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Effect of energy matrices on life cycle cost analysis of passive solar stills D.B. Singh a,⇑, G.N. Tiwari b, I.M. Al-Helal c, V.K. Dwivedi d, J.K. Yadav a a

Centre for Energy Studies, Indian Institute of Technology Delhi, HausKhas, New Delhi 11 00 16, India Bag Energy Research Society (BERS), SODHA BERS COMPLEX, Plot No. 51, Mahamana Nagar, Karaudi, Varanasi, UP 22 10 05, India c Department of Agricultural Engineering, College of Food & Agricultural Sciences, King Saud Univ., P.O. Box 2460, Riyadh 11451, Saudi Arabia d Department of Mechanical Engineering, GCET, Greater Noida, UP, India b

a r t i c l e

i n f o

Article history: Received 13 January 2016 Received in revised form 23 March 2016 Accepted 26 April 2016 Communicated by: Associate Editor Yogi Goswami Keywords: Exergoeconomic parameter Energy matrices

a b s t r a c t This paper presents the life cycle cost analysis of passive solar stills by incorporating the effect of energy payback period. Exergoeconomic and energy matrices have been evaluated for climatic condition of New Delhi. The annual exergy, yield and energy have been calculated considering the four climatic conditions for each month of year. The kW h per unit cost based on exergoeconomic parameter has been found to be 0.144 kW h/Rs. and 0.137 kW h/Rs. for single and double slope passive solar stills respectively. It is inferred that single slope solar still performs better than double slope solar still based on annual exergy analysis. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Most places on the earth are blessed with sun light and plenty of water. However, major portion of water available on earth is saline/brackish. Only, less than 3% of available water is fresh water. More than 2% water is locked up in ice caps and glaciers of Polar Regions and only less than 1% is within human reach. It has been reported that more than one out of six people would lack access to safe drinking water and more than two out of six would lack adequate sanitation as per UNICEF (2002). According to the WHO (2004) report, more than 3900 children die every day from water borne diseases. It has been estimated that 2/3rd of humanity will face shortage of water from 2025 onwards as per UN (2004). So, there is going to be an acute shortage of potable water for domestic and other uses such as agriculture and industry in remote places of many countries where electricity supply has not reached so far. The reason is that they are unable to use existing popular desalination technology as devices based on it need electricity supply to run. Moreover, global industrialization, fast growth in population and growth in agriculture have polluted water available in rivers and underground reservoir badly. Also, these water resources may not be able to fulfill requirements in future. It has been

⇑ Corresponding author. E-mail address: [email protected] (D.B. Singh). http://dx.doi.org/10.1016/j.solener.2016.04.039 0038-092X/Ó 2016 Elsevier Ltd. All rights reserved.

reported that an over 76 million people will die due to water borne diseases by the year 2020 (Pacific Institute of Oakland, California). In the present situation, an exploitation of solar energy for distillation can provide the best solution for rural as well as urban areas. It is a simple technology, eco-friendly, more economical and easily maintainable. It needs only sunshine to operate and unskilled labor to maintain. So, it can be most suitable for under developed and developing countries. Generally, the performance of passive solar still can be evaluated on the basis of first law of thermodynamics. On the basis of current literature review, the following researchers have carried out research in analyzing the performance of solar still such as a. Inclination (Aderibigbe, 1985; Singh and Tiwari, 2004) b. Dye (Rajvanshi and Hsieh, 1979) charcoal (Akinsete and Duru, 1979), black butyl rubber sheet and charcoal chips (Wibulswas and Tadtium, 1984) c. Wind velocity (Löf et al., 1961; Cooper, 1969; Morse and Read, 1968; El-Sebaii, 2003; Toure and Meukam, 1997; Agrawal, 1998) d. Water depth (Cooper, 1969; El-Sebaii, 2003), thermal capacity of water and depth (Morse and Read, 1968) e. Solar radiation (United Nations, 1970; Ahmed, 1988; Cooper, 1983; Akinsete and Duru, 1979; G.N. Tiwari and A.K. Tiwari, 2007) f. Ambient temperature (Morse and Read, 1968; Cooper, 1969)

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D.B. Singh et al. / Solar Energy 134 (2016) 9–22

Nomenclature L n0 Ag AgE Ab AgW Eout Esol Ein ðSPÞw F CR;i;n F SR;i;n UAC Ss Ps

a0

_ Ex Is ðtÞ ISE ðtÞ ISW ðtÞ l Y S R a b c d

g gp

EPBT EPF LCCE n i Gex;annual ln SS DS t R0 Ts

latent heat, J/kg number of clear days area of glass cover, m2 area of east glass cover, m2 area of basin, m2 area of west glass cover, m2 annual energy output, kW h annual solar energy, kW h embodied energy, kW h selling price of water, Rs. capital recovery factor sinking fund factor uniform end-of-year annual cost, Rs. salvage value, Rs. net present cost, Rs. emissivity absorptivity hourly exergy, W solar intensity, W/m2 solar intensity on east glass cover, W/m2 solar intensity on west glass cover, W/m2 thickness, m daily yield, kg daily solar energy, kW h revenue clear days (blue sky) hazy days (fully) hazy and cloudy days (partially) cloudy days (fully) efficiency, % productivity, % energy payback time, Year energy production factor, per year life cycle conversion efficiency life of solar still, Year rate of interest, % annual exergy gain, kW h natural logarithm single slope passive solar still double slope passive solar still time, h reflectivity temperature of sun, °C

g. Bottom insulation (Nayak et al., 1980), back wall as reflector (Wibulswas and Tadtium, 1984; Tamini, 1987), back wall with cotton cloth (Wibulswas and Tadtium, 1984), regenerative effect in back wall (Wibulswas and Tadtium, 1984), solar still with internal condenser (Ahmed, 1988) On the basis of second law of thermodynamics, following researchers have studied the performance of solar still. a. Dincer (2002) reported the linkage between energy and exergy. Hepbalsi (2007) used exergetic analysis extensively in the design, simulation and performance prediction of energy systems. b. Torchia-Nuñez et al. (2007) performed theoretical exergy analysis of passive solar still and reported that the greatest irreversibility is produced by interaction between the sun and the collector (basin liner). Further, Vaithilingam and Esakkimuthu (2014) investigated energy and exergy analysis of single slope passive solar still experimentally and validated the earlier findings of Torchia-Nuñez et al. (2007).

_ Ex Ex Exm

water temperature, °C ambient temperature, °C water temperature at t = 0, °C glass temperature at inner surface, °C monthly yield, kg monthly solar energy, kW h glass temperature at inner surface of east glass cover, °C glass temperature at inner surface of west glass cover, °C radiative heat transfer coefficient from water to inner surface of glass cover, W/m2 K convective heat transfer coefficient from water to inner surface of glass cover, W/m2 K evaporative heat transfer coefficient from water to inner surface of glass cover, W/m2 K evaporative heat transfer coefficient for east side, W/m2 K evaporative heat transfer coefficient for west side, W/m2 K mass of distillate from single slope passive solar still, kg mass of water in basin, kg maintenance cost annual yield from passive solar still, kg mass of distillate from east cover of double slope passive solar still, kg mass of distillate from west cover of double slope passive solar still, kg exergoeconomic parameter based on exergy gain, kW h/Rs. hourly exergy, kW h daily exergy, kW h monthly exergy, kW h

Subscript g b w E W in out eff

glass basin liner water east west incoming outgoing effective

Tw Ta Two Tgi m Sm T giE T giW hrwg hcwg hewg hewgE hewgW _ ew;s m Mw M Mew _ ew;E m _ ew;W m Rg;ex

c. Dwivedi (2009) studied energy and exergy analysis of passive solar still and concluded that thermal efficiency of double slope passive solar still is higher than the thermal efficiency of single slope passive solar still if basin area is taken as 1 m2 and 2 m2 for single slope passive solar still and double slope passive solar still respectively. d. Singh et al. (2011) studied energy and exergy analysis of various passive solar distillation systems and concluded that energy and exergy of single slope solar still is higher than that of double slope passive solar still. e. Zerouala et al. (2011) and Rajamanickam and Ragupathy (2012) investigated south-north oriented double-slope passive solar still with partially cooled condenser and reported an increase of 11.82% in the yield. f. Muftah et al. (2014) reviewed basin type solar still till 2012 and concluded that yield of solar stills is heavily influenced by climatic, operational and design parameters. Its output can further be improved via operational and design conditions as climatic conditions are beyond our control.

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D.B. Singh et al. / Solar Energy 134 (2016) 9–22

None of the above researchers have compared life cycle cost analysis based on second law of thermodynamics. Hence, in this paper a comparative study of basin type single slope and double slope passive solar still has been done on the basis of annual exergy, energy matrices, exergoeconomic parameter, productivity, and efficiencies for the climatic condition of New Delhi. The following weather conditions have been considered for analysis. (a) (b) (c) (d)

Water feed Jar Glass cover Saline/brackish water in basin

Clear days (blue sky), hazy days (fully), hazy and cloudy days (partially) and cloudy days (fully).

15o

0.2 m 2m

2. Methodology

Basin liner

1m

The following methodology has been adopted for annual exergy analysis of solar still.

Jar

Step I The climatic data namely solar radiation on a horizontal surface, ambient air temperature and number of days for the weather conditions (a), (b), (c) and (d) has been taken from Indian Metrological Department (IMD), Pune, India. Solar radiation for inclined surface at 30° north latitude has been calculated using Liu and Jordan formula with the help of MATLAB. Step II Single slope passive solar still is shown in Fig. 1a and double slope passive solar still is shown in Fig. 1b. Table 1a represents the specification of single and double slope passive solar stills. Table 1b represents the design parameter of single and double slope passive solar stills. Following Tiwari and Ghosal (2005) and Dwivedi (2009), water temperature in the basin ðT w Þ, glass temperature at inner surface ðT gi ; T giE and T giW Þ and glass temperature at outer surface ðT go ; T goE and T goW Þ can be evaluated as follows.

Fig. 1b. Schematic diagram of double slope passive solar still.

Table 1a Specifications of single slope and double slope passive solar still. Component

Specification

Single slope passive solar still Length Width Inclination of glass cover Height of smaller side Material of body Material of stand Cover material Orientation

2m 1m 15° 0.2 m GRP GI Glass South

Double slope passive solar still Length Width Inclination of glass cover Height of smaller side Material of body Material of stand Cover material Orientation

2m 1m 15° 0.2 m GRP GI Glass East–West

Water feed

Saline/brackish water in basin

Table 1b Design parameters used in computation for single slope and double slope passive solar still.

Glass cover

Single slope passive solar still

15o

Parameter

Value

Parameter

Value

a0b a0g a0w

0.82 0.01

a0b a0g a0w

0.82 0.01

lb lg Kb Kg CW Mw

V R0g

0.05 0.82 0.82 0.005 m 0.004 m 0.04 W/m °C 0.816 W/m °C 4200 J/kg °C 50 kg 5.67 108 W/m2°K4 1 m/s 0.05

V R0g

0.05 0.82 0.82 0.005 m 0.004 m 0.04 W/m °C 0.816 W/m °C 4200 J/kg °C 50 kg 5.67 108 W/m2°K4 1 m/s 0.05

R0w

0.05

R0w

0.05

w g

0.2 m 2m 1m Jar

Basin liner

Fig. 1a. Schematic diagram of single slope passive solar still.

Double slope passive solar still

lb lg Kb Kg CW Mw

r

w g

r

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D.B. Singh et al. / Solar Energy 134 (2016) 9–22

Tw ¼ T gi ¼

T go ¼

T giE

f ðtÞ ð1 ea1 t Þ þ T w0 ea1 t a1

ð1Þ

a_ g Is ðtÞAg þ h1w T w Ab þ U c;ga T a Ag

ð2Þ

U c;ga Ag þ h1w Ab Kg Lg

T gi þ h1g T a Kg Lg

T goE ¼

þ h1g

T giW ¼

T goW ¼

ð3aÞ

þ h1gE

ð4Þ

T giW þ h1gW T a Kg Lg

ð4aÞ

þ h1gW

The constants of Eqs. (1)–(4a) are given in Appendix A. The value of water temperature and glass temperature at inner surface can be calculated using Eqs. (1)–(4) with the help of MATLAB. Step III Exergy balance equation for solar still in steady state condition can be written as

_ in Ex _ out ¼ Ex _ des Ex

ð5Þ

_ in ðWÞ can be calculated using the expression Here, input exergy Ex given by Petela (2003) as

"

4 # _ in ¼ Ag IðtÞ 1 4 T a þ 1 T a Ex 3 Ts 3 Ts

ð6Þ

_ out ðWÞ can be calculated using the expression The output exergy Ex given by Nag (2004) as

_ out ¼ Ab hewg ðT w T gi Þ ðT a þ 273Þ ln ðT w þ 273Þ Ex ðT gi þ 273Þ where

he;wg ¼ 16:273 103 hc;wg hc;wg ¼ 0:884 ðT w T gi Þ þ Pw ¼ exp 25:317 and

Pgi ¼ exp 25:317

_ ew;E ¼ m

hewgE ½T w T giE 3600 L

_ ew;W ¼ m

B1 þ B2 T w P Kg Lg

hewg ½T w T gi 3600 L

ð3Þ

T giE þ h1gE T a Kg Lg

_ ew;s ¼ m ð2aÞ

A1 þ A2 T w ¼ P Kg Lg

and (d) in that month. The annual exergy can be evaluated by adding monthly exergy for 12 month. Step IV _ ew;E and m _ ew;W Þ for solar still can be _ ew;s ; m The hourly yield ðm calculated as follows.

Pw Pgi T w T gi

ð7Þ

ð8Þ

ðP w Pgi ÞT w

ð13Þ

3

268:9 10 Pw

5144 T w þ 273 5144 T gi þ 273

The daily exergy for clear days (condition (a)) can be calculated by adding hourly exergy obtained from Eq. (7) for 24 h and the same process has been adopted to calculate the daily exergy for other climatic conditions (b), (c), and (d). The monthly exergy for clear days (condition (a)) can be calculated by multiplying daily exergy with the corresponding number of clear days and the same process has been adopted to calculate the monthly exergy for other climatic conditions (b), (c), and (d). The total exergy for each month has been obtained by adding the exergy in the climatic conditions (a), (b), (c),

hewgW ½T w T giW 3600 L

ð9Þ ð10Þ ð11Þ

The evaporative heat transfer coefficients (hewg ; hewgE and hewg Þ can be calculated using Eq. (8). The daily yield for clear days (condition (a)) can be calculated by adding hourly yield for 24 h and the same process has been adopted to calculate the daily yield for other climatic conditions (b), (c), and (d). The monthly yield for clear days (condition (a)) can be calculated by multiplying daily yield with the corresponding number of clear days and the same process has been adopted to calculate the monthly yield for other climatic conditions (b), (c), and (d). The total yield for each month has been obtained by adding the yield in the climatic conditions (a), (b), (c), and (d) in that month. The annual yield can be evaluated by adding monthly yield for 12 month. Step V After evaluation of exergy and yield, energy matrices based on exergy as well as energy, annual productivity and exergoeconomic parameter have been calculated. 3. Analysis 3.1. Exergy analysis Exergy analysis is based on second law of thermodynamics. It tries to find the location, the magnitude and the causes of thermodynamic inefficiencies. Conventional exergy analyses locate components and processes with high irreversibility (Petrakopoulou et al., 2012). However, it has some limitations that can be overcome by advanced exergy analysis which tries to supply engineers with more useful information related to energy systems improvement potential. The advanced exergy analysis splits total exergy destruction into the parts (Tsatsaronis and Park, 2002). It can be divided into avoidable and unavoidable exergy destruction. It can also be divided into endogenous and exogenous exergy destruction. Exergy can be evaluated using the concept of entropy which comes from second law of thermodynamics. The term exergy analysis on the basis of entropy concept has been used by Jafarkazemi and Ahmadifard (2012) in exergetic evaluation of flat plate collectors. Following Eq. (7), the expression of hourly exergy gain for double slope passive solar still can be written as

Hourly exergy gain Ab ðT w þ 273Þ ¼ hewgE ðT w T giE Þ ðT a þ 273Þ ln ðT giE þ 273Þ 2 Ab ðT w þ 273Þ þ hewgW ðT w T giW Þ ðT a þ 273Þ ln ðT giW þ 273Þ 2 ð12Þ The daily exergy gain for single slope and double slope passive solar still can be calculated by adding hourly exergy gain from Eqs. (7) and (12) respectively for the period of 24 h. Daily, monthly and annual exergy gain for single slope and double slope passive solar

13

D.B. Singh et al. / Solar Energy 134 (2016) 9–22 Table 2 Daily, monthly and annual exergy gain for single slope passive solar still on the basis of entropy concept. Month

January February March April May June July August September October November December

Weather condition (type a)

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

Exa

n0a

Exma

Exb

n0b

Exmb

Exc

n0c

Exmc

Exd

n0d

Exmd

0.33 0.37 0.46 0.61 0.61 0.61 0.52 0.47 0.58 0.42 0.31 0.26

3 3 5 4 4 3 2 2 7 5 6 3

1.00 1.10 2.31 2.45 2.44 1.84 1.05 0.94 4.04 2.11 1.87 0.77

0.30 0.39 0.56 0.68 0.59 0.66 0.54 0.51 0.53 0.35 0.20 0.23

8 4 6 7 9 4 3 3 3 10 10 7

2.44 1.57 3.35 4.78 5.35 2.65 1.61 1.54 1.58 3.48 2.04 1.61

0.11 0.13 0.22 0.30 0.51 0.46 0.37 0.31 0.38 0.22 0.08 0.13

11 12 12 14 12 14 10 7 10 13 12 13

1.16 1.52 2.59 4.27 6.06 6.41 3.71 2.17 3.83 2.82 1.01 1.68

0.03 0.04 0.17 0.32 0.33 0.23 0.20 0.18 0.19 0.11 0.08 0.04

9 9 8 5 6 9 17 19 10 3 2 8

0.31 0.36 1.37 1.62 1.99 2.11 3.38 3.51 1.87 0.34 0.16 0.34

Annual exergy gain (Gex,annual) (kW h)

Monthly exergy 4.91 4.55 9.62 13.11 15.84 13.01 9.75 8.16 11.31 8.74 5.08 4.40 108.48

Table 3 Daily, monthly and annual exergy for double slope passive solar still on the basis of entropy concept. Month

Weather condition (type a)

January February March April May June July August September October November December

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

Exa

n0a

Exma

Exb

n0b

Exmb

Exc

n0c

Exmc

Exd

n0d

Exmd

0.23 0.23 0.35 0.54 0.59 0.55 0.48 0.39 0.41 0.24 0.16 0.12

3 3 5 4 4 3 2 2 7 5 6 3

0.69 0.69 1.75 2.14 2.35 1.66 0.96 0.78 2.85 1.22 0.94 0.36

0.17 0.25 0.43 0.59 0.57 0.64 0.50 0.44 0.40 0.22 0.12 0.12

8 4 6 7 9 4 3 3 3 10 10 7

1.33 1.01 2.57 4.13 5.13 2.55 1.50 1.31 1.20 2.24 1.20 0.85

0.07 0.09 0.17 0.28 0.49 0.44 0.35 0.28 0.31 0.15 0.06 0.08

11 12 12 14 12 14 10 7 10 13 12 13

0.73 1.08 2.10 3.91 5.84 6.17 3.48 1.93 3.05 1.89 0.67 0.98

0.03 0.03 0.14 0.30 0.32 0.23 0.19 0.18 0.16 0.09 0.05 0.03

9 9 8 5 6 9 17 19 10 3 2 8

0.24 0.29 1.13 1.50 1.92 2.04 3.25 3.35 1.62 0.27 0.11 0.25

Annual exergy gain (Gex,annual) (kW h)

ghourly;exergy ¼

0:933 ðAg IS ðtÞÞ

100 ð13Þ

Here, the factor 0.933 has been used to convert sun radiation to exergy and it can be calculated using the expression given by Petela (2003). The daily exergy can be evaluated by summing up the hourly exergy for 24 h. Hence, the daily exergy efficiency of single slope passive solar still using Eq. (13) can be expressed as

gdaily;exergy ¼

hewg Ab

P24

h

w þ273Þ ðT w T gi Þ ðT a þ 273Þ ln ðT ðT gi þ273Þ P 0:933 24 t¼1 ðAg IS ðtÞÞ

i

t¼1

100 ð14Þ Here, the solar intensity (Is) appearing in the denominator has zero value for off sunshine hour. Following Eq. (13), the hourly exergy efficiency of double slope passive solar still can be expressed as

ghourly;exergy

h i hewgE A2b ðT w T giE Þ ðT a þ 273Þ ln ðTðT w þ273Þ giE þ273Þ h i þhewgW A2b ðT w T giW Þ ðT a þ 273Þ ln ðTðT w þ273Þ giW þ273Þ ¼ 0:933 ðAgE ISE ðtÞÞ þ ðAgW ISW ðtÞÞ 100

2.99 3.08 7.55 11.68 15.24 12.42 9.19 7.38 8.73 5.62 2.93 2.44 89.24

still have been evaluated and presented in Tables 2 and 3 respectively. Following Eq. (7), the hourly exergy efficiency of single slope passive solar still can be expressed as

h i w þ273Þ hewg Ab ðT w T gi Þ ðT a þ 273Þ ln ðT ðT gi þ273Þ

Monthly exergy

ð15Þ

The daily exergy can be evaluated by summing up the hourly exergy for 24 h for given climatic condition. Hence, the daily exergy efficiency of double slope passive solar still using Eq. (15) can be expressed as i P h ðT w þ273Þ hewgE A2b 24 t¼1 ðT w T giE Þ ðT a þ 273Þ ln ðT giE þ273Þ i P h ðT w þ273Þ þhewgW A2b 24 t¼1 ðT w T giW Þ ðT a þ 273Þ ln ðT giW þ273Þ gdaily;exergy ¼ P 0:933 24 t¼1 ½ðASE ISE ðtÞÞ þ ðASW ISW ðtÞÞ

100

ð16Þ

3.2. Energy analysis Energy analysis has been done on the basis of first law of thermodynamics. The energy efficiency (G.N. Tiwari and A.K. Tiwari, 2007) is the ratio of the amount of thermal energy utilized to get a certain amount of distilled water to the incident solar energy within a given time interval. Following earlier researchers (Tiwari, 2002; A.K. Tiwari and G.N. Tiwari, 2007; Dwivedi and Tiwari, 2008, Dwivedi, 2009; Tiwari et al., 2015), the hourly thermal efficiency of single slope passive solar still can be expressed as

ghourly;thermal;SS ¼

_ ew;ss L m 100 ½Ag Is ðtÞ 3600

ð17Þ

The daily energy can be evaluated by summing up the hourly energy for 24 h. Hence, the daily thermal efficiency of single slope passive solar still using Eq. (17) can be expressed as

gdaily;thermal;SS ¼ P24

P24

_

t¼1 mew;ss

L

t¼1 ½Ag Is ðtÞ 3600

100

ð18Þ

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D.B. Singh et al. / Solar Energy 134 (2016) 9–22

Here, the solar intensity ðIs ðtÞÞ appearing in the denominator has zero value for off sunshine hour. Following Dwivedi (2009) and Tiwari et al. (2015), hourly thermal efficiency of double slope passive solar still can be expressed as

ghourly;thermal;DS ¼

_ ewE þ m _ ewW L ½m 100 ½ðAgE ISE ðtÞÞ þ ðAgW ISW ðtÞÞ 3600

The daily thermal energy output and thermal energy input to double slope passive solar still can be evaluated by adding hourly thermal energy output and hourly thermal energy input respectively for 24 h. Hence, the daily thermal efficiency of double slope passive solar still using Eq. (19) can be written as

P24

_

t¼1 ½mewE

_ ewW L þm

t¼1 ½ðAgE I SE ðtÞÞ þ ðAgW I SW ðtÞÞ 3600

Embodied enrgy ðEin Þ Annual energy output ðEout Þ Embodied enrgy ðEin Þ EPBT based on exergy ¼ Annual exergy output ðGex;annual Þ

EPBT based on energy ¼ ð19Þ

gdaily;thermal;DS ¼ P24

3.3.1. Energy payback time (EPBT) It is the time period needed to recover the total energy exhausted in preparing the materials (embodied energy) required for fabrication of passive solar still. Following Tiwari and Mishra (2012), it can be expressed as

100 ð20Þ

Here, the solar intensity falling on east glass cover ðISE ðtÞÞ and solar intensity falling on west glass cover ðISW ðtÞÞ have zero values for off sunshine hour. 3.3. Energy matrices Energy matrices consist of energy payback time, energy production factor and life cycle conversion efficiency. These are an important parameter for renewable technologies because the use of technology does not make any sense if the energy produced by them during the whole life time is less than the energy used in their manufacturing (Tiwari and Mishra, 2012).

ð21Þ ð22Þ

Embodied energy quantifies the amount of energy used to manufacture the material required for passive solar still. The calculation of embodied energy for single slope passive solar still and double slope passive solar still is presented in Table 4. The annual energy output can be evaluated by multiplying the annual yield with latent heat. The calculation of annual yield for single slope passive solar still and double slope passive solar still is presents in Tables 5 and 6 respectively. The value of latent heat has been taken as 2400 kJ/kg. The numerical value of EPBT for passive solar still should be as low as possible to make the passive solar still cost effective. Lower the value of EPBT, better is the system. EPBT for single slope and double slope passive solar still have been evaluated using Eqs. (21) and (22) and they have been presented in Table 6. 3.3.2. Energy production factor (EPF) It expresses the overall performance of the passive solar still. The ideal value of EPF on annual basis is 1. It is the reciprocal of EPBT. Following Tiwari and Mishra (2012), EPF for passive solar still on annual basis can be expressed as

Table 4 Daily, monthly and annual yield for single slope passive solar still. Month

January February March April May June July August September October November December

Weather condition (type a)

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

Ya

n0a

ma

Yb

n0b

mb

Yc

n0c

mc

Yd

n0d

md

4.69 5.20 6.03 7.19 8.45 7.53 6.89 6.36 7.49 5.72 5.39 4.44

3 3 5 4 4 3 2 2 7 5 6 3

14.06 15.60 30.15 28.76 33.80 22.59 13.78 12.72 52.43 28.60 32.34 13.32

4.42 5.42 6.53 7.90 8.16 7.79 6.81 6.78 8.22 5.70 4.10 3.89

8 4 6 7 9 4 3 3 3 10 10 7

35.36 21.68 39.18 55.30 73.44 31.16 20.43 20.34 24.66 57.00 41.00 27.23

2.27 2.71 4.10 5.57 6.96 6.50 6.04 5.46 6.04 4.26 2.35 2.72

11 12 12 14 12 14 10 7 10 13 12 13

24.97 32.52 49.20 77.98 83.52 91.00 60.40 38.22 60.40 55.38 28.20 35.36

1.17 1.39 3.49 2.36 5.64 4.98 4.31 3.89 4.21 2.93 2.26 1.42

9 9 8 6 6 9 17 19 10 3 2 8

10.53 12.51 27.92 13.49 33.84 44.82 73.27 73.91 42.10 8.79 4.52 11.36

Annual yield (kg)

Monthly yield 84.92 82.31 146.45 175.53 224.60 189.57 167.88 145.19 179.59 149.77 106.06 87.27 1739.15

Table 5 Daily, monthly and annual yield for double slope passive solar still. Month

January February March April May June July August September October November December Annual yield

Weather condition (type a)

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

Ya

n0a

ma

Yb

n0b

mb

Yc

n0c

mc

Yd

n0d

md

3.69 3.89 5.57 6.71 8.20 7.97 6.93 6.03 6.25 4.71 3.51 2.75

3 3 5 4 4 3 2 2 7 5 6 3

11.07 11.67 27.85 26.84 32.80 23.91 13.86 12.06 43.75 23.55 21.06 8.25

3.02 4.13 6.32 7.12 8.10 7.63 6.58 6.06 6.32 4.32 2.95 2.59

8 4 6 7 9 4 3 3 3 10 10 7

24.16 16.52 37.92 49.84 72.90 30.52 19.74 18.18 18.96 43.20 29.50 18.13

1.72 2.20 3.60 5.24 6.70 6.35 6.03 5.04 5.45 3.33 1.84 1.98

11 12 12 14 12 14 10 7 10 13 12 13

18.92 26.40 43.20 73.36 80.40 88.90 60.30 35.28 54.50 43.29 22.08 25.74

0.98 1.21 3.16 5.42 5.46 4.83 4.15 3.66 3.80 2.55 1.81 1.19

9 9 8 5 6 9 17 19 10 3 2 8

8.80 10.89 25.28 27.10 32.76 43.47 70.55 69.54 38.00 7.65 3.62 9.52

Monthly yield 62.95 65.48 134.25 177.14 218.86 186.80 164.45 135.06 155.21 117.69 76.26 61.64 1555.79

15

D.B. Singh et al. / Solar Energy 134 (2016) 9–22 Table 6 Embodied energy (Ein), energy payback time (EPBT) and energy production factor (EPF) for single slope and double slope passive solar still based on exergy. Name of component

Mass of component (kg)

Energy density (kW h/kg)

Embodied energy (kW h)

Single slope passive solar still GRP body GI angle iron Glass cover

44.49 30.00 20.7

25.64 13.88 8.72

1142.12 416.40 180.50

Total embodied energy = 1737.79 kW h Annual energy available from solar still = 1159.43 kW h Annual exergy available from solar still = 108.48 kW h Energy payback time (EPBT) based on energy = 1.49 years Energy payback time (EPBT) based on exergy = 16.02 years Energy production factor (EPF) based on energy = 0.67 per year Energy production factor (EPF) based on exergy = 0.062 per year Double slope passive solar still GRP body GI angle iron Glass cover

Annual yield = 1739.15 kg

34.59 30.00 20.7

25.64 13.88 8.72

886.89 416.40 180.50

Total embodied energy = 1483.90 kW h Annual yield = 1555.79 kg Annual energy available from solar still = 1037.19 kW h Annual exergy available from solar still = 89.24 kW h Energy payback time (EPBT) based on energy = 1.43 years Energy payback time (EPBT) based on exergy = 16.62 years Energy production factor (EPF) based on energy = 0.70 per year Energy production factor (EPF) based on exergy = 0.060 per year

Table 7 Annual solar energy (Esol) for single slope passive solar still. Month

January February March April May June July August September October November December

Weather condition (type a)

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

Sa

n0a

Sma

Sb

n0b

Smb

Sc

n0c

Smc

Sd

n0d

Smd

12.29 12.80 13.68 14.75 14.60 14.84 14.03 13.45 14.28 12.73 11.69 11.29

3 3 5 4 4 3 2 2 7 5 6 3

36.87 38.41 68.41 58.99 58.42 44.53 28.06 26.91 99.96 63.66 70.13 33.88

11.83 13.15 14.79 15.32 14.47 15.27 14.16 14.01 14.01 11.74 9.87 10.60

8 4 6 7 9 4 3 3 3 10 10 7

94.62 52.59 88.75 107.27 130.21 61.10 42.47 42.03 42.02 117.37 98.67 74.23

7.72 8.42 10.07 11.08 13.36 13.17 12.06 11.31 12.05 9.60 6.75 8.35

11 12 12 14 12 14 10 7 10 13 12 13

84.97 101.04 120.83 155.15 160.29 184.33 120.64 79.20 120.50 124.83 80.98 108.57

5.07 5.52 9.01 11.31 11.21 9.91 9.28 8.96 8.76 7.38 6.55 5.50

9 9 8 5 6 9 17 19 10 3 2 8

45.59 49.68 72.11 56.57 67.27 89.18 157.68 170.24 87.61 22.14 13.11 44.02

Annual solar energy (kW h)

Monthly yield 262.05 241.72 350.10 377.97 416.19 379.14 348.85 318.39 350.09 328.01 262.89 260.70 3896.09

EPF based on energy ¼

Eout Ein

ð23Þ

EPF based on exergy ¼

Gex;annual Ein

ð24Þ

where Eout , Ein Gex;annual are annual energy output, embodied energy and annual exergy gain respectively. The annual energy output can be evaluated as the product of annual yield and latent heat. EPF for single slope and double slope passive solar still has been evaluated using Eqs. (23) and (24) and presented in Table 6. 3.3.3. Life cycle conversion efficiency (LCCE) It is the net output of the system with respect to solar radiation falling on the system for the entire life time. The ideal value of LCCE is one. Higher the value of LCCE, better is the system. Following Tiwari and Mishra (2012), LCCE for passive solar still can be expressed as

where Esol is the annual solar energy falling on the solar still, T is the life time of solar still, Eout is the annual energy output, Gex;annual is the annual exergy gain and Ein is the embodied energy. The calculation of Esol for single slope and double slope passive solar still is presented in Tables 7 and 8 respectively. Annual solar exergy can be calculated by multiplying Esol with 0.93. Eout can be evaluated by multiplying the annual yield with latent heat. LCCE for single slope and double slope passive solar still has been evaluated using Eq. (25) and (26) and presented in Table 9. 3.4. Productivity ðgp Þ of single slope and double slope passive solar still

LCCE based on energy ¼

Eout n Ein Esol n

ð25Þ

Productivity represents the relationship between output and the factors used in achieving the output. Its objective is to get output as high as possible with less and less input of resources. It is the ratio of effectiveness and efficiency as defined by ILO (1979). Following Ashcroft (1950), Cox (1951), Benson (1952) and ILO (1979), the annual productivity for single slope passive solar still can be expressed as

LCCE based on exergy ¼

Gex;annual n Ein ðAnnual solar exergyÞ n

ð26Þ

gp ¼

M ew ðSPÞw 100 UAC

ð27Þ

16

D.B. Singh et al. / Solar Energy 134 (2016) 9–22

Table 8 Annual solar energy (Esol) for double slope passive solar still. Month

January February March April May June July August September October November December

Weather condition (type a)

Weather condition (type b)

Weather condition (type c)

Weather condition (type d)

Exa

n0a

Exma

Exb

n0b

Exmb

Exc

n0c

Exmc

Exd

n0d

Exmd

9.78 10.90 12.45 14.18 14.50 14.84 13.74 12.58 12.52 10.36 9.00 8.66

3 3 5 4 4 3 2 2 7 5 6 3

29.34 32.69 62.27 56.73 57.99 44.52 27.48 25.15 87.65 51.78 54.02 25.99

9.52 11.30 13.53 14.75 14.36 15.25 13.90 13.22 12.45 9.92 8.14 8.29

8 4 6 7 9 4 3 3 3 10 10 7

76.15 45.22 81.20 103.23 129.27 61.00 41.70 39.65 37.35 99.19 81.38 58.00

6.66 7.59 9.43 10.79 13.27 13.13 11.88 10.89 11.09 8.27 5.86 6.93

11 12 12 14 12 14 10 7 10 13 12 13

73.24 91.03 113.11 151.02 159.22 183.78 118.77 76.24 110.93 107.45 70.33 90.07

4.66 5.23 8.63 11.06 11.15 9.89 9.20 8.74 8.35 6.87 5.80 5.01

9 9 8 5 6 9 17 19 10 3 2 8

41.93 47.08 69.03 55.28 66.89 89.00 156.40 166.10 83.47 20.62 11.60 40.10

Monthly exergy 220.66 216.02 325.62 366.26 413.37 378.29 344.34 307.14 319.39 279.04 217.33 214.16

Annual solar energy (kW h)

3601.63

Table 9 Life cycle conversion efficiency (LCCE) for single slope and double slope passive solar still based on annual energy and annual exergy. Life time in year (n)

Energy output (Eout) in kW h Embodied energy (Ei) in kW h Solar energy for life time (Esol) in kW h Life cycle conversion efficiency (LCCE) based on energy Exergy output (Eout) in kW h Solar exergy for life time (Esol) in kW h Life cycle conversion efficiency (LCCE) based on exergy

Single slope passive solar still

Double slope passive solar still

30

50

30

50

34782.90 1737.79 116882.70 0.28 3254.40 108700.91 0.014

57971.50 1737.79 194804.5 0.29 5424.00 181168.18 0.020

31115.70 1483.90 108048.90 0.27 2677.20 100485.47 0.012

51859.5 1483.90 180081.50 0.28 4462.00 167475.79 0.018

Table 10 Capital investment. S. n.

Parameter

Cost of Single slope (Rs.)

Cost of double slope (Rs.)

1 2 3 4

Solar still Iron stand Labor and other charges Salvage value of the system after 30 years, if inflation remains @ 4% in India, [using present value of scrap material sold in Indian market] Salvage value of the system after 50 years, if inflation remains @ 4% in India, [using present value of scrap material sold in Indian market]

22,143 1000 4000 7506

18,183 1000 4000 6221

16,447

13,633

5

where Mew , ðSPÞw and UAC are annual yield for solar still, selling price of water and uniform end-of-year annual cost for solar still. The selling price of water has been taken as Rs. 5 per kg. The calculation of uniform end-of-year annual cost (UAC) is based on the present value method. Table 10 represents the cost of different components. The salvage value is based on the current price of different materials in Indian local market. The uniform end-of-year annual cost (Kumar and Tiwari, 2009; Tiwari and Ghosal, 2005) for a given initial investment of solar distillation systems can be expressed as

UAC ¼ Ps F CR;i;n þ M F CR;i;n Ss F SR;i;n

ð28Þ

where Ps, Ss and M are the net present cost, salvage value and maintenance cost of the solar still respectively. The first term in Eq. (28) represents the part of UAC corresponding to net present cost of the system, the second term represents the part of UAC corresponding to present value of maintenance cost and third term is the part of UAC corresponding to salvage value. The maintenance cost is generally taken as 10% of present value of the system. Hence, the maintenance cost can be written as M ¼ 0:1 Ps . FCR,i,n and FSR,i,n are capital recovery factor and sinking fund factor respectively. They are given by

n

F CR;i;n ¼

i ð1 þ iÞ n ð1 þ iÞ 1

and F SR;i;n ¼

i : n ð1 þ iÞ 1

where i and n are the rate of interest and life of the system respectively. The capital recovery factor and sinking fund factor (Tiwari, 2002) convert the present cost and the future cost respectively into uniform end-of-year annual cost. The uniform end-of-year annual cost for solar still ðUACÞ has been evaluated using Eq. (28) and presented in Tables 11 and 12. The annual productivity for single slope and double slope passive solar still have been calculated using Eq. (27) and they are presented in Table 13. 3.5. Exergoeconomic analysis Exergoeconomic analysis is economic analysis method based on exergy. It integrates exergy analysis with conventional cost analysis for improving the performance of energy systems (Tsatsaronis et al., 1993). The objective of this analysis is to estimate the costoptimal structure, the cost optimal values and facilitate designers to find ways to enhance the performance of a system in a cost effective manner. Exergoeconomic analysis has been applied by

17

D.B. Singh et al. / Solar Energy 134 (2016) 9–22 Table 11 Uniform annual cost (UAC) of capital investment, annual exergy gain and exergetic cost of single and double slope passive solar stills for life of 50 year. System

n (Year)

i (%)

Ps (Rs.)

M @ 10%

S (Rs.)

FCR,i,n

FSR,i,n

UAC (Rs.)

Gex,annual (kW h)

Rgex (kW h/Rs.)

Single Slope

50 50 50

2 5 10

27,143 27,143 27,143

2714.3 2714.3 2714.3

16,447 16,447 16,447

0.032 0.055 0.101

0.012 0.005 0.001

755.69 1556.92 2997.25

108.48 108.48 108.48

0.144 0.070 0.036

Double slope

50 50 50

2 5 10

23,183 23,183 23,183

2318.3 2318.3 2318.3

13,633 13,633 13,633

0.032 0.055 0.101

0.012 0.005 0.001

650.347 1331.757 2560.327

89.240 89.240 89.240

0.137 0.067 0.035

Table 12 Uniform annual cost (UAC) of capital investment, annual exergy gain and exergetic cost of single and double slope passive solar stills for life of 30 year. System

n (Year)

i (%)

Ps (Rs.)

M @ 10%

S (Rs.)

FCR,i,n

FSR,i,n

UAC (Rs.)

Gex,annual (kW h)

Rgex (kW h/Rs.)

Single Slope

30 30 30

2 5 10

27,143 27,143 27,143

2714.3 2714.3 2714.3

7506 7506 7506

0.045 0.065 0.106

0.025 0.015 0.006

1148.10 1829.28 3121.60

108.48 108.48 108.48

0.094 0.059 0.035

Double slope

30 30 30

2 5 10

23,183 23,183 23,183

2318.3 2318.3 2318.3

6221 6221 6221

0.045 0.065 0.106

0.025 0.015 0.006

985.284 1565.26 2667.34

89.240 89.240 89.240

0.091 0.057 0.033

Table 13 Annual productivity (gp ) of single slope and double slope passive solar stills. n

i

(SP)w

Single slope passive solar still

(Year)

(%)

(Rs./kg)

UAC (Rs.)

Annual yield (kg)

Rw (Rs.)

gp (%)

UAC (Rs.)

Dingle slope passive solar still Annual yield (kg)

Rw (Rs.)

gp (%)

30 30 30 50 50 50

2 5 10 2 5 10

5 5 5 5 5 5

1148.10 1829.28 3121.61 755.69 1556.92 2997.25

1739.15 1739.15 1739.15 1739.15 1739.15 1739.15

8695.75 8695.75 8695.75 8695.75 8695.75 8695.75

757.40 475.36 278.57 882.56 555.55 326.01

985.28 1565.26 2667.34 650.35 1331.76 2560.33

1555.79 1555.79 1555.79 1555.79 1555.79 1555.79

7778.95 7778.95 7778.95 7778.95 7778.95 7778.95

789.51 496.97 291.64 1196.12 584.11 303.83

many researchers (Ozgener and Hepbasli, 2005; Tsatsaronis and Winhold, 1985; D’Accadia and de Rossi, 1998; Kwon et al., 2001; Rosen and Dincer, 2003a,b; Ozgener and Hepbasli, 2005; Ozgener and Ozgener, 2009; Agrawal and Tiwari, 2012; Tiwari et al., 2015) to a variety of systems including power plants, cogeneration systems, heat pump systems, geothermal district heating systems and solar distillation system because it is thought that exergoeconomic analysis is one of the best suitable methods for the design, analysis, and performance improvement studies of energy conversion systems. They have considered the exergoeconomic parameter as the ratio of exergy loss to the cost. Their objective was to minimize the loss. However, the consideration of exergoeconomic parameter on the basis of exergy loss does not seem to be appropriate with solar system as we do not have to pay any penalty against exergy loss. The reason is that we do not have to pay anything for the corresponding input which is solar radiation. Also, solar radiation (input to solar distillation system) depends on climatic condition which cannot be controlled. So, we cannot provide same input to different solar distillation system while making comparison. Hence, exergoeconomic parameter on the basis of exergy gain with an aim to maximize the exergy gain for the same geometrical parameter and same climatic condition has been proposed for the comparison of different solar distillation systems. The exergoeconomic parameter (Rg,ex) based on exergy gain for passive solar still can be written as

Rg;ex ¼

Gex;annual UAC

ð29Þ

where Gex;annual and UAC are annual exergy gain for passive solar still and uniform end-of-year annual cost for the passive solar still

respectively. The exergoeconomic parameters for single slope passive solar still and double slope passive solar still have been calculated using Eq. (29) and presented in Tables 11 and 12 respectively. 4. Results and discussion The annual exergy of single slope and double slope passive solar stills have been found to be 108.48 kW h and 89.24 kW h respectively. The annual energy of single slope and double slope passive solar stills has been found to be 1159.43 kW h and 1037.19 kW h respectively. Single slope has been found to perform better than double slope passive solar still on the basis of exergy based EPBT, exergy based EPF, LCCE based on exergy as well as energy and exergoeconomic parameter. However, double slope performs better than single slope on the basis of EPBT based on energy, EPF based on energy and annual productivity. All relevant equations and data for the solar intensity and ambient temperature for the composite climatic condition of New Delhi have been transported to MATLAB computational program in order to compute exergy, yield, energy, energy matrices, exergoeconomic parameter and annual productivity. Figs. 2a and 2b represent the variation of intensity and average ambient temperature. The results obtained have been presented in Figs. 3–15. Figs. 3 and 4 represent the hourly variation of water temperature in basin, glass temperature, and ambient temperature for single slope and double slope passive solar stills for a typical day in the month of Jan and May respectively. It has been observed that water temperature in the basin of solar still is higher for single slope than double slope passive solar still because daily solar energy absorbed by single slope is higher by 20.42% and 0.68% for the month of January and May respectively due to the orientation of still.

TgiE,DS

30

TgiW,DS

20

Tgo,SS

10

TgoE,DS

0

TgoW,DS 6:00

40

4:00

Tgi,SS

2:00

50

0:00

Tw,DS

22:00

Tw,SS

60

20:00

70

18:00

6:00

4:00

2:00

0:00

22:00

20:00

yield (kg)

0.6

hew h1w yield

15

0.4

10 0.2

5

0.0 6:00

4:00

2:00

0

Ta

Time of the day (h) Fig. 3. Hourly variation of water temperature in basin, glass temperature and ambient temperature for single slope and double slope passive solar still for a typical day in the month of January.

Figs. 5 and 6 represent the hourly variation of yield, convective, radiative, evaporative and total heat transfer coefficients of single and double slope passive solar still respectively for a typical day in the month of January. Similarly, Figs. 7 and 8 represent the hourly variation of yield, convective, radiative, evaporative and total heat transfer coefficients of single and double slope passive solar still respectively for a typical day in the month of May. It has been observed from Figs. 5–8 that the maximum value of hourly yield occurs at 1:00 pm for both single and double slope

Fig. 5. Hourly variation of heat transfer coefficient and yield for single slope passive solar still for a typical day in the month of January.

35

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

30 25 20 15 10 5 0

hcwE hcwW

yield (kg)

Fig. 2b. Hourly variation of ambient temperature (Ta) for each month.

16:00

20

hcw hrw

Time of day (h)

Time of the day (h)

14:00

0.8

25

17:00

16:00

15:00

14:00

13:00

12:00

11:00

10:00

0

30

0:00

5

1.0

22:00

10

35

20:00

15

1.2

40

18:00

20

Ta

Fig. 4. Hourly variation of water temperature in basin, glass temperature and ambient temperature for single slope and double slope passive solar still for a typical day in the month of May.

16:00

25

9:00

TgoW,DS

14:00

30

12:00

20

12:00

35

8:00

TgoE,SS

8:00

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

40

8:00

30

8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00 2:00 4:00 6:00

45

10:00

Tgo,SS

10:00

Fig. 2a. Hourly variation of solar intensity on horizontal surface for each month.

Ambient Temperature Ta (oC)

40

Time of the day (h)

Time of the day (h)

Temperature (oC)

TgiW,DS

17:00

16:00

15:00

14:00

13:00

12:00

11:00

10:00

9:00

8:00

0

TgiE,SS

50

18:00

200

60

16:00

400

Tgi,SS

14:00

600

Tw,DS

70

10:00

800

Tw,SS

80

12:00

1000

90

8:00

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Heat transfer coefficient (W/m2-K)

Solar Intensity (W/m2)

1200

Temperature (oC)

D.B. Singh et al. / Solar Energy 134 (2016) 9–22

Heat transfer coefficient (W/m2-K)

18

hrwE hrwW hewE hewW h1wE h1wW yield

Time of day (h) Fig. 6. Hourly variation of heat transfer coefficient and yield for double slope passive solar still for a typical day in the month of January.

passive solar stills. However, maximum value of evaporative heat transfer coefficient occurs at 3:00 pm. Further, maximum value of difference between water temperature and glass temperature occurs at 12:00 noon as evident from Figs. 3 and 4. It happens because hourly yield depends on the product of evaporative heat transfer coefficient and temperature difference between water temperature and glass temperature. Fig. 9 represents the hourly variation of thermal exergy and energy of single and double slope passive solar stills for a typical day in the month of January and May. The hourly thermal exergy

19

Dec

Nov

Oct

Sep

Aug

Jul

DS

Jun

Jan

yield

May

h1w

Apr

hew

Mar

hrw

SS

18 16 14 12 10 8 6 4 2 0 Feb

hcw

Monthly exergy (kWh)

1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

yield (kg)

100 90 80 70 60 50 40 30 20 10 0 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00 2:00 4:00 6:00

Heat transfer coefficient (W/m2-K)

D.B. Singh et al. / Solar Energy 134 (2016) 9–22

Month

Time of day (h)

Fig. 10. Variation of monthly exergy gain for single slope and double slope passive solar stills.

hcwW

1.2

hrwE

0.8 0.6 0.4 0.2 0.0

yield (kg)

1.4 1.0

SS

hcwE

1.6

hrwW hewE hewW

DS

250 200

yield (kg)

100 90 80 70 60 50 40 30 20 10 0 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00 2:00 4:00 6:00

Heat transfer coefficient (W/m2-K)

Fig. 7. Hourly variation of heat transfer coefficient and yield for single slope passive solar still for a typical day in the month of May.

150 100

h1wE

50

h1wW

0

yield

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Time of day (h) Fig. 8. Hourly variation of heat transfer coefficient and yield for double slope passive solar still for a typical day in the month of May.

Fig. 11. Variation of monthly yield for single slope and double slope passive solar stills.

0.6 0.4 0.2 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00 2:00 4:00 6:00

0.0

Time of day (h)

Fig. 9. Hourly variation of thermal energy and exergy for single slope and double slope passive solar stills for a typical day in the month of January and May.

and energy for single slope have been found to be higher than double slope passive solar still. It happens because hourly solar energy absorbed by single slope is higher than double slope for both January and May due to its orientation which results in higher temperature difference in single slope than double slope passive solar still. Further, exergy of May is higher than the exergy of January for both single and double slope passive solar stills because hourly solar intensity for May is higher than hourly solar intensity of January which results in higher temperature difference between water surface in basin and glass temperature at inner surface. Fig. 10 represents the variation of monthly exergy gain for both single and double slope passive solar stills for all months of year. The maximum value of monthly exergy occurs in the month of May for both single slope and double slope passive solar stills

60

Exergy Eff.(%)

0.8

10 9 8 7 6 5 4 3 2 1 0

50 40 30 20 10 0 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

1.0

Jan-thermal energy-SS Jan-thermal energy-DS May-thermal energy-SS May-thermal energy-DS Jan-exergySS Jan-exergyDS May-exergySS May-exergyDS

Thermal Eff. (%)

Thermal Energy (kWh)

0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00

Exergy (kWh)

70 1.2

Time of day (h) Fig. 12. Hourly variation of thermal efficiency and exergy efficiency for single slope and double slope passive solar still for a typical day in the month of January and May.

because of the occurrence of maximum solar energy falling on the surface of solar stills in the month of May. The minimum value of monthly exergy occurs in the month of December for both single slope and double slope passive solar stills which occur because of the occurrence of minimum daily solar intensity in December for both single slope and double slope passive soar still. Also, monthly yield for single slope is higher than monthly yield of double slope solar still throughout the year which occurs due to occurrence of higher solar energy for single slope passive solar still throughout the year resulting in higher temperature difference between water surface in basin and inner surface of glass cover. Fig. 11 represents the variation of monthly yield for single slope and double slope passive solar still respectively for all months of

20

D.B. Singh et al. / Solar Energy 134 (2016) 9–22

0.80

15

0.70

13

0.60

11

0.50

9

0.40

7

0.30

5 3

0.20

1

0.10

-1

SS

EPBT based on energy

EPF (fraction)

EPBT (Year)

17

EPBT based on exergy EPF based on energy EPF based on exergy

0.00

DS

Typeof solar still

0.030

0.29

0.025

0.27

0.020

0.25

0.015

0.23

0.010

0.21

0.005

0.19

0.000

LCCE based on exergy (Fraction)

0.31

5 10 15 20 25 30 35 40 45 50 55 60 65

LCCE based on energy(Fraction)

Fig. 13. Variation of energy payback time (EPBT) and energy production factor (EPF) for single slope and double slope passive solar stills.

LCCE of SS based on energy LCCE of DS based on energy LCCE of SS based on exergy LCCE of DS based on exergy

Life of solar still (yr)

0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00

1200 Rgex,SS

1000 800 600 400 200

Annualproductivity (%)

Rgex (kWh/Rs.)

Fig. 14. Life cycle conversion efficiency (LCCE) of single slope and double slope passive solar stills.

Rgex,DS p,SS p,DS

0 2

4

6

8

10

12

14

16

Rate of interest (%) Fig. 15. Variation of exergoeconomic parameter (Rgex ) and annual productivity ðgp Þ of single slope and double slope passive solar stills with rate of interest for 30 year life time.

the year. The maximum value of monthly yield occurs in May for single slope passive solar still as well as double slope passive solar still. It happens because solar energy falling on the solar still has its maximum value in the month of May which is evident from Tables 7 and 8. The minimum value of monthly yield occurs in the month of December for both single slope and double slope passive solar stills which occur because of the occurrence of minimum daily solar intensity in December for both single slope and double slope passive soar still. Also, monthly yield for single slope is higher than monthly yield of double slope solar still throughout the year which occurs due to occurrence of higher solar energy for single slope passive solar still throughout the year.

Fig. 12 represents the variation of hourly exergy efficiency and hourly thermal efficiency of both single slope and double slope passive solar stills for a typical day in the month of May and January. It is observed that the hourly exergy efficiency and thermal efficiency for single slope passive solar still is higher than the corresponding values of double slope passive solar still till 2 pm because solar energy falling on the surface of single slope solar still is higher than double slope passive solar still due to the orientation of solar stills. However, double slope has been observed to give better hourly thermal exergy and energy efficiency after 2 pm due to its orientation. The daily thermal exergy efficiency of single and double slope passive solar stills for the month of May have been found to be 4.49% and 4.35% respectively. The daily thermal exergy efficiency of single and double slope passive solar stills for the month of January have been found to be 2.91% and 2.50% respectively. The daily thermal energy efficiency of single and double slope passive solar stills for the month of May have been found to be 45.03% and 42.67% respectively. The daily thermal energy efficiency of single and double slope passive solar stills for the month of January have been found to be 25.12% and 25.01% respectively. Hence, single slope has been found to give better performance than double slope passive solar still on the basis of daily thermal exergy and energy efficiency. It happens because of the occurrence of higher hourly thermal exergy and energy efficiency of single slope than double slope for a longer period. Fig. 13 represents the variation of energy payback time (EPBT) and energy production factor (EPF) for single slope as well as double slope passive solar stills. EPBT based on exergy has been found to be 16.02 year for single slope and 16.62 year for double slope passive solar still. EPBT based on exergy is lower for single slope passive solar still by 3.75% because embodied energy is higher by 14.61% and annual exergy gain is higher by 17.68%. EPBT based on energy has been found to be 1.49 year for single slope and 1.47 year for double slope passive solar still. EPBT based on energy for single slope solar still is higher by 1.36% because embodied energy for single slope passive solar still is higher by 14.61%, and annual energy available from single slope solar still is higher by 10.54%. EPF based on exergy has been found to be 0.062 for single slope passive solar still and 0.060 for double slope passive solar still. EPF based on exergy is 3.22% higher because annual exergy available from single slope is higher by 17.68% and embodied energy is higher by 14.61%. EPF based on energy has been found to be 0.67 for single slope solar still and 0.70 for double slope passive solar still. EPF based on energy for single slope has been found to be lower by 4.47% because annual energy available from single slope solar still is higher by 10.54% and embodied energy for single slope passive solar still is higher by 14.61% than double slope passive solar still. Fig. 14 represents the variation of Life cycle conversion efficiency (LCCE) with the life of single slope and double slope passive solar still. It has been observed that LCCE based on exergy as well as energy is higher for single slope than double slope passive solar still. It happens because annual exergy, embodied energy and annual solar exergy for single slope are higher than double slope passive solar still by 17.68%, 14.61% and 7.56% respectively. It means that the percentage increase in numerator is more than the percentage increase in denominator and hence the ratio is higher for single slope than double slope passive solar still. The difference of energy for n = 30 year and embodied energy for single slope is higher than double slope by 10.33%. The solar energy absorbed by single slope is higher than double slope passive solar still by 7.56%. It means the increase in numerator of Eq. (25) overcomes the increase in denominator and hence LCCE based on energy is higher for single than double slope passive solar still. Further, it can be noted from Fig. 14 that the difference in LCCE for single slope and double slope passive solar still increases as

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D.B. Singh et al. / Solar Energy 134 (2016) 9–22

the life of system increases. It happens because gap of difference between energy available from solar still and embodied energy for single slope and double slope increase as the life of system increases. Also, the gap of difference between exergy available from solar still and embodied energy for single slope and double slope increase as the life of system increases. The exergy based LCCE for single slope is higher than double slope passive solar still by 10% and energy based LCCE for single slope is higher than double slope passive solar still by 3.45% at n = 50 year. It happens because exergy gain is high grade energy. It can directly be used. Total amount of energy available cannot be used. Some part is bound to loss when put to use. Fig. 15 represents the variation of annual productivity and exergoeconomic parameter (Rgex) with the rate of interest for single slope and double slope passive solar stills. It has been observed that annual productivity as well as exergoeconomic parameter decreases with the increase in the rate of interest. It happens because the value of UAC increases with the increase in rate of interest. Further, the exergoeconomic parameter for single slope is higher than double slope by 3.19% for n = 30 year and rate of interest 2% because annual exergy gain and UAC for single slope passive solar still is higher by 17.68% and 14.18% respectively. The percentage increase in numerator of Eq. (29) is more than the percentage increase in denominator and hence the ratio increases by 3.19%. Similarly, annual productivity of double slope is higher than single slope by 4.07% for n = 30 year and rate of interest 2% because annual yield of double slope is lower than single slope passive solar still by 11.78% and UAC is lower for the same by 16.52%. Here, it can be seen that the percentage decrease in denominator is more than percentage decrease in numerator and hence the ratio increase by 4.97%. Also, annual productivity for both single slope and double slope passive solar stills is more than 100% which suggests the feasibility of system.

Appendix A Constants of Eqs. (1) and (2) are as follows. b þU t ÞAb a1 ¼ ðUM , for single slope passive solar still w Cw h i 1 2 ÞAb 2 ÞAb , for double slope pasþ h1wWðPB a1 ¼ Mw C w U b Ab þ h1wEðPA 2P 2P

sive solar still h i f ðtÞ ¼ 1 a0 IS A þ ðU t þ U ÞA T a , for single slope passive b b b eff Mw C w solar still f ðtÞ ¼ 1 Mw C w

h

a0w 2

i Ab 1wW B1 þ h1 a0b Ab ðISE ðtÞ þ ISW ðtÞÞ þ U b Ab T a þ h1wE A1 þh , P 2

for double slope passive solar still

a0eff ¼ a0w þ h1 a0b þ h01 a0g h1w ¼ hrwg þ hcwg þ hewg h1 ¼

hbw hbw þ hba

Ub ¼

hba hbw hbw þ hba

h1 ¼

h1w Ag U c;ga Ag þ h1w Ab

Ut ¼

h1w U c;ga Ag U c;ga Ag þ h1w Ab

0

K

g h1g l U c;ga ¼ K g g þ h1g lg

Constants of Eqs. (3) and (4) are as follows. 5. Conclusions A comparative study of single slope passive solar still and double slope passive solar still has been done on the basis of energy matrices based on exergy, exergoeconomic parameter, productivity, and efficiencies for the same geometrical parameter and same climatic condition. On the basis of the study, the following conclusions have been drawn. i. Annual exergy gain, annual energy output, thermal efficiency and exergy efficiency of single slope passive solar still is higher than double slope passive solar still for the same geometrical parameter and same climatic condition. ii. LCCE based on exergy as well as energy is better for single slope passive solar still than double slope passive solar still. Both EPBT and EPF based on exergy are better for single slope than double slope passive solar still for the same geometrical parameter and same climatic condition. However, EPBT and EPF based on energy are better for double slope than single slope passive solar still for the same geometrical parameter and same climatic condition. iii. Annual productivity of single slope passive solar still is higher than double slope passive solar still for the same geometrical parameter and same climatic condition. Also, annual productivity is more than 100% for both single slope and double slope passive solar still which suggest that both systems are feasible. iv. The value of exergoeconomic parameter is better for single slope passive solar still than double slope passive solar still for the same geometrical parameter and same climatic condition.

A1 ¼ R1 U 1 AgE þ R2 hEW AgW Ab Ab þ hEW h1WW 2 2 ! 2 h Ab AgW U 1 U 2 EW h1WW AgE 2

A2 ¼ h1WE U 2

P¼

U1 ¼

h1wE A2b þ hEW AgE þ U c;gaE AgE AgW

U2 ¼

h1wW A2b þ hEW AgW þ U c;gaW AgW AgE

B1 ¼

ðR2 P þ A1 hEW ÞAgW U 2 AgE

B2 ¼

Ph1wW A2b þ hEW AgW A2 U 2 AgE

R1 ¼ a0g ISE ðtÞ þ U c;gaE T a R2 ¼ a0g ISW ðtÞ þ U c;gaW T a h i hEW ¼ 0:034 5:67 108 ðT giE þ 273Þ2 þ ðT giW þ 273Þ2 ½T giE þ T giW þ 546

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D.B. Singh et al. / Solar Energy 134 (2016) 9–22 K

g h1gE l U c;gaE ¼ K g g þ h1gE lg

K

g h1gW l U c;gaW ¼ K g g þ h1gW lg

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