Comparative study of two weir type cascade solar stills with and without PCM storage using energy and exergy analysis

Energy Conversion and Management 133 (2017) 97–109

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Comparative study of two weir type cascade solar stills with and without PCM storage using energy and exergy analysis Faramarz Sarhaddi a, Farshad Farshchi Tabrizi b,c,⇑, Halimeh Aghaei Zoori c, Seyed Amir Hossein Seyed Mousavi d,c a

Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan, Iran d Department of Chemical Engineering, Tarbiat Modares University, Tehran, Iran b c

a r t i c l e

i n f o

Article history: Received 8 August 2016 Received in revised form 17 November 2016 Accepted 18 November 2016

Keywords: Weir type cascade solar still Energy efficiency Exergy efficiency Irreversibility rate Phase change material (PCM)

a b s t r a c t In this paper, the comparative study of energy and exergy performance of two weir type cascade solar stills with and without PCM storage in sunny and semi-cloudy days is carried out. The governing equations of energy analysis include a set of nonlinear equations which is obtained by writing energy balance for the various components of a solar still (i.e. glass cover, brackish water, absorber plate, phase change materials). A detailed exergy analysis is carried out and various irreversibility rates in the solar still system and its exergy efficiency are introduced. In order to solve the governing equations a computer simulation program is developed. The results of a numerical simulation of the present study are in good agreement with the experimental data of previous literatures. The numerical results of the present study show that the energy and exergy performance of solar still without PCM storage is better than the solar still with PCM storage in sunny days. On the other hand, the solar still with PCM storage is preferred for semi-cloudy days due to its better energy and exergy performance. The maximum value of the energy and exergy efficiencies of the solar still without PCM for a typical sunny day are 76.69% and 6.53%, respectively. While, the maximum energy and exergy efficiencies of the solar still with PCM for a sample semicloudy day are 74.35% and 8.59%, respectively. Furthermore, it is observed that the highest irreversibility rate belongs to the absorber plate and its value for the solar still without PCM on typical sunny day and the solar still with PCM on semi-cloudy days is 83.1% and 78.8% of the whole of system irreversibility rates, respectively. Whereas, the irreversibility rate of glass cover and brackish water can be neglected. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Nowadays, burning fossil fuels to provide different kinds of energy causes many environmental problems such as climate change and air pollution; therefore, tendency to use renewable energy especially solar energy as an alternative choice has increased [1–3]. Solar energy also has many application [4,5] such as brackish water desalination [6–8]. Providing a clean source of drinking water becomes more demanding every year and it has turned to a problem in human societies [9]. Because of the population growth and industrial activities, the different sources of potable water including rivers, lakes, and underground aquifers have been contaminated [10,11]. An appropriate way to supply potable ⇑ Corresponding author at: Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran. E-mail address: [email protected] (F. Farshchi Tabrizi). http://dx.doi.org/10.1016/j.enconman.2016.11.044 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

water in arid and remote areas is the utilization of solar energy by solar stills [12]. Cascade solar stills are one of the most common types of solar stills due to the simple operation and low construction and maintenance costs. As it is revealed in Fig. 1, in a cascade solar still, water flows down the steps as a thin layer. Solar light heat up the water and the evaporated water is collected at the bottom of the solar still. Due to the small distance between the glass cover and absorber plate, the still becomes rapidly saturated with water and it has higher efficiency compared with the other types of solar stills. A weir, with 2 cm height and 59 cm length, was applied on the edge of each step to distribute the brine water flow equally onto the evaporation surface. Moreover, the weirs help to raise the time spent on the evaporation surface [13]. The brackish water is supplied from a storage tank. Storage tank contains 500 lit of brackish water and it is placed about 1.5 m above the still to retain the mass of water at the constant value. About 50 L of brackish water from storage tank is consumed in one course of experiments.

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Nomenclature A (m2) area C (J/kg
°C) specific heat capacity d (m) distance between water surface and glass cover dEn (W) accumulated energy rate dt En (W) energy rate Ex (W) exergy rate dEx dt

(W)

accumulated exergy rate

Fr exergy fraction gravitational acceleration g (m/s2) Gr Grashof number Gr0 modified Grashof number h (W/m2
°C) overall heat transfer coefficient h1 (W/m2
°C) convective heat transfer coefficient from absorber plate to water h2 (W/m2
°C) overall heat transfer coefficient from water surface to the inner surface of glass cover hfg (J/kg) latent heat of vaporization of water I(t) (W/m2) solar irradiation Ion (W/m2) solar irradiation on a plate perpendicular to irradiation direction out of the atmosphere Ir (W) irreversibility rate L (kJ/kg) PCM heat of fusion k (W/m
°C) thermal conductivity m (kg) mass M (J/°C) heat capacity of PCM _ (kg/min) mass flow rate m _ ew (kg/m2
h) hourly productivity m n number of experiments in each day P (Pa) partial vapor pressure Pr Prandtl number t (h) time T (°C) temperature RMSD (%) root mean square percentage deviation U (W/m2
°C) heat loss coefficient V (m/s) fluid velocity x0 (m) rectangle characteristic length x (m) thickness xi,exp experimental data xi,sim simulation data

Also, cascade solar stills have higher efficiency and productivity than the basin type solar stills [14]. The main deficiency of solar stills is their low productivity in semi-cloudy days. A semicloudy day is defined as a day with cloudiness index 3–5 [15]. A latent heat storage system is usually connected to cascade solar still in order to increase its productivity in semi-cloudy days [16]. The heat storage system contains phase change materials (PCM). Phase change materials (PCM) are substances that absorb and release thermal energy during the process of melting and freezing. When a PCM freezes, it releases a large amount of energy in the form of latent heat at a relatively constant temperature [17]. The performance evaluation of cascade solar stills gives some criteria for the improvement of their productivity and efficiency. It can be investigated in terms of energy analysis or exergy analysis. Exergy analysis usually provides a more realistic and practical view of the process than energy analysis [18]. Many researchers have studied the performance evaluation of solar stills based on energy or exergy analysis [6,7,16]. Aybar [19] has investigated the water productivity of an inclined cascade solar still in the various levels of solar radiation intensity.

Subscripts a b c des e equ ex in ins g l loss m out p PCM t th r s sun v w

ambient black convection destruction evaporation equivalent exergy inlet insulation glass liquid loss melting out absorber plate phase change material top thermal radiation solid, sky sun humid air water

Greeks

a

absorption coefficient glass cover angle thermal expansion coefficient s reflection coefficient sb transmission coefficient for diffusing photons/beams sd transmission coefficient for diffusing photons/beams q (kg/m3) density l (N
s/m2) fluid viscosity d0 incremental rise h zenith angle hz angle between solar irradiance and glass cover DT (°C) temperature difference DT0 (°C) effective temperature difference g (%) efficiency b (°) b0 (K1)

They have observed that the daily fresh water productivity of the system is between 3.5 and 5.4 kg/day. Torchia et al. [20] have carried out the exergy analysis of a passive basin solar still. Their results show that the collector component has the highest irreversibility rate in solar still. On the other hand, the irreversibility rates of solar still increases with the increase of solar radiation intensity due to the increase of the temperature of various components of solar still. El-Sebaii et al. [21] have developed a transient mathematical model for the performance analysis of a single basin solar still with and without PCM. They have reported that the basin solar still equipped to PCM has more productivity for the time interval of 24 h of day and night because PCM provides the possibility of fresh water productivity especially at night. Zoori et al. [22] have investigated the effect of mass flow rate of brackish water on the energy and exergy efficiency of a weir type cascade solar still under sunny days conditions. Their simulation results have shown that the maximum energy and exergy efficiencies are obtained at the minimum inlet brine flow rate of 0.065 kg/min. Tabrizi et al. [16] have carried out the energy performance evaluation of a weir-type cascade solar still connected to a latent heat storage system. Their results have shown that the

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Fig. 1. Schematic view of a cascade solar still [13].

connection of latent heat storage system to cascade solar still improves significantly the fresh water productivity on semicloudy days. Ziabari et al. [23] have carried out some modifications on the design of a cascade solar still in order to prevent the channelization of brackish water flow on the steps of cascade solar still. Their modifications cause the increase of 26% in fresh water productivity with respect to the primary design of cascade solar still. Ansari et al. [24] have used phase change materials to store thermal energy in a passive solar still connected to a heat energy storage system. They have indicated that the excess absorbed solar energy of absorber plate during sunshine is stored in a phase change material to utilize later during the night. Moreover, they have specified that the choice of the PCM type depends on the maximum water temperature in basin. Alaudeen et al. [25] have investigated the energy performance of a stepped solar still connected to a flat plate collector. They have pointed out that the flat plate collector preheats of brackish water in the entrance of solar still; therefore, its connection to step solar still increases the fresh water productivity. Hansen et al. [26] have investigated the usage of various wick materials on the performance of an inclined type solar still, experimentally. The wick materials include wood pulp paper wick, wicking water coral fleece fabric and polystyrene sponge. They have reported that the inclined type solar still with coral fleece and weir mesh-stepped absorber plate has more productivity. Its fresh water productivity is 4.28 L/day. In the previous studies [26] the exergy performance evaluation of a weir type cascade solar still equipped to PCM thermal storage is not carried out. Also, the determination of irreversibility rates of different parts a weir type cascade solar still with PCM and without PCM is not carried out. Therefore, in this research a comparative study of two weir type cascade solar stills with and without PCM storage using energy and exergy analysis for a sunny and semi-cloudy days is carried out. Our research is based on numerical simulation. A thermal model presented by Dashtban et al. [13] is used to obtain the thermal parameters and the energy efficiency of cascade solar still. A detailed exergy analysis is carried out in order to introduce the various irreversibility rates of cascade solar still and its exergy efficiency. The validation and parametric studies of the simulation results are the other parts of the present research.

2. Energy analysis The goal of energy analysis is the derivation of a set of equations in order to calculate the temperature of various components of cascade solar still. The various components of the cascade solar still includes glass cover, brackish water, absorber plate and PCM layer. The set of governing equations is obtained by writing energy balance for the mentioned components. The following assumptions are used in the development of energy balances [13]:  There is no leak from the solar still.  Heat loss from the sides of the solar still has been considered negligible.  Water and glass temperature are considered uniform along their path.  No convection in PCM layer.  Considering small thickness of phase change material, there is no temperature gradient throughout the PCM. The schematic diagram of energy rates for both solar stills (with and without PCM) is shown in Fig. 2. 2.1. Solar still with PCM Based-on the aforementioned assumptions, energy balance for the different elements of the still can be derived as follows. 2.1.1. Glass cover Energy balance for glass cover is expressed as follows [13].

ag IðtÞAg þ h2 Aw ðT w  T g Þ ¼ hc;ga Ag ðT g  T a Þ þ hr;gs Ag ðT g  T s Þ þ ðmg C g Þ


 dT g dt

ð1Þ

According to Eq. (1), parameter h2 equals to the summation of heat transfer coefficients from water to inner surface of the glass cover (h2 = hrw + hcw + hew) and hrw, hcw and hew are convection, radiation, and evaporation heat transfer coefficient, respectively. It is worth to note that details about calculation of the mentioned

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Fig. 2. (A) Energy balance of glass cover. (B) Energy balance of brackish water. (C) Energy balance of absorber plate (with PCM). (D) Energy balance of PCM. (E) Energy balance of absorber plate (without PCM).

heat transfer coefficients are presented in [13,22,27]. Besides, hc;ga and hr;gs are convection and radiation heat transfer coefficient from glass to environment and sky, respectively [22].




ap sg sw IðtÞAp ¼ h1 Ap ðT p  T w Þ þ Ap

2.1.2. Brackish water Energy balance for brackish water is expressed as follows

sg aw IðtÞAw þ h1 Ap ðT p  T w Þ ¼ h2 Aw ðT w  T g Þ þ ðmw C w Þ

2.1.3. Absorber plate Energy balance for the absorber plate can be written as [13]


 dT w dt ð2Þ

where convective heat transfer coefficient from the absorber plate to the brackish water, h1 , is indicated in Ref. [13].


  kPCM dT p ðT p  T PCM Þ þ ðmp C p Þ xPCM dt ð3Þ

2.1.4. Phase change material (PCM) The phase change material stores the transferred energy from the absorber plate and dissipates low amount of heat to the environment via the cascade solar still bottom [13].

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 kPCM kins M equ dT PCM ðT p  T PCM Þ ¼ ðT PCM  T a Þ þ xPCM xins Ap dt

ð4Þ

where Exew and Exsun are evaporative exergy rate and sun exergy rate, respectively, which are given in Appendix A [4,16,28].

where Mequ is the equivalent heat capacity of PCM [28], and it is indicated in different phases of the PCM during the process of state change from solid to liquid as follows [13]

3.1.2. Brackish water Exergy balance for brackish water is obtained from following equation

M equ ¼ mPCM C s;PCM M equ ¼ mPCM LPCM

for T PCM < T m for T m 6 T PCM 6 T m þ d0

M equ ¼ mPCM C l;PCM

for T PCM > T m þ d0

ð5Þ

Irw ¼ Exdes;w ¼ aw sg Exsun þ Expw  Exew 

dExw dt

ð12Þ

The transferred exergy rate from the absorber plate to the brine is

2.2. Solar still without PCM In this case, only equation relevant to absorber plate has been changed. Therefore, energy balance for the absorber plate is obtained as follows [13]

ap sg sw IðtÞAp ¼ h1 Ap ðT p  T w Þ þ U b Ap ðT p  T a Þ þ ðmp C p Þ


 dT p dt

ð6Þ

The energy efficiency of a cascade solar still is the ratio of evaporative heat transfer to the solar radiation intensity on the absorber plate, which is given by [13,29]

P

_ ew hfg m P 3600Ap IðtÞ

3.1.3. Absorber plate Exergy balance for the absorber plate can be written as:

hew Aw ðT w  T g Þ3600 hfg

ð8Þ

dExp dt

ð14Þ

The transferred exergy rate from the absorber plate to PCM layer is

Expins ¼

ð7Þ

_ ew is where hfg is the latent heat of vaporization of water [23] and m the fresh water productivity which has been revealed by [13,29]

_ ew ¼ m

ð13Þ

Irp ¼ Exdes;p ¼ ap sg sw Exsun  Expw  Expins 

2.3. Energy efficiency

gth ¼


 T a þ 273 Expw ¼ h1 Ap ðT p  T w Þ 1  T p þ 273



 kPCM T a þ 273 Ap ðT p  T PCM Þ 1  T p þ 273 xPCM

ð15Þ

3.1.4. Phase change material (PCM) Exergy balance equation for PCM layer is developed as follows

IrPCM ¼ Exdes;PCM þ Exinsa ¼ Expins 

dExPCM dt

ð16Þ

Exergy loss rate of the insulation to the surrounding is equal to 3. Exergy analysis

Exinsa ¼ Exergy is preserved only when all processes occurring in a system and the environment are reversible [18]. Exergy of a system which is in equilibrium with the environment is equal to zero. However, because the irreversibilities of the actual processes lead to the entropy generation, exergy efficiency will be destroyed [17]. Therefore, in order to decrease the irreversibility, efforts should be carried out to determine irreversibility effects. The exergy balance is written for different components of both weir type cascade solar stills with PCM and without PCM in order to determine irreversibility rates. Irreversibility is defined as the summation of exergy loss from control volume and exergy destruction in control volume [17,30].

Ir ¼

X

Exloss þ

X

ð9Þ

Exdes

Exergy balance for the different components of the solar still is developed in the next section.

3.1.1. Glass cover Exergy balance for glass cover is expressed as

dExg dt

Exga

3.2. Solar still without PCM Exergy balance for the absorber plate is obtained as follows

Irp ¼ Expa þ Exdes;p ¼ ap sg sw Exsun  Expw 

dExp dt

ð18Þ

The exergy loss rate from the absorber plate to ambient can be evaluated as follows


 T a þ 273 Expa ¼ U b Ap ðT p  T a Þ 1  T p þ 273

ð19Þ

3.3. Exergy efficiency

gex ¼ ð10Þ

Exergy loss rate from the glass cover to ambient is obtained as follows


 T a þ 273 ¼ ht;ga Ag ðT g  T a Þ 1  T g þ 273

ð17Þ

The exergy efficiency of the solar still is expressed as the ratio of the desired output exergy from the solar still (evaporative exergy) to the net input exergy to the solar still (sun exergy) [31].

3.1. Solar still with PCM

Irg ¼ Exga þ Exdes;g ¼ ag Exsun þ Exew 



 kins T a þ 273 Ap ðT PCM  T a Þ 1  T PCM þ 273 xins

ð11Þ

Exout Exew ¼ Exin Exsun

ð20Þ

Following equation is a relationship between energy and exergy efficiencies which has been introduced in Ref. [22].

gex

  1  TTwa þ273 þ273 Ap ¼ gth h  4  i Ag 1 þ 1 T a þ273  4 T a þ273 3

6000

3

6000

ð21Þ

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F. Sarhaddi et al. / Energy Conversion and Management 133 (2017) 97–109 Table 1 Design parameters of cascade solar still [33]. Design parameter

Value

PCM type d0 (°C) Tm (°C) Cs,PCM (kJ/kg
°C) Cl,PCM (kJ/kg
°C) Ls,PCM (kJ/kg) mPCM (kg) kPCM (W/m2
°C) xPCM (m)

Paraffin wax 3 56 2.95 2.51 226 18 0.24 0.02 0.9 0.95 0.05 0.05 0.9 30 1 1 0.033 0.03 204 0.002 0.57 0.02 999 9.52 4190 800 896 14

sg sw ag aw ap b (°) Ap (m2) x0 (m) kins (W/m2
°C) xins (m) kp (W/m2
°C) xp (m) kw (W/m2
°C) xw (m) qw (kg/m3) Prw Cw (J/kg
°C) Cg (J/kg
°C) Cp (J/kg
°C) Ub (W/m2
°C)

Fig. 3. Flowchart of numerical calculations.

It should to be noted that the energy and exergy calculations depend on the input solar intensity. Its calculation is carried out for Zahedan, Iran, which is located at 60°:540 E longitude and 29°:320 N latitude with the aid of equations of Ref. [32] (see Appendix A).

4. Validation of numerical simulation

Fig. 4. Hourly variation of solar radiation intensity and ambient temperature for all typical days.

Eqs. (1)–(6) constitutes a set of nonlinear ordinary differential equations for the unknown temperatures Tw, Tg, Tp and TPCM. MATLAB software is used to solve the mathematical model. A computer simulation program (MATLAB ode45 subroutine), based on the fourth-order Runge–Kutta method is developed to solve the aforementioned set for both weir type cascade solar stills with and without PCM storage in typical sunny and semi cloudy days. The flowchart of numerical calculations has been shown in Fig. 3. The numerical results of solar still components temperature have been validated with the corresponding experimental temperatures of Ref. [16]. The experiments of Ref. [16] have been carried out on the constructed cascade solar still in Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan, Iran, which is located at 60°:540 E longitude and 29°:320 N latitude. The experiments have been conducted for typical sunny (23/05/2009) and partially cloudy (13/05/2009) days. The value

of the design parameters applied in numerical calculations are given in Table 1 [33]. Hourly variation of solar radiation intensity and ambient temperature for all typical days are shown in Fig. 4. According to Fig. 4, the maximum value of solar radiation intensity is occurred at noon. On the other hand, the ambient temperature increases initially and then decrease; however, its variation is almost negligible. Fig. 5(A and B) depicts the variation of experimental data [16] and simulation values of different temperatures of the still with and without PCM in sunny and semi-cloudy days, respectively. It should be noted that, the temperatures presented in Fig. 5 are the hourly average values. It is clear from Fig. 5A that absorber plate, water and glass cover temperatures increase with time until they reach a

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Fig. 5. (A) Hourly variations of absorber plate, water and glass cover temperatures of the still without PCM in sunny day and (B) hourly variations of absorber plate, water, glass cover and PCM temperatures of the still with PCM in semi-cloudy day.

Fig. 6. A. Hourly variations of simulated and experimental water temperature for still with and without PCM in typical sunny day, B. Hourly variations of simulated and experimental water temperature for still with and without PCM in semi-cloudy day.

maximum value at about 13:30 PM and then reduce till sunset. Also, it can be observed that the simulation result for absorber plate temperature, water temperature and glass cover temperature is in good agreement with the experimental data and their RMSD is 7.31%, 4.52% and 5.14%, respectively. Moreover, Fig. 5B indicates that the trend of temperatures variation of the water, absorber plate and glass cover with time is similar to hourly variations of temperatures in Fig. 5A. It can also be observed from Fig. 5B, that when the solar radiation intensity increases, the PCM temperature is increased. In fact, higher solar irradiation helps the increase of heat transfer rate from the absorber

plate to the PCM. Further, it is seen that between 14 PM and 16 PM, the PCM temperature is approximately constant, because PCM reaches to its melting point about 56 °C, so, it means that the phase change process is started. After that, it is possible to beginning of the discharge process; it means that the PCM temperature decreases gradually until its solidification temperature. According to Fig. 5B, there is a good agreement between simulation results with the experimental data for the temperature of brine, glass cover, absorber plate and PCM with RMSD of 6%, 5.4%, 3.57% and 4.2%, respectively.

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Fig. 7. (A) Hourly variations of simulated and experimental productivity for still with and without PCM in typical sunny day and (B) hourly variations of simulated and experimental productivity for still with and without PCM in semi-cloudy day.

5. Results and discussion In this section, a comparison between the performance of two weir type cascade solar stills with and without PCM storage in sunny and semi-cloudy days is carried out. Also, daily parametric studies on the various operating parameters of cascade solar still including water temperature, hourly productivity, different exergy rates, different irreversibility rates, energy and exergy efficiency are carried out. Hourly variations of simulated and experimental water temperature for still with and without PCM in sunny and semi-cloudy days are shown in Fig. 6A and B, respectively. It can be concluded from Fig. 6A that water temperature for still without PCM in the sunny day is higher than the still with PCM during the sunshine till 15:30 because solar radiation increases. Afterwards, the water temperature of the still with PCM is higher than the still without PCM. The reason behind this behavior can be explained due to the fact that after time 15:30 solar radiation decreases and PCM releases its stored heat in lack of solar radiation. Fig. 6B also shows that in the semi-cloudy day water

temperature in still without PCM is higher during the sunshine till 12 PM. This period is shorter in compare with the sunny day. Hourly variations of simulated and experimental productivity with time for the still with and without PCM in the sunny and semi-cloudy days are shown in Fig. 7A and B, respectively. According to Fig. 7A, it is clear that the hourly productivity of solar still without PCM is higher than solar still with PCM during sunshine hours (8:30 AM to 15:30 PM). This result originates from this fact the temperature difference between water and glass cover (during the sunshine hours) in solar still without PCM is higher than solar still with PCM. In sunshine hours, the still with PCM is utilized the part of the absorbed solar energy to increase the PCM temperature. Such phenomenon contributes to lower heat transfer rate from absorber plate to water which consequently leads to a decline in temperature difference in the still with PCM. On the other hand, hourly productivity in still with PCM is higher than solar still without PCM during afternoon time; because, PCM releases its stored heat in low solar radiation conditions, therefore the temperature difference between the water and the glass cover Increases and it leads to a higher productivity. Fig. 7B reveals that

Fig. 8. (A) Hourly variations of the evaporative, convective and radiative exergy rate for the still without PCM in sunny day and (B) hourly variations of the evaporative, convective, and radiative exergy rate for the still with PCM in semi-cloudy day.

F. Sarhaddi et al. / Energy Conversion and Management 133 (2017) 97–109

the productivity of the still without PCM is significantly lower than the still with PCM in semi-cloudy day. According to Fig. 7(A and B), It is observed that total productivity of the still without PCM is partly higher than the still with PCM in the sunny day (7.05 kg/m2
day for still without PCM and 6.63 kg/m2
day for still with PCM). Also, total productivity of the still with and without PCM in the semi-cloudy day is 4.94 kg/m2
day and 3.84 kg/m2
day, respectively. Nevertheless, as can be seen there is a significant difference in the total productivity for the semi-cloudy day whereas there is nearly the proximity values for the sunny day. Fig. 8(A and B) depicts simulation results of the hourly variations of the evaporative, convective, and radiative exergy rate for the still without PCM and with PCM in the sunny and semicloudy days, respectively. It should be noted that the equations of exergy rates is given in Appendix A. According to Fig. 8(A and B), it is illustrated that three modes of exergy rates increase when solar radiation intensity increases. The evaporative exergy is more significant in comparing to the convective and radiative exergy. In fact, the convective exergy rate and especially the radiative exergy rate could be neglected.

105

Fig. 9(A and B) demonstrates the hourly variations of the evaporative exergy rate for the still without and with PCM in the sunny and semi-cloudy days, respectively. The evaporative exergy is higher when the water temperature is high. This is due to the fact that, increasing in water temperature, increases the evaporation rate of water and this enhances the evaporation exergy. Therefore, it is evident from Fig. 9A that for higher values of water temperature, evaporative exergy in the still without PCM, is higher than still with PCM due to high solar radiation intensity, which increase water temperature in the still without PCM, as illustrated on Fig. 6A; whereas in the low solar radiation intensity, evaporative exergy in the still without PCM is lower than still with PCM. It is also observed from Fig. 9B, that the trend of variations of evaporative exergy is inverted in semi-cloudy day. It means that dependency of evaporative exergy for the still without PCM on solar radiation is lower than evaporative exergy for the still with PCM. In other words, the still with PCM due to using of PCM storage, has better and higher performance than the still without PCM in the semi-cloudy day.

Fig. 9. (A) Hourly variations of the evaporative exergy for the still with and without PCM in sunny day. (B) Hourly variations of the evaporative exergy for the still with and without PCM in semi-cloudy day.

Fig. 10. (A) Variations of the energy and exergy efficiencies with the solar radiation intensity in sunny day and (B) effect of solar irradiation on the energy and exergy efficiencies in semi cloudy day.

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Fig. 10(A and B) depicts the influence of solar radiation intensity on the energy and the exergy efficiencies for the still without and with PCM in the sunny and semi-cloudy days, respectively. Fig. 10(A and B) reveals that the energy and the exergy efficiencies increase by increasing solar radiation intensity. In fact, higher solar irradiation causes increasing the evaporation rate and distilled water production. It is due to the higher operational temperature which finally leads to improvement in exergy and energy efficiencies. As was expected, Fig. 10(A and B) reveals that the energy and the exergy efficiencies for the still without PCM in the sunny day and for the still with PCM in the semi-cloudy day are more sensitive to the solar radiation intensity, as can be seen from the variations in hourly productivity and evaporative exergy in sunny and semi cloudy days, respectively. It is seen that the energy and exergy efficiencies reach to 75.68% and 6.33% for the still without PCM in the sunny day. On the other hand, the maximum value of energy and exergy efficiencies for the still with PCM in the sunny day are 56.45% and 3.9% respectively. Moreover, the energy efficiency for the still with and without PCM in the semi-cloudy day is 73.68% and 65.04% and for the exergy efficiency is 8.63% and 5.41%, respectively. Therefore, it is clear that the still with PCM is more efficient than the still without PCM in the semi-cloudy day and the still without PCM is more suitable for the sunny day.

The effect of ambient temperature on the energy and the exergy efficiencies for the still without and with PCM in the sunny and semi-cloudy days is shown in Fig. 11. Fig. 11(A and B) illustrates that increasing the ambient temperature from 27 to 47 °C, leads to a significant decline in the exergy and energy efficiencies. Since the ambient temperature varies during the day, to achieve the maximum exergy and energy efficiencies, other parameters and solar still operating conditions should vary during the day. Daily variation of the various irreversibility rates for solar still without PCM in sunny day and solar still with PCM in semicloudy day is shown in Fig. 12. It is observed from Fig. 12(A and B) that the irreversibility rate of absorber plate, glass cover, water and PCM increase with time and solar radiation intensity. The irreversibility rates reach to their maximum value at 13:30 PM and then reduce till sunset. It can also be observed that the trend of variation of the irreversibility rate in absorber plate is much more than irreversibility rate in other parts of the solar still system without PCM and with PCM in the sunny and semi-cloudy days, respectively. It means that, dependency of irreversibility rate in absorber plate on solar radiation is much more than irreversibility rate in other parts of system. However, it is known that these high values of irreversibility rate in absorber plate is due to the temperature difference between absorber plate

Fig. 11. (A) Variations of the energy efficiency and the exergy efficiency with ambient temperature in sunny day and (B) effect of ambient temperature on the energy and exergy efficiencies in semi-cloudy day.

Fig. 12. (A) Daily variations of the irreversibility rate of absorber plate, glass cover and water for the still without PCM in the sunny day and (B) daily variations of the irreversibility rate of absorber plate, glass cover, water and PCM for the still with PCM in the semi-cloudy day.

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08:30 09:30 10:30 11:30 12:30 13:30 14:30 15:30 16:30 17:30

Solar still without PCM in the sunny day

Solar still with PCM in the semi-cloudy day

_ ew (kg/m2
h) m

gth (%)

gex (%)

Ir (W)

_ ew (kg/m2
h) m

gth (%)

gex (%)

Ir (W)

0.3 0.59 0.83 0.94 1.04 1.08 0.97 0.53 0.34 0.23

40.18 55.25 64.68 67.36 72.75 76.69 74.75 49.26 45.39 39.43

1.39 3.08 4.63 5.38 6.13 6.53 5.97 3.29 2.43 1.41

190.55 288.04 363.78 406.94 430.51 423.64 384.21 307.84 208.28 94.91

0.08 0.17 0.36 0.47 0.49 0.62 0.56 0.48 0.36 0.27

25.56 31.18 52.26 58.11 58.75 74.35 68.78 68.35 66.23 51.48

0.69 1.82 4.33 5.61 6.35 8.59 7.33 6.39 5.45 3.32

157.41 232.10 284.31 315.12 329.19 334.19 298.73 240.16 163.10 70.14

Fig. 13. (A) Hourly variations of the exergy fractions for the still without PCM in sunny day. (B) Hourly variations of the exergy fractions for the still with PCM in semi-cloudy day.

and the sun and also greater exergy loss rate of absorber plate to the surrounding. Whereas, the irreversibility rates in the other parts of the solar still can be neglected. Therefore, solar radiation is a parameter that strongly affects the irreversibility rates. Considering Fig. 12A, average values from the irreversibility rates of water, glass cover, and absorber plate in the solar still system without PCM on a typical sunny day are 3.88 W, 33.25 W, and 202.1 W respectively. Also, according to Fig. 12B, average values from the irreversibility rates of water, glass cover, absorber plate and PCM in the still with PCM in semi-cloudy day are 3.91 W, 26.02 W, 136.68 W and 6.86 W respectively. Moreover, average value of irreversibility rate of the whole system for the solar still without PCM in the sunny day and the still with PCM in semicloudy day is 239.25 W and 173.47 W, respectively. Therefore, the irreversibility rate of absorber plate on typical sunny and semi-cloudy days is 83.1% and 78.8% of all of the systems irreversibility rates, respectively. Therefore, in order to decrease irreversibility rate, efforts should be performed to introduce better absorber plate designs and still cover materials. After all, because the exergy efficiency can be expressed in the form of common parameters in solar engineering like energy efficiency, temperature, mass flow rate, etc. Unlike other optimization methods, exergy analysis reduces internal irreversibility rates, which is more significant. The daily values of productivity, thermal efficiency, exergy efficiency and irreversibility rate for the still without PCM in the sunny day and the still with PCM in semi-cloudy day are reported in Table 2. According to Table 2, the maximum energy and exergy efficiencies for the solar still without PCM are 76.69% and 6.53%, respec-

tively. Moreover, the maximum energy and exergy efficiencies for the solar still with PCM are 74.35% and 8.59%, respectively. Therefore, the solar still without PCM is considered for sunny days and the solar still with PCM is preferred for semi-cloudy days due to the higher productivity and the energy and exergy efficiencies. Fig. 13(A and B) demonstrates the hourly variations of exergy fractions for the still without PCM in the sunny day and with PCM in semi-cloudy day, respectively. It should be mentioned that the exergy fraction equations are given in Appendix A. According to Fig. 13(A and B), the higher exergy fraction belongs to evaporative exergy fraction. On the other hand, radiative exergy fraction can be neglected. The higher value for evaporative exergy fraction leads to higher evaporation from the water surface. On the other hand, the higher value for the convective exergy fraction causes the faster transfer of evaporated water vapor (due to free convective currents) on the inner condensing surface of the glass cover. Therefore, both these fractions need to be higher to increase the productivity and efficiency. 6. Conclusions In this paper, a theoretical analysis based on transient exergy model was successfully developed for both cascade solar stills with and without PCM. The temperatures used in the exergy analysis have been already obtained from energy balance written for different components of both solar stills. The effect of different parameters such as solar radiation intensity and ambient temperature on the energy and exergy efficiencies of both solar still during sunny and semi-cloudy days was investigated. In addition, the comparison between the irreversibility rates of different components of

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both solar stills were carried out. Simulation results showed that the maximum energy and exergy efficiencies for the still without PCM are 76.69% and 6.53%, in the sunny day, respectively. Moreover, the maximum energy and exergy efficiencies for the still with PCM are 74.35% and 8.59% in the semi-cloudy day, respectively. Therefore, the still without PCM is considered for sunny day and solar still with PCM is preferred for semi-cloudy day due to the higher productivity and the energy and exergy efficiencies. Furthermore, simulation results proved that there is a direct relationship between the variations of energy and exergy efficiencies in both the solar stills with the variations of solar radiation intensity and an inverse relationship with respect to the variations of ambient temperature. According to the obtained results, it was found out that exergy efficiency of both weir-type cascade solar stills is much lower than its energy efficiency. The reason is that the energy analysis does not consider the internal irreversibility rates, whereas high irreversibility rate in the different components of the solar still leads to a decline in exergy efficiency. Also, simulation results showed that the largest value of irreversibility rate among all of the irreversibility rates of the still with and without PCM belongs to absorber plate. The irreversibility rate of absorber plate on a typical sunny day for cascade still without PCM and for the still with PCM on semi-cloudy day is 83.1% and 78.8% of the whole systems irreversibility rates, respectively. Whereas, the irreversibility rates in other elements of the solar still can be neglected. Therefore, in order to decrease irreversibility rate, efforts should be performed to introduce better absorber plate designs and still cover materials. After all, because the exergy efficiency can be expressed in the form of common parameters in solar engineering like energy efficiency, temperature, mass flow rate, etc., the exergy efficiency is a suitable parameter for optimization and design of solar still. Unlike other optimization methods, exergy analysis reduces internal irreversibility rates, which is more significant.

h2 ¼ hrw þ hcw þ hew _ w ¼ qw V w Aw ¼ m

qw xw Aw t

b0 gd q2v DT 0 3

Gr0 ¼

l2v

DT 0 ¼

ðT w  T g Þ þ ðPw  Pg ÞðT w þ 273Þ ð268:9  103  P w Þ

lv C v

Pr ¼

kv Tw þ Tg 2

Ti ¼

C v ¼ 999:2 þ 0:1434T i þ 1:0101  104 T 2i  6:7581  108 T 3i

qv ¼

353:44 T i þ 273

kv ¼ 0:0244 þ 0:7673  104 T i

lv ¼ 1:718  105 þ 4:62  108 T i
 5144 Pi ¼ exp 25:317  T i þ 273 b0 ¼

1 T i þ 273

RMSD ¼

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP h  i2 x x u n t i¼1 exp;ix sim;i  100 exp;i

n

Appendix A


IðtÞ ¼ Ion

 ð1 þ cosbÞ ð1  cosbÞ þ 0:2ðsb þ sd Þ coshz sb cosh þ sd coshz 2 2

Exew


 T a þ 273 ¼ hew Aw ðT w  T g Þ 1  T w þ 273

Excw


 T a þ 273 ¼ hcw Aw ðT w  T g Þ 1  T w þ 273 "

Exrw


4
# 1 T a þ 273 4 T a þ 273 ¼ hrw Aw ðT w  T g Þ 1 þ  3 T w þ 273 3 T w þ 273 "

Exsun


4
# 1 T a þ 273 4 T a þ 273 ¼ Ag IðtÞ 1 þ  3 6000 3 6000

Fr ex;ew ¼

Exew Exew þ Excw þ Exrw

Fr ex;cw ¼

Excw Exew þ Excw þ Exrw

Fr ex;rw ¼

Exrw Exew þ Excw þ Exrw

h1 ¼ 0:54


 kw ðGrPrw Þ0:25 x0

hfg ¼ 3:1615ð106  761:6T i Þ;

T i > 70

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