Comprehensive experimental and theoretical study of a novel still coupled to a solar dish concentrator

Accepted Manuscript Comprehensive experimental and theoretical study of a novel still coupled to a solar dish concentrator Milad Bahrami, Vahid Madadi Avargani, Mohammad Bonyadi PII: DOI: Reference:

S1359-4311(18)36749-8 https://doi.org/10.1016/j.applthermaleng.2019.01.103 ATE 13283

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

2 November 2018 3 January 2019 30 January 2019

Please cite this article as: M. Bahrami, V. Madadi Avargani, M. Bonyadi, Comprehensive experimental and theoretical study of a novel still coupled to a solar dish concentrator, Applied Thermal Engineering (2019), doi: https://doi.org/10.1016/j.applthermaleng.2019.01.103

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Comprehensive experimental and theoretical study of a novel still coupled to a solar dish concentrator Milad Bahrami1, Vahid Madadi Avargani2, *, and Mohammad Bonyadi3 1

MS Student, Department of Chemical Engineering, Faculty of Engineering, Yasouj University, Yasouj, Iran, E-mail: [email protected] 2, * Assistant Professor, Department of Chemical Engineering, Faculty of Engineering, Yasouj University, Yasouj, Zip Code: 75918-74831, P. O. Box 353, Iran (corresponding author). Tel: (+98)74-31005064, E-mail: [email protected] 3 Assistant Professor, Department of Chemical Engineering, Faculty of Engineering, Yasouj University, Yasouj, Zip Code: 75918-74831, P. O. Box 353, Iran, E-mail: [email protected]

Abstract This work presents a solar parabolic dish collector system with a new design of a solar still mounted at its focal point for saltwater desalination. The system was investigated both experimentally and theoretically. A detailed and accurate mathematical model was developed for the system described. The proposed model includes two main parts: the modeling of saltwater heating in the evaporator before evaporation process starts, and the modeling of water vaporization in the evaporator and condensation of vapor produced in the condenser. Validation and verification of the model were done with experimental data, and the results of errors analysis showed that the model is reliable. A parametric study for some optical properties, structural and operational parameters was performed for the system. The results show that the collector optical efficiency, absorber reflectivity, dish aperture diameter, and absorber plate size have a significant effect on the distilled water produced and initial saltwater temperature, salinity and the amount of saltwater in the evaporator have no impressive effect. For a dish with an aperture of 2 m, when the absorber plate reflectivity reduces from 0.7 to 0.4 and parabolic dish optical efficiency increases from 0.5 to 0.8, the distilled water produced increases up to 120 and 80% respectively, while the influence of initial water salinity, temperature and its amount in the evaporator on distilled water produced is less than 10%. For a dish concentrator with an aperture diameter of 3 m and for specified conditions about 75 kg distilled water can be produced in a day for system time operating from 8:30 to 17:30. Keywords: Solar Desalination; Solar Still; Parabolic Dish Collector; Mathematical Modeling

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1. Introduction Sustainable development of the world needs two vital water and energy resources [1]. A severe shortage of both resources in the 3rd world countries is entirely tangible and in some countries is disturbing and crisis. The water challenge for drinking, agricultural needs, and other usages is one of the most critical encounters in remote areas. Many countries are struggling with a lack of drinking water although the water resources are available in abundant quantity in nature. Most of the freshwater resources are destroying due to some unscheduled and unpremeditated mechanisms created by man-made activities. Seawater and icebergs in the polar regions are two main available water resources on the earth. A considerable portion of the water on earth is salty and less than 3% of it is fresh, and eventually, from available freshwater, less than 1% is within human reach [1,2]. Desalination process is one of the best methods that can provide part of the freshwater needed. Based on separation mechanisms, the desalination technologies are categorized into thermal and membrane desalination systems. In thermal desalination systems, the salts are separated from water due to water vaporization whereas in membrane desalination systems the water diffuses through a membrane and salts are almost retained. The main processes that are included in the thermal desalination classification are multi-stage flash (MSF), multi-effect distillation (MED), thermal and mechanical vapor compression processes (TVC & MVC). Reverse osmosis (RO), electrodialysis (ED), and ion exchanges (IE) are classified into the membrane desalination processes. From thermal desalination systems, the multi-stage flash, and from the membrane desalination systems, the reverse osmosis are most widely used in the world. In desalination processes, especially in the thermal category, a large amount of energy is needed to remove a portion of pure water from a saltwater source. Many oil-rich countries that are involved in the water shortage crisis, use fossil fuels as energy supply in their commercial desalination processes. However, in addition to the cost of fossil fuel sources, the environmental destructive aspects of using these resources, encourage the governments to use the renewable energy resources such as solar, wind, geothermal and biomass energy as far as possible in desalination systems. In areas which are struggling with the potable water crisis, the coupling of renewable energy resources with desalination processes can be a practical and economical way to supply drinking water. One of the most promising and attractive renewable energy resources that can be used in the thermal desalination processes is solar energy. The country Iran has a good level of solar irradiation and abundant seawater resources as the Persian Gulf, Oman Sea, and the Caspian Sea. Therefore, due to the severe shortage of drinking water, especially in recent years in Iran, the use of solar energy for seawater desalination can be a very fine option for drinking water supply. Solar desalination systems can either be direct or indirect. In the direct solar desalination systems, the solar energy is directly used in a solar collector to produce distilled water and in 2

indirect systems, combining conventional desalination techniques with solar collectors are used. Coupling solar thermal energy with a power cycle by using direct mechanical power can also be used in some desalination processes [3]. From the perspective of the collector used in solar water desalination systems, two conversion modes were proposed. For temperatures lower than 100 oC the flat collectors are used and for a higher temperature more than 100 oC the solar concentrators are used [4]. A number of researchers studied indirect solar thermal desalination processes implemented in different locations. Kalogirou studied a MSF desalination system using solar collectors with 10 m3/day capacity in Safat, Kuwait [5]. Abu-Jabal et al. investigated a MSF desalination system using thermal collectors and PV cells with 0.2 m3/day capacity in Al Azhar University in Gaza [6]. Several types of research have been carried out on solar desalination systems using parabolic trough collectors. Kalogirou introduced a parabolic solar trough collector for seawater desalination and revealed that the multiple-effect boiling evaporator is conducted to be the most suitable method that used solar energy [7]. Mohamed and El-Minshawy used parabolic trough concentrators in a humidification-dehumidification desalination system [8]. Jafari Mosleh et al. studied a combined system consists of a heat pipe, evacuated tube and parabolic trough collector for desalination application [9]. The performance of a single effect thermal desalination system coupling with a small scale concentrating solar power (CSP) was studied by Cioccolanti and Renzi [10]. The results showed that the described system has interesting potential, especially in small-scale applications to supply the freshwater demand in rural and remote areas. Combination of a reverse osmosis system with CSP and PV plants has been studied by Laissaoui et al. under variable load conditions [11]. Since storing electricity is not a particularly efficient process, the CSP plants in which the energy gained from the solar sunlight source is converted to electricity or the PV plants are only effective during daylight hours. Therefore, for large-scale energy production systems, the solar thermal technologies are so attractive. Because in these systems, the storage of heat is a far easier and more efficient method. Before now, direct types of solar desalination systems have been studied numerously. Some researchers have been focused on solar desalination processes using types of solar collectors. A multi-effect desalination system coupled with a flat plate solar collector was studied experimentally by Chorak et al. [12]. Riffat et al. evaluated the performance of a v-trough solar collector for desalination applications. This type of collector compared to the common trough collectors does not need high precision tracking system and its cost is also lower [13]. To concentrate the solar energy on the small surface absorbers, a point focusing collector is one of the best options due to lower thermal losses from the absorber to the ambient. Since the thermal losses from the absorber are proportional to its surface, therefore higher temperature can be achieved under concentrated conditions. A parabolic dish collector concentres the solar energy on a central receiver that is placed at its focal point [14,15]. Madadi et al. studied a solar parabolic dish collector with a cylindrical cavity receiver based on simultaneous energy and 3

exergy analysis [16]. Li et al. proposed an approach for designing parabolic mirrors using optimized compliant bands [17]. The parabolic dish collector or concentrator with point focusing system is more efficient and advantageous over other collectors such as parabolic trough and flat plate collectors due to minimal thermal losses [18,19]. In the solar desalination processes, to achieve higher distilled water rate, the concentrator is coupled with a solar still in order to increase the temperature of saltwater in the evaporator. The natural and forced circulation modes can be used to supply water in the receiver. The coupling of a solar concentrator and a solar still enhance the distilled water productivity [20,21]. When a concentrator is placed inside or outside of the still, the energy reached to the still increases and consequently the distilled water productivity is increased compared to that obtained with a conventional still [22]. A coupling desalination system consists of a pipe and simple heat exchanger at the focal line of a parabolic trough collector with a conventional desalination system was developed by Zeinab and Ashraf [23]. The results of this work indicated that an increase of 18% in freshwater productivity can be obtained due to the system modification. A triple basin solar desalination using a parabolic dish concentrator was investigated by Srithar et al. [24]. The results showed that the triple basin solar still (TBSS) with charcoal and TBSS with river sand enhance the distillate by 34.2 and 26.5% compared to conventional TBSS. Prado et al. investigated a parabolic dish concentrator experimentally and theoretically for water desalination [25]. The distilled water produced by the system varied from 4.95 to 4.11 kg/m2day for 0-4% of seawater concentrations. In this study, a novel solar desalination system is investigated both experimentally and theoretically. A parabolic dish collector (PDC) with novel solar still as its receiver that is located at the focal point of the dish is designed and manufactured. The design of solar still is such a way that both evaporator and condenser are considered in a package. The incident solar irradiation to the dish surface is reflected and collected to the absorber surface of the solar still. The saltwater in the still is evaporated and the generated vapor is condensed by a plate condenser which is embedded at the top of solar still. Innovation in the design of the solar still is such a way that there is a possibility of using inlet saltwater for vapor condensation. This can be very effective in pre-heating of saltwater before entering the evaporator and consequently can increase the distilled water productivity. In addition to novelty in system operation, a comprehensive mathematical model is presented for the system described and effect of some optical properties, operational and structural parameters on the thermal performance of the system are investigated.

2. Experimental setup An experimental setup for desalt water production was designed and manufactured. The detailed schematic and the photo of complete experimental setup are shown in Fig. 1(a), and (b) respectively. The setup is made of two main sections, the dish collector and solar still. The 4

optical properties, geometrical and operational parameter values and ranges in experimental setup and conditions are given in Table 1. Saltwater in a salinity range of 10 to 40 gr salt per kilogram of water was prepared in a saltwater storage tank. A water pump is used to pump the saltwater from sample tank to the solar still. By a float level controller, the amount of saltwater in the evaporator is controlled. The maximum amount of saltwater in the evaporator is 10 kg. The solar still is made of a stainless steel sheet with a thickness of 2 mm, to prevent deposition of sediment and salts in the water on the internal walls of the evaporator. The size of the absorber plate in the solar still is a 0.2 × 0.2 m rectangular plate, which is covered with a black color. In order to minimize the thermal losses from the wall side of the solar still, a rock wool insulation of 3 cm in thickness was used. The temperature of coolant (water) in the condenser at inlet and outlet, the bulk temperature of saltwater in the evaporator, and the inlet temperature of saltwater to the evaporator were measured by PT100 thermocouples, which were stored to an Autonics KRN1000 date recorder. The weather conditions, ambient temperature, and wind velocity were measured by a multi-function HVAC meter model Testo 480 and a Testo vane probe, with 4" diameter (100 mm). The Direct solar irradiation intensity at the location of the experiment was measured by a solar power meter model TES-1333R, which was installed on the dish surface and was moving with dish collector movement. In order to consider the effects of ambient conditions, such as ambient air velocity, its temperature and instantaneous solar irradiation intensity on the thermal performance of the system, the measuring devices were turned on at the start of the system operating. The advantage of this is the use of real data in the input of the developed model for the system. The system started operating at the beginning of the day, and all data was recorded at the same time. A dual-axis tracking system was used to set up the solar energy direction in the normal direction of the dish surface or parallel with the focal line of the dish. The system in the base axis turns from north to south and 360 o freedom is available for adjustment the solar azimuth angle. On the other hand, an adjustable arm was employed to regulate the dish tilt angle to achieve the maximum normal direction of solar irradiation on the dish surface. These settings are carried out manually and in the next phase, its settings should be done automatically. The dual-axis tracking system is shown schematically in Fig. 1(a). The solar still in the system is designed in such a way that in the first configuration, the saltwater can preheat in the condenser before it enters the evaporator. This configuration has two advantages. The coolant in the condenser can be provided from the saltwater source that can be sea water. On the other hand, preheating of saltwater before entering the evaporator can enhance the rate of desalting water produced and consequently enhance the thermal performance of the system. In the second configuration, the coolant in the condenser can be provided from another source, or even another coolant rather than water can be used to increase the cooling condenser efficiency. Since the first configuration is suitable for large-scale plants like the setup explained, in this work the second configuration was applied in the experiments, and the hot water outlet from the condenser was collected in a storage tank. The experiments were performed in Yasouj city, Iran, with the latitude and longitude of 30.6684° N, 5

51.5875° E, respectively. In the experiments, average solar irradiation of 850-900 W/m2 was available, and the effects of initial saltwater salinity, temperature and amounts of saltwater in the evaporator on distilled water produced by the system were investigated at different weather conditions and solar irradiation intensities.

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Fig. 1: Experimental setup, (a) detailed schematic diagram, (b) the photo of the whole experimental setup Table 1: Geometrical and operational parameter values and ranges in the experimental setup

Dish Collector and Solar Still Geometries and Optical Properties Parameter Value Concentrator aperture diameter 2.0 m Concentrator focal length 1.4 m Absorber plate size 0.2 m × 0.2 m Condenser size 0.2 m × 0.4 m Plates gap distance (Condenser) 0.02 m Concentrator optical efficiency 0.70 Absorber Plate Reflectivity 0.60 Absorber Plate Emissivity 0.55

7

Operational range in experiments Parameter Range Saltwater amount in evaporator 1.0 -10.0 kg Salinity 10-40 gr salt/kg water Irradiation intensity 200–1050 W/m2 Wind velocity 0-5 m/s Ambient Temperature 25-35 °C Water rate in the condenser 0.01-0.125 kg/s Condenser inlet temperature 20-30 °C Average solar irradiation intensity 850-900 W/m2

3. Mathematical modeling Mathematical modeling technique is a powerful and appropriate tool for the parametric study of a system and can be used efficiently in order to improve the performance of a system by investigating the effective parameters. For the solar desalination system described in the previous section, a comprehensive and accurate mathematical model was developed. The system operates at unsteady-state. The solar systems are inherently dynamic due to changing in environmental conditions such as ambient air temperature, wind velocity, solar irradiation intensity, and other parameters. In the proposed model and deriving of system governing equations some assumptions are used, which are summarized as below: ˗ The radiative properties of absorber plate embedded in the solar still such as absorptivity, reflectivity, and emissivity are considered constant, and the effects of temperature on these properties are negligible. ˗ The distribution of the saltwater temperature in the evaporator is uniform. ˗ The heat losses from the wall of solar still to the ambient is negligible due to wall insulation for the heating process. However, after the evaporation process started, the heat losses from the evaporator wall can be considered in the energy balance equation due to large boiling heat transfer coefficient. ˗ The thermo-physical properties of absorber plate are considered constant. The proposed model in this study is divided into two sections, the model for the system before the saltwater in the evaporator begins to evaporate, and the model for the system after the evaporation process started. Since in the system before and after the evaporation process the governing equations are different, this approach is employed in system modeling.

3.1. System modeling before the evaporation process starts (Batch heating of saltwater) 3.1.1. Energy balance for the absorber plate A schematic energy balance for the evaporator is shown in Fig. 2 for batch heating of saltwater in the evaporator Fig. 2(a), and for continuous evaporation process, Fig. 2(b). In the first step, the modeling of the batch heating process is carried out. The amount of solar energy which is reflected from the dish surface and reaches to the absorber plate is transferred to the saltwater in the evaporator by free convection mechanism. The saltwater in the evaporator starts to warm up and when it comes to its boiling point, the evaporation process starts. Part of solar energy that reached to the absorber plate is reflected and another part of it is lost to the ambient by convection and radiation mechanisms.

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Fig. 2: The schematic energy balance for the absorber plate and saltwater in the evaporator, (a) before the evaporation process starts and (b) after the evaporation process started

According to the mentioned explanations, the energy balance for the absorber plate can be written as follows: 4 Qsolar  RsQsolar   s As Ts4  Tamb   hext ,conv. As Ts  Tamb   hint ,conv. As Ts  Tsw  

  ms c p , sTs  t

(1)

where, As, ms and cp,s are the surface, mass, and heat capacity of absorber plate respectively, the Qsolar is the amount of solar energy which is reflected from the dish surface on the absorber plate. The second term in Eq. (1) is the amount of energy which is reflected from the absorber plate to the ambient, the two next terms are heat losses from the absorber plate to the ambient by radiation and convection mechanisms, and the last convective term is the amount of energy that is transferred to the saltwater in the evaporator by free convection mechanism. The Rs and  s are the reflectivity and emissivity of absorber plate. The  is the Stefan-Boltzmann constant and is approximately 5.67 x 10-8 W/m2. K4. In Eq. (1), the Qsolar can be estimated from Eq. (2): Qsolar  opt . Ac Ib

(2)

where, opt is the optical efficiency of the dish, which depends on the optical properties of the materials involved such as reflectance of the dish and the optical properties of the receiver, the geometry of the collector, and the various imperfections arising from the construction of the collector [26]. The optical efficiency of a dish collector is defined as a fraction of incident solar energy on the concentrator surface that is reflected on its focal point. In this study, the optical efficiency of the dish is estimated at 0.70 in the experiments. The Ac is the dish aperture area and I b is the instant beam solar irradiation. 9

The external convective heat transfer coefficient for heat transfer from absorber plate to the ambient in windy conditions for an inclined surface is calculated from the Eq. (3) [27]:

hext ,conv.

0.5 kair * 0.325 Re0.6255 1  sin       Lc

(3)

In Eq. (3), the Re is the Reynolds number, kair is the thermal conductivity of air,  is the angle between absorber plate and vertical and Lc is the characteristic length of the absorber plate. All thermo-physical properties of air are calculated in the average temperatures of ambient and absorber plate. The internal free convection heat transfer coefficient for heat transfer from the absorber plate to the saltwater is calculated by below equation [28]: 2

hint ,conv.

1   0.387 Ra 3   ksw * 0.825   9 16 8 27 1   0.492 Pr         (4)  Lc

where, ksw is thermal conductivity of saltwater, Ra and Pr are Rayleigh and Prandtl numbers respectively. All properties of saltwater are calculated based on its salinity and average temperatures of saltwater and absorber plate. The Rayleigh and Prandtl numbers are calculated by Eqs. (5) and (6) as follows:

Pr 

c p , sw sw

(5)

ksw

g cos  *  (T  T ) L3c s sw Ra  * Pr 2

(6)

 sw

3.1.2. Energy balance for the saltwater in the evaporator The energy balance equation for the saltwater in the evaporator before it begins to evaporate can be written as below. Before evaporation, since the temperature of the absorber plate is not high, the heat is transferred to the saltwater by free convection mechanism which is more dominant than the radiation mechanism. Therefore, the energy balance equation for the saltwater is given by Eq. (7):

hint ,conv. As Ts  Tsw   U overall ,h Aw Tsw  Tamb  

  mswc p ,swTsw  t 10

(7)

A part of heat gained by saltwater is lost to the ambient. In Eq. (7), the Aw is the wall area of the evaporator and U overall ,h is the overall heat transfer coefficient and subscript h indicates that it can be considered for heating process, or in other words for saltwater in the evaporator before it begins to evaporate. The overall heat transfer coefficient can be calculated from Eq. (8), as follows:

U overall ,h

  t 1 1   insulation   h  ext ,conv. Aw kinsulation Aw hint ,conv. Aw 

1

(8)

In heat losses from the saltwater to the ambient, both convective heat transfer in saltwater and air sides and also conductive heat transfer from the insulation are considered. By solving Eqs. (1) and (7), the temperatures of the absorber plate and saltwater in the evaporator as a function of time can be achieved. After the process starts, the temperature of the absorber plate and consequently the temperature of the saltwater increase until the saltwater inside the evaporator starts to boil. When the saltwater in the evaporator boils, the energy balance equation for absorber plate and saltwater are different with before evaporation process due to water vapor rising from the saltwater surface. Therefore, in the next section the energy balance equations for absorber plate, saltwater in the evaporator and condenser are derived.

3.2. System modeling after the evaporation process started (Continuous evaporation and condensation process) The schematic energy balance for the solar still for when the saltwater evaporation starts is shown in Fig. 2(b). As the energy streams in the figure show, the governing equations for the system before and after the boiling process are different. When the evaporation process starts, since the temperature of the absorber plate is higher than before the evaporation process begins, the amount of absorber plate energy is transferred to the saltwater by radiation and boiling process mechanisms. By starting evaporation of saltwater, a part of the energy of saltwater exits with rising vapor from the saltwater surface. During the evaporation process in order to condense the rising vapor, the coolant in the condenser must be entered. 3.2.1. Energy balance for the absorber plate By using the schematic energy balance for the solar still shown in Fig. 2(b), the energy balance equation for the absorber plate is written as: 4 Qsolar  Rs Qsolar   s As Ts4  Tamb   hext ,conv. As Ts  Tamb 

hboiling As Ts  Tsw,b    s As T  T 4 s

4 sw ,b



  ms c p , sTs  t 11

(9)

According to the temperature difference between the absorber plate and saltwater temperatures, the type of boiling in this process is film boiling. The boiling heat transfer coefficient is given by the following equation [29]: 1

hboiling

 2k 2  gh (   v )  3  0.234  v v fg l   T v gc  

(10)

where, kv ,  v and v are thermal conductivity, density and dynamic viscosity of vapor, h fg is the difference between the enthalpy of saltwater and water vapor and l is the density of saltwater. All properties of saltwater are calculated at instant salinity and boiling temperature. All properties of air stream outside the absorber plate are calculated in the average temperature of absorber plate and ambient air. Also, instant wind velocity and ambient air temperature at any time are considered as the model input. 3.2.2. Energy balance for the saltwater in the evaporator The energy balance equation for boiling saltwater in the evaporator is given by Eq. (11):

msw,in c p , sw,inTin  hboiling As Ts  Tsw,b    s As Ts4  Tsw4 ,b  mv   U overall ,b Aw Tsw,b  Tamb  

  mswc p , swTsw,b 

(11)

t

In Eq. (11), the overall heat transfer coefficient for heat losses from the wall of the evaporator to the ambient, U overall ,b , is similar to that in Eq. (8), with the difference that hboiling should be placed instead of hint ,conv. . 3.2.3. Energy balance for condenser The condenser energy balance according to the schematic shown in Fig. 2(b) can be written as:

T T    mcwc p ,cwTcw  mcw,in c p ,cw,inTin  mv   mcw,out c p ,cw,outTout  hext ,conv. Acond .  in out  Tamb   2 t  

(12)

3.3. Mass balance for salt and water vapor in the evaporator It is assumed that all produced vapor in the evaporator is condensed in the condenser. On the other hand, the amount of saltwater in the evaporator is constant, since it is controlled by a level controller. Therefore, by a simple mass balance equation for the saltwater in the evaporator, it can be said that: 12

msw,in  mv

(13)

The mass balance equation for salt in the evaporator can be written as:

msw,in Sin 

  msw S  t

(14)

3.4. Thermo-physical properties of saltwater before and after evaporation process Since the temperatures of the absorber plate, saltwater in the evaporator and ambient temperature and also, the salinity of water during desalination process changes, the properties of saltwater and ambient air outside the solar still must be modified at any time. Therefore, the properties of air outside the plate are calculated at the average temperature of ambient air and absorber plate. On the other hand, for saltwater in the evaporator before evaporation process starts since water salinity does not change and only the temperature of saltwater increases, the properties of saltwater are calculated in the average temperatures of saltwater and absorber plate. For when the saltwater is evaporating, the salinity and consequently boiling point of saltwater changes, and as a result, the properties of saltwater must be modified based on instant salinity, and average temperature of absorber plate and boiling temperature of saltwater. All needed correlations for calculation of saltwater properties are given in the appendix.

4. Numerical solution methodology 4.1. Discretization of governing equations For the developed mathematical model, a numerical solution methodology is described in this section. Since in the obtained equations, the radiation mechanism exists, the finalized equations are nonlinear ordinary differential equations. In this study, the finite difference method is used to solve derived equations numerically. Here, a methodology is described step by step in order to find the temperature of saltwater in the evaporator, temperature of absorber plate, the temperature of outlet water from the condenser and the rate of distilled water produced. At first, the equation of desalination process before the saltwater begins to evaporate must be solved to find of the temperature variation of saltwater and absorber plate temperature with time, and consequently the time that saltwater starts to evaporate. The governing equations of absorber plate and saltwater in the evaporator, Eqs. (1) and (7), after discretization by finite difference method are simplified as:

Tst 1 

 A I t 1  R     A  T t 4  T t 4    amb    s s s  s   opt . c g  t *   t t t t t t hext  A T  T  h A T  T , conv. s  s amb  int , conv. s  s sw    ms c p , s

13

 Tst

(15)

t 1 sw

T







t t t t t t t t t t * hint ,conv. As Ts  Tsw   U overall , h Aw Tsw  Tamb   Vsw  swc p , swTsw

Vsw  c

t 1 t 1 sw p , sw

(16)

The stepwise solution method is explained as: 1- The procedure of solution is a try and error technique. The average temperature is guessed for absorber plate. The arithmetic mean of saltwater and absorber plate temperatures and also, the arithmetic mean of absorber plate and ambient air temperatures are calculated. 2- For inside and outside of evaporator, the properties of saltwater and air around the absorber plate are calculated at appropriate mean temperatures. 3- By using Eqs. (3), (4) and (8) the heat transfer coefficients are calculated and by inserting the value of these quantities in Eqs. (15) and (16), the temperatures of saltwater and absorber plate are achieved. 4- The absorber plate temperature obtained from the previous step is compared with its guess value and modified. The described procedure continues until the true values of temperatures are obtained. By solving Eqs. (15) and (16), the temperature changes of saltwater in the evaporator and absorber plate with time and the time that saltwater begins to evaporate can be achieved. After the temperatures of saltwater in the evaporator and absorber plate were obtained, the program code shifts to the second section of the model to obtain the temperature of absorber plate, saltwater boiling temperature, the temperature of outlet water from the condenser and the rate of distilled water produced. In the second section of the model, the governing equation for when the saltwater in the evaporator starts to evaporate are Eqs. (9), (11), (12) and (14). The discretization forms of these equations are given as follows:  A I t 1  R     A  T t 4  T t 4    amb   s s s  s   opt . c g   t *   t t t t t t T t  4  T t  4   hext A T  T  h A T  T    A     , conv. s s amb boiling s s sw,b s s  s sw,b     Tst 1   Tst ms c p , s

Tswt ,1b 

4 t t t t t  mt c  t 4   v p , sw,inTin  hboiling As Ts  Tsw,b    s As Ts   Tsw,b    t t t t *    Vsw  swc p , swTsw,b t t t t mv   U overall ,b Aw Tsw,b  Tamb     t 1 t 1 Vsw  sw c p , sw

14

(17)

(18)

t mcw,in c p ,cw,inTint  mvt   mcw,out c p ,cw,outTout    t 2* t *  t   Tint  Tout t   Tamb  hext ,conv. Acond .   2      T t 1  T t  T t t 1 Tout  in in out mcwc p ,cw

S t 1 

t tmsw,in Sin  Vsw  sw St

(19) (20)

t 1 Vsw  sw

5- For when the saltwater in the evaporator starts to evaporate, the Eqs. (17)-(20) must be solved. All properties of saltwater are calculated at the appropriate mean temperature and salinity.

4.2. Model validation and verification In the experiments, the effects of some parameters on the rate of distilled water produced for various conditions were considered. Effects of the initial amount of saltwater in the evaporator, the initial salinity of water and different rates of inlet water to the condenser at different weather conditions during various days were investigated. On the other hand, the goal of mathematical modeling of such systems is to explore the effect of some optical properties, operational and structural parameters on the performance of the system in order to enhance significantly its performance. Before a parametric study of each modeled system, the developed model must be validated and verified. In this study, various tests were performed at different weather conditions such as sunny days, partly cloudy days, windy and calm weather conditions. The developed model for the system was validated and then verified at all conditions. But, since the number of experiments is so much, in order to compare the model results with experimental data, only the results of one of the mentioned conditions with the maximum deviation between model results and experimental data are reported here. Two statistical parameters, the root mean square error, RMSE and the coefficient of determination, R2 are used to report the spreading error. Moreover, another statistical parameter, the mean bias error, MBE is used to report the bias error. These indicators are defined as:

R2  1 

 O  m  i

2

i

(21)

i

  Oi  O 

2

i

RMSE 

 O  m  i

2

i

i

(22)

N

15

MBE 

1 N

N

 i 1

mi  Oi Oi

(23)

where, mi is the i-th model data, Oi is the corresponding experimental value, N is the total number of data, and O is the mean value of the experimental data. The values of R2 varies between 0 and 1. Larger numbers indicate better agreement between the model and experimental data, and 1 represents a perfect agreement. Also, smaller numbers of RMSE and MBE indicate better agreement.

5. Results and discussion Temperature variations for saltwater in the evaporator, ambient temperature, condenser inlet, and outlet, and distilled water productivity with time are shown in Fig. 4. The experimental data in Fig. 4 are for Saturday, June 2, 2018. The ambient conditions for the test day, such as solar irradiation intensity, ambient temperature and wind velocity with time are shown in Fig. 3(a) and (b). The day was partially cloudy, which the small drop in solar irradiation around 13:00 to 13:40 in Fig. 5 represents this issue. That's why, in a range of times, it seems that solar irradiation is constant. The ambient temperature and wind velocity are required to estimate the amount of heat losses from the absorber plate to the ambient air.

Fig. 3: Ambient conditions, (a) the solar irradiation intensity, (b) the wind velocity and ambient air temperature for Saturday, June 2, 2018

The results in Fig. 4 show that for an initial amount of saltwater of 6.15 kg, salinity of 20 (g salt/kg water) and water rate in condenser of 0.10 kg/s, for when the process starts at about 11:40, the saltwater in the evaporator is warmed up and starts to evaporate at around 12:40. In the experiments about 6.75 kg distilled water produced from 11:00 to about 14:30, during the time of saltwater boiling, while the model predicts that about 6.90 kg distilled water must be produced. This difference can be due to the error in calculating the heat losses from the solar still 16

to the ambient, or it may be due to the fact that part of the vapor generated in the evaporator does not liquefy in the condenser and discharged with distilled water from the device and released in the ambient air. However, the proposed model, in most cases predicts precisely the amount of distilled water produced by the system with a very little error. The temperature variations are affected by environmental conditions, especially the intensity of solar irradiation. When the wind velocity increases, the thermal losses due to heat convection from the absorber plate to the ambient increases and consequently the performance of the system is decreased. The solid lines in Fig. 4 show the results of the model and indicate that good agreements between model results and experimental data exist. Condenser Water_out Ambient Air

2.50

370

2.00

Temperature(K)

360 350

1.50

340

Salinity = 20 (g/kg) Condenser Water Rate = 0.1 (Kg/s)

330

1.00

320 310

0.50

300 290 11:30

Distilled Water Productivity, kg/h

380

Condenser Water_in Evaporator Tank DW Productivity

0.00 12:00

12:30

13:00

13:30

14:00

14:30

15:00

15:30

Time Fig. 4: Left side, temperature variations for saltwater, condenser inlet and outlet, ambient temperature, and right side, distilled water productivity for Saturday, June 2, 2018

Table 2: The results of error analysis

Parameters

R2

Saltwater temperature

0.9955 2.125242 0.00181

RMSE

MBE

Condenser outlet temperature 0.8882 0.934374 0.00214 Distilled water productivity

0.9812 0.124844 0.00598

The results of error analysis for distilled water productivity, the saltwater temperature in the evaporator and condenser outlet temperature for these experimental conditions are given in Table 2. The values of calculated errors show that there is a good agreement between mathematical modeling results and experimental data. 17

After model validation and verification in various conditions, a system parametric study was done by the model. The effect of some optical properties such as PDC optical efficiency and absorber reflectivity, operational parameters such as the initial amount of saltwater in the evaporator, initial saltwater temperature, salinity and structural parameters such as PDC aperture diameter, and absorber plate size were investigated and the rate of distilled water produced by the system was studied. The solar irradiation intensity and weather conditions for Monday, September 17, 2018, are considered as model input which are shown in Fig. 5(a) and (b) respectively.

Fig. 5: Ambient conditions, (a) solar irradiation intensity, (b) the wind velocity and ambient air temperature for Monday, September 17, 2018

For the parametric study of the system using the developed model, all structural parameters outlined in Table 1 were used except for the parameter or property that has been aimed to investigate its effect on the performance of the system. The optical efficiency of the dish collector of 0.8 and the absorber plate reflectivity of 0.4 were considered in the model as optical properties. The condenser water rate of 0.05 kg/s, the condenser inlet temperature of 20 oC, the saltwater initial amount of 8 kg, the initial saltwater temperature of 25 oC, and salinity of 30 g/kg were considered as operational parameters in the model.

5.1. Effect of some structural parameters 5.1.1. Effect of PDC aperture diameter One of the most important structural parameters that affect the performance of these systems and the amount of distilled water produced is the PDC aperture diameter. By increasing in the diameter of the PDC aperture, the larger amount of solar irradiation is received, and 18

consequently, a larger amount of solar irradiation is reflected from the dish surface to the absorber plate. As a result, by increasing in the dish aperture diameter, the rate of distilled water produced is increased significantly. The effect of dish aperture diameter on the rate of distilled water produced by the system during the day is shown in Fig. 6. The results in Fig. 6 indicate that the rate of distilled water produced by a dish collector with an aperture diameter of 3 m is approximately 2.15 times of a dish with an aperture diameter of 2 m. For a dish with an aperture of 3 m, during a specified day that its weather conditions and solar irradiation data were mentioned before, about 50 kg of distilled water is produced, while the dish with an aperture of 2 m produces about 20 kg distilled water in the same conditions. Also, saltwater in the evaporator boils for a dish with a larger aperture diameter at an earlier time. For example, for a dish with 3 m aperture, the 8 kg saltwater with an initial salinity of 30 g/kg boils after only 20 minutes, while it takes about 40 minutes for a dish with 2 m aperture. By comparing the results in Fig. 6 with ambient conditions, the data in Fig. 5, the dominant changes in the trend of distilled water rate during the day is caused by changes in the intensity of solar radiation, and the reduction of distilled water rate during the day is due to increasing in salinity and consequently increasing in saltwater boiling point.

Distilled Water Rate, kg/h

9

Dish Aperture Diameter = 1.5 m

Dish Aperture Diameter = 2.0 m

Dish Aperture Diameter = 2.5 m

Dish Aperture Diameter = 3.0 m

8 7 6 5 4 3 2 1 0 9:00

10:00

11:00

12:00

13:00

14:00

15:00

16:00

17:00

Time Fig. 6: Effect of dish aperture on distilled water produced during the day

5.1.2. Effect of absorber plate size Another important structural parameter that affects the performance of the system and the rate of distilled water produced is the absorber plate dimensions. In the model, a square plate with a length of L is considered as absorber plate. The effect of absorber length on the rate of distilled water produced during the desalination process is shown in Fig. 7. The absorber plate in the solar 19

still has a dual effect. Concentrating characteristics of a PDC have important effects on the optical-thermal conversion efficiency of collector and its receiver. As described the solar energy concentration area (SECA) in details in previous work [30], for absorber plate with smaller area than SECA, a part of solar irradiation reflected from dish surface reaches to the absorber plate and total reflected solar irradiation does not hit to the absorber plate and consequently the thermal performance of the solar still is decreased. On the other hand, for absorber plate greater than SECA although the total reflected solar irradiation hits to the absorber plate but, the surface that exposed to the ambient air and consequently thermal losses increase. For the system under study in this work, the SECA of the dish is a circular surface with a diameter of 0.2 m. Absorber Length = 0.1 m Absorber Length = 0.3 m

Absorber Length = 0.2 m Absorber Length = 0.4 m

Distilled Water Rate, kg/h

4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 9:00

10:00

11:00

12:00

13:00

14:00

15:00

16:00

17:00

Time Fig. 7: Effect of absorber plate size on distilled water produced during the day

The results in Fig. 7 demonstrate that the maximum distilled water rate can be produced for the absorber plate with a length of 0.3 m. For this absorber plate, the total solar energy reflected from the dish hits to the plate and for larger sizes, the thermal losses are increased while the amount of heat gained by the absorber is almost constant. During the day for a dish collector with 2 m aperture diameter, about 22.5 kg distilled water can be produced with a solar still that its absorber plate has 0.3 m length, while for an absorber plate with 0.1 m in length, the total produced distilled water is about 3.5 kg.

5.2. Effect of some optical properties 5.2.1. Effect of PDC optical efficiency For a specified PDC, its optical efficiency has a great effect on its performance. The results in Fig. 8 show that the rate of produced distilled water is greater for a PDC with greater optical 20

efficiency. According to Eq.(2), for PDCs with greater optical efficiency or more ideal PDCs, greater amounts of incident solar irradiation on PDC surface is reflected on the absorber plate. For a PDC with an optical efficiency of 0.8, the amount of total distilled water produced during the day is about 22.5 kg while for the optical efficiency of 0.5 is about 11 kg. By increasing about 60% in PDC optical efficiency, the production of distilled water doubles. On the other hand, when the desalination process starts at 9:30, for PDC with an optical efficiency of 0.8, the saltwater boils after about 30 minutes while for the optical efficiency of 0.5 it takes about 60 minutes. Optical Efficiency= 0.5 Optical Efficiency= 0.7

Distilled Water Rate, kg/h

4.0

Optical Efficiency= 0.6 Optical Efficiency= 0.8

3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 9:00

10:00

11:00

12:00

13:00

14:00

15:00

16:00

17:00

Time Fig. 8: Effect of dish optical efficiency on distilled water produced during the day

5.2.2. Effect of absorber plate reflectivity Another optical property of the system that can affect significantly the performance of the system is the absorber plate reflectivity. The rate of distilled water produced for a solar still and absorber plate with different reflectivity is shown in Fig. 9. By increasing in absorber reflectivity, the distilled water produced is reduced due to reflecting a part of the solar energy which is reached by the absorber. The absorber plate that is used as material in solar still construction, can be selected in such a way that in addition to its high absorptivity coefficient, has a low reflectivity. This can be achieved by coloring the absorber plate or coating it with high absorptivity and low reflectivity materials. For the PDC under study in this work, when the absorber reflectivity decreases from 0.7 to 0.4, the distilled water produced by the system increases from 10.2 to 22.8 kg.

21

Distilled Water Rate, kg/h

4.0

Reflectivity = 0.4

Reflectivity = 0.5

Reflectivity = 0.6

Reflectivity = 0.7

3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 9:00

10:00

11:00

12:00

13:00

14:00

15:00

16:00

17:00

Time Fig. 9: Effect of absorber plate reflectivity on distilled water produced during the day

5.3. Effect of some operational parameters 5.3.1. Effect of initial saltwater temperature Operational parameters such as saltwater initial temperature and salinity and the amount of saltwater in the evaporator were investigated both experimentally and theoretically. The rate of distilled water produced for different initial temperatures of saltwater is shown in Fig. 10. It is important from this point of view that saline water resources are available at different temperatures in different areas for desalination. But, from the results of Fig. 10, it is observable that the initial temperature of the saltwater has no great effect on the performance of the system. By increasing the initial saltwater temperature from 15 to 30 oC, the total distilled water produced during the desalination process increases from 22 to 23.2 kg. On the other hand, the initial temperature of saltwater also has no significant effect on the boiling time of it. 5.3.2. Effect of initial saltwater salinity Like the explained statement in section 5.3.1 for initial saltwater temperature, the investigating of initial salinity of water can be important from this aspect that several salty water resources exist in nature. The rate of distilled water produced for the initial salinity of 20 to 50 g salt per kg of water is presented in Fig. 11. The results show that initial salinity like the initial temperature of the saltwater has no tangible effect on the rate of distilled water produced. By increasing the salinity from 20 to 50 g/kg, the total distilled water during the desalination process decreases from 23.4 to 21.8 kg. On the other hand, the initial salinity of saltwater also has no significant effect on the boiling time of it. 22

Salt Water Inlet Temperature = 15 °c Salt Water Inlet Temperature = 25 °c

Salt Water Inlet Temperature = 20 °c Salt Water Inlet Temperature = 30 °c

4.0 3.9 3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0

Distilled Water Rate, kg/h

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 9:00

10:00

11:00

12:00

13:00

14:00

15:00

16:00

17:00

Time Fig. 10: Distilled water rate during the day for salty water with different initial temperatures

Distilled Water Rate, kg/h

4.5

Initial Salinity = 20 g/kg

Initial Salinity = 30 g/kg

Initial Salinity = 40 g/kg

Initial Salinity = 50 g/kg

4.4

4.0 3.5

4.2

3.0

4.0

2.5

3.8

2.0

3.6

1.5

3.4

1.0

3.2

0.5 0.0 9:00

3.0 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

Time Fig. 11: Distilled water rate during the day for salty water with different initial salinities

5.3.3. Effect of saltwater amount in the evaporator In one hand, the larger amounts of saltwater in the evaporator can prolong the saltwater heating process and as a result, the saltwater boils in the evaporator at later times. On the other hand, since the salinity of water in the evaporator increases during the process, it can decrease the rate 23

of distilled water produced in the evaporation process. In addition, for smaller amounts of saltwater, it is essential that there is an outlet stream for brine removing from the evaporator during the process in order to prevent the accumulation of salt in the evaporator. The rate of distilled water produced during the desalination process for various amounts of saltwater from 4 to 10 kg is shown in Fig. 12. For smaller amounts of saltwater in the evaporator, the heating process will be done at earlier times and also the evaporation process starts at earlier times. But the rate of distilled water produced for smaller amounts of saltwater is lesser than larger amounts of saltwater. It can be explained that for larger amounts, the boiling point of saltwater will not increase so much and as a result, the evaporation rate is more much. For 4 kg of saltwater, the boiling point increases from 373.65 to 376.3 K while it increases from 373.65 to 374.75 K for 10 kg of saltwater. Although the 10 kg of saltwater boils at later times compare to 4 kg, but the total distilled water produced is larger (21 kg compared to 23 kg). For 4 kg saltwater in the evaporator, the salinity increases from 30 to 191.16 g/kg during the process while for 10 kg increases from 30 to 97.76 g/kg.

Distilled Water Rate, kg/h

4.5

Initial Volume = 4 kg

Initial Volume = 6 kg

Initial Volume = 8 kg

Initial Volume = 10 kg

4.0

4.5 4.3

3.5

4.1

3.0 2.5

3.9

2.0

3.7

1.5

3.5

1.0

3.3

0.5 0.0 9:00

3.1 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

Time Fig. 12: Distilled water rate during the day for salty water with different amounts in the evaporator

5.3.4. Variations of saltwater temperature in the evaporator The variations of saltwater temperature in the evaporator during the day for PDCs with various apertures is shown in Fig. 13(a), for absorber plates with various lengths in Fig. 13(b), for PDC with different optical efficiencies Fig. 13(c), and for absorber plate with different reflectivity in Fig. 13(d). The results in Fig. 13(a) indicate that for PDCs with smaller apertures, the saltwater 24

boils at later times. Before starting the evaporation process, the saltwater is warmed up to reach its boiling point, and when it started to boil, it evaporates and gradually increases its salinity. For a PDC with 3 m aperture diameter, the salinity increases from 30 to about 210 g/kg during evaporation process and its boiling point increases from 373.65 to 376.60 K, while for a PDC with an aperture of 2 m, the salinity varies from 30 to 113.2 g/kg and boiling point increases from 373.65 to 375.00 K. Also, the results show that the rate of increase in saltwater boiling point in the evaporator for larger PDCs is greater than smaller PDCs due to salinity increasing.

Fig. 13: Variation of saltwater temperature in the evaporator for various (a) dish aperture diameter, (b) absorber plate length, (c) dish optical efficiency, and (d) absorber plate reflectivity

It is observable in Fig. 13(b) that the absorber size greater than SECA has no great effect on boiling time of saltwater in the evaporator for specified conditions and for absorber plate size smaller than SECA, the boiling time of saltwater is strongly dependent on the absorber plate size. For absorber plate with a size of 0.1 m, it takes about 150 minutes to boil the saltwater in the evaporator.

25

From results in Fig. 13(c) it is clear that the saltwater starts to boil at an earlier time for PDCs with greater optical efficiency. Also, the boiling point temperature of the saltwater inside the evaporator increases with a greater rate for more ideal PDCs, due to greater evaporation rate and increased salinity. By comparing the results in Fig. 13(c) and (d), it is clear that when the absorber reflectivity is small, the saltwater boils at earlier times and also, the rate of increase in water salinity in the evaporator is greater for absorber plate with smaller reflectivity. It can be explained that for absorber with smaller reflectivity, the rate of evaporation is more much and consequently the accumulation of salt in the evaporator increases.

6. Conclusions In this study, a design, manufacturing and mathematical modeling of a PDC with novel solar still mounted at its focal point for saltwater desalination are presented. A two-axis manual tracking PDC and a new solar still design were investigated both experimentally and theoretically. In the parametric study of the system, for structural parameters, the effects of PDC aperture diameter and solar still absorber size, for optical parameters, the effects of PDC optical efficiency and absorber reflectivity and for operational parameters, the effects of the initial saltwater temperature, salinity and amount of saltwater in the evaporator on the distilled water rate during the desalination process were investigated. The results of the model show that the optical and structural parameters of the system have a significant effect on the distilled water produced by the system and the operational parameters have no impressive effect on the performance of the system. For a PDC system like the system under study in this work, by increasing the PDC aperture diameter from 1.5 to 3 m, for the system time operating from 9:30 to 16:30, the total distilled water produced increases from 11.5 to 50 kg. By an increasing in PDC optical efficiency from 0.5 to 0.8, the distilled water produced almost doubles. By a decreasing in absorber plate reflectivity from 0.7 to 0.4, the distilled water produced is more than double. The effect of other parameters such as the amount of saltwater in the evaporator, initial saltwater temperature and salinity at maximum impact is less than 10%. These results provide a clear path in the use of such systems that the construction of a dish with higher optical efficiency, and accurate design of the absorber plate in the evaporator are very important. In the comparison of the operation of the studied system with other types of solar desalination, it can be said that the performance of the system is acceptable. The system under study, in a typical day with average solar irradiation of 800-900 W/m2, can produce about 20-23 kg for 7 hours operating time (5.7-6.5 kg/m2day). These results can comparable with previous studies, 4.11-4.95 kg/m2day in Prado et al. [25], 2.0 kg/m2day for conventional still and 2.5 kg/m2day for modified still in Abdel-Rehim and Lasheen [23]. From an economic point of view, it is difficult to say that the system is an affordable desalination system for short operating period. The solar 26

systems have shorter payback period due to lower operating costs, although need a higher initial investment. Therefore, a comprehensive cost analysis is needed to found out the system cost assessment. But it can be said that in thermal desalination systems that are based on the distillation of saltwater with thermal energy, these systems are economical. Because the source of requisite energy can be supplied from solar energy and no extra operating cost is needed within the system, even the required electrical energy for pumping saltwater to the evaporator also can be provided by a solar photovoltaic panel.

Nomenclature Alphabetical Symbols Definition Area (m2) A Specific heat capacity (J/kg.K) cp Convective heat transfer coefficient (W/m2. K) h Specific enthalpy of evaporation (kJ/kg) hfg Solar irradiation intensity (W/m2) I Condenser height (m) L i-th model value mi Mass flow rate (kg/s) m Total number of data n i-th experimental data Oi Mean value of the experimental data O Prandtl number Pr Heat (W) Q Ratio R 2 Coefficient of determination R Rayleigh number Ra Reynolds number Re Reflectivity of absorbent surface Rs Temperature (K) T Thickness t Time difference t

Greek Symbols 

 

Definition Thermal expansion coefficient Emissivity Efficiency 27

 v  

Thermal conductivity Latent heat of vaporization Dynamic viscosity Kinematic viscosity Density Stefan-Boltzmann constant

Subscript Definition amb b c cond conv cw ext g in int l opt out rad s sw v w

Ambient Boiling Collector Conduction Convection Cooling water External Direct Inlet Internal Liquid Optical Outlet Radiation Absorber surface Saltwater Vapor Wall

Abbreviation CSP ED HTF IE MBE MED MSF MVC

Definition Concentrating Solar Power Electro Dialysis Heat Transfer Fluid Ion Exchanges Mean Bias Error Mechanical Vapor Compression Processes Multi-Effect Distillation Multi-Stage Flash

k



28

PDC RMSE RO SECA TVC

Parabolic Dish Collector Reverse Osmosis Root Mean Square Error Solar Energy Concentration Area (SECA) Thermal Vapor Compression Processes

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and its salinity. The heat capacity of saltwater as a function of salinity and temperature is calculated from below equation [31]:

 kJ  2 3 c p , sw    A1  B1T  C1T  D1T  kg.K 

(A-1)

where, T is in K, S is salinity in gr salt per kilogram water, and constants of Eq. (A-1) are given as: A1  5.328   9.76*102  S   4.04*104  S 2

(A-2)

B1  6.913*103   7.351*104  S   3.15*106  S 2

(A-3)

C1  9.6*106  1.927*106  S  8.23*109  S 2

(A-4)

D1  2.5*109  1.666*109  * S   7.125*1012  S 2

(A-5)

The density of saltwater is a function of its salinity, relevant temperature and density of water. The density of saltwater, based on the density of water as a function of salinity and temperature is calculated by using Eq. (A-6) [32]:

 kg   sw     w  A2 S  B2 S 1.5  C2 S 2  m3 

(A-6)

In Eq. (A-6), the temperature is in oC, and the density of water and constants are given as:

 kg   w    999.842594  6.793952*102 T  9.09529*103 T 2  1.001685*104 T 3  m3  1.120083*106 T 4  6.536336*109 T 5

(A-7)

A2  0.824493  4.0899*103T  7.6438*105 T 2  8.2467*107 T 3  5.3875*109 T 4

(A-8)

B2  5.72466*103  1.0227*104 T 1.6564*106 T 2

(A-9)

C2  4.8314*104

(A-10)

The thermal conductivity of saltwater is calculated from Eq. (A-11) [33], where P is in MPa and T is in oC :

W  4 3 7 3 ksw    0.55286  3.4025*10 P  1.8364*10 T  3.3058*10 T  m.k 

(A-11)

The dynamic viscosity of saltwater as a function of salinity and temperature is calculated from Eq. (A-12) [34], where T is in oC: 32

 kg  2 sw    w 1  A3 S  B3 S   m.s 

(A-12)

For using Eq. (A-12), the dynamic viscosity of water as a function of temperature and constants are given as:

A3  1.474*103  1.5*105 T  3.927*108 T 2

(A-13)

B3  1.073*105  8.5*108 T  2.23*1010 T 2

(A-14)

604.129   w  exp  10.7019   139.18  T  

(A-15)

33

Highlights     

A novel solar still in a direct solar desalination system was studied. A solar still in a PDC system was considered as key component. A comprehensive mathematical model was developed for the system described. Model showed the system is promising for small to medium scale desalination. The system with a 3 m PDC can produce 75 kg distilled water per day.

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