Numerical study of an inclined photovoltaic system coupled with phase change material under various operating conditions

Applied Thermal Engineering 141 (2018) 958–975

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Research Paper

Numerical study of an inclined photovoltaic system coupled with phase change material under various operating conditions

T

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Meriem Nouira , Habib Sammouda Laboratory of Energy and Materials (LabEM) (LR11ES34), University of Sousse, ESSTHSousse, Abbassi Lamine Street, 4011 Hammam Sousse, Tunisia

H I GH L IG H T S

numerical study of PCM layer attached behind PV panel is performed. • APhase process of a PCM is studied under Tunisian climate. • 9 g/m change of dust deposition reduces PV panel power output of about 3 W at midday. • Wind direction increase from 30° to 60° rises PV panel temperature from 64 °C to 69 °C. • 2

A R T I C LE I N FO

A B S T R A C T

Keywords: PCM PV-PCM panels BIPV Efficiency Thermal regulation Dust deposition density

Photovoltaic panels suffer from high temperatures. A large part of absorbed solar radiation is converted into heat, which causes heating of PV cells and therefore leads to decrease PV efficiency. The effect of integrating different PCMs with different thicknesses is studied. Coupling photovoltaic panel with the suitable macroencapsulated phase change material layer is important for having better thermal regulation of PV panel. In the current thermodynamic investigation, melting and solidification processes of the selected PCM are carried out. To achieve a realistic simulation of heat and mass transfer of PV-PCM system, it is very important to analyze the effects of the following exterior operating conditions on PV panel performance: wind direction, wind speed and dust accumulation. Dust deposition density of 3 g/m2, 6 g/m2, and 9 g/m2 reduces electrical power of about 1.2 W, 2.8 W and 3 W, respectively. Moreover, the increase of wind speed leads to increase the heat losses due to forced convection and therefore reduces PV panel temperature. Eventually, wind azimuth angle increase causes an increase in the operating temperature of the PV panel.

1. Introduction One of the renewable energy technologies that are being promoted is solar energy; such energy is known to have the potential of generating electricity directly by using solar photovoltaic or by converting heat into electricity from solar thermal energy. Photovoltaic cells can absorb up to 80% of the incident solar radiation available in the solar spectrum. However, only a limited amount of the absorbed incident energy is converted into electricity depending on the conversion efficiency of the PV cell technology. The high temperature of PV modules reduces the efficiency of a PV system by 0.4–0.5% per K [1,2]. The operating temperature of the PV panel usually varies between 40 °C and 85 °C in hot climates [3] and could exceed the upper range in some real cases in summer as presented in [4]. Several studies have considered PV panel as a building element. Therefore, thermal regulation of a building integrated photovoltaic (BIPV) module is required to enhance its

⁎

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

https://doi.org/10.1016/j.applthermaleng.2018.06.039 Received 2 November 2017; Received in revised form 22 April 2018; Accepted 12 June 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.

electrical efficiency and to increase its power output. So far, several methodologies have been used for thermal regulation of PV panel such as active cooling or passive cooling methods. Active cooling methods require external devices, such as pumps to pump water or fans to force air, in order to maintain the temperature of the BIPV system at a level consistent with higher power output. For instance, pumping water for cooling in locations characterized by great potential of solar energy, like deserts, may be unsuitable because water is rare. Moreover, it causes an insupportable maintenance that leads to increase the operating costs. To reduce the temperature rise of a BIPV system using active techniques, Yun et al. [5] have studied the effect of ventilated wallintegrated PV system with an opening behind the PV. The findings have led to a rise of about 2.5% in the electrical output of PV panel. Lu et al. [6] studied the annual thermal performance of a BIPV system. In this paper, authors have discussed mainly the impact of the

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β βref Δτ εglass εal γpv γw ηpv μ ν ρ ρg ρD σ τ (τα )(θ) θ θr

Nomenclature A Apv Ai B Cp D F FT FF f Gr GT g k K τα Lf Lc M Mref P Pr Q Re Ra T Te,amb Tsky TPV Tref Tf TES T u v vair vpv,cell ΔT

upper surface of the PV panel (m2) surface area of PV panel (m2) anisotropy index liquid fraction of PCM specific heat capacity (J/kg K) Dirac delta function the view factor absorbed solar radiation with dust deposition (W/m2) fill factor correction coefficient Grashof number incident solar radiation (W/m2) acceleration due to gravity (m/s2) thermal conductivity (W/m K) Incidence angle modifier latent heat (J/kg) characteristic length (m) air mass modifier reference air mass modifier pressure (Pa) Prandtl number internal heat generation (W/m3 K) Reynolds number Rayleigh number temperature (°C) exterior ambient temperature (°C) sky temperature (°C) PV panel temperature (°C) temperature at standard condition (°C) fusion temperature (°C) thermal energy storage time (s) velocity of PCM in x direction (m/s) velocity of PCM in y direction (m/s) wind velocity (m/s) volume of the PV cells (m3) transition temperature (°C)

Abbreviation AM BIPV HDKR PCM PV PV-PCM STC

air mass building integrated photovoltaic Hay, Davies, Klucher, Reindl phase change material photovoltaic Photovoltaic phase change material standard test conditions

Subscripts a al b b,n c d e,amb g liq n r solid T

Greek symbols α αp αp

thermal expansion coefficient of PCM (1/K) temperature coefficient (1/K) transmittance reduction surface emissivity of the glass aluminum emissivity PV panel orientation (°) wind direction (°) electrical efficiency dynamic viscosity (Pa s) kinematic viscosity (m2/s) density (kg/m3) ground reflectance (albedo) dust deposition density (g/m2) Stefan–Boltzmann constant (W/m2 K4) transmittance of polluted panel transmission/absorptance product incidence angle of solar radiation (°) refraction angle (°)

angle of inclination with the horizontal (°) thermal expansion factor of air (1/K) absorptivity of the glass cover

air aluminum beam radiation beam radiation at normal incidence angle characteristic diffuse exterior ambient ground liquid phase normal incidence angle refraction solid phase titled

PCMs are mainly classified as non-organic, organic and eutectics PCMs [12]. Non-organic PCM: Hydrated salts are the most frequently used PCM in this category. They have high latent heat storage capacity, nonflammable and they are available at low prices. However, their main disadvantage is that their super cooling problem during phase change process which leads to irreversible transition phase [13]. Organic PCMs: Paraffin, carbohydrate and fatty acids are the most used PCMs for thermal energy storage in this group. Being recyclable, having the ability of melting congruently, having high heat of fusion and freezing without much under-cooling compared to inorganic PCMs [14] are their most known advantages. However, they have low thermal conductivity in their solid state and can be available at high prices [11]. Eutectic: Eutectic is a mixture of pure compounds with a volumetric storage density slightly higher than organic substances. However, their thermo-physical properties data are limited because the use of such materials is new for energy storage applications.

thickness of an air duct on the thermal performance of the system. A global comprehensive review could be observed in the researches of Sargunanathan et al. [7]. Passive cooling methods are based on the application of absorbing materials of heat excess released by the photovoltaic panel. The integration of PCM on the back side of a PV panel is a preferable passive cooling method since it needs less operating and maintenance costs compared to active cooling techniques [8], it does not require any intervention of external devices and additional energy [9] thanks to its ability of storing and releasing heat [10]. PCMs undergo a reversible phase change process depending on their fusion temperature. They absorb/release heat during their fusion/solidification phase change. The selection of the ideal PCM for a better thermal regulation of PV panel is very important. Hence, an appropriate PCM for such application must bear several criteria: large latent heat of fusion, high thermal conductivity, chemically stable, non-corrosive, non-toxic and its melting temperature must be within the PV system’s operating range [11]. 959

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1.0–1.5% compared to the conventional PV panel. Laura et al. [27] have studied a BIPV-PCM prototype, installed on Solar XXI office building's vertical façade, under Lisbon outdoor conditions. Hasan et al. [28] have investigated experimentally the performance of PV-PCM system for Dublin, Ireland and Vehari, Pakistan locations. They have observed a reduction of 7 °C and 10 °C in PV panel' temperature using salt hydrate (CaCl26H2O) and a eutectic mixture of fatty acids with Capric-palmitic acid as PCMs respectively. Browne et al.[29] have investigated a novel PV-T-PCM system under Dublin, Ireland environmental conditions. They have found that using PCM leads to improve heat extraction amount from PV panel about 7 times. An experimental investigation carried out by Browne et al. [30,31] show that coupling PV-PCM system with a pipe network filled with water could be a good approach to utilize the heat stored by PCM. Al-Waeli AH et al. [32] have showed in his paper that the use of 3 wt % Nano-SiC-water improves the electrical efficiency by up to 24.1% in comparison with the reference system and the thermal efficiency reached 100.19% in comparison with the reference system. Moreover, Al-Waeli AH et al. [33] have investigated experimentally the effect of SiC nanoparticles added in paraffin as a PCM on the efficiency of the PV/T systems. This investigation has showed that the studied system reduces PV cell temperature to 30 °C and therefore increases its power output from 61.1 W to 120.7 W. Apart from the experimental researches, several studies have reported numerical studies of PV-PCM system. Most numerical studies do not take into account the convective heat transfer inside the PCM. However, Liu et al. [34] have mentioned the vital role of convective heat transfer mode on the phase change process. Taking into account the presence of convective mode for macro-encapsulated phase change material allows the displacement of macroscopic fluid particles and therefore leads to speeding up fusion process and enhancing the extraction of heat from PV panel. The following studies have considered only the conductive heat transfer mode:

Hence, using paraffin for solar system cooling, requiring high latent heat storage is preferable. But, such materials have usually low thermal conductivity leading then to poor performance of the TES system. For this reason, Chaichan et al. [15] have studied the effect of improving the thermal conductivity of paraffin wax with different mass fractions of nanoparticles of Al2O3 and TiO2. They have found that increasing the mass fraction leads to an increase in its thermal conductivity and thus increasing the heat release rate of the studied material. He et al. [16] have investigated experimentally new nanofluids PCMs. Its thermal conductivity is enhanced and its supercooling degree is reduced by adding TiO2 nanoparticles in BaCl2-H2O (aqueous BaCl2 solution). The studied TiO2-BaCl2-H2O can be considered as a promoting candidate for cooling storage. Chaichan et al. [17] have performed an experimental study, in Baghdad-Iraqi weathers, to enhance the thermal conductivity of paraffin wax by adding aluminum powder as an additive and therefore to enhance its heat transfer rate. An improvement on its thermal conductivity is found as compared to the pure PCM. The different types of PCMs, mentioned previously, have been used for several applications. For instance, Sharma et al. [18] have considered the use of PCM in various building components. Sun et al. [19] have studied the effect of its integration in Trombe walls. Lin et al. [20] have studied the use of PCM for floor heating. Moreover, several studies have recently been studying the use of PCMs for thermal regulation of BIPV panel. Such application to decrease the rise of PV panel temperature has recently been studied. Most experimental investigations on PV-PCM modules have been studied under controlled external conditions. The following investigations have revealed the experimental studies of the PV-PCM system. The first experimental and numerical study of a BIPV system coupled with paraffin wax (RT25) as a PCM has been carried out by Huang et al. under externally controlled conditions [21]. In this research, a macro encapsulated PCM into aluminum container has been attached behind a solar selective absorbing material and exposed to 750–1000 W/m2 of solar radiation. Their numerical results have been compared with the numerical results and a good agreement has been found. Hasan et al. [8] have investigated the use of various types of PCM for thermal regulation of four different cell-size BIPV systems under 500–1000 W/m2 of solar radiation. They have found that the use of pure salt hydrate mixed with Eutectic mixture of Capric-lauric acid, commercial blend and Eutectic mixture of palmitic acid and paraffin wax reduce PV panel's temperature to about 18 °C, 16 °C and 14 °C, respectively. Maiti et al. [22] have studied the effect of integration PCM (paraffin wax) on the back side of PV system. PV panel's temperature is reduced to 65–68 °C at 2300 W/m2 while it attains 90 °C without using PCM. Biwole et al. [23] have revealed in his investigation that the integration of a PCM layer behind PV panel leads to reduction of PV panel's temperature to 40 °C. Sharma et al. [24] have investigated the thermal regulation of a building integrating concentrated PV system using PCM. An enhancement in its electrical efficiency has been observed by 6.80%, 4.20% and 1.15% under 1200, 750 and 500 W/m2 respectively. Atkin and Farid [25] have analyzed through an experiment, the thermal response of a PV-PCM panel under controlled peak incidentlight of 960 W/m2. Four different techniques have been studied to analyze the efficiency of the studied PV-PCM system. A few experimental studies have been investigated under actual environmental conditions. For instance, Park et al. [26] have examined a vertical BIPV-PCM module in an experiment under actual climatic conditions. Their results reveal that adding a PCM layer behind the PV panel decreases the PV temperature rise coming from overheating by absorbing a considerable amount of heat during the phase change. In addition, the amount of electric power generation is increased by

Park et al. [26] have analyzed the effects of orientation on vertical BIPV-PCM system as well as the thickness of PCM on PV panel's electrical output. Elarga et al. [35] have studied a one dimensional numerical model of a PV-PCM system with double skin façade in different climates. A reduction within 20–30% in the monthly cooling requirement is found for hot climates. Additionally, about 8% of an increase in peak value of PV efficiency is noticed when the double skin façade is combined with the PV-PCM system. Atkin and Farid [9] have studied the thermal regulation of the PV panel using infused graphite as PCM integrated with finned heat sink. Results show that using PCM creates a shift in temperature peak. Moreover, the efficiency of PV cell rises to 13% using PCM for PV panel. Smith et al. [36] have analyzed from a global numerical study the electrical power output from the PV-PCM system for countries all over the globe. They have found an improvement of 6% on PV panel power output in different countries such as eastern Africa and Mexico. Ho et al. [37,38] have studied numerically a three dimensional model of PV system coupled with microencapsulated PCM and taking into account only the conductive heat transfer mode into the PCM. Kibria et al. [39] have investigated a one-dimensional numerical study of a BIPV-PCM system. The thermal response of BIPV-PCM has been treated using various PCMs, neglecting wind speed effect and convective mode effect in PCM on PV panel power generation. All the previous numerical studies mentioned below do take into consideration neither the effect of wind orientation on PV-PCM panel 960

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temperature nor the effect of dust on the electrical power produced of PV-PCM panel. Great interest has been paid to thermal PV-PCM systems in recent years. However, researches on such modules under actual environmental conditions in hot regions like Tunisia have seldom been found. To the best of our knowledge, the study of the effect of wind direction as well as the effect of dust on the performance of the system has been rarely studied in the open literature. In order to deepen the study of the PV-PCM, further improvements have been made in the present study, including convective heat transfer into the liquid PCM to study its phase change process (fusion and solidification), heat loss by forced and natural convection from both sides of the PV-PCM panel to the environment, radiation heat loss, actual climatic conditions using the Hay, Davies, Klucher, Reindl (HDKR) to model solar radiation received by an inclined PV-PCM system, wind speed, wind direction and dust deposition on the performance of the system have been investigated. The current work is organized as follows: A numerical model description is presented in Section 2. The mathematical model of the considered PV-PCM system is given in Section 3. The current results have been validated against previous experimental results from literature in Section 4. In Section 5, the effect of the integration of different PCMs behind PV panel as well as the effect of its thickness on operating PV-PCM panel temperature has been investigated. Additionally, the effects of the operating conditions such as wind direction, wind speed, dust deposition density on the temperature of PV-PCM system, on its efficiency and on its electrical power generation have been studied. Eventually, conclusions have been yielded in Section 6 and future work direction is given in Section 7. Thus, an evaluation of the system behavior under various operating conditions could be assessed from the current thermodynamic work by studying the influence of pretty important factors that have not been taken into consideration hitherto.

Table 1 PV panel material properties [35,36]. Thermo-physical properties of PV panel and aluminum layer

Glass EVA Silicon cells Tedlar Aluminum

Density (kg/m3)

Specific heat (J/(kg K))

Thickness (m)

Thermal conductivity (W/ (m K))

3000 960 2330 1200 2675

500 2090 677 1250 903

0.003 0.0005 0.0003 0.0005 0.002

1.8 0.35 148 0.2 211

Table 2 Thermo-physical properties of the PCM used by Park et al. (2014) [15]. Thermo-physical properties

Value

Thermal conductivity (solid) (W/(m K)) Density (solid) (kg/m3) Density (liquid) (kg/m3) Specific heat capacity (kJ/(kg K)) Melting temperature (K) Latent Heat of Fusion (kJ/kg)

0.2 880 760 2.1 298 184

frame which its effects are not considered in the model because its surface area in comparison with the panel area is very low, thus, it have a negligible effect on the variation of PV panel temperature [40]. The angle α represents the tilt angle relative to the horizontal. The thermophysical properties of each layer used in the current study are given in Table 1. Moreover, the thickness of the chosen PCM layer used in the present work is macro encapsulated in 2 mm thick aluminum sheets. The properties of the selected PCM are presented in Table 2. The above described thermal model was studied for a selected city, namely Sousse (35.82539_N, 10.63699_E) for Tunisian climate on July 15th.

2. Numerical model description As usual, a PV module is composed of five layers depending on the photovoltaic technology used as presented in Fig. 1. The PV module in this work is polycrystalline and it is assumed to be fixed in a metal

Fig. 1. Physical model of PV/PCM panel. 961

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(36). σ is the Stefan–Boltzmann constant, εglass is the surface emissivity of the glass cover taken as 0.91 [41], Ff-sky and Ff-g are correspond to the view factors between the PV panel front surface and the sky or the ground, respectively. Tglass, Te,amb and Tsky are, respectively, the glass, the exterior ambient and the sky temperatures. On the bottom surface of PV-PCM system, long wave radiation heat loss from aluminum layer to the ground and convection term heat loss had been considered as follows:

3. Thermal equations and boundary conditions The processes that describe the phenomenon of electricity production at the level of the semiconductor material as well as the operating temperature of the photovoltaic module are very intricate. In fact, the electricity production and the extra heat released by the photovoltaic module occur by the bombardment of photons onto the solar cell. For these reasons, the following assumptions have been considered: (i) Properties of each layer in PV panel are considered to be isotropic and homogeneous. (ii) The solar radiation falling on the front surface of the PV panel is equally distributed. (iii) The contact resistances in the PV cell are not taken into account in this work. (iv) The flow of the melted PCM is considered Newtonian, incompressible and unsteady. (v) All absorbed solar radiation that is not converted to electricity will be dissipated into heat. (vi) The fusion of PCM is controlled by the convection and conduction modes of heat transfer. (vii) Rain effect, which probably affect dust accumulation density, is not considered

where Tal and Tg are, respectively, the aluminum back layer surface and ground temperature. The value of the aluminum surface emissivity, εal , is set to 0.85 [42]. Ff-sky and Ff-g are the view factors between the PV panel back surface and the sky or the ground, respectively.

The simulation of the variation of the temperature of the PV module is performed by considering the heat transfer from the module to the surroundings and the energy absorbed by the PCM.

qrad = qirradiance−(q ground + q sky)

∂T −kal ⎛ ⎞ = (hb, free + hb − forced )(Te, amb−Tal ) + σεal Fb − g (Tg 4−Tal 4 ) ⎝ ∂y ⎠ + σεal Fb − sky (Tsky 4−Tal 4 ) ⎜

⎜

qirradiance = αglass G T A

(6)

All the necessary equations for the calculation of the incident solar radiation on the front PV panel and absorbed solar radiation by the PVPCM panel are mentioned below.

⎟

(1)

• Solar radiation modeling on the level of the PV panel surface

where Q is a heat source and it is applied to the heat transfer equation of the PV cells layer as an internal heat generation. As mentioned in the above assumptions, the remaining absorbed solar radiation that is not converted to electricity will be dissipated into heat. Hence, an increase in PV panel temperature is obtained because of this internal heat source. Q is evaluated using the expression below:

Q=

(5)

where qirradiance, qground and qsky define, respectively, the solar radiation absorbed by the PV-PCM panel, the heat loss leaving the panel towards the ground and sky. The irradiance model input on the PV-PCM panel’s front surface depends on cover glass’s absorptivity and can be calculated as follows:

The conduction mode is the only mode that governs the heat transfer in all solid domains (PV and aluminum layers). Hence, the diffusion heat transfer equation applied to the solid parts of the system, after simplifications using hypothesis cited above, is expressed by Eq. (1):

∂T ∂ 2T ∂ 2T = k⎛ 2 + 2 ⎞ + Q ∂t ∂ y⎠ ⎝∂ x

(4)

3.2.1. Radiation modeling The total solar radiation absorbed by the PV-PCM panel depends effectively on the incident radiation on the front surface of the panel studied and on the total radiation produced by the PV-PCM panel. Thus, the total resulting radiated energy can be estimated as:

3.1. Within solid domains

ρCP

⎟

(1−ηPV )FT A VPVcell

The prediction of real PV cells variation requires information on the solar energy radiation received by an inclined PV panel. To mimic a real time application, the daily solar radiation incident on inclined PV panel surface, GT, is simulated in this paper using the HDKR model (Hay, Davies, Klucher, Reindl model) [43]. In details, the hourly total incident irradiance on inclined surface consists of three components as presented in Eq. (7) [44]:

(2)

G T = (G T,b + G T,d + G T,ref )

where FT is the absorbed solar radiation as properly expressed in Eq. (25), ηpv is the electrical efficiency of the PV cells which is defined in Eq. (54), A is the upper surface of the PV panel and Vpv,cell is the volume of the PV cells in the panel.

(7)

In details: Beam radiation GT,b : The beam radiation on titled surface describes the solar radiation traveling from the sun, passing through the atmosphere without any scattering and directly received by the surface. As presented in Eq. (8), GT,b can be estimated by multiplying the value of beam radiation received by horizontal surface, Gb, by the geometric factor, Rb.

3.2. On the level of the PV panel surface At the upper interface of the PV panel, we have considered the solar radiation, the long-wave radiation of the glass surface and the convection terms as presented below:

GT , b = Gb Rb

∂T k glass ⎛ ⎞ = αglass GT + (hcvfree + hcvforced )(Te, amb−Tglass ) ⎝ ∂y ⎠

where Rb denotes a geometric factor depending on the zenith and incidence angles. Rb is calculated using the following expression [45-47].

⎜

⎟

+ σεglass Ff − sky (Tsky 4−Tglass 4 ) + σεglass Ff − g (Tg 4−Tglass 4 )

(3)

Rb =

where αglass and GT are the absorptivity of the glass cover and the incident solar radiation on the PV-PCM panel (expressed in Eq. (7)) respectively. hcvfree and hcvforced are, respectively, the heat transfer coefficient for natural and forced convection as expressed in Eqs. (35) and

cos(θ) cos(θz )

(8)

(9)

where θ and θz are the incidence angle and the zenith angle respectively and both of them can be evaluated according to [45]. Thus, the beam radiation received by titled surface, GT,b, is giving by: 962

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cos(θ) ⎞ GT , b = Gb ⎛⎜ ⎟ ⎝ cos(θz ) ⎠

GT = GT , b + GT , d + GT , ref (10)

= Gb Rb + Gd ⎡ (1−Ai ) ⎣

Gb is the beam radiation incident on horizontal surface which can be expressed as follow [48]:

G b = G b,ncos(θz)

Gb G

Ai =

Gb Go

3 α 2

i

M = Mref

)

(18)

4

∑ ai (AM )i

(19)

i=0

where AM is the air mass which is given according to [60] as presented in Eq. (20), a0, a1, a2, a3 and a4 are constants for different PV cells materials and their values for polycrystalline PV cells are 0.918093, 0.086257, −0.024459, 0.002816, −0.000126 respectively [60].

AM =

1 cos(θz ) + 0.5057(96.080−θz )−1.634

(20)

K τα, b , K τα, d and K τα, g are the incidence angle modifiers for beam, diffuse and ground-reflected radiation components, respectively, where the incidence angle modifier is defined as:

(12)

K τα =

(τα ) (τα )n

(21)

where (τα )(θ) is the transmission/absorptance product through a PVPCM cover system by a simple air-glazing model. (τα )(θ) is calculated according to [61]:

1 sin2 (θ −θ) tan2 (θr −θ) ⎞ ⎤ + (τα )(θ) = e−(KL /cos θr ) ⎡1− ⎛ 2 r 2 (θ + θ ) ⎥ ⎢ 2 ⎝ sin (θr + θ) tan r ⎠⎦ ⎣

(14)

⎟

(22) -1

where θ and θr are the incidence and refraction angles, K (m ) is the glazing extinction coefficient, and L (m) is the glazing thickness. The refraction angle is defined as θr = sin−1 (θ /(nr / n)) where the refraction index (nr/n) for glass is set to 1.526.

here G is the global radiation received by horizontal surface. It is calculated using the Eq. (15) below: (15)

• Absorbed solar radiation with dust deposition

Go is the horizontal extraterrestrial radiation over a time step and it can be calculated referring to [59]. Ground reflected component GT,ref: describes the reflected solar radiation by the ground and reached by the tilted surface. All models presume that this component is isotropic as expressed below [46,47,52,53]

1−cos α ⎞ 2 ⎠

1 − cos α 2

where (τα )n is the transmittance/absorptance product of the PV cover for incoming solar radiation at a normal incidence angle. Gref is the solar radiation at standard conditions (1000 W/m2) where sref = Gref (τα )n and Mref = 1[44]. M and Mref are the air mass modifier and the reference air mass modifier respectively. The air mass modifier is modeled using the empirical relation expressed by the below equation [60]:

⎜

GT , ref = ρg G ⎛ ⎝

g

GT , ref GT , d GT , b ST K τα, d + K τα, g ⎞⎟ K τα, b + = M (τα )n ⎜⎛ G Gref G Sref ref ⎠ ⎝ ref

(13)

G = Gb + Gd

b

The absorbed solar radiation without dust deposition is evaluated using the radiation and optical model. In details, it is a function of the incident radiation on titled PV panel surface GT, air mass M and incidence angle modifier K τα . The model is defined by the following equation [44]:

where α is the inclination angle of the considered surface relative to the horizontal. Ai and f are the anisotropy index and the correction coefficient, respectively, which are given as follow [59]:

f=

) (1 + f sin ( ) ) + A R ⎤⎦ + ρ G (

• Absorbed solar radiation without dust deposition

(11)

1 + cos α ⎛ α ⎞ 1 + f sin3 ⎛ ⎞ ⎞ + Ai Rb⎤ ⎥ 2 ⎠⎝ ⎝ 2 ⎠⎠ ⎦

1 + cos α 2

(17)

where Gb,n is the energy of solar radiation falling with right angle on square meter of the ground in a unit of time and can be calculated according to [48]. Diffuse radiation GT,d: describes the sunlight that reach the sloping surface after its dispersion through molecules and particles into the atmosphere. It should be known that modeling the sky diffuse component on titled surface is considered the most complex problem. In fact, this diffuse component is characterized by its anisotropic and not uniformity of its distribution in the sky over the time. Many researchers used many models in order to evaluate this component which is basically classified on three types: Isotropic, circum-solar and anisotropic models. The isotropic models assume that the distribution intensity of this component is isotropic and uniform over the entire hemisphere sky. Many authors evaluated solar radiation on titled surface for any orientation using the isotropic diffuse sky model [49,50]. In spite of its popularity, this model should not be used because it does not give a real picture of solar conditions in comparison with other theoretical as well as with other experimental results [51]. The second type model (the circum-solar model) assumes that the diffuse component is evaluated similarly to the direct component [52,53]. However, it is not preferable to use this model because it could only be applied for totally clear skies [53]. Finally, the anisotropic model presumes the anisotropy of this component in the circumsolar region as well as the isotropy diffuse component distribution from the rest of the sky dome. This model is pretty used for clear and cloudy days [46]. Many researchers used a large number of models considering the anisotropic model [54–58]. In this paper, the diffuse radiation received by titled surface is modeled using the HDKR (Hay, Davies, Klucher, Reindl) model [51]. According to HDKR model, the diffuse radiation received by inclined surface is expressed as:

GT , d = Gd ⎡ (1−Ai ) ⎛ ⎢ ⎝ ⎣

(

▪ Transmittance-Dust deposition modeling

Many previous experimental investigations studied the effect of dust deposition density on PV panel transmittance and therefore on PV panel’s efficiency. In this context, the decreasing of PV’s performance due to the increasing of the dust concentration on PV panel surface has been investigated in [62–64]. Several experimental studies investigated the effect of dust deposition density on the transmittance. Therefore, various correlations were derived for the evaluation of transmittance reduction in [65–68]. Thus, the correlation quoted in [68] is used in the present study due to its application in various regions and various weather conditions and it is given by Eq. (23):

(16)

where ρg is the ground reflectance (albedo). Thus, as mentioned previously, the HDKR model will be applied in this paper and the total solar radiation incident on oblique surface can be expressed as: 963

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Δτ (%) = −0.001335ρD6 + 0.04398ρD5 −0.5427ρD4 + 3.05ρD3 −7.703ρD2 + 11.19ρD −2.25

surfaces of the PV panel, respectively.

• For the top side of the PV panel, the convective heat transfer coef-

(23)

ficient, hf-pv, is given as:

where ρD is the dust deposition density in (g/m ). Once the transmittance reduction is evaluated, the transmittance of polluted PV panel can be calculated as follows: 2

τ = (1−Δτ )(τα )(θ)

hf − pv = hf , free + hf − forced

where hf,free and hf-forced are the natural and forced convective heat transfer coefficients for the front PV panel surface respectively. hf-pv is given below as follows [71]

(24)

Here (τα )(θ) present the transmission of a clean glass cover, and its evaluation is deduced from the Eq. (22). Thus, the absorbed solar radiation by a photovoltaic module under the effect of dust deposition, FT, is expressed as follows:

GT , ref GT , d GT , b K τα, d + K τα, g ⎞⎟ K τα, b + FT = (1−Δτ ) Sref M (τα )n ⎛⎜ G G G ref ref ref ⎠ ⎝

hf − pv

(25)

hf , free =

(27)

The sky temperature, Tsky, can be calculated by the modified relationship of [69] as expressed in Eq. (28):

Tsky = 0.037536 Te,amb1.5 + 0.32Te,amb

⎜

1

Ff − sky = 2 (1 + cos α ) Ff − g =

1 (1−cos α ) 2

⎟

(29)

cos(α w ) = cos(90−α ) cos(γ ) = sin(α ) cos(γ )

(36)

(37)

where γ is the angle given as γ = |γpv−γw |, as shown in Figs. 13 and 14. γw is the wind direction and γpv donates PV panel orientation with reference to the south (angle between south direction and the horizontal projection of normal to PV panel where γpv = 0 for south orientation). Hence, the heat transfer coefficient due to forced convection is given by the following equation:

⎫ ⎪ ⎪

⎨ Fb − sky = 1 (1 + cos(π −α )) ⎬ 2 ⎪ ⎪ ⎪ Fb − g = 1 (1−cos(π −α )) ⎪ 2 ⎭ ⎩

(35)

where υis the kinematic viscosity of the air and vair is the wind velocity. αw is the wind incident angle and defined as the angle between the wind direction vector and the normal to the PV module surface vector as figured out in Figs. 13 and 14. In order to determine the wind incident angle, Eq. (37) below is derived from spherical trigonometry and used as following [71]:

where Tamb and ΔTamb are, respectively, the average value and the oscillation amplitude of the exterior ambient temperature during a period of time TS (one day = 24 h). The view factor F acts on the heat loss of the PV-PCM structure and it is properly expressed as follows:

⎧ ⎪ ⎪

⎧ [0.13{(GrPr )1/3−(GrC Pr )1/3} + 0.56(GrC Pr sin α )1/4] K a ⎪ / Lc if α > 30∘ ⎨ ⎪ [0.13(GrPr )1/3] K a/ Lc if α ⩽ 30∘ ⎩

hf − forced = 0.848ka [cos α w vair Pr / υ]0.5 (Lc /2)−0.5

(28)

The exterior ambient temperature could be modeled as a sinusoidal function of the form [70]:

2πt ⎞ Te, amb = Tamb + ΔTamb sin ⎛ ⎝ TS ⎠

(34)

where Grc is the critical Grashof number which can be given as: GrC = 1.327 × 1010 exp(−3.708(π /2−α )) , this critical number correspond to the transition zone from laminar to turbulent flow, Pr define the Prandtl number, ka is the air thermal conductivity, Lc is the characteristic length. The evaluation of heat losses by forced convection caused by the wind speed is very important for calculating the thermal response of the studied PV panel. The appropriate empirical equation of the heat transfer coefficient due to forced convection is given by the following equation [71]:

(26)

In the present study, the ground temperature is considered to be equal to the exterior ambient temperature. The net heat loss radiation, qsky, is described as follows:

qsky = εglass Ff − sky σA (Tsky 4−Tglass 4 ) + εal Fb − sky σA (Tsky 4−Tal 4 )

hf − forced ifGr / Re 2 ⩽ 0.01 ⎧ ⎪ 7/2 + h 7/2 ) 2/7if 0.01 < Gr / Re 2 < 100, α = 0∘ ( h ⎪ f , free f − forced = 3 ⎨ (hf , free + hf − forced3)1/3if 0.01 < Gr / Re 2 < 100, α > 0∘ ⎪ ⎪ hf , free ifGr / Re 2 ⩾ 100 ⎩

where Re is the Reynolds number and Gr is the Grashof number. The heat transfer coefficient due to natural convection the top surface is given as follows [72]

3.2.2. Thermal radiation heat losses modeling The effective heat loss from front and back sides of the studied PV panel radiated towards the ground and sky follows the Stefan–Boltzmann's law. It depends essentially on the surface emissivity, the exterior ambient temperature, the upper and rear surface temperatures of the PV panel and tilt angle. The net heat loss radiation, qrad, to the ground is expressed as follows:

qground = εal Fb − g σA (Tg 4−Tal 4 ) + εglass Ff − g σA (Tg 4−Tglass 4 )

(33)

hf − forced = 0.848ka [sin α cos γvair Pr /υ]0.5 (Lc /2)−0.5 (30)

(38)

• At the back side of the PV panel, the overall convective heat transfer coefficient, hb-pv, is given as:

3.2.3. Convective heat losses modeling At the top and back surfaces of the PV panel, convective heat losses are taken into account for the present research. The heat transfer by convection mode takes place by the combination between natural and forced convection heat transfer. Thus, the heat losses, qf-convection and qb-convection, due to convection mode in this case for the front and for the back sides, respectively, are defined as follows:

qf − convection = hf − pv (Tpv−Te, amb) A

(31)

qb − convection = hb − pv (Tal−Te, amb) A

(32)

hb − pv = hb, free + hb − forced

(39)

where hb,free and hb,forced are the natural and forced convective heat transfer coefficients for the back side of the PV panel, respectively. The heat transfer coefficient due to natural convection, hb,free , is obtained by evaluating the Eq. (40) as follows [72]:

hb, free =

where hf-pv and hb-pv are the overall convective heat coefficients that include both natural and forced convection for the front and back 964

⎧ ⎪ ⎪

(

1/6

)

2

⎡ 0.825 + 0.387(Ra . sin α ) ⎤ ka/ Lc if α ⩾ 30 (1 + (0.492 / Pr )9/16)8/27 ⎣ ⎦ [0.56(Ra. sin α )1/4] ka/ Lc if 2 < α < 30 and 105 < Ra.

⎨ ⎪ sin α < 1011 ⎪ 1/5 6 11 ⎩ [0.58(Ra) ] ka/ Lc if 0 ⩽ α ⩽ 2 and 10 < Ra < 10

(40)

Applied Thermal Engineering 141 (2018) 958–975

M. Nouira, H. Sammouda

where Ra and αp are the Rayleigh number and the thermal expansion factor, respectively, which are given as:

gαp ρ2 cP |TPV −Tamb |Lc 3

Ra =

αp =

state, it absorbs the latent heat (Lf) which can be modeled as a change in its specific heat during the phase transition period.

ka μ

1 ⎛ ∂ρ ⎞ ρ ⎝ ∂TPV ⎠P ⎜

0 T < (Tf −ΔT ) ⎧ ⎪ (T − Tf + ΔT ) B (T ) = (Tf −ΔT ) ⩽ T < (Tf + ΔT ) 2ΔT ⎨ ⎪ 1 T > (Tf + ΔT ) ⎩

(41)

⎟

(42)

(47)

The latent heat and the latent heat of the selected PCM are modeled as follows

The heat transfer coefficient due to forced convection at the back side of the PV panel surface is given as [73] and [74]:

Cp (T ) = Cp, solid + (Cp, liq−Cp, solid ) B (T ) + Lf D (T )

(48)

k

hb − forced

⎧ (0.664 Re1/2 Pr 1/3) Lae for la min ar flow (Re<4. 105 and Pr ⩾ ⎪ ⎪ 0.6) ⎪ k ⎪ (0.037 Re 0.8Pr 1/3) Lae for turbulent flow (5.105 < Re < 108 ⎪ = and 0.6 ⩽ Pr ⩽60) ⎨ ⎪ ((0.037 Re 0.8 - (0.037 Re 0.8 - 0.664 Re 0.5 )) Pr 1/3) ka for mixed c c Le ⎪ ⎪ 5 5 and 0.6⩽ < < flows Re (4.10 5.10 ⎪ ⎪ Pr ⩽ 60) ⎩

where Cp,liq and Cp,solid are the specific heat capacities of the chosen PCM in liquid and solid phases respectively. D(T) is Dirac delta function and its main role is to distribute the latent heat of fusion in a similar manner nearby the melting point of PCM. It is set to 0 everywhere except in interval [Tf − ΔT,Tf + ΔT] and can be modeled as follows:

D (T ) = e

where Re = the Reynolds number (x is the position along the panel), Pr is the Prandtl number and Rec is the critical Reynolds number which is set to 4 · 105.

A(T) = C

)

⎨ ⎪ρ ⎪ ⎪ ⎪ ⎪ ⎩

(

(

)

∂v ∂t

∂v

∂v

)

∂P

+ u ∂x + v ∂y = − ∂y + μ

(

)

∂2v ∂x 2

+

∂2v ∂y 2

)

⎞ ΠΔT 2 ⎟ ⎠

(49)

(50)

(1−B(T))2 (B3 (T) + q)

(51)

where the constant q is typically a small number and it is fixed to 10-3 in order to make the PCM density effective even when the melt fraction is zero. C defines the mushy zone constant and its value depends on the morphology of the medium. The mushy zone constant describes how steeply the velocity is totally reduced to zero when the material becomes completely solid. The value of C is often varying between 104 and 108 kg/m3 s. In this research, the value of C is taken 106 because of the high viscosity of solid PCM.

⎧ ρcp ∂T = ∂ k ∂T −ρcp uT + ∂ k ∂T −ρcp vT ∂t ∂x ∂x ∂y ∂y ⎪ ⎪ ∂u ∂u ∂u ∂P ∂2u ∂2u ⎪ ρ ∂t + u ∂x + v ∂y = − ∂x + μ ∂x 2 + ∂y 2 + Wx ⎪ ⎪ + ρliq (1−β (T −Tf )) gx sin α

(

ΔT 2

where A(T) is used in order to mimic Carman-Kozeny equations for flow in a porous media and it is defined as follows[75]:

By applying the heat transfer diffusion equation and the NavierStokes equations for Newtonian and incompressible fluid as presented in equations below, the temperature of the studied PV-PCM system as well as the instantaneous velocities of the melted PCM can be found:

(

−(T − Tf )2

Wx = −A(T)·u Wy = −A(T)·v

3.3. PCM modeling

)

(

Moreover, Wx and Wy are the Darcy’s law source terms in x and y directions that are added to modify the momentum equations in the mushy zone and can be written as:

(43) Vair x is νair

(

⎛ ⎜ ⎝

)+W

y

+ ρliq (1−β (T −Tf )) gy cos α ∂u ∂x

+

∂v ∂y

=0

3.4. Electrical efficiency and power output

(44)

where ρ, cp and k are the density, the specific heat capacity and the thermal conductivity of the PCM respectively. u and v represent the velocities of the fused PCM in x and y direction respectively. P is the pressure, g is the acceleration due to gravity, β is the thermal expansion coefficient and μ is the dynamic viscosity. The density, ρ(T), as well as the thermal conductivity, k(T), of PCM are modeled using the following equations:

ρ (T ) = ρsolid + (ρliquid −ρsolid ) B (T )

(45)

K (T ) = Ksolid + (Kliq−Ksolid ) B (T )

(46)

The power output of PV cells can be simulated using the following correlation [76]:

Pout = Imp Vmp = (FF ) Isc Voc = ηpv APV FT

(52)

where Imp and Vmp are the current and voltage output at maximum power output, respectively. Apv is the surface area of the PV panel. FF is the fill factor; Isc and Voc are the open circuit current and voltage respectively. Also, the PV cell electrical output efficiency is a function of PV cell power output, solar radiation and PV cell surface area as shown in Eq. (53):

where ρliq and ρsolid describe the density of the PCM at its liquid and solid phase respectively. Moreover, ksolid and kliq are the thermal conductivity of the PCM at its solid and liquid phases respectively. The function, B (T) as mentioned in Eq. (47), is defined as the liquid fraction of the PCM in order to model the modifications of the thermo-physical properties that appear during the phase transition. It is clear that from Eq. (47) B(T) takes zero as value when the PCM is totally in solid state and takes 1 as value when it becomes fully melted. During the phase transition, B(T) increases linearly from 0 to 1between the two states [75]. Here, Tf and ΔT are the fusion temperature and the transition temperature of PCM respectively. When the PCM begins to change its

ηPVcell = Pout /(APV FT )

(53)

Moreover, the module efficiency can be represented as follows [77]:

ηPV = ηref (1−βref (TPV −Tref ))

(54)

where ηref, βref, and Tref are respectively the panel’s electrical efficiency, temperature coefficient, and temperature at STC. The value of βref is 0.004 1/K for polycrystalline PV panel [78]. Thus, the total power output is given by:

Pout = ηref (1−βref (Tpv−Tref )) AFT 965

(55)

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4. Numerical procedure, mesh independence study and model validation

investigation are presented in the following subsections: (5.1) Transient study of PV-PCM panel (5.2) Effect of the integration of different PCMs on operating PV panel temperature (5.3) Effect of thickness of PCM layer (5.4) Effect of wind azimuth angle (wind direction) (5.5) Effect of wind velocity on PV panel’s temperature (5.6) Effect of dust deposition.

COMSOL Multiphysics software is used to solve numerically the concurrent equations mentioned previously in Section 3 and subjected to the boundary conditions based on the finite element method. The dimensions of PV-PCM layers as well as the PCM thermo-physical properties were properly defined in the commercial software COMSOL Multiphysics. The numerical simulation is carried out according to the following steps: Discretization of the considered domain (size, element and type), defining the appropriate time step as well as the relative and absolute tolerances and use the appropriate solver techniques. In order to get the most suitable solution, a mesh dependence study was performed carefully for the current investigation. A triangular meshing with a regular refinement method was used for the global mesh as shown in Fig. 2. For all domains, maximum element size and element growth rate are set to 0.03 and 1.1 respectively. 26,852 finite elements are considered initially for the entire model and mesh sizes of 31,048 and 48,628 finite elements are considered when using a finer mesh. It is well noted that were not a significant difference in the obtained results for all mesh sizes. For better precision and exactness, a mesh size with 48,628 elements will be chosen for our research. The Backwards differentiation formulas (i.e. Backward Euler) time stepping method is selected for the time-dependent resolution. The maximum and minimum order of backwards differentiation principles are 5 and 1 respectively. An absolute tolerance of 0.00001 and a relative tolerance of 0.001 are applied. The time stepping is selected with an initial time step of 0.01 s and a maximum time step of 100 s. The initial temperature for all PV-PCM layers is set to 293.15 K. The two dimensional simulated model was performed for the atmospheric conditions of July 15th , for the City of Sousse, Tunisia (35.82539_N, 10.63699_E). The variation of exterior ambient temperature and solar radiation for the considered day are plotted in Fig. 3. For validation, initial calculations were carried out using the developed methodology of the present research for which similar system geometry, boundary conditions and the same material properties were used as defined by Park et al. [26]. The thermo physical properties of the PCM used for the validation of our thermodynamic model are presented in Table 2. The PV-PCM model is validated against the experimental results of Park et al. [26]. As plotted in Figs. 4 and 5, a good match between the simulated temperature of PV cell, with and without PCM, along three days using the present work and between those of Park et al. [26] with a difference within the range of ±2 °C.

5.1. Transient study of PV-PCM system The variation in temperature and velocity field in PCM (RT44HC) domain at various time intervals is shown in Fig. 6. The results show that, at the initial state, the PCM is totally in solid phase due to the fact that the solar radiation falling on PV panel surface does not exist. At daytime, PV panel temperature starts increasing with time and PCM starts absorbing and storing energy extracted from PV panel in the form of sensible heat in its solid state. In this situation, heat extracted from PV panel is very low. After a period of time, PV panel temperature decreases due to the fact that the PCM starts melting and the energy is stored in the form of latent heat. When PCM is totally melted, the total latent heat is absorbed and the PV panel temperature grows rapidly with time. As figured out in Fig. 6, the movement of the melted PCM due to natural convection is represented by arrows. The melted PCM which characterized with high velocity is represented with large arrow size and the melted PCM with low velocity is represented with small arrow size. When solar radiation decreases with time, solidification process starts when PCM reaches its solidification temperature and finally it become fully in solid phase with absence of arrows (zero velocity). 5.2. Effect of integration of different PCMs In order to study the effect of different PCMs on PV cells temperature and on the produced electrical power, three PCMs were selected where their thermo physical properties are listed in table 3. The corresponding variations of PV cells temperature with time for different PCMs along two consecutive days are plotted in Fig. 7. Interestingly, the results in Fig. 7 show that the RT44HC which is characterized with a melting temperature of 44 °C leads to lower PV temperature at daytime. These results can be justified by the latent thermal energy of RT44HC which is higher compared to RT25HC and RT35HC. The variation in temperature of PV panel and velocity field in different PCMs at t = 11 AM are shown in Fig. 9. It can be seen that at 11 AM, RT25HC and RT44HC are almost in liquid phase and in solid phase respectively. Hence, from Figs. 7 and 9 it can be illustrated that fusion process of RT25HC is much faster and starts earlier than RT35HC and RT44HC because RT25HC has the lowest fusion onset temperature of about 26.6 °C. The liquid fraction variation with time of different PCMs is shown in Fig. 8. It is well observed that the melting and solidification phenomenon of PCMs for variable solar irradiation starts at different

5. Results and discussion The performance of the PV and PVPCM systems had been analyzed in the current paper. The results and discussion of the current

Fig. 2. Mesh at different number of element of the numerical model. 966

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40

1200 Exterior ambiant temperature Solar radiation

38

800

34 32

600

30 400

28

200

2

26

Solar radiation (W/m )

Exterior ambiant temperature (°C)

1000 36

24 0

22 0

2

4

6

8

10

12

14

16

18

20

22

24

Time (hour) Fig. 3. Exterior ambient temperature and solar radiation variation with time.

in the next day due to its low fusion temperature and because of its low latent heat of fusion as plotted in Fig. 8. Hence, the amount of RT25HC to be melted in the next day is not the same and the impact in temperature reduction is not the same (the panel temperature is lower by a maximum of 9 °C and 8 °C in the first and in the next day respectively as shown in Fig. 7). For these reasons, the energy production increase is the same for the two days when using RT44HC and RT35HC but it is not the same reduction when using RT25HC as figured out in Fig. 10. For instance, the maximum generated electrical power reaches of about 12.7 W at midday of the considered days when using RT44HC and it reaches of about 12 W and 11.6 W in the first and next day when using RT25HC, respectively. RT44HC will be selected for the rest of the present research.

times. For instance, the fusion process of RT35HC and RT44HC starts at 08:00 AM and at 09:30 AM respectively and both of them will be totally melted after three hours. Moreover, each PCM remains at his fully liquid state in a different period of time of about 5 h and 7 h for RT44HC, RT35HC respectively. Therefore, as shown in Fig. 7 the same reduction in PV cells temperature at daytime, for the two days, is obtained when using RT44HC and RT35HC due to the presence of the same amount of PCM to be melted in the first day and in the next day (i.e. RT44HC and RT35HC are totally at their solid state before the solar radiation starts falling on PV panel surface as illustrated in Fig. 8 where the liquid fraction of those PCMs is zero). However, RT25HC remains at his fully liquid state of about 10 h in the first day and of about 11 h in the next day because the solidification process of RT25HC is not totally achieved

70

Present results Park et al. results

65 60

PVPCM Temperature (°C)

55 50 45 40 35 30 25 20 15 10 5 0 0

5

10

15

20

25

30

35

40

45

50

Time (h) Fig. 4. PV-PCM panel temperature variation with time. 967

55

60

65

70

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75 Our results Park et al. results

70 65 60

PV temperature (°C)

55 50 45 40 35 30 25 20 15 10 5 0 0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

Time (hours) Fig. 5. PV panel temperature variation with time without PCM.

Fig. 6. Variation in temperature (°C) and velocity field of PV-PCM panel at various time intervals.

plotted in Fig. 11. The operating temperature variation depends on the thickness of PCM layer for constant wind velocity (1 m/s) as shown in Fig. 11. The considered thermodynamic model is solved for different PCM layer thickness i.e. 1 cm, 1.5 cm, 2 cm, 2.5 cm and 3 cm. From

5.3. Effect of thickness of PCM layer As mentioned in Section 5.2 above, RT44HC is used for our research. The effect of thickness of PCM layer on PV panel temperature is

Table 3 Thermo-physical properties of the selected PCMs [34]. Melting temperature (°C)

Latent Heat of Fusion (kJ/kg)

Specific heat (kJ/kgK)

Density (kg/m3)

Thermal conductivity (W/(m K))

RT25HC

26.6

232

RT35HC

35

240

1.8 solid phase 2.4 liquid phase 2 both phases

0.19 solid phase 0.18 liquid phase 0.2 both phases

R44HC

44

250

2 both phases

785 749 880 770 800 700

968

solid phase liquid phase solid phase liquid phase solid phase liquid phase

0.2 both phases

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80

without PCM with RT25HC with RT35HC with RT44HC

76 72 68 64

Temperature (°C)

60 56 52 48 44 40 36 32 28 24 20 16 12 04 4

00 0

08 8

12

16

20

24 00

Time (h)

04 28

08 32

36 12

40 16

44 20

48 00

Fig. 7. Variation of PV cells temperature with time coupled with different PCMs.

5.4. Effect of wind azimuth angle

these results, it is clearly shown that as the thickness of the PCM layer increases, the operating temperature of the PV panel decreases with a half-hour offset at each increase of 0.5 cm of the selected PCM layer thickness. These results can be explained due to the increase of PCM melting period. In fact, once the thickness of RT44HC increases, the storage time of the energy in the form of latent heat will be greater and therefore the PV panel temperature will decrease as the thickness of the PCM layer increases. Moreover, the variation of the PCM liquid fraction and the PV panel temperature for two consecutive days for the case of PCM with 3 cm thick is figured out in Fig. 12. Interestingly, at the end of the first day the PCM does not solidify completely as illustrated in Fig. 12 (i.e. at 00:00 AM the liquid fraction is not zero (reaches 0.15)) until it remains at his fully solid state from 01:00 AM to 09:30 AM of the following morning (i.e. from 01:00 AM to 09:30 AM the melt fraction remains zero)). Therefore, the same amount of PCM to be melted the next day will be the same at daytime (with the presence of solar radiation falling on PV panel surface) and the impact in temperature reduction of the PV panel temperature is the same as shown in Fig. 12. 1,2

Prior to study the effect of the wind direction on the PV panel temperature, the wind incident angle should be evaluated. The wind incident angle is the angle comprised between the normal to PV module vector and the wind direction vector as shown in Fig. 13. Hence, an angle γ formed by the orientation vector of the PV panel, γpv , and the vector of the direction of the wind, γw , as figured out in Figs. 13 and 14, should be determined. In our case (i.e. south orientation), γ = γw as shown in Fig. 14, because γpv = 0. The variation of average PV-PCM panel temperature along the day for different wind azimuth angle for a clean system keeping south orientation and α = 30° are figured out in Fig. 15. On the basis of these results, it is clear that as wind azimuth angle is higher, the average PV panel temperature increases. It's well observed that the PV-PCM temperature increases with the increase of wind azimuth angle. These results can be explained as follows, when the wind azimuth angle decreases, the wind flow will be almost normal at the surface of the panel and therefore heat losses due to forced

RT25HC RT35HC RT44HC

1,1 1,0 0,9

Liquid fraction

0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 -0,1 00

04

08

12

16

00

20

04

08

12

Time (h) Fig. 8. Variation of liquid fraction of different PCMs with time. 969

16

20

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Fig. 9. Temperature (°C) and velocity field of PV panel coupled with different PCM at t = 11 AM.

13

without PCM with RT44HC with RT35HC with RT25HC

12 11 10

DC power (W)

9 8 7 6 5 4 3 2 1 0

0 00

04 4

12 12

8 08

16

20

24 28 00 04 Time (h)

32 08

36 12

40 16

44 20

00

Fig. 10. Variation of DC power of PV power coupled with different PCM for two consecutive days keeping α = 30°, vair = 1 m/s and γw = 30° for south orientation.

Without RT44HC

80

1 cm 1,5 cm

70

PV panel temperature

2 cm 2,5 cm

60

3 cm 50 40 30 20 10 0

2

4

6

8

10

12

14

16

18

20

22

24

Time (h) Fig. 11. Effect of thickness of PCM (RT44HC) layer for a clean system for south orientation keeping vair = 1 m/s and γw=30°.

970

Applied Thermal Engineering 141 (2018) 958–975

M. Nouira, H. Sammouda

1,1

80 Liquid fraction without RT44HC with RT44HC

1,0

75 70

0,9

65

0,8

60

Liquid fraction

55

0,6

50

0,5

45

0,4

40 35

0,3

30

0,2

PV panel temperature (°C)

0,7

25

0,1

20

0,0

15

-0,1

10

0

4

8

12

16

20

24

28

32

36

40

44

48

Time (h) Fig. 12. Effect of integration of a 3 cm of PCM (RT44HC) layer for a clean system for south orientation keeping vair = 1 m/s and γw = 30° for two consecutive days.

5.6. Dust effect

convection will be greater. Thus, a decrease in the average temperature of the PV panel is obtained.

Several previous researches on thermal modeling of PV panels coupled with PCMs had not considered the effect of dust on the performance and the operating temperature of PV panels. Dust deposition plays a vital role on the amount of solar energy absorbed by the panel and therefore on the temperature of the PV cells. Thus, it is very important to consider the dust density deposition in our modeling The developed model with 2 cm thickness of the chosen PCM (RT44HC) is studied for various dust deposition density i.e. 3 g/m2, 6 g/m2, 9 g/m2 for south orientation keeping 30° as an inclination angle. . The efficiency variation of PV panels with time is plotted in Fig. 17. It can be seen that as the density of dust deposition increases the efficiency of PV panel increases. These results are explained due to the reduction of the absorbed solar energy when dust deposition increases as shown in

5.5. Effect of wind speed It is necessary to study the impact of various wind speed values on the operating temperature of PV panel (in PV-PCM system). The effect of wind velocity on PV panel operating temperature variations with time is plotted in Fig. 16. The developed thermal model is studied for various wind velocity (i.e. 1 m/s, 2 m/s, 3 m/s and 4 m/s) at 30° angle of inclination for south orientation. From results in Fig. 16, it is well shown that as wind speed is higher, the PV panel operating temperature decreases. These results are explained due to the increase of heat losses due to forced convection when wind speed increases.

Fig. 13. PV panel orientation, wind incident angle and wind direction for PV panel not facing south. 971

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Fig. 14. PV panel orientation, wind incident angle and wind direction for PV panel facing south (our case).

6. Conclusion

Fig. 18a. For instance, the maximum absorbed energy the PV-PCM module reaches 922 W/m2, 850 W/m2, 705 W/m2 and 695 W/m2 for a clean panel, 3 g/m2, 6 g/m2 and 9 g/m2 of dust deposition density, respectively. Hence, a reduction in electrical power generated by the PVPCM panel of about 1.2 W, 2.8 W and 3 W is obtained as figured out in Fig. 18b for 3 g/m2, 6 g/m2 and 9 g/m2 of dust deposition density, respectively. Therefore, the increase of the density of the dust deposition covering the panel reduces the quantity of the absorbed solar radiation and thus an improvement on the efficiency of the PV panel is obtained. Consequently, a reduction in the produced electrical power is noticed.

In light of the current investigation, the developed thermodynamic PV-PCM model has been well investigated in order to recognize the heat, mass and momentum transfer phenomena of a PCM attached behind PV panel. The simulated studies are performed for the month of July and for the Tunisian climatic conditions of the City of Sousse (35.82539_N, 10.63699_E) which hold high quality PV panel installation potential. Some important findings and conclusions can be derived. It is observed that at midday of the two considered days, the operating temperature of the PV panel with the integration of RT35HC and

90 85

w

80

w

75

w

PV-PCM temperature (°C)

70

w

65

w

60

w

=15°

=30° =45° =60° =75° =90°

55 50 45 40 35 30 25 20 15 10 5 0

2

4

6

8

10

12

Time (h)

14

16

18

20

22

24

Fig. 15. Variation of average PV-PCM panel temperature over the day time for different wind azimuth angle for a clean system keeping vair = 1 m/s, south orientation and α = 30°. 972

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80 With RT44HC and Vair=1ms

75

With RT44HC and Vair=2ms

-1

With RT44HC and Vair=3ms

-1

65

With RT44HC and Vair=4ms

-1

60

Without RT44HC and Vair=1ms

70

Temperature (°C)

-1

-1

55 50 45 40 35 30 25 20 15 10 0

2

4

6

8

10

12

14

16

18

20

22

24

Time (h) Fig. 16. Wind Speed effect on a clean panel operating temperature keeping α = 30° and γw = 30° for south orientation.

study reveal that the maximum operating temperature reaches approximately 87 °C, 72.5 °C, 69 °C, 66 °C, 64 °C and 63 °C for wind azimuth angle of 90°, 75°, 60°, 45°, 30° and 15° respectively. A dramatic decrease in the maximum operating temperature during peak time of the day is illustrated reaching therefore 67 °C, 63 °C, 58 °C and 53 °C for wind speed of 1 m/s, 2 m/s, 3 m/s and 4 m/s respectively. As a final finding, the maximum PV-PCM efficiency reaches 13.1%, 13.4% and 13.5% for dust deposition density of 3 g/m2, 6 g/m2, and 9 g/m2 respectively leading therefore to a reduction in the maximum absorbed solar radiation of about 72 W/m2, 217 W/m2 and 227 W/ m2respectively. Hence, a reduction in PV panel power output is noticed of about 3 W, 2.8 W and 1.2 W at midday for 9 g/m2, 6 g/m2 and 3 g/m2

RT44HC behind its back surface is lower by about a maximum of 10 °C and 12 °C, respectively, when attached to the conventional PV module. However, the reduction in the maximum temperature of the PV panel is not the same when attaching RT25HC behind its back surface and it is reduced by a maximum of 9 °C and 8 °C at midday of the first day and during peak time of the next day respectively. Hence, RT44HC is the appropriate PCM and leads to increase the produced electrical power to a maximum of about 12.7 W. An obvious increase in the total period required to reach the full liquid state of the PCM layer is observed due to the increase of its thickness. Thus, the maximum operating temperature of the PV panel is reduced from 70.36 °C to 56 °C due to increase the PCM thickness from 1 cm to 3 cm. The results of the current

17,0 16,5 16,0

Efficiency (%)

15,5 15,0 14,5 14,0 13,5 13,0 12,5

clean and without RT44HC clean and with RT44HC -2 with RT44HC and D =3 gm

12,0

with RT44HC and

D

with RT44HC and

11,5 0

2

4

D

6

=6 gm

-2

=9 gm

-2

8

10

12

14

16

18

20

22

24

Time (h) Fig. 17. Effect of dust deposition density keeping α = 30°, γw = 30° and vair = 1 m/s for south orientation on PV panel efficiency with time. 973

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1000

3,4

clean panel 3 g/m2 of dust deposition density

900

6 g/m2 of dust deposition density 2

9 g/m of dust deposition density

800

2

3,2

3 g/m of dust deposition density

3,0

6 g/m of dust deposition density

2,8

9 g/m of dust deposition density

2 2

2,6 2,4 2,2

600

Power reduction (W)

2 Absorbed energy ( W/m )

700

a)

500 400 300

2,0

b)

1,8 1,6 1,4 1,2 1,0 0,8

200

0,6 0,4

100

0,2 0

0,0 0

2

4

6

8

10

12

14

16

18

20

22

24

Time (h)

0

2

4

6

8

10

12

14

16

18

20

22

24

Time (h)

Fig. 18. Effect of dust deposition density keeping α = 30°, γw = 30° and vair = 1 m/s for south orientation: (a) on the absorbed energy reduction and (b) on the electrical power reduction with time.

of dust deposition density respectively. It can be concluded that the type of the selected PCM, thickness of PCM layer, wind speed, wind azimuth angle and dust deposition density has significant effects on PV panel operating performance. Hence, such effects on PV-PCM system should be taken into consideration for many practical applications.

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