(photovoltaic/thermal) active solar still

Energy xxx (2015) 1e11

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Optimization of a PV/T (photovoltaic/thermal) active solar still F. Saeedi, F. Sarhaddi*, A. Behzadmehr Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 January 2015 Received in revised form 4 April 2015 Accepted 24 April 2015 Available online xxx

In this paper, the optimization of a PV/T (photovoltaic/thermal) active solar still is carried out. Analytical expressions for glass cover temperature, basin temperature, brackish water temperature and fresh water productivity are obtained by writing energy balance for different components of PV/T active solar still. The output electrical power of PV/T active solar still is calculated by four-parameter IeV (current evoltage) model. Objective function in present study is the energy efficiency of PV/T active solar still. A computer simulation program has been developed in order to obtain thermal and electrical parameters, respectively. The simulation results of the present study are in fair agreement with the experimental data of previous literatures. Finally, the optimization of PV/T active solar still has been carried out and the optimized value of mass flow rate, number of PV/T collector and the objective function have been obtained. Furthermore, the effect of various operating parameters on energy efficiency have been investigated. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Basin solar still PV/T collector Optimization

1. Introduction Nowadays, freshwater scarcity endangers the continuation of human life. About 1% of available water sources on the earth is drinkable and the rest of them are brackish (97%) or frozen in polar glaciers (2%) [1]. Most of warm arid countries in Middle East and North Africa are involved with water scarcity problem. Water purification causes heavy economic costs in these countries, annually [2]. Solar desalination technology is a good option to produce freshwater in remote areas and arid regions due to great solar potential and abundance of saline/brackish water sources in these zones. The most common type of solar desalination systems are basin solar stills because of their simplicity in construction, operation and low cost. Active basin solar stills have higher efficiency than passive basin solar stills because they are equipped to solar collectors [3]. Solar collector plays the role of brackish water pre-heater in PV/T active solar still and increases the average temperature of brackish water in basin. In order to circulate brackish water in solar collector, an external electrical source is needed. In order to supply the consumed electrical power of pump, the solar still is combined with PV/T (photovoltaic/thermal) solar collector. This type of system is called hybrid PV/T active solar

* Corresponding author. Tel.: þ98 54 33426206; fax: þ98 54 33447092. E-mail address: [email protected] (F. Sarhaddi).

still. The EPBT (energy payback time) of a PV/T active solar still is about 5 years [4]. If PV/T active solar still works in its optimum operating mode, its EPBT can be reduced. Therefore, the optimum performance evaluation of PV/T active solar still is important. Many researchers have investigated the assessment of solar stills performance. Tiwari et al. [5] have studied the effects of water depth and absorptivity of basin on the performance of a passive solar still in the presence of viz. concentration dye, analytically. Their analytical thermal model gives more accurate results for large water depth and low absorption coefficient. Tiwari et al. [6] have optimized the glass cover inclination of a passive basin solar still. Their numerical computations for winter and summer climate conditions have shown the yield of passive solar still increases with increase of inclination in winter and viceversa in summer. Kumar and Tiwari [7] have carried out the optimization of an active solar still integrated to FPC (flat plate solar collector). Their numerical results have shown that the optimum area of FPC collectors are 8 m2 for a 1 m2 basin area and 0.15 m water depth. Akash et al. [8] have conducted some experiments on a passive basin solar still with various cover tilt angles of 15, 25, 35, 45 and 55 in Jordan climate. They have reported that the optimum tilt angle of passive solar still is 35 . Voropoulos et al. [9] have compared the performance of a solar still which is coupled to hot water storage tank with a conventional

http://dx.doi.org/10.1016/j.energy.2015.04.062 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Saeedi F, et al., Optimization of a PV/T (photovoltaic/thermal) active solar still, Energy (2015), http://dx.doi.org/ 10.1016/j.energy.2015.04.062

2

F. Saeedi et al. / Energy xxx (2015) 1e11

passive solar still, experimentally. Their experimental results have shown that the solar still-storage tank system has better performance than the passive solar still. Abdel-Rehim and Lasheen [10] have investigated the performance of an active solar still connected to solar parabolic trough collector, experimentally. Their results have shown that the freshwater productivity of their solar still 18% is more than the conventional basin solar stills. Gaur and Tiwari [11] have obtained the optimum number of collectors for a hybrid PV/T active solar still in constant mass flow rate of PV/T collector. They have observed that the maximum exergy efficiency of hybrid PV/T active solar still occurs when the number of collectors is four. Boubekri and Chaker [12] have studied the effect of external and internal reflectors on the performance of an active solar still, numerically. Their numerical results have shown that the increase in yield of active solar still is about 27.54%, 21% and 23.28% respectively for winter, spring and summer. Sampathkumar and Senthilkumar [13] have investigated the performance of an active solar still connected to ETC (evacuated tube collector), experimentally. They have observed that the productivity of ETC solar still is twice the productivity of a conventional basin solar still. Rahbar and Esfahani [14] have developed a correlation for the productivity of basin solar still based on CFD (computational fluids dynamics) simulation. Their correlation is in a good agreement with the available well-known models. Also, they have shown that there is an optimum length in which the productivity is maximized. Kabeel et al. [15] have examined the effect of aluminum-oxide nanofluids and external condenser on the performance of a basin solar still, experimentally. Their results have shown that the usage of nanofluids and external condenser improves the solar still water productivity by about 116%. Shanmugan et al. [16] have proposed a thermal asymmetry model for basin solar still with sponge liner. Their results have shown that the system with black color sponge gives better result with a productivity of 5.3 kg/m2. Appadurai and Velmurugan [17] have investigated the fresh water production of conventional solar still, fin type solar still and fin type solar pond integrated with fin type solar still, experimentally. They observed that fin type mini solar pond integrated with conventional solar still, fin type single basin solar still and fin type mini solar pond integrated with fin type single basin solar still increase the water collection gain, which is about 47%, 45.5% and 50%, respectively.

1.1. Necessity of the present research In Refs. [6e8,11] the simple optimization of basin solar stills with respect to one design variable have been carried out. Tiwari et al. [6] and Akash et al. [8] have obtained the optimum inclination of glass cover in passive basin solar stills based on experimental observations. Kumar and Tiwari [7] and Gaur and Tiwari [11] have obtained the optimum number of solar collectors (FPC or PV/T) in active basin solar stills. On the other hand, the electrical model of the previous literatures [1e17] has some deficiencies as follows. It has a significant error at low solar radiation intensity. The output electrical power of PV/T collector is negligible when the solar radiation intensity is low. While the electrical model of the previous literatures gives the output electrical power of PV/T collector near to the nominal output electrical power of PV

module at the reference conditions (Gref ¼ 1000 W/m2, Tc,ref ¼ 25 C and air mass ¼ 1.5). It does not include the consumed electrical power by pump. The consumed electrical power of pump is significant at high mass flow rate of brackish water. The novelties of present study are as follows. The comprehensive optimization of a PV/T active basin solar still with respect to two design parameters (number of PV/T collectors and mass flow rate of system). The usage of better electrical model for the calculation of electrical parameters of PV/T active basin solar still. Our research is based on numerical simulation and included the following items. Thermal analysis is done in order to obtain the thermal parameters of solar still and PV/T collector. Electrical analysis is done in order to obtain the electrical parameters of PV module. Formulation of optimization problem is introduced. Validation of numerical simulation is carried out. Finally, some parametric studies are done in order to investigate the effect of design parameters on efficiency.

2. Thermal analysis Thermal analysis of PV/T active solar still is carried out in order to obtain analytical expressions for glass cover temperature, basin temperature, brackish water temperature, etc. Therefore, energy balance equation is written for various components of PV/T active solar still [11]. 2.1. Energy balance for glass cover condenser

ag Gs Ag þ hwg Ab Tw Tg ¼ hga Ag Tg Ta

(1)

where Tg, Tw, Ta, Gs, Ag, Ab, ag, hwg and hga are glass cover temperature, brackish water temperature, ambient temperature, solar radiation intensity on solar still, area of glass cover, area of basin, absorptivity of glass cover, overall heat coefficient between water and glass cover and overall heat coefficient between glass cover and surrounding, respectively. An expression for the glass cover temperature can be obtained from Eq. (1) as follows

Tg ¼

ag Gs þ hga Ta þ AAbg hwg Tw

(2)

hga þ AAbg hwg

2.2. Energy balance for brackish water

tg aw Gs Ab þ hbw Ab ðTb Tw Þ þ

N X

q_ u;i

i¼1

¼ Mw Cw

dTw þ hwg Ab Tw Tg dt

(3)

P _ where Tb, hbw, Mw, Cw, aw, tg and N i¼1 qu;i are basin temperature, overall heat coefficient between basin and water, mass of brackish water in basin, heat capacity of brackish water, absorptivity of brackish water, transmitivity of glass cover and the rate of useful thermal energy of PV/T collectors, respectively.



2.3. Energy balance for basin liner

b¼ tg tw ab Gs Ab ¼ hbw Ab ðTb Tw Þ þ hba Ab ðTb Ta Þ

(4)

where ab, tw and hba are absorptivity of basin liner, transmitivity of brackish water and overall heat coefficient between basin liner and ambient, respectively. Basin temperature can be obtained from Eq. (4) as follows

Tb ¼

tg tw ab Gs þ hbw Tw þ hba Ta hbw þ hba

(5)

3

Ab Ac ðatÞeff;s Gs þ NFR hp1 hp2 ðatÞeff ;c Gc Mw Cw Ab ) N FR Ac UL;c X Ac _ þ UL;s þ NFR UL;c Ta ðN iÞqu;i _ w Ab Ab mC i¼1

(10) where (at)eff,s and UL,s are the product of effective absorptivity and transmissivity of solar still and overall heat loss coefficient of solar still, respectively. They are defined as follows

ðatÞeff;s ¼ tg aw þ tg tw ab

ag hwg hbw þ hbw þ hba hga þ Ab hwg

(11)

Ag

2.4. Energy balance for PV/T collectors The details of energy balance for PV/T collectors are not mentioned to have a brief note. The proof of them is mentioned in Ref. [18]. The rate of useful thermal energy of each PV/T collector in series is calculated from the following equation [18].

8 > > < > > : q_ u;N

h i q_ u;1 ¼ FR Ac hp1 hp2 ðatÞeff;c Gc UL;c ðTw Ta Þ ; " !# 1 X 1 N ¼ FR Ac hp1 hp2 ðatÞeff ;c Gc UL;c q_ u;i þ Tw Ta ; _ w mC

UL;s ¼

hga hwg hbw hba þ hbw þ hba hga þ Ab hwg

(12)

Ag

The average temperature of brackish water in time interval Dt can be obtained from the solution of Eq. (8) as follows

9 N ¼ 1> > = > ; N 2>

(6)

i¼1

_ FR and (at)eff,c are area of solar collector, solar where Ac, Gc, UL;c , m, radiation intensity received by solar collector, overall heat loss coefficient of solar collector, mass flow rate of brackish water in solar collector, heat removal factor and the product of effective absorptivity and transmissivity of solar collector, respectively. Also, hp1 and hp2 are penalty factors. For the case of FPC collectors, the value of (at)eff,c, hp1 and hp2 are considered 0.85, 1 and 1, respectively. For N number of PV/T collectors which are connected in series with the aid of Eq. (6), the rate of useful thermal energy of PV/T collectors can be obtained as follows N X i¼1

q_ u;i ¼ q_ u;1 þ q_ u;2 þ q_ u;3 þ … þ q_ u;N

FR Ac UL;c _ w mC

ðN iÞq_ u;i

q_ ev ¼ hev Ab Tw Tg

(14)

The freshwater productivity of active solar still in time interval

Dt is given by q_ ev Dt hfg

(15)

3. Electrical analysis

(8)

where Tw0 is the temperature of brackish water at t ¼ 0 and the coefficients a and b are defined as follows

Ab Ac UL;s þ NFR UL;c Mw Cw Ab

After calculating the average temperature of brackish water by Eq. (13), we obtain the average temperature of glass cover and basin from the Eqs. (2) and (5). The rate of evaporative energy of solar still is given as

(7)

An ordinary differential equation for brackish water temperature is obtained by substituting Eqs. (2), (5) and (7) into Eq. (3).

a¼

(13)

where hfg is the latent heat of water vaporization.

i¼1

8 < dTw þ aT ¼ b w dt : Tw ð0Þ ¼ Tw0

b 1 expð aDtÞ 1 expð aDtÞ 1 þ Tw0 a aDt aDt

mw ¼

h i ¼ NFR Ac hp1 hp2 ðatÞeff ;c Gc UL;c ðTw Ta Þ N X

Tw ¼

(9)

In the previous literatures [1e17], the output electrical power of PV/T collector has been calculated from

h

i q_ el ¼ hel;ref 1 0:0045 Tc Ta;ref Gc Ac

(16)

where hel,ref, Ta,ref and Tc are electrical efficiency of PV module in reference conditions, ambient temperature in reference conditions and PV/T collector temperature, respectively. This equation has some deficiencies; first, at low solar radiation intensity, it gives the output electrical power of PV/T collector equals the output electrical power of PV module at reference conditions (q_ el zq_ el;ref s0). The equivalence of PV/T collector temperature and ambient


4


temperature is the reason of this fact. Second, Eq. (16) does not include the consumed electrical power of pump. In present study, the foureparameter IeV (currentevoltage) model are used to calculate the electrical parameters of PV/T collector. This model and its parameters in reference conditions is given by Ref. [19].

voltage temperature coefficient, respectively. Vmp and Imp is the coordinate of a point on the IeV characteristic curve. This point corresponds the maximum area of rectangle under the IeV curve. The consumed electrical power of pump needed to circulate water in the PV/T active solar still is calculated from

V þ IRs 1 I ¼ IL Io exp a

q_ p ¼

2Vmp;ref Voc;ref

aref ¼

Imp;ref Isc;ref Imp;ref

þ ln 1

(17)

!

(18)

Imp;ref Isc;ref

Voc;ref aref

!

aref ln 1 Rs;ref ¼

4. Energy efficiency of PV/T active solar still Energy efficiency of PV/T active solar still is defined as the ratio of net output (desired) energy rate to net input energy rate.

Imp;ref Isc;ref

Vmp;ref þ Voc;ref (21)

Imp;ref

where I, V, Voc, Vmp, Isc, Imp, a, IL, Io and Rs are PV current, PV voltage, open-circuit voltage, maximum power point voltage, short-circuit current, maximum power point current, ideality factor, light current, diode reverse saturation current and series resistance, respectively. The subscript ‘ref’ indicates the value of parameters at the reference conditions (Tc,ref ¼ 25 C , Ta,ref ¼ 25 C , Gref ¼ 1000 W/ m2). The value of Voc, Vmp, Isc and Imp at reference conditions is given by PV module manufactures. In order to calculate the electrical parameters at actual operating conditions (Gc, Tc), a set of translation equations is used as follows [18].

a Tc ¼ aref Tc;ref

IL ¼

¼

(32)

(20)

!

Io;ref

where DP, r and hp are pressure drop in PV/T active solar still, density of water and pump efficiency, respectively. The electrical output of PV/T active solar still is given by

(19)

Io;ref ¼ Isc;ref exp

Tc

(31)

q_ el ¼ Vmp Imp q_ p

IL;ref ¼ Isc;ref

Io

_ mDP rhp

!3

Tc;ref

εNc exp aref

Tc;ref 1 Tc

i Gc h IL;ref þ a Tc Tc;ref Gref

DT ¼ Tc Tc;ref ! Gc DI ¼ a DT þ Gref

(33)

Fig. 1 shows the control volume of PV/T active solar still and the various components of energy rate in the control volume. The general form of energy balance equation for the control volume of Fig. 1 is written as

X

_ En in

X

_ out ¼ En

dEn dt cv

(34)

(22)

P _ P _ Enin , Enout and (dEn/dt)cv are inlet energies rate, outlet where energies rate, and the change of energy rate within the control volume, respectively. Substituting the various energy rates of control volume of Fig. 1 into the Eq. (34), we obtain an equation for the desired output energy rate as follows

(23)

X

!

dTw _ En out;des ¼ q_ ev þ q_ el ¼ q_ solar;s þ q_ solar;c q_ loss Cw Mw dt (35)

(24) (25)

! Gc 1 Isc;ref Gref

P _ Enout;des hen ¼ P _ En in;net

In our problem, the net input energy rate includes solar radiation intensity received by solar still and PV/T collectors.

X

_ En in;net ¼ q_ solar;s þ q_ solar;c

(36)

(26) Substituting Eqs. (35) and (36) into Eq. (33), we can obtain the energy efficiency of PV/T active solar still as follows

DV ¼ bDT Rs DI

(27)

Isc ¼ Isc;ref þ DI

(28)

Voc ¼ Voc;ref þ DV

(29)

Rs zRs;ref

(30)

where ε, Nc, a and b are semiconductor band gap energy, solar cells number in PV module, current temperature coefficient and

hen ¼

_ Vmp Imp mDP rhp hev Ab Tw Tg þ Cf

Ab Gs þ NAc Gc

¼1

w q_ loss þ Cw Mw dT dt Ab Gs þ NAc Gc

(37)

The quality of thermal energy and electrical energy are not the same. Here, Cf is a conversion factor which converts the output electrical power of PV/T active solar still to its equivalent thermal power [11]. Eq. (37) can be rewritten in the following form



5

Fig. 1. Control volume of PV/T active solar still and the various components of energy rate in the control volume.

Table 1 Design parameters of PV/T active solar still. Parameters

Value

PV module type Area of PV/T collector Number of PV modules on PV/T collector Area of PV module Area of basin Area of glass cover Angle of glass cover Angle of PV/T collector Time interval Short-circuit current at reference conditions Open-circuit voltage at reference conditions Maximum power point current at reference conditions Maximum power point voltage at reference conditions Current temperature coefficient Voltage temperature coefficient Semiconductor band gap energy Number of solar cells in PV module Transmitivity of glass cover Transmitivity of water Absorptivity of glass cover Absorptivity of basin liner Absorptivity of water Pump efficiency Energy conversion factor

glass to glass mono-crystalline silicon, 75 W Ac ¼ 2 m2 Nm ¼ 3 Am ¼ 0.66 m2 Ab ¼ 1 m2 Ag ¼ 1.16 m2 qg ¼ 30 qc ¼ 45 Dt ¼ 3600 s Isc,ref ¼ Nm 4.8 A Voc,ref ¼ 21.7 V Imp,ref ¼ Nm 4.4 A Vmp,ref ¼ 17 V a ¼ 2.06 mA/C b¼ 0.077 V/C ε ¼ 1.12 eV Nc ¼ 36 tg ¼ 0.95 tw ¼ 0.360.08log(Hw) ag ¼ 0.05 ab ¼ 0.9 aw ¼ 1tw hp ¼ 0.8 Cf ¼ 0.38


6


hev Ab ðTw Tg Þ Ab Gs

hen ¼

¼

1þ

NAc Gc Ab Gs

hth;s c Gc 1 þ NA A Gs b

Table 2 The operators used in real coded genetic algorithm.

_ Vmp Imp mDP rh p

þ NAc Gc Ab Gs 1 þ NA Cf c Gc hel;c Cf

þ Ab Gs 1 þ NA c Gc

(38)

Operator

Type

Selection Crossover Mutation

Linear ranking selection Arithmetical variable point crossover Real number uniform mutation

6. Validation of numerical simulation where hth,s and hel,c are the thermal efficiency of basin solar still and the electrical efficiency of PV/T collectors, respectively. In the previous studies [1e17], the energy efficiency of PV/T active solar still has been considered the summation of thermal efficiency of basin solar still and the electrical efficiency of PV/T collectors as follows

hen ¼ hth;s þ

hel;c Cf

(39)

The PV/T active solar still includes two main components: basin solar still and PV/T collector. Eq. (38) is obtained based on energy balance approach. According to this equation, it is seemed that the Eq. (39), which is the summation of the efficiency of two different components, is not true. The design parameters of PV/T active solar still are described in Table 1.

5. Formulation of optimization problem The optimization of PV/T active solar still increases its efficiency and reduces its EPBT. In order to solve the governing equations obtained from the thermal and electrical models of the previous sections, a computer simulation program has been developed. The formulation of optimization problem, considering the quantities ag, aw, ab, tg, tw, a, b, ε, hp, Nc, Ta, Ta,ref, Tc,ref, Gs, Gc, Gref, Mw, Dt, Ag, Ab, Ac, etc. as constant parameters is given by

Our research is based on numerical simulation. The results of numerical simulation of present research have been validated by the experimental results of Kumar and Tiwari [3] for a sample hybrid PV/T active solar still. Kumar and Tiwari has been designed and tested a PV/T active solar still for composite climate at I.I.T. New Delhi. They have observed that the PV/T active solar still gives a higher yield (more than 3.5 times) than the passive solar still. Their experimental setup includes a basin solar still and two FPC collectors. The area of each FPC collector is 2 m2. One of them is equipped by a PV module (glass to glass type, 75 W) with area of 0.66 m2. The area of basin and glass cover are 1 and 1.16 m2, respectively. The mass of water in basin is 50 kg. More details of their experimental setup can be found in Ref. [3]. The experimental data of Kumar and Tiwari [3] include solar radiation intensity received by solar still and solar collectors, freshwater productivity and output electrical power. The simulated values of freshwater productivity and output electrical power have been validated by their corresponding experimental values in Ref. [3]. In order to compare the simulated results with the experimental measurements, a relative error has been evaluated by following equation

n X 1X sim;i Xexp;i Er ¼ 100 n Xexp;i

(40)

i¼1

where n is the number of the experiments carried out.

8 Maximize hen ¼ Eq:ð37Þ; > > > subject to > > > > > Eqs: ð1Þ ð32Þ > > > > > and > < 0:001 m_ 0:25 kg=s; > 1 N 50; > > > N is integer; > > > > > Tg ; Tb ; Tw ; Tc ; mw ; Cw ; r; Io ; IL ; Rs ; a; Isc ; Voc ; Imp ; Vmp ; q_ ev ; q_ el ; q_ p ; q_ u;i ; > > > > > UL;s ; UL;c ; hwg ; hga ; hbw ; hba ; hfg ; DP; ðatÞeff ;s ; ðatÞeff;c ; FR ; hp1 ; hp2 > 0; : other nonlinear constraints:

The comprehensive optimization of PV/T active solar still is carried out with respect to the mass flow rate of system and the number of PV/T collectors. The objective function and its constraint equations are nonlinear. Therefore, a real coded genetic algorithm program has been developed to optimize the objective function [20]. The structure of real coded genetic algorithm is similar to the simple genetic algorithms. However, the definition of operators in real coded genetic algorithm is different from simple genetic algorithm. Table 2 summarizes the operators used in real coded genetic algorithm of present study [20].

The variations of solar radiation intensity received by solar still and solar radiation intensity received by solar collectors during the test day are shown in Fig. 2. According to Fig. 2, the maximum value of solar radiation intensity has been occurred at noon. There is a discrepancy between the solar radiation received by solar collectors and that received by the solar still. The main reason of this discrepancy is the difference of tilt angle of solar collectors (45 ) and solar still (30 ). A comparison between the experimental and simulated values of output electrical power of PV/T active solar still is carried out in Fig. 3.



It is observed from Fig. 3 that there is a fair agreement between the simulated and experimental values of this parameter and its relative error is 16.33%. The main reasons of difference between the simulated and experimental values of output electrical power can be expressed as follows. the temperature coefficients of current and voltage have been assumed constant. In practical cases, there is slight fluctuation due to the solar radiation intensity and PV module temperature variations; the experimental results of Ref. [3] has been obtained from the figures of Ref. [3] by interpolation and curve fitting methods. This subject decreases the precision of measured data; hourly wind speed during the course of experiments has not been reported in Ref. [3]. A wind speed of 1 m/s is assumed to have a comparison with the experimental data. This subject has a direct effect on the values of simulated results. However, additional calculations for various wind speeds are carried out in the next section. The simulated and experimental values of freshwater productivity during the test day are shown in Fig. 4. According to this figure, it is observed that there is a fair agreement between the simulated and experimental value of this parameter with a relative error of 26.94%. This relative error value can be considered fair agreement because the relative error value of freshwater productivity reported in the previous literature has greater values (for example Er ¼ 36.98% in Ref. [21]). When the variations range of a parameter is very low, so even a small error produces a great percentage error. In this state, the linear coefficient of regression is evaluated by using the following expression [21]:

n

Pn

i¼1

! Xexp;i $Xsim;i

Pn

i¼1

! Xexp;i $

Pn

i¼1

7

Fig. 5 shows the variations of energy efficiency with respect to mass flow rate and number of PV/T collectors. According to Fig. 5, it is observed that there is one global maximum point. The coordinate of this point shows the values of optimized parameters. The calculated values of global maximum point are m_ opt ¼ 0:044 kg=s, Nopt ¼ 7, hen,max ¼ 21.56%. In the optimum value of number of PV/T collectors (Nopt ¼ 7) it is observed that by increasing mass flow rate from 0.001 to 0.25 kg/s, initially the energy efficiency increases from ~17% to its optimum value (21.56%) and then it decreases to ~16%. The value of 0.044 kg/s is the optimum value of mass flow rate for the given design parameters of Table 1. The increase of mass flow rate increases pressure drop, therefore the consumed electrical power of pump increases and it causes a significant drop in the energy efficiency. In the previous literatures, it is assumed that the consumed electrical power of pump is negligible. This assumption is not true for high mass flow rates. 7.2. Parametric studies In parametric studies process, the design parameters of PV/T active solar still are considered according to Table 1. The rest of needed parameters are mentioned above each figure. The main purpose of optimization of PV/T active solar still is higher production of freshwater. Fig. 6 shows the daily freshwater productivity of PV/T active solar still in the various number of PV/T collectors. It is observed from Fig. 6 that daily freshwater productivity increases with the increase of number of PV/T collectors. The increase of number of PV/T collectors increases water temperature in basin and it causes the increase of daily freshwater productivity. However, the increase of daily freshwater productivity is not

! Xsim;i

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! !2ffi v ! !2ffi u u u u P P P P n n n n tn 2 2 $tn i¼1 X exp;i i¼1 Xexp;i i¼1 X sim;i i¼1 Xsim;i

(41)

Upper bound of ‘r’ is 1. The linear coefficient of regression between the simulated and experimental values of freshwater productivity is very close to 1.

7. Results and discussion The relations of water properties and heat transfer coefficients of basin solar still and PV/T collector (r, Cw, UL,s, UL,c, hwg, hga, hbw, hba, hfg, (at)eff,s, (at)eff,c, FR, hp1, hp2) are found in Refs. [11,18]. They are not mentioned to have a brief note.

7.1. Optimization results The optimization of PV/T active solar still is carried out for the selected design parameters according to Table 1. The objective function is the energy efficiency of PV/T active solar still. It should be maximized. The optimization independent parameters are the mass flow rate of brackish water and the number of PV/T collectors.

Fig. 2. Variations of solar radiation intensity received by solar still and solar radiation intensity received by solar collectors during the test day.


8


Fig. 5. Variations of energy efficiency with respect to mass flow rate and number of PV/T collectors. Fig. 3. Simulated and experimental values of output electrical power of PV/T active solar still during the test day.

Fig. 4. Simulated and experimental values of freshwater productivity during the test day.

considerable after N 30. In other words, there is an upper bound for the daily freshwater productivity of active PV/T solar still. P mw ¼ 8:37 kgÞ: ð daily

The effect of usage of additional output electrical power of PV/T collector to preheat brackish water on daily freshwater productivity is investigated in Fig. 7. The cost of the bottled water in Indian market is about Rs. 10/kg [4]. On the other hand, the cost of distilled water obtained from a PV/T active solar still is about Rs. 1.93/kg. Therefore, the production of distilled water by a PV/T active solar still is economic. The cost of distilled water obtained from a PV/T active solar still can be reduced to Rs. 1.5/kg if the additional output electrical power of PV/T collector is used to preheat brackish water in basin. Fig. 8 shows the simultaneous effect of mass of water in basin and number of PV/T collectors on the energy efficiency. According to Fig. 8, it is observed that the energy efficiency decreases with the increase of mass of water in basin. This decrease

Fig. 6. Daily freshwater productivity of PV/T active solar still in the various number of PV/T collectors.

is significant for N 7. The decrease of mass of water from 50 to 1 kg decreases water depth in basin, therefore the evaporative heat transfer in solar still increases and it causes a significant increase in the energy efficiency. It is concluded that from the figure, the maximum value of energy efficiency is strongly connected to the mass of water in basin. Energy efficiency is higher for the low values of the mass of water in basin. Fig. 9 shows the variations of the energy efficiency with respect to ambient temperature. According to Fig. 9, it is observed that by increasing ambient temperature from 27 to 47 C, the energy efficiency decreases from 21.56% to ~20%. The increase of ambient temperature increases the temperature of glass cover condenser, therefore the distillated water decreases and it causes energy efficiency decrease. The variations of the energy efficiency of the present study and the energy efficiency based on the electrical model of the previous literatures with respect to solar radiation intensity are shown in Fig. 10.



Fig. 7. Effect of usage of additional output electrical power of PV/T collector to preheat brackish water on daily freshwater productivity.

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Fig. 10. Variations of the energy efficiency with respect to solar radiation intensity.

Fig. 8. Simultaneous effect of mass of water in basin and number of PV/T collectors on the energy efficiency.

Fig. 11. Variations of the energy efficiency with respect to wind speed.

Fig. 9. Variations of the energy efficiency with respect to ambient temperature.

According to Fig. 10, it is observed that by increasing solar radiation intensity from 4 to 1000 W/m2, initially the energy efficiency of the present study increases from 0% to ~23.5% and then it decreases to ~19.8%. The energy efficiency based on the electrical model of the previous literatures has the same behavior with respect to solar radiation intensity. Since it does not include the consumed electrical power of pump, its relative values are more than the energy efficiency values of the present study. On the other hand, it is observed that the energy efficiency based on the electrical model of the previous literatures has a significant error at low solar radiation intensity. The electrical model of the previous literatures gives the output electrical power of PV/T collector equals the output electrical power of PV module at reference conditions (q_ el zq_ el;ref s0). The equivalence of PV/T collector temperature and ambient temperature is the reason of this fact. In actual conditions, the output electrical power of PV/T collector is negligible when the solar radiation intensity is low.


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by increasing ambient temperature and the mass of water in basin, the energy efficiency of PV/T active solar still decreases. There are the various kinds of energies (heat and electricity) in a PV/T active solar still. As we know, the quality of these two kinds of energies is not the same. Using exergy analysis, we can compare these two kinds of energies, which are different in their quality. Therefore, our future work will be on the exergy optimization of PV/ T active solar stills. Nomenclature a A Cf Cw Er _ En Fig. 12. Variations of the energy efficiency with respect to the area of basin.

Fig. 11 shows the variations of the energy efficiency with respect to wind speed. According to Fig. 11, it is observed that the energy efficiency increases with the increase of wind speed. The increase of wind speed decreases the temperature of glass cover condenser, therefore the distillated water increases and it causes a significant increase in the energy efficiency. Fig. 12 shows the variations of the energy efficiency with respect to the area of basin. It is observed from Fig. 12 that the energy efficiency increases with the increase of the area of basin. The absorbed solar energy is increased by increasing the area of basin. Therefore, water temperature in basin increases and it causes a significant increase in the energy efficiency. 8. Conclusion The use of PV/T active solar stills to produce freshwater is limited due to low production per unit area. Therefore, the optimization of PV/T active solar stills is needed to increase their yield. In this research, energy optimization have been carried out to enhance the efficiency of PV/T active solar stills. The following concluding remarks have been obtained from the present study: the numerical simulation results of the present study are in fair agreement with the experimental measurements of Kumar and Tiwari [3]; the electrical model of the previous literatures has a significant error at low solar radiation intensity. This deficiency has been corrected in the modified energy efficiency of the present study; since the energy efficiency based on the electrical model of the previous literatures does not include the consumed electrical power of pump, its relative values are more than the energy efficiency values of the present work. the assumption of negligible amount of the consumed electrical power of pump is not true for high mass flow rate in PV/T active solar still. the comprehensive optimization presents a range of operational and design conditions where the energy efficiency takes a global maximum value; by increasing wind speed and the area of basin, the energy efficiency of PV/T active solar still increases;

FR G h hfg H hp1 hp2 I IeV mw Mw m_ n N Nc Nm P q_ r Rs t T Tw0 UL V X

ideality factor (eV) area (m2) energy conversion factor specific heat capacity of water (J/kg.K) relative error (%) energy rate (W) heat removal factor solar radiation intensity (W/m) overall heat transfer coefficient (W/m2.K) latent heat of water vaporization (J/kg) water depth (m) penalty factor due to the presence of solar cell material, glass and EVA penalty factor due to the presence of interface between absorber plate and working fluid circuit current (A) currentevoltage mass of distillated water (kg) mass of water in basin (kg) mass flow rate of water (kg/s) number of the experiment carried out number of PV/T collectors number of cells in PV module number of PV module pressure (Pa) energy rate (W) linear coefficient of regression series resistance (U) time (s) temperature (K) initial temperature of brackish water (K) overall heat loss coefficient from the PV/T collector or solar still to the environment (W/m2.K) circuit voltage (V), wind speed (m/s) experimental or simulated parameter

Greek symbols a absorptivity, current temperature coefficient (mA /C) (at)eff product of effective absorptivity and transmittivity b voltage temperature coefficient (V/ C) q tilt angle ( ) D difference in current, pressure, temperature, time, voltage ε semiconductor band gap energy (eV) h efficiency (%) r density (kg/m3) t transmittivity Subscripts a ambient b basin ba basin to ambient bw basin to water



c daily des el en ev exp g ga i in loss L m max mp net o oc opt out p ref s sc sim solar th u w wg

cell, collector daily desired electrical energy evaporative experimental glass cover glass cover to ambient i-th parameter inlet loss light current module maximum maximum power point net reverse saturation open-circuit optimum outlet pump reference still short-circuit simulated solar thermal useful water, wind water to glass cover

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