Effects of operational and environmental parameters on the performance of a solar photovoltaic-thermal collector

Energy Conversion and Management 205 (2020) 112428

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Effects of operational and environmental parameters on the performance of a solar photovoltaic-thermal collector

T

Anandhi Parthibana, K.S. Reddya, , Bala Pesalab, T.K. Mallickc ⁎

a

Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India Council of Scientific and Industrial Research – Central Electronics Engineering Research Institute, Chennai 600 113, India c Environment and Sustainability Institute, University of Exeter, Penryn, UK b

ARTICLE INFO

ABSTRACT

Keywords: Solar collector Thermal modeling of PV/T Sheet-and-tube heat exchanger Techno-economic analysis

A steady, three-dimensional model considering all the layers of a solar photovoltaic-thermal collector with sheet and tube heat exchanger is developed. The model takes the solar heat loading as the thermal input to estimate the temperature distribution in the collector for variation in incident radiation, ambient temperature, wind velocity, flow rate and inlet water temperature. Based on the numerical results, the parameter that highly influences collector performance is the coolant mass flow rate. For the range of flow rates considered, a maximum efficiency of 93.01% is obtained for 44 LPH. Further, a techno-economic comparison of the photovoltaic-thermal system is made with a photovoltaic system and a flat plate thermal system. The increase in electrical efficiency of the photovoltaic-thermal system is only marginal to that of the photovoltaic system but the overall efficiency of the former is high. The annual cost of energy that the photovoltaic-thermal system can supply is found to be 0.13 USD/kWh from economic analysis.

1. Introduction The incident solar energy can be directly converted to electrical energy by photovoltaic technology. However, only a fraction is converted to useful electrical energy while the remainder of the incident energy constitutes the wasteful thermal energy that builds up inside the photovoltaic cell leading to an increase in the cell temperature. The photo-electric conversion efficiency decreases by 0.45% per unit rise in the cell temperature. Therefore, the photo-electric efficiency is a strong function of cell operating temperature [1]. High operational temperatures of the panels lead to the development of thermal stresses which, over time, leads to mechanical damage [2]. Additionally, the electrical stresses in the panel that arise due to the flow of reverse currents increase in magnitude with increase in the panel temperature [3]. Therefore, photovoltaic panels operating at high temperatures suffer from thermal stresses as well as increased electrical stresses resulting in a reduction of panel life. Peng et al. [4] investigated the effect of panel temperature on the electrical performance of a photovoltaic system with and without cooling. They concluded that reducing the panel temperature results in better electrical efficiency and consequently a lower payback period than operating at high panel temperatures. A critical need to cool the photovoltaic systems can be identified, as cooling offers better electrical performance and increased panel life. ⁎

The passive methods of cooling the panels include the use of phasechange materials [5,6], fins/finned plate attached to the bottom surface of the panel [7,8] and modifications to the panel surface such as perforation [9] to augment the natural convective heat removal from the panel. The active methods of cooling the panels include the forced convective heat transfer using air or water as the working fluid. The conventional air-cooled photovoltaic thermal collector involves the forced circulation of air over the panel surface. Tonui and Tripanagnostopoulous [10] explored the possibilities of modifying the conventional design by placing a flat metal sheet in the middle of the air channel and by providing fins in the channel back wall. From their experimental and numerical attempts, they concluded that providing fins in the channel back wall offers better performance. Photovoltaic systems can be cooled using water by either spraying water on the surfaces of the panel [11,12] or by internal forced convection through tubes/ducts below the panel surface [13], the latter being the most commonly adopted option. Nizetic and his co-workers provide a comprehensive analysis of the available cooling methods and also assess the viability of the methods by economic analyses [14,15]. The applications of photovoltaic-thermal systems are listed categorically in [16]. Prakash [17] theoretically analysed the performance of a photovoltaic-thermal system and concluded that water-cooled systems perform better than air-cooled ones. He also reported that the hybrid

Corresponding author. E-mail address: [email protected] (K.S. Reddy).

https://doi.org/10.1016/j.enconman.2019.112428 Received 3 October 2019; Received in revised form 27 November 2019; Accepted 21 December 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

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density, kg m−3 Stefan-Boltzmann constant, = 5.67 × 10-8 W m−2 K−4 scattering coefficient s τ transmissivity solid angle, sr phase function Subscripts amb ambient c collector cell solar cell conv convection ele electrical EVA EVA layer g glass cover layer in inlet (water) m photovoltaic module out outlet (water) p plate (of thermal collector) PV photovoltaic layer rad radiation ref reference RC Rankine efficiency (0.38) sky sky th thermal tot total w wind x,y,z directional coordinates Abbreviations EVA ethylene-vinyl acetate FPC flat plate collector LPH liters per hour O&M operation and maintenance PV photovoltaic PV/T photovoltaic/thermal USD United States dollar

Nomenclature

ρ σ

Latin symbols A area, m2 CC capital cost, USD m−2 cp specific heat, J kg−1 K−1 FR collector heat removal factor g gravitational acceleration, m s−2 h heat transfer coefficient, W m−2 K−1 i interest rate per year, % I intensity of radiation, W m−2 k thermal conductivity, W m−1 K−1 M number of useful years m mass flow rate, kg s−1 n refractive index P pressure, Pa q heat flux, W m−2 Q volumetric heat generation, W m−3 Qu useful energy, W r position vector, m s direction vector s’ scattering vector direction S incident radiation, W m−2 T temperature, K U velocity, m s−1 UL overall heat loss coefficient, W m−2 K−1 V wind velocity, m s−1 λ volume, m3 Greek symbols α absorptivity β temperature coefficient, = 0.0045/°C βc packing factor emissivity efficiency, % µ dynamic viscosity, Pa s photovoltaic-thermal system is more efficient than the conventional photovoltaic system. Joshi and Dhoble [18] provide an excellent review on the experimental and numerical investigations focusing on photovoltaic-thermal systems. They recommend water-based systems, from the power output and efficiency points-of-view, and air-based systems for space heating purposes. Arcuri et al. [19] tested the performance of a photovoltaic system, which is cooled using air and water, with variation in constructional aspects. Based on the results, they concluded that for the water-cooled system the temperature difference between the ducts can be reduced by the use of metal sheet between the photovoltaic layer and the cooling system, thereby resulting in a reduction in the number of ducts used. A maximum temperature difference of 3 °C is reported between the ducts with absorber plate for a tube pitch of 159 mm. Rahman et al. [20] conducted experiments to study the influence of radiation, flow rate, humidity and dust on the performance of a photovoltaic system, with and without cooling. They reported that the module output increases for decreasing module operational temperature and increasing incident radiation. On the other hand, increase in humidity and increase in the dust cover were detrimental to the performance of the module. The influence of heat exchanger configuration on system performance was studied experimentally by Fudholi et al. [21] and numerically by Ibrahim et al. [22]. Bianchini et al. [23] conducted experimental performance-monitoring of a photovoltaicthermal system in Central Italy to assess the benefits of the simultaneous production of thermal energy and electrical energy from a photovoltaic-thermal system. They concluded that cooling offers negligible returns in terms of increase in electrical efficiency but the simultaneous heat and electricity generation from the system outweighs the output

from a separate photovoltaic and a flat plate thermal collector. The attempts to model the performance of the photovoltaic-thermal system have, by and large, been one-dimensional models based on energy balance [18]. Aste et al. [24] developed a one-dimensional model by considering the spectral efficiency, losses due to temperature, the real angle of incidence and the collector thermal inertia. They reported that the efficiency of a photovoltaic-thermal system was higher than that of a photovoltaic system. Touafek et al. [25] developed a one-dimensional model for a hybrid photovoltaic-thermal system with a sheet-and-tube heat exchanger. Using energy balance, the temperature distribution was obtained for the different layers of the collector. They concluded that the considered sheet-and-tube design had better heat absorption and lower production cost. Spertino et al. [26] investigated the effect of water cooling on the electrical performance of the photovoltaic module by performing outdoor experiments and by developing a one-dimensional model based on energy balance. They recommended that the flow rate of the coolant must be changed according to the geographic location and the season of the year to produce high energy yield. The one-dimensional models based on energy balance do not sufficiently capture the multi-physical nature of the heat transfer phenomena in a photovoltaic-thermal system, especially the coolant recirculation and backflow in the tubes, span-wise and length-wise conduction in the different layers of the system, and cannot be used to model other complex heat exchanger designs [27]. Three-dimensional thermal models have been developed for flat plate thermal collectors for quantifying the different modes of heat losses and for studying the influence of operational parameters on system performance [27,28]. Herrando et al. [29] compared the performance of different photovoltaic-thermal collectors using a three2

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temperature distribution across the various layers of the photovoltaicthermal system. Further, the study considers a three-dimensional numerical model of a photovoltaic-thermal system and analyzes the effect of various environmental and operational parameters on system performance. This is also a novel feature of this work. Using this method, more accurate results can be obtained, thereby providing considerable cost saving with regard to prototype testing. The validity of the proposed model is established upon comparison with the experimental results reported by Sakellariou and Axaopoulos [37]. The proposed model is more accurate than the state-of-the-art models because of its three-dimensional nature, the consideration of solar heat loading as thermal input for the model and the consideration of the dependence of the photo-electric conversion efficiency on panel temperature.

dimensional structural analysis. They reported that for sheet-and-tube photovoltaic-thermal systems, the variation in tube diameter showed insignificant effect on thermal output whereas the increase in number of tubes led to an increase in the thermal and electrical outputs. The photovoltaic-thermal system is unique, because in order to improve the overall system performance, the objectives of increasing the electrical power output and increasing the thermal power output are conflicting in nature. Duck et al. [30] developed a theoretical basis for the economic analysis of any photovoltaic cooling system. They recommend that the cooling method be chosen by considering the local conditions and system design. Aldossary et al. [31] numerically investigated the technical feasibility of the various cooling methods for a concentrated photovoltaic system for harsh ambient conditions. They demonstrated that for ambient temperatures above 35 °C, the passive methods fail and active cooling by water is capable of maintaining the cell temperature independent of the ambient temperature. Vera et al. [32] developed a methodology to optimize the design parameters simultaneously for maximum overall performance from a photovoltaicthermal system. The design parameters chosen were fluid mass flow rate, packing factor, the air gap between the PV and the glazing, and the collector length. They adopted a multi-objective optimization strategy as the objectives of improving the electrical and thermal generation from a photovoltaic-thermal system are conflicting in nature and reported the trade-off for different combination of design parameters. From these studies, the need to consider all the operational and environmental parameters in the analysis of such systems, to optimize the system, can be identified. Aste et al. [33] developed a three-dimensional thermal model of a water-cooled photovoltaic-thermal system and analysed the temperature distribution in the panel for serpentine and harp-type heat exchanger designs. They reported that the harp-type heat exchanger leads to a more uniform temperature distribution in the panel. Temperature homogeneity is a crucial requirement as the cells operating at different temperatures in a panel lead to considerable ohmic losses when the cells are connected in parallel [34]. However, cells in series show negligible ohmic losses when operating across a panel temperature gradient [35,36]. In this work, a steady, three-dimensional model that considers all the layers of the water-cooled photovoltaic-thermal collector with a sheet and tube heat exchanger is developed. The novelty of the work is the consideration of the remaining portion of the incident energy, after photo-electric conversion, which is converted into heat (called the solar heat loading [30]), and using the same as a volumetric heat generation input in the photovoltaic cell layer. The cell efficiency is taken as a function of average photovoltaic temperature and is iterated to obtain the volumetric heat generation in the photovoltaic layer, to study the

2. System configuration and energy transfer The solar photovoltaic-thermal collector consists of a photovoltaic module on top which converts the incident solar energy into electrical energy and the solar thermal collector provided at the bottom of the photovoltaic module extracts the thermal energy from the photovoltaic module. This extraction of both electrical and thermal energy increases the overall system output. The thermal energy extraction is achieved by attaching the absorber plate with cooling tubes onto the bottom of the photovoltaic module. 2.1. System description Fig. 1 shows the solar photovoltaic-thermal collector system configuration. The thermo-physical properties of the various layers of a photovoltaic-thermal collector are detailed in Table 1. The photovoltaic layer is enveloped with layers of EVA, Tedlar and glass cover preventing the entry of moisture and dust, and also providing stability and electrical insulation. By the virtue of low iron content, the glass cover used has high transmissivity to solar insolation. The EVA layer provides electrical insulation and cushion to protect the solar cell from mechanical damage that may occur due to increased stresses. The Tedlar, also called the back-sheet, is made of polyvinyl fluoride provides mechanical stability and robustness to the solar cell. The thermal absorber constitutes a conventional flat plate collector in which the cooling tubes of circular cross section are welded onto the rear surface of the absorber plate. The cooling tubes which are made of copper, a high thermal conductive material, are attached to the aluminium absorber plate. The model is developed with an aim of optimising the performance of a 380Wpe panel in which the cells are arranged in 12 × 6 array. The idea is to maximise the heat removal from the photovoltaic module which can be achieved by increasing the number of cooling tubes. With

Fig. 1. Schematic of the solar PV-T collector system. 3

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Table 1 Thermo-physical properties of various layers of PV-T collector [39]. Layer

Thickness (mm)

Thermal conductivity (W/m K)

Density (kg/m3)

Specific heat capacity (J/kg K)

Glass cover EVA top layer PV EVA bottom layer Tedlar Absorber plate (Aluminium) Cooling tube (Copper, outer diameter 16 mm) Water Insulation Thermal bond

3.2 0.5 2 0.5 0.33 4 1 – 50 –

1 0.4 148 0.4 0.4 204 386 0.63 0.05 0.92

3000 960 2330 960 1200 2710 8940 998.2 180 2260

500 2090 677 2090 1250 910 390 4183 1515 1050

weight and cost constraints, a twelve-tube configuration is considered for analysis. The cooling tubes are arranged in a manner so that each row of solar cells is cooled by two riser tubes underneath it. Further enhancement of heat transfer is achieved by the use of thermal bond between the absorber plate and the cooling tubes. The bottom of the collector is thermally insulated with rock wool and the entire collector unit is enclosed in an aluminium frame. Water is then circulated through the cooling tubes to extract thermal energy and to cool the photovoltaic module to ensure that the panel is operated within safe temperature limits, without any hotspots or thermal stress build-up.

depicts a solar PV/T collector with sheet and tube heat exchanger along with the basic energy transfer pathways. 3. Numerical model The steady state, three-dimensional thermal model was developed using ANSYS 18.2. The photovoltaic-thermal collector is simulated to obtain its temperature distribution across various layers. In order to reduce the computational cost, the system unit corresponding to one cooling tube is taken for modelling since the flow distribution among all the riser tubes is expected to be uniform because of low pressure drops associated with single-phase flow for the range of flow rates considered in the current study.

2.2. Energy transfer in a photovoltaic-thermal collector The energy incident on the photovoltaic module passes through glass cover and EVA layer before reaching the solar cell. The amount of energy reaching the solar cell depends on the transmissivity and absorptivity of the preceding layers, and the solar angle of incidence. The optical properties of various layers that constitute the photovoltaicthermal collector are mentioned in Table 2. The incident energy, after transmission and absorption in the glass cover and EVA layer, reaches the solar cell where a portion of incident energy is converted into electrical energy and the remaining incident energy constitutes the thermal energy that builds up in the module. This conversion of incident energy into electrical energy is a function of solar cell temperature and it increases with decrease in cell temperature. The conversion efficiency of the solar cell is very low and the maximum possible conversion efficiency of a commercial cell is around 20%. The photo-electric conversion is a function of average cell temperature and is given by [38], cell

=

ref

[1

(Tcell

Tref )]

3.1. Computational domain The computational domain consists of a photovoltaic semiconductor material layer with its insulating and protective layers – glass cover, photovoltaic layer sandwiched between two EVA layers, Tedlar/back sheet, absorber plate, cooling tube and insulation. The computational domain is depicted in Fig. 3. The three-dimensional geometry was generated using ANSYS DesignModeler. The geometric model is then meshed with structured hexahedral elements to generate the computational domain. To capture the boundary layer phenomena, a suitable inflation of seven layers from the wall in the fluid domain was provided. 3.2. Numerical methodology

(1)

Steady state modelling is performed to study the influence of environmental and operational parameters on the photovoltaic-thermal collector performance. The fluid flow problem is analysed in addition to conduction, convection and radiation modes of heat transfer simultaneously. In the fluid domain, mass, momentum and energy equations are solved while in the solid regions the energy equation is sufficient to capture the physics. The system is modelled for the range of mass flow rates for which the flow is incompressible and laminar.

where the reference efficiency is 20% obtained at a reference temperature of 25 °C, is the temperature coefficient of silicon solar cell (0.0045/°C). The remainder of the incident energy which constitutes the solar heat loading in the photovoltaic layer reaches the absorber plate, by conduction through the bottom EVA layer and Tedlar, from where it is actively removed by internal forced convection of water in the cooling tubes. To prevent any heat loss from the absorber plate to the ambient, the bottom surface is completely insulated with rock wool. The removal of heat from the absorber plate depends on the water mass flow rate and the inlet water temperature. The waste heat from the top surface of the photovoltaic module is dissipated to the environment by convection and radiation from the glass surface, after conduction through the top EVA layer and glass cover.

qconv = h w (Tg qrad =

4 g (T g

Tamb) 4 Tsky )

3.2.1. Governing equations The governing equations and the mathematical models that are used to model the photovoltaic-thermal collector are discussed in this section. The panel is assumed to be at zero tilt, hence the body force due to Table 2 Optical properties of various layers of PV-T collector [40].

(2) (3)

This convection and radiation from the glass cover to the environment highly depends on wind velocity and ambient temperature. Fig. 2 4

Layer

Transmissivity

Absorptivity

Reflectivity

Emissivity

Glass cover EVA PV

0.93 0.92 0.002

0.04 0.08 0.88

0.03 – 0.12

0.93 – –

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Fig. 2. Solar PV/T collector with sheet and tube heat exchanger.

gravitation along x and z-directions is zero, and along y-direction, it is (− gy ). The equations for conservation of mass (Eq. (4)), conservation of momentum (Eq. (5)) and conservation of energy (Eq. (6)) for a steady-state, single phase flow is given as,

P(

)u =

. u) =

P+

. (k

g + µ

T ) + ( q)

2u

(5) (6)

The energy equation is solved for each of the individual layers of the collector. The thermo-physical properties are assumed to remain constant with temperature. The top surface of the collector is subjected to convection and radiation. The heat transfer coefficients for convection from the top and bottom surfaces of the collector are assumed to be equal and calculated based on wind velocity. The internal heat source term in energy equation ( q) is calculated for the glass cover, top EVA and the solar cell using Eqs. (7), (8) and (9) [40], respectively. Since the solar cell transmissivity is zero, the layers that follow the solar cell, and are below it, have no heat generation.

Qg =

S

g Ag

(7)

g

QEVA =

S

g EVA AEVA

(8)

EVA

QPV =

S

EVA cell (1 cell

s ) I (r ,

s ) = an2

T4

+

S

4

4 0

I (r , s ) (s ·s ) d

(10)

3.2.2. Numerical procedure The numerical procedure that is adopted in this work is illustrated in the flow chart given in Fig. 4. An iterative method is employed to compute the internal heat source term in the photovoltaic layer. The initial iteration is performed by considering 15% solar cell efficiency with which the governing equations are solved to obtain the average photovoltaic layer temperature. The newly obtained average photovoltaic layer temperature is then substituted in Eq. (1) to obtain the photo-electric conversion efficiency. Based on the calculated efficiency, the heat generation term in the photovoltaic layer is updated for the succeeding iteration. The procedure is repeated till the difference in average cell temperature between successive iterations is less than 0.001 °C. ANSYS FLUENT is a commercial package which employs finite volume method to solve thermo-fluid problems. The non-linear partial differential equations are reduced to algebraic equations upon discretization and appropriate linearization. The discretisation of pressure, momentum and energy is done using the second-order upwind scheme with the gradients being evaluated using the least squares cell-based algorithm. The pressure and velocity coupling is achieved using the SIMPLE algorithm in which an initial pressure field is assumed and substituted in momentum equation to obtain velocity field. If the obtained velocity field satisfies the continuity equation then the guessed pressure field is retained else a pressure correction factor is used till the velocity field satisfies continuity equation. The equations governing the model are all non-linear and coupled. Hence, these equations are solved simultaneously until the convergence criteria are met – residuals for all the equations should be less than 1x10-6. Once the temperature distribution is obtained, the efficiency and

(4)

. ( u) = 0

(u .

I + (a + xi

cell ) A cell

(9)

The radiation heat transfer from the glass cover to the sky is modeled using the discrete ordinate (DO) radiation model. The DO model is implemented using the uncoupled method in which the energy and radiation intensity equations are solved one after the other.

Fig. 3. PV/T collector computational domain. 5

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heat. Hence the solar cell is modelled as a heat generation source whose volumetric heat generation is calculated using the solar cell efficiency which decays with increasing cell temperature. Similarly, the volumetric heat generation in glass cover and top EVA is calculated using their absorptivities. The outer surface of the collector is subjected to both convection and radiation and hence a mixed boundary condition is needed to capture the multi-physical phenomena. For simplicity, the current model considers convection occurring only at the top and bottom of the collector and hence the top surface of the glass cover and bottom surface of the backside insulation is assigned with the wind convection coefficient and free stream temperature which is equal to the ambient temperature. The wind convection coefficient is calculated using the correlation proposed by McAdams [41]. The photovoltaicthermal collector radiates energy to the sky which is driven by the temperature difference between the collector and the sky. To model the radiative heat exchange between the glass cover and the sky, it is required to specify the sky temperature and emissivity of radiating surfaces. The fluid flow problem is modelled by providing a velocity boundary condition at the inlet with an exit pressure boundary condition at the outlet. The details of the boundary conditions can be seen in Fig. 3. 3.4. Mesh sensitivity study For any numerical simulation, it is critical to ensure that the solution is independent of the resolution of the computational grid. It is for this purpose that the mesh sensitivity study is performed, which involves obtaining the solution for successively refined computational grids. With continued successive mesh refinement, the numerical solution asymptotically approaches the analytical solution. Practically, the accuracy of a particular grid is determined by estimating the change in solution with that obtained from the next finer grid. If the accuracy of the current grid is sufficient to preclude the use of a computationally expensive finer grid, then the current grid is selected. The outlet water temperature is computed for 8 grids of progressively refined element sizes, and the accuracy of a particular grid is established by computing the percentage deviation of the outlet water temperature between the two consecutive grids in relation to the grid under consideration. The variation in the solution (outlet water temperature) with increase in the number of elements is plotted in Fig. 5 along with the details of the case chosen for the sensitivity study. The outlet water temperature initially increases with grid resolution up to 1.41 million elements, beyond which the solution exhibits a grid-independent behaviour. The accuracy

Fig. 4. Flow chart – solution methodology of the numerical model.

power output are calculated. The electrical efficiency, thermal efficiency and the combined total efficiency of the photovoltaic-thermal collector are given by Eqs. (11), (12) and (13) respectively. ele

=

th

=

tot

=

(11)

cell Am c

mcp (Tout

Tin )

SAm th

+

(12)

ele RC

(13)

3.3. Boundary conditions To solve the governing equations, it is necessary to specify the conditions that exist at the boundaries of the computational domain. The three-dimensional model of PV/T collector involves concurrent heat transfer and fluid flow phenomena which necessitates the specification of thermal and flow boundary conditions. With the collector being placed in open atmosphere, the system is modelled for the physical conditions that exist in the immediate actual environment. The solar cells convert only a small portion of incident energy into electricity and the remainder of incident energy is dissipated in the form of

Fig. 5. Mesh sensitivity study – variation of outlet water temperature with number of elements. 6

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temperature of the photovoltaic layer is high at low mass flow rates and reduces with increasing mass flow rate. The average temperature of the photovoltaic layer at 6 LPH is 61.44 °C and the same at 44 LPH is 46.81 °C. At any length, the temperature of photovoltaic layer is the highest among all the layers, because of low photo-electric conversion efficiency and high absorptivity of the solar cell material. The temperatures of glass cover and Tedlar are close to the PV cell temperature because of low heat conduction resistance owing to the small thicknesses of the corresponding layers. The heat generated by the photovoltaic later is conducted to the aluminium absorber plate where it is effectively removed by convection by the flow of water through the cooling tube thereby extracting the waste heat from the cell. This waste heat extraction reduces the temperature of the cells and helps in improving the photo-electric conversion efficiency. The temperature of the bottom case remains fairly constant because of the poor thermal conductivity of glass wool. With increase in fluid velocity, the thickness of the thermal boundary layer decreases which increases the heat transfer rate from the surface. The extent of heat transfer is governed by the temperature difference between the wall and the fluid; with increase in inlet velocity by the virtue of augmented bulk motion fresh liquid comes in contact with the surface leading to improved panel cooling. Operating at higher mass flow rates leads to higher pressure drop which in turn implies increased pumping power requirement to compensate for the flow losses.

Table 3 Mesh sensitivity study. No. of elements (millions)

0.29 0.45 0.58 0.94 1.41 3.45 5.14 7.89

Outlet water temperature Tout (°C) 56.72 58.46 60.14 60.44 60.51 60.54 60.56 60.58

j Tout

(%)

j+1 Tout j Tout

× 100

3.07 2.87 0.49 0.11 0.05 0.03 0.03 –

of the grids, along with the numerical values of the solution, is listed in Table 3. Based on this study, the element size found optimal for the numerical model is 7.15 × 10−4 m for which the corresponding number of elements is 3.45 million. 3.5. Validation of the solver The developed thermal model is then validated against the experimental results obtained from the study by Sakellariou and Axaopoulos [37]. The photovoltaic-thermal module has 8 risers, each of 8 mm diameter and 120 mm tube pitch. The details of the module dimensions, thermo-physical properties and optical properties can be obtained from [37]. Fig. 6 shows the variation of collector outlet water temperature with incident radiation, obtained using the current model and the experimental results reported in [37], for these conditions − 95.43 LPH (mass flow rate), 24.58 °C (water inlet temperature), 1.45 m/s (wind velocity) and 24.50 °C (ambient temperature). The three-dimensional geometry is developed for a single cooling tube with its corresponding layers and then the geometry is computationally meshed using a structured grid. Grid independence study is done by taking the following element sizes- 3.76 × 10−3 m, 1.88 × 10−3 m, 1.25 × 10−3 m, 8.95 × 10−4 m, and 9.40 × 10−4 m. Based on the results of the grid sensitivity study, the solution is found to stabilize at an element size of 1.25 × 10−3 m for which the number of elements generated is 5.4 million. The modelling is performed using the iterative procedure described earlier by considering a nominal solar cell efficiency of 14.3%. The comparison of experimental and numerically predicted outlet water temperature indicates good agreement between the two, with a maximum deviation of 3.65%.

4.1.2. Influence of inlet water temperature The next operational parameter of interest is the inlet water temperature of the collector. Modelling is done by considering three different inlet water temperatures – 25 °C, 30 °C and 35 °C – for flow rate of 11 LPH, incident radiation of 1000 W/m2, wind velocity of 2.5 m/s and ambient temperature of 35 °C. Fig. 8 shows the temperature variation, along the length, in the photovoltaic layer and the temperature contours for the inlet water temperatures considered in the current study. With decreasing inlet temperature of the thermal energy extraction fluid, the PV cell temperature decreases. For a fully developed laminar flow with constant heat flux boundary condition, the local Nusselt number is constant implying that the convective heat transfer coefficient is also constant. For constant heat flux condition, the bulk fluid temperature increases along the length of the flow because of sensible heating and therefore the absorber plate temperature is directly related to the bulk fluid temperature since the ratio of the heat flux and the heat transfer coefficient is constant. Decreasing the fluid

4. Results and discussion Once the element size, and consequently the grid, is fixed, the computational domain is then modelled to study the collector performance for various conditions. The modelling is performed for various operational and environmental conditions to study the parametric influences of the same. 4.1. Influence of operational parameters The operational parameters for which the collector performance is analysed are inlet mass flow rate and inlet water temperature. 4.1.1. Influence of mass flow rate The collector performance is studied for various inlet mass flow rates: 6 LPH to 44 LPH. For the range of flow rates considered, the flow is found to be laminar. The modelling is done for incident radiation of 1000 W/m2, inlet water temperature of 30 °C, wind velocity of 2.5 m/s and ambient temperature of 35 °C. Fig. 7 shows the temperature variation, along the length, in the photovoltaic layer and the temperature contours for the flow rates considered in the current study. The

Fig. 6. Validation of the present model by comparison with experiments in [37]. 7

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Fig. 7. Influence of mass flow rate – Temperature profiles along the collector length and temperature contours of the PV layer.

inlet temperature decreases the bulk fluid temperature leading to reduced solar cell temperatures. By lowering the inlet temperature, the outlet temperature of the fluid is correspondingly lowered for the same heat removed resulting in better temperature normalization in the inlet reservoir leading to the elimination of additional heat exchange systems to bring down the outlet water temperature to the required inlet temperature. The obtained rise in water temperature from inlet to outlet is 37.56 °C, 33.25 °C and 28.87 °C for inlet temperatures of 25 °C, 30 °C and 35 °C respectively. Thus lowering the inlet water temperature lowers the PV cell temperature and increases the overall power output from the panel.

Fig. 8. Influence of inlet water temperature – Temperature profiles along the collector length and temperature contours of the PV layer.

Since the collector is static, its performance varies throughout the day due to the variation in incident radiation leading to variation in the radiation intensity. The performance is studied for three incident radiation fluxes – 600 W/m2, 800 W/m2 and 1000 W/m2 – for flow rate of 11 LPH, collector inlet water temperature of 30 °C, wind velocity of 2.5 m/s and ambient temperature of 35 °C. Fig. 9 shows the temperature variation, along the length, in the photovoltaic layer and the temperature contours for different incident radiation fluxes. The average temperature of the PV cell is found to be 57.15 °C at 1000 W/ m2 and 47.21 °C at 600 W/m2 implying that the temperature of PV cell increases with increase in incident radiation. The decrease in photoelectric conversion efficiency, with increase in cell temperature, is responsible for the photovoltaic layer temperature increasing with increasing radiation. The remainder of the incident energy, after photoelectric conversion, is converted to heat which leads to thermal energy

4.2. Influence of environmental parameters The environmental parameters for which the collector performance is analysed are solar insolation, wind velocity and ambient temperature. 4.2.1. Influence of solar insolation Incident radiation is the sole input to a solar collector. The incident radiation varies throughout the day as the sun moves along the sky. 8

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length, in the photovoltaic layer and the temperature contours for different wind velocities considered in the current study. With increase in wind velocity, the heat transfer by convection from the periphery of the collector increases which reduces the temperature of the photovoltaic layer which consequently improves the photo-electric conversion efficiency. The average photovoltaic layer temperature is 61 °C, 57.15 °C and 52 °C for wind velocities of 1 m/s, 2.5 m/s and 5 m/s respectively; the corresponding conversion efficiencies being 16.76%, 17.1% and 17.51%. 4.2.3. Influence of ambient temperature Ambient temperature is another environmental parameter that highly influences the collector performance as the minimum possible temperature of the collector is dependent on the ambient temperature.

Fig. 9. Influence of solar insolation – Temperature profiles along the collector length and temperature contours of the PV layer.

buildup in the panel, leading to increasing panel temperature and the tendency for thermal stresses. The conversion efficiency at 1000 W/m2 is 17.11% while that at 600 W/m2 is 18% showing that cell efficiency decreases with increasing incident radiation flux because of increase in photovoltaic layer temperature. 4.2.2. Influence of wind velocity Another important environmental parameter that influences the collector performance is the local wind velocity. With the collector subjected to convection by wind, both from the top and bottom surfaces, the performance of the collector is found to increase with increasing wind velocity. Simulations are carried out for three wind velocities – 1 m/s, 2.5 m/s and 5 m/s – for flow rate of 11 LPH, incident flux of 1000 W/m2, fluid inlet temperature of 30 °C and ambient temperature of 35 °C. Fig. 10 shows the temperature variation, along the

Fig. 10. Influence of wind velocity – Temperature profiles along the collector length and temperature contours of the PV layer. 9

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efficiency of 20%, electrical efficiencies of 17.10% and 17.72% were obtained at ambient temperatures of 35 °C and 25 °C respectively. Thus the increase in ambient temperature decreases the solar cell efficiency and consequently reduces the overall system output. 4.3. Overall performance of the PV/T collector Table 4 shows the comparison of performance of the photovoltaicthermal collector under different conditions considered in the current study. Based on the analysis it is found that mass flow rate is an important operational parameter that highly influences the collector performance and it is the only parameter that can be easily controlled operationally. Both the thermal and electrical efficiencies increase with increasing mass flow rate for reasons already discussed. Figs. 12 and 13 depict the temperature contours of various layers – glass cover, photovoltaic layer, absorber plate and the water domain – for the cases with the least (Case A in Table 4) and the best (Case F in Table 4) overall efficiencies respectively. 4.4. Techno-economic comparison of PV/T collector with PV and FPC systems The performance of the photovoltaic-thermal system is then assessed by comparing the efficiency of the photovoltaic-thermal system with that of a separate solar photovoltaic system and a solar thermal system, having the same collector area. The temperature of the solar photovoltaic module, as a function of incident radiation, ambient temperature and wind velocity, is calculated using the correlation given by Chenni et al. [42] as,

TPV = 0.943Tamb + 0.028 S

1.528 V + 4.3

(14)

Once the operating temperature of the photovoltaic module is obtained, its efficiency is calculated using Eq. (11). The thermal system, considered for comparison, is the standard solar flat plate collector. The system configuration of the flat plate collector is assumed to be the same as that of the photovoltaic-thermal system. The details of the thermal analysis of FPC can be found in [43]. The absorber plate mean temperature and the useful energy gain are given by Eqs. (15) and (16), respectively.

Tp = Tin +

Qu (1 FR UL AC

Qu = Ac FR [S

g

p

FR )

UL (Tin

(15)

Tamb)]

(16)

Fig. 14 presents the comparison of the efficiencies of the three systems for the different cases considered in the current study. The model can be utilized to optimize the operational parameters of a photovoltaic-thermal collector which can aid in the subsequent commercialisation of the same. After the performance comparison among the three systems, an economic analysis is performed to obtain the annual cost of thermal energy for the photovoltaic-thermal system, separate photovoltaic and flat-plate collector systems. The initial costs of the photovoltaic-thermal system, photovoltaic module and flat-plate collector are taken as 1036 USD/m2, 350 USD/m2 and 745.5 USD/m2, respectively. By considering 12% annual interest rate and 15 years useful life, the capital recovery factor is calculated [44], following which the annualized cost of the system is calculated. The operational and maintenance cost of the photovoltaic-thermal and flat-plate collector systems are estimated as 10% of the annualized uniform cost [45] whereas for the separate photovoltaic system, it is estimated as 2% of the annualized uniform cost.

Fig. 11. Influence of ambient temperature – Temperature profiles along the collector length and temperature contours of the PV layer.

With increase in ambient temperature, the output voltage reduces resulting in reduced power output from the panel. Fig. 11 shows the temperature variation, along the length, in the photovoltaic layer and the temperature contours for different ambient temperatures considered in the current study. Modelling is done for three ambient temperatures: 25 °C, 30 °C and 35 °C for incident radiation of 1000 W/ m2, inlet water temperature of 30 °C, wind velocity of 2.5 m/s and flow rate of 11 LPH. The panel temperature is found to increase with increase in ambient temperature because the extent of heat removal by natural convection currents set up in air and the outgoing radiation from the collector is governed by the difference between the system periphery temperature and the ambient temperature. The cooling rates by natural convection and radiation reduce with increasing ambient temperature. The average photovoltaic layer temperature for the three cases modelled is 50.32 °C, 53.72 °C and 57.15 °C for ambient temperatures of 25 °C, 30 °C and 35 °C respectively. Assuming a base cell

Capital re covery factor , CRF =

i (1 + i ) M (1 + i ) M 1

Annualized Cost of the system = CRF × CC + O &M 10

(17) (18)

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Table 4 Performance comparison of PV/T collector. Case

S (W/m2)

Tin (°C)

Tamb (°C)

m (LPH)

V (m/s)

Tpv (°C)

Tout (°C)

(%)

(%)

(%)

A B C D E F G H I J K L M N

1000 1000 1000 1000 1000 1000 800 600 1000 1000 1000 1000 1000 1000

30 30 30 30 30 30 30 30 30 30 25 35 30 30

35 35 35 35 35 35 35 35 35 35 35 35 25 30

6 8.64 11 22 33 44 11 11 11 11 11 11 11 11

2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 1 5 2.5 2.5 2.5 2.5

61.44 59.01 57.15 51.49 48.51 46.81 52.17 47.21 61.04 52.7 55.7 58.59 50.32 53.72

66.58 64.98 63.25 55.56 50.32 46.69 57.19 51.14 69.02 56.89 62.64 63.87 54.91 59.06

16.72 16.94 17.11 17.62 17.88 18.04 17.55 18.00 16.76 17.51 17.24 16.98 17.72 17.41

13.61 18.74 22.68 34.88 41.59 45.54 23.18 24.04 26.62 18.35 25.68 19.69 16.99 19.83

57.61 63.32 67.71 81.24 88.64 93.01 69.37 71.41 70.73 64.42 71.05 64.38 63.62 65.64

ele

th

tot

Fig. 12. Temperature contours for the least efficiency case – (a) glass cover (b) solar cell (c) absorber plate (d) water domain.

The useful energy gain is calculated by taking the efficiency values for the three systems, based on energy analysis corresponding to Case H from Table 4, for which the incident radiation is 600 W/m2. The efficiencies were found to be 71.41% for the photovoltaic-thermal system, 56.65% for the flat-plate thermal system and 17.72% for the photovoltaic system. The annual total insolation is taken to be 1752 kWh/m2. The results of the economic analysis are detailed in Table 5.

• •

5. Conclusions

• In this work, a steady state three-dimensional thermal model is

•

developed for solar photovoltaic-thermal collector with sheet and tube heat exchanger. The thermal modelling is done by considering 11

all the material layers of the collector-glass cover, photovoltaic layer sandwiched between two EVA layers, Tedlar/back sheet, absorber plate, cooling tube and back insulation. With the developed model, the system is analysed for variation in operational parameters – mass flow rate and inlet water temperature – and environmental parameters – incident radiation, ambient temperature and wind velocity. For the range of flow rates the system is modelled, the best performance was obtained for the flow rate of 44 LPH with 18.04% electrical efficiency and 45.54% thermal efficiency. A techno-economic comparison of photovoltaic-thermal system with separate photovoltaic and flat-plate collector systems is performed. The efficiency analysis shows that the combined efficiency of the

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Fig. 13. Temperature contours for the best efficiency case – (a) Glass cover (b) solar cell (c) absorber plate (d) water domain.

•

photovoltaic-thermal system is more than the individual efficiencies of the separate photovoltaic and flat-plate collector systems. Based on the results obtained from economic analysis, the annual cost of energy for a photovoltaic-thermal system, operating under an average insolation of 600 W/m2, is estimated as 0.13 USD/kWh. As a part of on-going activity, rigorous experiments are being planned to be conducted on the bespoke photovoltaic-thermal system with the aim of optimizing the system performance with subsequent commercialization.

CRediT authorship contribution statement Anandhi Parthiban: Data curation, Investigation, Methodology, Software, Validation, Writing - original draft. K.S. Reddy: Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Visualization, Writing - review & editing. Bala Pesala: Formal analysis, Funding acquisition, Investigation, Project admiistration, Visualization, Writing - review & editing. T.K. Mallick: Formal analysis, Investigation, Resources, Supervision, Writing - review & editing.

Fig. 14. Efficiency of PV/T, PV and FPC systems for the cases considered in the present study.

Declaration of Competing Interest

Table 5 Economic analysis – PV/T, PV and FPC systems. Economic metric

PV/T

PV

FPC

Initial cost (USD/m2) Annualized uniform cost (USD/m2) Operation and maintenance cost (USD/m2) Useful energy (kWh/m2) Annual cost of energy (USD/kWh) Simple payback period (years)

1036 152.08 15.21 1251.1 0.13 6.19

350 51.38 1.02 816.98 0.06 6.67

745.5 109.44 10.94 992.51 0.12 6.19

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The financial support provided by the Department of Science and Technology, Government of India through the project, DST/TM/SERI/ C278(C) is duly acknowledged. 12

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