture.
With the development of nanotechnology in recent years, several types of nanoparticles have been synthesized and dispersed in typical base fluids. Compared with a medium dispersed with micro-scale or larger particles, the suspension with nanoparticles may be more stable. In addition, the clogging and fouling would be less significant for suspension with nanoparticles. Many researches have shown the improvement in radiative properties of base fluids by the addition of a moderately small amount (<1% by volume) of nanoparticles. Spectral transmittance and absorption of various nanofluids have been reported experimentally (Bertocchi et al., 2004, Mu et al., 2009, Sani et al., 2010, Mercatelli et al., 2011, Kameya and Hanamura, 2011, Han et al., 2011, Taylor et al., 2011a, Otanicar et al., 2013) and a number of researchers have investigated the nanofluids optical characteristics using mathematical theories such as Rayleigh scattering approach (Taylor et al., 2011a, Tyagi et al., 2009, Saidur et al., 2012), Maxwell–Garnett effective medium theory (Taylor et al., 2011a), and Mie scattering theory (Otanicar et al., 2013, Mahendia et al., 2011, Zhu et al., 2013).
Several experimental and numerical studies on direct absorption collectors have shown efficiency improvement by using nanofluids as the fluidic medium. In an early work, Tyagi et al. (2009) theoretically investigated the performance of a nonconcentrating direct absorption solar collector and compared it with that of a typical flat-plate collector. A mixture of water and aluminum nanoparticle showed up to 10% higher efficiency than that of a flat-plate collector. Experimental study on a direct absorption solar collector setup based on carbon nanotubes, graphite, and silver nanofluids demonstrated efficiency improvements of up to 5% (Otanicar et al., 2010). Taylor et al. (2011b) investigated the feasibility of using nanofluids in laboratory-scale concentrating DASC using graphite nanoparticles disperse in therminol VP-1. A 0.125% volume fraction of graphite resulted in approximately an 11% improvement in efficiency over the base fluid. Lenert and Wang (2012) experimental investigation on a concentrating solar absorption-column with graphite coated cobalt in therminol VP-1 nanofluid showed system efficiencies exceeding 35% in optimum conditions. The numerical simulation by Lee et al. (2012) estimated that gold coated SiO2 nanoparticle can enhance the DASC efficiency by 70% under a particle concentration of 0.05% by volume. Bandarra Filho et al. (2014) reported the photothermal conversion capability of water based silver nanofluids under realistic conditions. They observed up to 144% enhancement in the stored thermal energy for a nanoparticle concentration of 6.5 ppm. Luo et al. (2014) experiments on a concentrating direct absorption-column using texatherm oil showed photothermal efficiencies of nanofluids of 0.01 vol.% graphite and 0.5 vol.% Al2O3, are 22.7% and 17.5% higher, compared to a conventional coating absorbing collector. Parvin et al. (2014) theoretical study on a Cu–water nanofluid direct absorption solar collector showed enhanced heat transfer performance and entropy generation for volume fractions less than 3%.
The literature review hereinabove shows that most of the previous studies focused on photothermal conversion efficiencies of nanofluids in a predesigned DASC and did not consider any optimization analysis regarding the collector geometry. The objective of the present work is to evaluate the effect of varying geometry on the overall thermal performance a nanofluid based DASC. Box–Behnken design and response surface methodology are applied to study the main and interaction effects of the dimensions on the system overall thermal performance. An optimization analysis is performed to find the optimum geometry based on maximum thermal efficiency and minimum entropy generation.
Section snippets
Evaluation procedure
The evaluation procedure of the current study is shown in Fig. 1. The collector geometries are firstly arranged by the Box–Behnken factorial design. The collector efficiency and entropy generation rate are obtained for each design point by computational fluid dynamics (CFD) simulation. Then, response surface methodology (RSM) is applied to the collected simulation data to establish the functional relationships between three dimensions of the aqueous graphite nanofluid-based DASC. In RSM after a
Numerical model
In this work, the heat transfer and nanofluid flow characteristics in DASC are obtained by numerical simulation. This section presents the computational domain, governing equations, boundary conditions, solution methods, grid generation and model validation results.
Box–Behnken factorial design
In this study, the Box–Behnken factorial design was chosen to find out the number of numerical simulations. Box–Behnken design requires a number of experiments according to N = n2 + n + rn, where n is the variable number and (rn) is the replicate number of the central point (Aslan, 2007, Aslan and Cebeci, 2007). For the three-level Box–Behnken experimental design, a total of 15 numerical runs are needed. Independent variables and their coded/actual levels used in this study are listed in Table 1.
Response surface methodology
Numerical results
As shown in Fig. 1, to obtain the responses, CFD calculations are performed according to the design matrix generated by Box–Behnken factorial design. Collector dimensions were adjusted at the required levels as per the Box–Behnken design, whereas other operational parameters of the collector were kept constant (flow rate, solar intensity, nanofluid properties). Using the relationships in Table 1, actual levels of variables for each numerical run in the design matrix were calculated as given in
Summary and conclusion
In this study, a three-level Box–Behnken factorial design combining with a response surface methodology was employed for optimizing the dimensions of a nanofluid filled direct absorption solar collector. To predict the thermal efficiency and entropy generation rate within the collector, a numerical model was proposed by combining the radiative heat transfer in particulate media with conduction and convection heat transfer in the DASC. A three-level Box–Behnken factorial design was applied to
References (39)
- et al.
Development of a “volume heat-trap” type solar collector using a fine-particle semitransparent liquid suspension (FPSS) as a heat vehicle and heat storage medium. Unsteady, one-dimensional heat transfer in a horizontal FPSS layer heated by thermal radiation
Sol. Energy
(1984) Modeling and optimization of multi-gravity separator to produce celestite concentrate
Powder Technol.
(2007)- et al.
Application of Box–Behnken design and response surface methodology for modeling of some Turkish coals
Fuel
(2007) - et al.
Experimental investigation of a silver nanoparticle-based direct absorption solar thermal system
Energy Convers. Manage.
(2014) - et al.
Heat transfer in molten salt direct absorption receivers
Sol. Energy
(1989) - et al.
Enhancement of solar radiation absorption using nanoparticle suspension
Sol. Energy
(2011) - et al.
Optimization of nanofluid volumetric receivers for solar thermal energy conversion
Sol. Energy
(2012) - et al.
Performance improvement of a nanofluid solar collector based on direct absorption collection (DAC) concepts
Int. J. Heat Mass Transf.
(2014) - et al.
Performance of a “black” liquid flat-plate solar collector
Sol. Energy
(1975) - et al.
Optical properties of liquids for direct absorption solar thermal energy systems
Sol. Energy
(2009)