Long-term environmental impacts of a small-scale spectral filtering concentrated photovoltaic-thermal system

Energy Conversion and Management 184 (2019) 350–361

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Long-term environmental impacts of a small-scale spectral filtering concentrated photovoltaic-thermal system

T

Marcelo Rodrigues Fernandes , Laura A. Schaefer ⁎

Department of Mechanical Engineering, Rice University, Houston, TX 77005, USA

ARTICLE INFO

ABSTRACT

Keywords: Spectral filtering Concentrated photovoltaic thermal Long-term analysis Environmental impact

Recent years have seen a sharp increase in the range and implementation of solar energy conversion systems, with the goal of reducing fossil fuel dependence. One example is a concentrated photovoltaic-thermal (CPV-T) system that uses nanofluid-based optical filters, which can generate electricity and absorb heat from sunlight. Although spectral filtering CPV-T systems have been explored in the literature for power generation, they have not been investigated for domestic applications. In this work, dynamic simulations of a small-scale spectral filtering CPV-T system under the climatic conditions of Tucson, Arizona, are performed. The long-term simulations indicate that the proposed CPV-T system can offset a total of 1.317 tons of carbon dioxide (CO2 ) per year per household. If implemented in 10% of the households in the U.S., the total offset by the proposed system would be equivalent to the greenhouse gas emissions from 3.19 million passenger vehicles per year.

1. Introduction The current worldwide framework for energy production strongly relies on non-renewable sources for primary energy production, with energy from fossil fuels accounting for more than 80% of total primary energy production [1]. Over the past century, the scientific community and policy makers have been giving increasing attention to the effects of fossil fuel-based energy production on the climate [2,3]. Around the world, this has resulted in a gradual change in energy policies towards a greater development of renewable energy systems. Although most of the energy consumed in the United States is from fossil fuels, there is an increasing share of power utilization from renewable sources [4]. Over the past decade, the energy consumption from renewable sources, other than biofuels and hydro-energy, has grown over 80%, and this share in energy consumption is predicted to increase still further. Solar and wind power generation are projected to grow by 64% by 2050, leading the energy growth by renewables in the period [4]. The trend of increasing energy production by renewable sources, especially from solar photovoltaics, is expected to diminish the electricity-related carbon dioxide emissions in the United States by 12% by 2050 compared to previous projections, according to the Department of Energy [4]. The expansion of solar power generation in the United States and around the world has been accompanied by an increase in solar energy research. Recent research in solar energy includes experimental and

⁎

Corresponding author. E-mail address: [email protected] (M. Rodrigues Fernandes).

https://doi.org/10.1016/j.enconman.2019.01.026

Available online 02 February 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

theoretical investigations of hybrid solar photovoltaic-thermal systems (PV-T), including concentrated PV-T (CPV-T) systems, which can generate electricity and absorb heat at the same time, increasing the overall efficiency when compared to the individual systems [5]. More recent works on hybrid PV-T systems explore the use of liquid spectral filters with the intent of absorbing a specific range of wavelengths of the solar spectrum. These spectral filtering PV-T systems are generally divided in single-pass channel systems [6–8], and coupled and decoupled double-pass channel systems [9–13]. Pure fluid filters and fluids that contain nanoparticles have been investigated, where the latter can entail different combinations of nanoparticles and base fluids. Pure fluids such as water [14], heat transfer fluids [6,15], and natural oils [16] have been used in previous works. Most of the studies on PV-T systems with nanoparticle-based fluid filters include the use of metal [9,12] and metal oxide [10,11] particles. Investigations by Otanicar et al. [6] focused on the parametric analysis of a single-pass CPV-T system using a heat transfer fluid as an optical filter. The authors analyzed the effect of temperature and solar concentration on the thermal and electrical efficiency of the system. More importantly, in that work, the authors highlighted the potential of using heat transfer fluids with better spectral absorptivity. That group also investigated the spectral absorptivity of other pure fluids such as water, ethylene glycol, propylene glycol, and diphenyl oxide, and emphasized the use of nanoparticles in fluids to tailor its optical characteristics [14].

Energy Conversion and Management 184 (2019) 350–361

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Thin-film filters have also been investigated and compared to optical fluid filters applied to PV-T systems, considering the non-idealities of the filters [7]. That paper analyzed the effects of non-idealities inside and outside the transmittance window in reducing the overall system efficiency by reducing either the solar cell or thermal efficiency. That work also stresses the use of nanoparticles in fluids to absorb heat and transmit light at a reduced fluid thickness when compared to thin-film solid filters. Saroha et al. [9] developed a one-dimensional model of a coupled CPV-T system with spectral filtering. Gold and silver nanoparticles in water were used as the optical filter and the theoretical and experimental spectral absorbance of each nanofluid was compared. The thermal efficiency of the proposed model was found to be higher than that of a similar PV-T system in the literature, and this difference was argued to be due to the capability of the nanofluids to absorb specific wavelengths of the incoming solar radiation. The effect of the filter cutoff wavelengths on the thermal and electrical efficiencies of a CPV-T system has also been investigated [11]. By analyzing the temperature at the fluid filter outlet and the solar cell temperature at varying filter cutoff wavelengths, the authors observed that by using a filter cutoff length of 850 nm, the outlet temperature can be about 70 °C higher than that of the solar cell at a concentration ratio of 15. This operating point is desirable for power generation applications, since it provides a higher thermal efficiency with a considerably lower solar cell temperature. Decoupled CPV-T systems have also been studied by various researchers. Hassani et al. [12] analyzed the performance of a twochannel CPV-T system with optical filtering, where the temperature of the PV cell is decoupled from the temperature of the optical filter. The authors compared the performance of these systems with that of a coupled system and found that the gradient of the efficiency over solar concentration can be minimized using the system proposed, especially when concentration ratios are larger than ten. The decoupling of the temperatures allows the concentration ratio to be larger, since the coupling is limited by the temperature of the solar cell. Therefore, the system proposed has the potential to be used in higher solar concentration applications (i.e. larger than 100). The same authors also performed for the first time an exergy and environmental impact analysis of various decoupled CPV-T systems and compared them with typical CPV-T systems without optical fluid filters [13]. Besides comparing the electric and exergetic performance of the proposed and typical CPV-T systems, the authors analyzed their system’s payback time, energy savings, and reduction of pollutant emissions. The best performing system in the analyses had a payback time of two years, energy savings of 30 MWh per year, and prevented emissions of 448 kg of equivalent CO2 per meter square per year. Jing et al. [10] reported the fabrication procedure of silicon oxide nanofluids and performed a simulation in ANSYS of a double-pass CPVT system. The authors investigated the effects of the nanoparticles in the thermal conductivity of the fluid and calculated the spectral transmittance of the fabricated nanofluid for different volume fractions. Using this nanofluid as an optical filter, the authors observed that the exergetic efficiency of a nanofluid-based optical filter is always higher of that of water, obtaining an exergetic efficiency increase of up to 9.5%. An et al. [8] developed and experimentally validated a model for analysis of a nanofluid-based optical filter CPV-T system for power generation applications. In this work, the authors analyzed the role of the spectral splitting window on the heat to electricity ratio and found that for a system using Silicon solar cells, the optimal spectral window is between 700 and 900 nm. Furthermore, the authors analyzed the change in electrical efficiency for different flow rates considering that the optical fluid filter could operate at its maximum allowable temperature. The contribution of this work in experimental analysis is significant for the development of high temperature CPV-T systems for power generation.

Fig. 1. CPV-T system schematic.

In this article, the performance of a small scale CPV-T system with a nanofluid-based optical filter is investigated for domestic electricity generation and water heating. The yearly performance of the overall system is analyzed, as well as the energy savings and environmental impact of the proposed system. Although previous works have investigated the environmental impact and energy savings of similar systems [13], the long-term operation of CPV-T systems to formulate a more comprehensive proof-of-concept is rarely explored [5]. Therefore, the simulations and analyses presented in this work continue to advance the research on CPV-T systems with nanofluid-based optical filtering. 2. System description and modeling 2.1. System design The design of the system analyzed in this work was inspired by similar work in the literature [9,6]. Fig. 1 depicts the construction of the system. The system is composed of two separate channels that are connected through a loop. The fluid in the primary channel serves as a coolant to the photovoltaic cell, with the intent of maintaining the efficiency of the solar cell at reasonable levels. The outlet of the primary channel is connected to the inlet of the secondary channel, where the fluid works as an optical filter. The fluid in the secondary channel will absorb the solar radiation according to its spectral transmittance, or absorbance. Glass slabs are used in this design to permit transmission of solar radiation to the secondary channel and solar cell. Two air gaps, shown in Fig. 1, are used to reduce heat exchange with the ambient air (top air gap) and the fluid in secondary and the solar cell (bottom air gap). An insulator is placed on the bottom of the primary channel to reduce heat exchange with the ambient air. In Fig. 1, the subscripts g1, g 2, and g3 mean glass 1, glass 2, and glass 3. Therefore, Tg1, top is the temperature of the top of glass 1. The subscripts p , s , and ins mean primary channel, secondary channel, and insulator, respectively. The overall system design is shown in Fig. 2. In this work, it is assumed that a linear Fresnel concentrator is used to concentrate light along a region of width W and length L. The width, W, is defined in the system as the width of a solar cell, 156 mm. The length of the system is analyzed and defined in the Results section. The view shown in Fig. 1 is described in Fig. 2 along the length L. Although the heat transfer model used in this work is only two-dimensional, the width of the CPV-T system is used to calculate the rates of heat transfer in the simulations. 351

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The extinction coefficient for a nanofluid depends on the extinction coefficient of both the nanoparticles and the base fluid, and is given by [18]: ext

=

particles

+

(3)

basefluid

where basefluid and particles are the extinction coefficient of the base fluid and of the nanoparticles, respectively. For the particles, the extinction coefficient can be calculated using Eq. (4) according to Taylor et al. [18]: particles

basefluid

Table 1 Physical system parameters.

Other parameters (mm) Width of the system, W Diameter of primary channel Diameter of secondary channel Air gap distance

5.0 0.5 5.0 50 156 10 10 10

basefluid

(5)

m2 1 m2 + 2

+ 4 p·Im

2 p

m2 1 15 m2 + 2

2

m4 + 27m2 + 38 2m2 + 3 (6)

Qsca =

8 3

4 p ·Re

m2 1 m2 + 2

2

(7)

where m is the relative complex refractive index of the nanofluid. From Eq. (7), one can observe that the scattering of light by nanoparticles can be neglected when compared to the absorption, assuming Rayleigh scattering approximation, since it depends on p4 . The values of the refractive index m and index of absorption basefluid were obtained from the literature for water [19], ethylene glycol [14,20], gold [21], and silver [21]. The optical filter model was compared with results from the literature. Fig. 3 depicts the comparison of the model present in this work and a reference model [9] for the transmittance of a gold nanofluid. For this comparison, the base fluid is water and parameters such as the volume fraction and size of particles were taken from the reference model. The results obtained from the optical filter model match well with the results in the reference model. The mismatch observed in Fig. 3 is due to the differences in the refractive index data source used in the

The absorption of light by nanoparticles can be derived from Mie theory and Rayleigh scattering, where the choice of model depends on the diameter of the particle compared to the wavelength of interest [17]. In this work, the Rayleigh scattering approximation is valid, as will be explained in this section. Using this approximation, the spectral absorbance and transmittance of a nanofluid can be obtained and integrated into the heat transfer and electrical models. The Rayleigh scattering approximation can be used when the particle size parameter ( p ) is much less than unity [17]. The particle size parameter can be calculated as [17]:

D

=4

Qabs = 4 p·Im

2.2. Rayleigh scattering approximation

=

(4)

where basefluid is the index of absorption of the fluid. Assuming the Rayleigh scattering approximation is valid, the absorption and scattering efficiencies for the nanoparticles are given by the following equations [17]:

The thickness of each conductive layer and the width and diameter of the fluid channels shown in Figs. 1 and 2 are listed in Table 1. The solar cell material is silicon, the metal plate under the solar cell is made of aluminum, and fiberglass plates are used as insulators. The thermophysical properties of these materials are described in the Appendix.

p

3 fv (Qabs + Qsca ) 2 D

where fv is the volume fraction of nanoparticles, and Qabs and Qsca are the absorption and scattering efficiencies, respectively. The extinction coefficient of the base fluid is given by [18]:

Fig. 2. Overall system design.

Thickness (mm) Glass (1, 2, and 3) PV cell Metal plate Insulator

=

(1)

where D is the diameter of the particles, and is the wavelength of the incident radiation. Since the solar spectrum ranges approximately from 250 to 2500 nm in wavelength and the particle diameter used in this work is 10 nm, the Rayleigh scattering approximation can be used. The amount of radiation transmitted through a nanofluid can be calculated once the extinction coefficient of the fluid ( ext ) is obtained [17]:

It = Ii exp(

ext · h )

(2)

where It is the transmitted radiation intensity, Ii is the incident radiation intensity, and h is the pathlength of the sample or channel. From Eq. (2), a higher extinction coefficient and sample thickness will transmit less of the incident radiation. The ratio It / Ii represents the spectral transmittance of the nanofluid (T).

Fig. 3. Transmittance of the nanofluid composed of water and gold particles. Reference data from [9]. 352

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reference model and in this work. In summary, this comparison demonstrates the ability of the optical filter model in this work to predict the transmittance of nanofluids. The optical transmittance of a nanofluid is usually calculated in the literature throughout the solar spectrum [9] to provide a good match between the solar cell spectral response and the optical filter absorption spectrum. This approach is also used in this work, although a bulk transmittance for the optical filter must be calculated to be later used in the heat transfer model. This is due to the heat transfer model utilizing solar heat flux as a lumped energy input, and not accounting for the solar heat flux for each wavelength of the spectrum. The choice for using solar heat flux as a lumped energy input is due to the heat transfer model accounting for climatic parameters, such as the lumped solar heat flux. The procedure of obtaining the bulk transmittance considers a standard direct and circumsolar spectrum used in photovoltaic applications [22]. Sunlight is transmitted by two glass slabs (glass 1 and 2) before passing through the optical filter, where the bulk transmittance of glass is taken as 0.9 [9]. Using the spectral transmittance of the nanofluid, as shown in Fig. 3, the solar spectrum is reduced and the energy available before and after the optical filter can be calculated. The bulk transmittance of the optical filter, therefore, is obtained based on the ratio of the available energy after the optical filter over the available energy before the optical filter.

this work was taken from [27], and is the ratio of the number of photons used for electricity conversion to the number of photons received by the solar cell [24]. The photon flux represents the available energy that can be converted in the PV cell [25]. The open circuit voltage, which is the voltage at which there is no current through the diode, can be calculated in Volts as follows [24]:

FF =

exp

Tc2 (Tc + g )

pv

g

0.25µm

eVmax kB Tc

1

eVoc kB Tc

1

(12)

eVmax kB Tc

1+

eVmax I = C sc + 1 kB Tc I0

(13)

(8)

Eg (9)

mkB Tc

e ·QE · · F d

=

Voc ·Isc ·FF incident solar power

(14)

where the incident solar power that is delivered to the solar cell is the reduced solar power after absorption by the glass slabs, and the optical fluid filter. The resulting cell efficiency calculated in this section is then used in the heat transfer model. The electrical model was validated against experimental data from the National Renewable Energy Laboratory (NREL) [28] and the results are depicted in Fig. 4. In that experiment, Silverman et al. tested the solar cells at NREL’s Outdoor Test Facility in Golden, Colorado, where they analyzed the effects of the cell temperature on Isc , Voc , and FF under solar irradiance between 950 W·m 2 and 1000 W·m 2 . The results were then normalized to a solar irradiance of 1000 W·m 2 and the temperature coefficients were obtained. For this validation, the transmittance of the nanofluid was set to 1, in the photovoltaic cell model, since the experiments were performed on a single solar cell directly exposed to solar radiation. Furthermore, a solar flux identical to the one used in the experiments (1000 W/m2 ) is

where K is an empirical parameter, Eg is the energy gap in eV, kB is the Boltzmann constant in eV/K , and m and n are empirical parameters that depend on the quality of the diode. The value of K is 0.03 [23], and m and n are equal to 1.15 and 0.96, respectively [12]. The short-circuit current, which is the maximum current when the voltage across the diode is zero, can be expressed in amperes as [9]:

Isc =

( ) exp ( )

exp

and C is the light concentration ratio. The solar cell efficiency can, therefore, be calculated as [23]:

where Tc is the solar cell temperature in K, Eg (0) is the bandgap of the solar cell at a reference temperature, and and g are the empirical parameters shown in Table 2 [26]. The dark saturation current, which is the diode leakage current when there is no light, can be calculated using the following expression [23]: 3

Vmax 1 Voc

where the maximum voltage Vmax is given by the following expression [23]:

The electrical model used in this work was developed based on previous work in the literature [23,24,9]. The bandgap of a solar cell, Eg , is defined as the minimum energy required for an incident photon to be absorbed by the solar cell and be converted into electricity and heat [25]. This energy gap can shift depending on the temperature of the diode, according to the following expression [23]:

I0 = K Tcn exp

(11)

where is the diode factor, considered as unity [23]. Another necessary parameter is the fill factor (FF) of the solar cell. The fill factor is the ratio of the actual maximum power that can be obtained by the solar cell to the maximum theoretical solar cell power considering the open circuit voltage and short-circuit current [24]. This ratio can be calculated as [23]:

2.3. Photovoltaic cell model

Eg = Eg (0)

kB Tc I ln sc + 1 e I0

Voc =

(10)

where e is the electron charge in coulombs, QE is the spectral quantum efficiency of the solar cell, is the spectral transmittance of the optical filter, and F is the photon flux. The spectral quantum efficiency used in Table 2 Solar cell energy gap parameters. Material

Eg (0) (eV )

Silicon

1.1557

(K )

(eV·K 1) 7.021 × 10

4

1108

Fig. 4. Validation of the electrical model. Experimental data from [28]. 353

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M. Rodrigues Fernandes and L.A. Schaefer

considered. The results obtained from the electrical model described in this work match well with the data from experiments. Overall, the electrical model slightly underestimates the electrical efficiency in the range analyzed, especially at low cell temperatures. This underestimation could be related to the empirical parameters used in Table 2, as they determine the shift in bandgap with temperature for a silicon cell. Fig. 5. Control volume over the top surface of glass 1.

2.4. Thermal model

Eqs. (15) and (16) describe the energy balance on the top and bottom surfaces of glass 1. Eqs. (17) and (18) describe the energy balance on top and bottom surfaces of glass 2. The energy balance applied to the secondary channel yields Eq. (19), where Ts is the temperature in the secondary channel, and the rate of radiative heat transfer, Qrad,4 , is partially absorbed by the fluid, due to the fluid being a participating medium [29]. Similarly, the rate of solar radiation CGAeff is also reduced through the optical fluid filter, noted by (1 f ) in the same equation. Eqs. (20) and (21) describe the energy balance on the top and bottom surfaces of glass 3, respectively. The energy balance of the paired solar cell and metal plate are described by Eq. (22), where the efficiency of the solar cell pv is obtained by the electrical model. In the heat transfer model described here, all of the solar radiation is considered to have been absorbed by the paired solar cell and metal plate. Because the heat transfer model requires the solar cell efficiency that, in its turn, depends on the temperature of the solar cell, the process of obtaining the system temperatures requires an iterative approach. Eq. (23) describes the energy balance on the primary channel, where Tp is the temperature in the primary channel. The last two equations (24) and (25) describe the energy balance on the top and bottom surfaces of the insulator. The energy balance Eqs. (15)–(25) were rewritten in terms of the heat transfer coefficients and thermal conductivities, and solved simultaneously using MATLAB. Another important parameter in the CPVT system is the thermal efficiency. The thermal efficiency of the system is the ratio of the energy absorbed by the nanofluid to the input energy, and can be calculated using the following expression [30]:

2.4.1. Heat transfer model The heat transfer model used in this work was developed using a control volume analysis, where energy and mass are conserved. Each physical surface in the system, e.g. the top and bottom surfaces of the glass slabs and insulator, was considered within the boundaries of a control volume, as shown in Fig. 5, except for the solar cell and metal plate. The solar cell and metal plate were considered to be one layer of the system. The lumped analysis assumed for the solar cell and metal plate was verified by using a lumped capacitance method. In Fig. 5, the rate of heat transfer through convection, radiation, and conduction are represented by Qconv , Qrad , and Qcond , respectively, as well as the rate of heat transfer due to concentrated solar radiation, CGAeff . The rate of radiative heat transfer between the top of glass 1 and the environment is represented by Qrad,1, and between the top of the glass and the sky is represented by Qrad,2 . The temperature of the sky, in this model, is taken as the temperature of the ambient minus 4 °C [11]. The rate of heat transfer due to convection between the top of the glass and the environment is represented by Qconv,1. The effective area of heat transfer, Aeff , is the equivalent area of heat transfer due to discretization. The application of the steady-state first law of thermodynamics to this control volume yields the expression shown in Eq. (15). The same procedure was applied to the control volumes for all of the surfaces shown in Fig. 1, and Eqs. (16) to (25) describe the compact version of these equations. In these equations, the subscript i refers to the current node, and i + 1 and i 1 represent the next and previous nodes, respectively. Control volume equations used in the heat transfer model

(Qconv,1 + Qrad,1 + Qrad,2 + Qcond,1)i

Q(cond, i

1)

+ Q(cond, i + 1)

th

CGAeff = 0 (15)

(Qconv,2 + Qrad,3 + Qcond,1 )i

Q(cond, i + 1) + Q(cond, i

g CGA eff

1)

Qcond,2 )i

Q(cond, i + 1) + Q(cond, i

1)

g CGA eff

1)

2 g CGA eff

=0

=0 (17)

(Qconv,3 + Qrad,4 + Qcond,2 )i + Q(cond, i + 1)

Q(cond, i

+

=0 (18)

[Qconv,3

Qconv,4 + (1

f ) Qrad,4 ]i + mcp (Ts, i

1

Ts,i ) + (1

f)

2 g CGA eff

=0

(19)

(Qconv,3 +

f

Qrad,4

Qcond,3 )i

Q(cond, i + 1) + Q(cond, i

1)

+

2 f g CGA eff

=0 (20)

(Qconv,5 + Qrad,5

Qcond,3 )i

Q(cond, i + 1) + Q(cond, i

1)

+

3 f g CGA eff

1)

+(

1)

=0 (21)

(Qconv,6 + Qrad,5 + Qrad,6 + Qcond,5 )i + Q(cond,i + 1)

Q(cond, i

pv

3 f g CGAeff

=0

(22)

[Qconv,6 (Qconv,7 +

Qconv,7 + (1 f

Qrad,6

(Qconv,8 + Qrad,7

f

) Qrad,6 ]i + mcp (Tp, i + 1

Qcond,6 )i

Tp, i) = 0

Q(cond, i + 1) + Q(cond, i

Qcond,6 )i + Q(cond, i + 1)

Q(cond, i

1)

1)

=0

=0

mcp (Ts, out CGA

Tp, in ) 2 glass

(26)

where cp is the specific thermal capacity of the fluid, m is the mass flow rate of the system, Ts, out is the outlet temperature in the secondary channel, and Tp, in is the inlet temperature in the primary channel. The transmittance of the glass slabs 1 and 2 also needs to be included in this expression, since the glass slabs absorb and reflect part of the solar flux. The two-dimensional heat transfer model was validated against data on CPV-T systems in the literature. Zondag et al. [31] described the yield of various PV-T systems, including a set up that is similar to the one used in this work, and will be referred to as the reference model. The reference model developed by Zondag et al. considers an ambient temperature of 20 °C, solar irradiance of 800 W·m 2 , wind speed of 1 m·s 1, water mass flux of 76 kg·m 2·h 1, and a collector angle of 45°. All of these parameters and others such as the thickness of the cover and solar cell glass, as well as the width of the fluid channel and air layer were set to the same values in the model developed in this work during the validation procedure. One difference between the heat transfer model present in this work and the reference model is the control volume approach. In this work, the physical dimensions that compose the heat transfer area are important, whereas the model used as the reference considers all the heat exchanges as heat fluxes, and only the length of the collector is given. For that reason, the reference model utilizes mass flux instead of mass flow rate. This difference causes the two models to not be perfectly comparable, since the model in this work utilizes mass flow rate, but the reference model was used as a base for validation. The parameters used in the validation are the same as those used in the reference

(16)

(Qconv,2 + Qrad,3

=

(23) (24) (25) 354

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according to data obtained in the literature [32]. If there is water usage at the current iteration, the algorithm checks if the temperature in the tank is higher than the water temperature that is desired, which is 49 °C (120.2 °F) [33]. If this is positive, the cycle repeats normally with energy being transferred from the tank to the water. If this is negative, the system registers a failure in providing hot water. A thermal storage unit was selected from available commercial options, the choice of which both depends on the system year-long performance and environmental impacts. Therefore, the selection of the thermal storage unit is described in more detail in the Results secion. The pump chosen for the system is a Micro High Temperature Metering Pump Model 531 from Analytical Scientific Instruments and its maximum power consumption is estimated by the manufacturer as 60 W [34]. The pump can provide mass flow rates from 0 to 1 gallon per minute and withstand temperatures up to 200 °C, according to the manufacturer. During the simulations, it was assumed that the pump works at its peak capacity whenever the system is running. Similar to the approach used in the heat transfer model, the heat transfer calculation in the DWH model is based on a control volume analysis. The equation that describes the energy balance in the thermal storage tank can be written as:

Fig. 6. Outlet flow temperature compared to the inlet flow temperature.

model. The validation results are shown in Fig. 6. In this figure, the temperature exiting the system is compared to the inlet temperature of the system at given conditions. Although the validation matches well, with an error margin of 5%, the model in this work accounts for more heat losses than the reference case. This higher heat loss is due to the differences between the two models, namely the rate of heat transfer used in this model compared to the heat flux used in the reference model, and the mass flow rate used in the model compared to the mass flux used in the reference model.

dEtank = Ein, CPV dt

Eout , CPV

T

T

Eout , DWH

(27)

where Etank is the energy in the tank at an instant t , Ein, CPV T and Eout , CPV T are the rate of energy coming in and out of the tank from the CPV-T system, respectively, and Eout , DWH is the rate of energy exchanged with the water in the DWH system. The rates of energy related to the CPV-T and the DWH system can be calculated using Eqs. (28) and (29):

ECPV

2.4.2. Domestic water heating model The simulations developed in this work consider that the CPV-T system is utilized for domestic water heating (DWH). The DWH model is composed of a thermal storage tank, a pump for recirculation of the fluid, and a heat exchanger that further heats the water to the desired temperature. The temperature in the tank is calculated based on the output from the heat transfer model, the heat losses in the tank, and the heating of the water. The algorithm for domestic water heating is described in Fig. 7. The temperature of the flow out of the secondary channel in the heat transfer model is input into the DWH model, and at the current iteration the system checks if there is hot water consumption at that time

T

= mcp TCPV

Eout , DWH =

(28)

T

mDWH cp, water (Thot HX

Tcold ) (29)

where mDWH is the mass flow rate (i.e., consumption) of water during the simulation time, and cp, water is the specific thermal capacity of water, considered to have a constant value of 4.2 kJ/kg K . Eq. (28) is applicable to both the rate of energy in and out of the tank. For the rate of energy going out of the tank, TCPV T = Ttank . For the rate of energy coming into the tank, TCPV T = Ts, out . Thot and Tcold are 49 °C and 20 °C, which are the hot water temperature recommended by ASHRAE and the assumed tap water temperature, respectively. The heat exchanger is considered to have an efficiency, nHX , of 90%. 2.4.3. Climatic data The climatic parameters used in the simulations include ambient temperature, solar flux, and wind speed. This data is available hour-byhour through NREL [35] for various locations in the United States. The analyses performed consider that the CPV-T system will be implemented in Tucson, Arizona, due to the higher solar irradiance of that region [22]. As an example of the data used in the simulations, Fig. 8 depicts the ambient temperature and wind speed during a whole year in Tucson. 2.4.4. Calculation of the environmental impact The environmental impact of the proposed CPV-T is measured in terms of its Global Warming Potential (GWP) and compared with a household where electricity is consumed through the grid and water heating could be obtained using electricity or natural gas as fuel. The carbon dioxide emissions are estimated according to the Greenhouse Gas Equivalencies Calculator, provided by the United States Environmental Protection Agency (EPA) [36]. According to the EPA, 1 kWh of electricity consumed from the grid in the United States is equivalent to 0.0007 tons of carbon dioxide (CO2 ) emitted to the atmosphere. The same analysis can be made for the case of using natural

Fig. 7. Algorithm for the domestic water heating model. 355

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Fig. 8. Ambient temperature and wind speed data for Tucson, Arizona. Climatic data obtained from [35].

gas as fuel. For natural gas, 1 million cubic feet (MCF ), which is equal to 293 kWh of energy, is equal to 0.055 tons of equivalent CO2 . Therefore, 1 kWh of energy from natural gas is equivalent to 1.877 × 10 4 tons of CO2 . The calculations of the impact of the proposed system are described in the Results section.

Fig. 9. Spectral transmittance of gold, silver, and platinum nanoparticles in ethylene glycol for different volume fractions and a channel thickness of 6 mm. Table 3 Parameters of the selected nanofluid filter and channel. Nanoparticle material Base fluid Volume fraction

3. Results 3.1. Nanofluid optical filter

Channel height

First, the characteristics of the candidate nanofluid optical filters are evaluated and the best filter is selected. The choice of an optical fluid filter is dependent on the material of the solar cell used in the system, and on the desired transmittance of the fluid filter. The material of the solar cell is important because it determines the transmittance window that one would like to achieve. In this work, the solar cells are made of silicon, which has a bandgap energy of 1072.8 nm (1.1557 eV ) [26]. The ideal spectral window was defined as in previous works [9], and considered to be between 0.8 µm and 1.1 µm . Although this spectral window is merely a representation of the real non-linear spectral window of silicon solar cells, it serves as a basis for comparing the applicability of different nanoparticles as optical filters. Gold, silver, and platinum nanoparticles in ethylene glycol were considered in this analysis, and the spectral transmittance of these nanofluids at different volume fractions is shown in Fig. 9. The ideal spectral response of the silicon solar cell is also represented for comparison. The results displayed in Fig. 9 show that gold nanoparticles have an overall shorter spectral transmittance window, and represent a better match compared to the ideal filter, with silver being the second-best candidate for ideal filter fit. At a same volume fraction ( fv ), however, silver nanoparticles have a slightly higher transmission than gold nanoparticles. Moreover, Fig. 9 shows that there is a minimum volume fraction that should be considered for all of the nanoparticles. Volume fractions lower than 5.0 × 10 5 significantly increase the transmittance outside of the ideal filter window, and therefore should be disregarded. A volume fraction of 10 × 10 5 shortens the spectral window closer to the ideal filter window, while maintaining considerably high transmittance inside the windows. This volume fraction, therefore, is used in the simulations of the CPV-T system. Since gold nanoparticles offer the shortest window of transmittance, compared to silver and platinum nanoparticles, they will be used for the CPV-T system analysis. The parameters of the nanofluid used in the CPV-T system are described in Table 3.

Parameters

Gold Ethylene glycol

1.0 × 10 6 mm

4

3.2. Long-term analysis The selection of the system parameters, such as mass flow rate, length of the collector, and concentration ratio of the linear Fresnel lens, was based on a parametric analysis of the proposed CPV-T system. The temperature of the fluid at the outlet and the average temperature of the solar cell were analyzed, as well as the solar cell and thermal efficiencies. The parametric analysis revealed that the increase in mass flow rate increases the system thermal efficiency, while reducing the outlet temperature of the fluid. The opposite occurs with an increase in the length of the system. An increase in the length of the system promotes a higher temperature at the outlet, while reducing the thermal efficiency of the system due to the increase in heat loss area. The concentration ratio also increases the outlet and solar cell temperature, due to higher heat flux availability. Moreover, the increase in concentration ratio can decrease the thermal and electrical efficiencies. The diminishing thermal efficiency is related to the modest increase in outlet temperature with increased solar concentration, whereas the decrease in electrical efficiency is related to the solar cell temperature increase. However, the year-long simulation of the proposed CPV-T system provides a better understanding of the capacity of the system in producing electrical energy and heat under variable climatic conditions. The pump used in the CPV-T system is described in Section 2.4.2, and has a maximum power of 60 W. Initially, a commercial thermal storage tank from GSW, model G680TDE-30 [37], was selected for the DWH model. The stand-by heat loss is estimated by the manufacturer as 78 W, and the tank volume is 287 L. However, a heating failure analysis should be performed for selection of a more suitable storage tank. A failure of the system is characterized by a lack of high enough temperatures in the tank to provide heating to the DWH system. The number of failures, therefore, is a simple representation of the reliability of the CPV-T system in providing domestic hot water. In this 356

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Table 4 Selected system parameters. Concentration ratio Collector length Mass flow rate

Parameters

10 4.0 m 0.01 kg/s

Fig. 11. Tank temperature during the month of September.

Fig. 10. Tank temperature and failures at different tank volumes.

analysis, the 287 liter tank from GSW was compared to a larger 500 L tank currently not manufactured by the company. The heat loss for the 500 L tank was extrapolated from the stand-by loss provided by the manufacturer [37], and the value obtained was 120 W. The selection of system parameters such as concentration ratio, collector length, and mass flow rate considered the performance of the system at a range of values, which were compared using a parametric analysis. The selected system parameters are shown in Table 4. Fig. 10 describes the temperature in the tank and failures associated with different tank volumes. The temperatures in the tank fluctuate throughout the year, depending on the consumption of domestic hot water, ambient temperature, and solar flux. The percentage of failures using the 287-L tank is 2.17%, whereas using the larger tank the percentage of failures is only 0.71%. Therefore, the tank volume for the proposed CPV-T system is set at 500 L. The thermal storage unit used in the proposed CPV-T system has considerably larger volumetric capacity compared to tanks used in conventional solar DWH systems. The Department of Energy [38] recommends a thermal storage unit for a residential solar DWH system of approximately 80 gallons, or 304 L, for a family of four. However, this recommendation assumes that there is a backup water heater connected to the DWH system. In the proposed CPV-T system, a backup water heater is not considered and, therefore, a larger thermal storage unit is required. As described before, for a 287-L tank, the failure rate is 2.17%. This failure rate could be negligible if the proposed CPV-T system contained a backup water heater while using the smaller, 287-L thermal storage unit. The temperature in the tank depends strongly on the solar flux available, as expected from a solar collector. The considerable drops in the tank temperature seen in Fig. 10 are associated with lower solar flux while hot water is still being consumed for domestic use, as shown in Fig. 11. In this figure, the solar flux and tank temperature during the month of September are depicted. The temperature in the thermal storage drops considerably when the solar flux is reduced, especially in the first two weeks of the month. As soon as the solar flux is increased, the temperature in the tank also grows, as seen approximately in the middle of the month of September. Fig. 12 shows the energy produced by the solar cells and the energy in the tank during approximately 10 days in the summer. The amount of energy stored in the tank is significantly higher than the energy generated by the solar cells, which can be explained by the limited quantity of solar cells in the CPV-T system. Also, the shift in energy production by the PV cells and the energy in the thermal storage unit are depicted

Fig. 12. Energy stored in tank and energy produced by solar cells during 10 days in the summer.

in Fig. 12. The energy generation by the solar cells occurs as soon as solar flux is available, whereas the energy in the tank changes gradually during the days, and decreases when there is no solar flux, due to the thermal losses in the tank. The energy stored in the tank is calculated according to Eq. (27). The energy produced by the solar cells is calculated from the power generated in all the solar cells in one hour. The energy stored in the tank is two orders of magnitude larger than the energy produced by the solar cells, and this difference is due to the small number of solar cells (26 cells) in the proposed CPV-T system. The use of linear Fresnel lenses, as shown in Fig. 2, limits the number of solar cells that can be used in the system since the photovoltaic cells are required to be connected in a linear fashion. Increasing the electric power generation, therefore, would require the use of a different type of lens, or a different arrangement of linear Fresnel lenses. The efficiency of the solar cells varying with the solar cell temperature is shown in Fig. 13. The values shown in this figure are from

Fig. 13. Efficiency and temperature of solar cells during 21 days in the spring. 357

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use 33.9% of energy from electricity, and 66.1% of energy from natural gas. Thus, the proportional offset of emissions by the proposed system is equal to 1.317 tons of CO2 equivalent per year. If 10% of the households in the United States, or approximately 11 million [40], utilized the CPVT system proposed in this work, a total of 14.49 million tons of CO2 emissions per year could be avoided, compared to the average water heater assumed. This total of carbon dioxide emissions is equivalent to the greenhouse gas emissions from 3.19 million passenger vehicles per year, the total CO2 emissions from 1.61 million homes per year, or the CO2 emissions from 3.7 coal-fired power plants in one year [36]. All of the equivalencies described here assume an average electric grid profile across the United States. Fig. 14. Thermal efficiency and system temperatures during 25 h in September.

4. Conclusions and future directions

mid-March to mid-April, over a total of 21 days. The solar cell efficiency changes up to 2% in a day during that period, caused by the change in solar cell temperature throughout a day. The temperature of the solar cell depends directly on the incoming solar flux, and is calculated at every hour. Therefore, the temperature of the solar cell could possibly vary significantly during a day depending on the solar flux. Moreover, the larger changes in solar cell temperature throughout the whole period are reflected in the efficiency of the solar cell during that same period, in an inverse proportion. Throughout the whole year, the average efficiency of the solar cell was 18.58%, which is comparable to experimental studies in the literature [28]. The influence of the temperatures in the tank (Ttank ), CPV-T (TCPV T ), and environment (Tamb ) on the thermal efficiency is shown in Fig. 14. The results displayed in this figure represent the values of the simulation during 25 h in September. The temperature exiting the CPV-T has a similar shape to the solar flux at those hours, since the solar irradiance is the source of energy for the system. The temperature in the tank varies according to the temperature coming from the CPV-T, and increases gradually up to a maximum point seen around 7 p.m. This gradual increase depends on the volume of the tank and the temperature in the tank in the previous hour. The temperature in the tank decreases after reaching a maximum during that day, which is caused by the stand-by thermal losses of the tank. The temperature of the tank and from the CPV-T have a strong effect on the thermal efficiency of the system. The thermal efficiency of the system around 8 a.m. is close to 45%, and decreases from that hour until the end of the day. This diminishing of the efficiency is related to the smaller temperature difference between Ttank and TCPV T at every following hour, due to the increase in tank temperature.

4.1. Conclusions The development of a simulation for a CPV-T system with a nanofluid-based optical filter provides a better understanding of the longterm performance and the reliability of these systems. The simulations are based on the integration of an optical filter, a photovoltaic electrical model, and a heat transfer model, which includes water heating. An optical filter with gold nanoparticles with a volume fraction of 10 4 was selected for the CPV-T due to the better matching of the spectral transmittance of the gold particles to the spectral window of silicon cells. The gold nanoparticle suspension in ethylene glycol was then used in the simulations. A two-dimensional heat transfer model was developed, in which temperature variations along the fluid and solid (surface) nodes of the system are calculated. Once the temperatures of the solar cells are calculated using the heat transfer model, the photovoltaic efficiency can be obtained. Finally, the three models are integrated through an algorithm that incorporates thermal energy storage and hot water consumption for a household. The long-term simulation assessed the performance of the overall system under the climatic conditions of Tucson, Arizona, during a year. The simulations show that the system can provide water heating for a household of four persons during a year while generating a surplus of electricity. The system can provide 2230.3 kWh of thermal energy per year, which in terms of environmental impact is equal to a reduction of 1.317 tons of CO2 equivalent per year (compared to an average water heater). The system can also generate a net total of 731.89 kWh of electricity per year, which is equal to an offset of 0.418 tons of CO2 equivalent per year. The environmental impacts of this system are significant and, if adopted by 10% of the households in the United States, could reduce the emissions of carbon dioxide to the atmosphere by, approximately 14.49 million tons per year, based on the average water heater considered. This reduction in GWP would contribute to the decrease of electricity-related carbon dioxide emissions in the United States, as reported by the Department of Energy [4]. In addition, the long-term analysis showed that the proposed system is capable of providing hot water during over 97% of the year. As expected, failures in the system occur more often during the winter in Tucson, from December through February, and rarely in the summer months, from June through August. As discussed earlier in this paper, the system failures could be negligible if a backup water heater is used with the smaller 287-L water tank. The findings from the year-long simulation demonstrate the feasibility of CPV-T systems for domestic applications. This work, therefore, contributes to the advancement of research in small-scale CPV-T systems and confirms the potential of these systems to induce a positive environmental impact. Moreover, this work builds a framework for future experimental investigations to continue the research efforts in the field of concentrated photovoltaic-thermal systems.

3.3. Environmental impacts The environmental impacts of the system were also evaluated based on the year-long simulation. The total energy produced by the solar cells is 964.63 kWh per year, whereas the energy consumed by the pump is 232.74 kWh per year. The net energy produced by the solar cells is, therefore, 731.89 kWh per year. Instead of obtaining electricity from the grid, using this energy would mean a reduction of 0.512 tons of CO2 equivalent per year. The total energy that would be used to increase the temperature of the water from 20 °C to 49 °C is 2230.3 kWh per year. Compared to using an electric heater, this amount of energy obtained from the grid would be equivalent to emissions of 1.56 tons of CO2 . Compared to a natural gas water heater, the amount of energy from the fuel would be equal to 0.418 tons of CO2 equivalent. According to the EIA, 33.9% of the households in the United States use electricity as the main heating source, and over 50% of the households use natural gas as fuel for water heating [39]. An average water heater is, therefore, approximated to 358

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4.2. Future work

A life cycle assessment (LCA) would also be valuable to better understand the environmental impact of the system. Additionally, although the long-term simulations done in this work are valuable in understanding the performance of a spectral filtering CPV-T system, other important factors such as the cost of implementation and system maintenance were not explored. The development of an experimental setup similar to the one proposed by this work would be beneficial to validate the results obtained from the simulations, creating a basis for future investments in domestic CPV-T systems from the industry.

A more comprehensive analysis of this system could utilize a multiobjective optimization of the system parameters. This optimization would be important to define the best operating parameters of the system under various conditions. As described before, the parametric analysis is not sufficient to determine the best operating parameters, since the efficiencies of the system depend on multiple factors. A multiobjective optimization should include the selection of a base fluid, nanoparticle and nanoparticle volume fraction, physical system dimensions, and thermal storage unit size. Appendix A. Heat transfer relations and thermophysical properties

The forced convection heat transfer coefficient was obtained based on the Nusselt number for channels with rectangular cross sections and fully developed flow, assuming that the heat flux is constant along the wall of the channel. The aspect ratio of the rectangular channel plays an important role in the Nusselt number value. For the proposed system, the aspect ratio is 15.6, according to the values shown in Table 1, and, therefore, the Nusselt number used is 8.23 [41]. The thermal conductivity of the materials and fluid used in the simulations are described in Table A.1. The specific heat capacity of ethylene glycol is taken as 2.4 kJ/kg K [42]. The forced convective heat transfer coefficient can be calculated as follows:

hconv, forced =

NuD · kfluid

(A.1)

D

where NuD is the Nusselt number for internal flow, and D is the diameter of the channel. The heat transfer coefficient due to the wind on the top of the glass 1 and on the bottom of the insulator are obtained from an empirical expression given by [43]: (A.2)

hconv, wind = 2.8 + 3V where V is the velocity of the wind, in m/s . The natural convection heat transfer calculation depends on the Rayleigh number [41]:

Table A.1 Thermal conductivity of materials used in the CPV-T system in W/ mK. Values taken from [41]. Thermal conductivity at 1 atm and 300 K Glass PV cell (silicon) Metal plate (aluminum) Insulator (glass fiber) Ethylene glycol

1.4 148 237 0.04 0.252

Table A.1 Thermophysical properties of air at 300 K. Values taken from [41]. Pr g

Properties

0.71

9.81 m/s2

15.89 × 10

RaL = Pr·

T2 ) Lc3

g (T1

6 m2 /s

(A.3)

2

where Pr is the Prandtl number, which correlates diffusion momentum with the diffusion of heat, g is the acceleration of gravity in m/s2, is the coefficient of thermal expansion in K 1, T is the temperature in Kelvin, Lc is the characteristic length in which heat transfer occurs in meters, and is the kinematic viscosity of the fluid in m2 /s . For natural convection in a channel, the characteristic length is equal to the diameter. The following table describes the parameters used in the heat transfer model (Table A.1), The coefficient of thermal expansion, , is calculated by [41]:

=

1 1

(T1 + T2)· 2

(A.4)

The empirical Nusselt number for confined cavities is described by [41]: 359

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Table A.2 Emissivity of the materials used in the heat transfer model. Values taken from [31]. Glass Insulator Silicon solar cell

1708 RaLcos

¯ L = 1 + 1.44 1 Nu

1708sin(1.8 )1.6 RaL cos

1

+

RaL cos 5380

Emissivity

1/3

0.9 0.75 0.9

1 (A.5)

where is the inclination angle of the cavity. The terms marked with [] should be set to zero if negative. The solar tracking in the CPV-T system was ignored, and the value of the inclination was defined as 45°. The emissivity of the glass, insulator, and photovoltaic cells was taken from [31]. These values are described in the following table (see Table A.2). The rate of radiative heat transfer can be separated into two groups: heat exchange between a surface and the surrounding environment, and heat exchange between two surfaces. The heat transfer coefficient due to radiation between a surface and the surrounding environment is given by the following expression [41],

hr =

surface

2 2 (Tenvironment + Tsurface )(Tenvironment + Tsurface )

(A.6)

where is the Stefan-Boltzmann constant, 5.67 × 10 8 W·m 2·K 4, surface is the emissivity of the surface, and T is the temperature in Kelvin. The heat transfer coefficient due to radiation between two surfaces is given by the following expression [41],

hr = where

2 2 (Tsurface,1 + Tsurface,2 )(Tsurface ,1 + Tsurface,2 )

(

surface,1

1 surface,1

and

+

1 surface,2

surface,2

)

1

(A.7)

are the emissivity of the surfaces 1 and 2, respectively, and T is the temperature in Kelvin.

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