Optimisation of geometry and surface wettability for enhanced efficiency of the solar still-based desalination unit

Evaporative solar desalination systems offer an economical method to produce pure water from brine solutions. In the present study, the effects of geometry (top surface inclination) and the surface wettability of the condensation plate on the performance of the basin-type solar desalination unit was investigated through the route of CFD (computational fluid dynamics) simulations. It was observed that inclination angle and surface patterning influence the overall rate of condensation. With the 26o top surface inclination, the rate of water production was 33.33% more than that of the 15o and 35o top surface inclinations. Surface wettability influences the production rate of pure water. A novel patterned condensation surface has been proposed, which can enhance the rate of condensation by 12.8% to produce more purified water. The patterned surface was obtained by placing alternate patches of hydrophilic and hydrophobic layers.


Introduction
The scarcity of water in different regions projected a severe worldwide concern.Although several water purification technologies are emerging in the market, most are energy intensive and not sustainable for resource-limited areas.Solar energybased desalination units offer an easy alternative for producing fresh water from saline water in an economically viable manner (Sharon and Reddy 2015).Basin-type of solar stills is the most common type of solar desalination unit because of their simplicity in design and fabrication.However, such type of solar stills suffers the limitations of lower efficiency and slow production rate.Many researchers have attempted to increase the efficiency of such solar still by incorporating various modifications.For example, there were attempts to recover energy from condensed vapors (Rajaseenivasan et al. 2012;Rajaseenivasan, Elango, and Kalidasa Murugavel 2013;Rajaseenivasan and Kalidasa Murugavel 2013;Elango and Murugavel 2015;Feilizadeh et al. 2015a;Feilizadeh et al. 2015b;Feilizadeh et al. 2016;Karimi Estahbanati et al. 2015;Rajaseenivasan, Kalidasa Murugavel, and Elango 2015;Reddy and Sharon 2016;Srithar et al. 2016), adding condensers (Bhardwaj, ten Kortenaar, and Mudde 2016), using energy-storing materials (Asbik et al. 2016;Kabeel, Abdelgaied, and Mahgoub 2016;Shalaby, El-Bialy, and El-Sebaii 2016;Thirumalai Venkataraman et al. 2016), utilising reflectors to absorb more energy (Karimi Estahbanati et al. 2016;Omara et al. 2016), coupling the still with solar thermal collectors (Eltawil and Omara 2014;Taghvaei et al. 2014;Thirumalai Venkataraman, Raja, and Srithar 2014;Morad, El-Maghawry, and Wasfy 2015;Taghvaei et al. 2015;Faegh and Shafii 2017), adding fins to the basin (El-Sebaii et al. 2015;Rajaseenivasan and Srithar 2016), utilising wick to increase evaporation area (Alaian, Elnegiry, and Hamed 2016)  fabrication costs or consume extra energy making the operating cost higher.By modifying the system geometry, there is a possibility to increase the efficiency of the solar still, as reported by Feilizadeh et al. (2017).The effect of height, length and width of a single-slope basin-type solar still on the production efficiency was investigated therein, and it was found that geometric parameters significantly influence the net production rate of the water.El-Swify and Metias (2002) studied the effect of aspect ratio (ratio of the length of the still to its width) on the incidence of solar radiation inside the still.It was found that for a single slope solar basin, the aspect ratio value should be two for utilising maximum solar radiation.Tripathi and Tiwari (2004) reported the effect of a single slope solar basin's geometric dimensions (length, width and height) on the water production rate considering the solar intensity of a particular day.Although most of these reports dealt with the geometric modifications of the solar still, very few of them considered the effect of surface wettability on the overall rate of production.Surface wettability significantly influences the rate of condensation, and it is a well-established fact (Niu 2016;Goswami, Pillai, and McGranaghan 2021).Since the production efficiency of a basintype solar desalination unit is directly proportional to the rate of condensation of the generated vapor, it is worth investigating the effect of the condensing surface characteristic on the overall efficiency.
In the present work, the angle of inclination of the top glass surface was optimised considering several cases with the help of computational fluid dynamics (CFD) based simulations, and a modified design of solar still is proposed.In the next phase, the wettability of the condensing surface was changed by varying the contact angle-based boundary conditions and its effect on the overall condensation rate were analyzed.

Methodology
Continuum-based CFD simulations were carried out to study the basin-type solar still with a single slope.

Geometry and meshing
A single slope basin type of solar still having 30 cm width and 40 cm length and made of steel (side walls) and glass (top surface) have been designed in CAD environment (ANSYS Workbench) and shown in Figure 1(a).In conventional solar still design, the condensed water is continuously collected outside the still.Here, we propose a modification in the geometry and place a barrier (of 10 cm height) inside the solar still, separating the still into two chambers.In the right-hand chamber, saline water is kept, and the condensed water will be collected in the left-hand chamber, as pointed out in Figure 1(b).The height of the left wall of the solar still is 10 cm while that of the right wall is 30 cm when the angle of inclination of the top glass surface is 26°(Figure 1(a)) for a representative case.Obviously, these wall heights will change as the inclination angle is varied.The entire side and bottom walls are made of steel while the top cover is made of glass with a thickness of 0.5 cm.The sunlight falls on the top cover of the glass and produces heat inside the still, and as a result, evaporation will start in the saline water chamber, producing vapour.The vapour moves up and releases its heat and is finally condensed on the inner wall of the inclined glass cover.Condensed water will be collected in the condensation chamber, which can be connected to a suitable outlet (not shown for simplicity).Figure 1(c) and (d) show the geometry of the same solar still with modified inclination angles of 35°a nd 15°, respectively.In Figure 1(e), the angle of inclination of the top surface is 26°; however, surface modifications have been provided on the internal surface of the top cover on the condensation chamber.Consecutive strips of the hydrophobic and hydrophilic layers have been provided in this section to check the effect of variable wettability gradient on the overall rate of condensation.
After creating the geometry of each case, meshing was done properly.Meshed geometry of a representative case is shown in Figure 2, along with the details of the meshing parameters.It was observed that the total number of nodes is above 9 lac and the skewness and quality values indicate a satisfiable meshing quality.

Governing equations
The present simulation study contains two phases, including the phase change process like evaporation and condensation.Conservation equations of mass, momentum and energy are the primary governing equations here.

Continuity equation
The continuity equation for the mixture is Here, ν m is the mass averaged velocity, ρ m is the density.

Momentum equation
By combining the momentum equation for each phase, the momentum equation for the mixture can be stated as follows: Here, ∇P is the pressure gradient, μ m is the viscosity, α i is the phase volume fraction, g is the acceleration due to gravity.

Energy equation
The mixture's energy equation is provided below (Vaibhav Rai et al. 2017) Here, K eff is the effective conductivity, E i is the energy, S E is the source term and T is the temperature.

Boundary conditions
The following initial and boundary conditions were specified to solve the governing equations: • The brine solution chamber was initially filled with water to a height of 10 cm.• No-slip boundary conditions were imposed on all the solid walls.• Sunlight was assumed to fall on the top inclined glass surface of the unit.Radiative heat flux was calculated based on the time and location using the built-in solar model of Ansys Fluent.The study was carried out considering the time of 1 pm on 21st June at Durgapur, West Bengal (India).• The top glass surface is given a transitivity of 0.2 and absorptivity of 0.5.
• The preliminary temperature of the water pool was taken to be 298 K at 101,325 Pascal.• Volume of Fluid (VOF) based interface tracking algorithm was considered along with the continuous surface tension force model of Brackbill et al.(1992).The VOF model additionally offers the ability to choose a wall adhesion angle in conjunction with the surface tension model.The fluid's presumed contact angle with the wall was employed to modify the surface normal in cells close to the wall rather than imposing this boundary condition at the wall itself.The curvature of the surface close to the wall is altered due to this dynamic boundary condition.If θ w is the contact angle at the wall, The surface normal at the cell next to the wall is where and are the unit normal and tangential vectors to the wall, respectively.
The local curvature of the interface is determined by combining this contact angle with the regularly calculated surface normal one cell away from the wall.This curvature is then utilised to modify the body force term in the surface tension calculation.

Simulation details
The following assumptions have been considered during the simulation of the present cases from Mahmoud, Eliman, and Heqazy (2020): (1) No leakage of water vapor from the solar still (2) Insulation covers, and absorbent materials have minimal heat capacity.
(3) The water in the basin and the glass cover of the solar still are at the same temperature.
It is noteworthy to mention that similar assumptions were considered in the earlier study of Mahmoud, Eliman, and Heqazy 2020.For calculating solar radiation, a built-in solar ray tracking algorithm has been adopted in the present study.In this approach, solar load is incorporated as a heat source in the energy equations.Under this framework, the Rosseland model was adopted (Rosseland radiation model theory,, 2018), which provides the solar radiation intensity based on the given latitude, altitude and ambient temperature of the application site.For calculating the solar intensity, we have specified the location of Durgapur (West Bengal, India) and considered the standard day for the month of June.Since this is a multiphase system containing liquid and vapor phases along with solid walls, the volume of fluid (VOF) method is adopted as the interface tracking algorithm.A phase change phenomenon was implemented by considering the evaporation-condensation model of Ansys Fluent, also known as the Lee Model (Lee 1979).In the Lee model, evaporation and condensation frequency were set to 0.05 and saturation temperature was kept at 373 K. Since the vapor flow forms turbulence inside the system, proper turbulence modelling is essential in such cases.Here, the standard k-epsilon model is used for modelling the turbulence.Time step size has been taken at 0.005s for each iteration.

Results & discussion
In the present study, variation of the inclination angle of the top surface and its effect on the overall performance was checked initially.The effect of surface wettability (contact angle) on the overall rate of condensation was considered subsequently.

Validation of model
Experimental data of the exact geometry that we considered in the present study is not available.Hence, for validating our adopted methodology, we considered a similar study of Badusha (2013), where experimental data were available.We did simulations based on that geometry and the results were compared with the experimental ones (Figure S1).The comparison shows a satisfiable match to validate our methodology.Details of this validation study is mentioned in the Supplementary Information.

Effect of variation of the angle of inclination of the top surface
To analyze the performance efficiency of the solar stills, unsteady state simulations were carried out for 2 sec, and the amount of water accumulated in the condensing chamber was monitored.Temporal variation of this accumulated water is shown in Figure 3 for different configurations of the solar still.Three different angles of inclination (15°, 26°, 35°) of the top covering surface were considered.The plot profile reveals that with the increase of angle of inclination, initiation of condensation becomes faster.It was observed that in the case of a 35°slope, condensation starts almost instantaneously and reaches saturation very fast.The influence of gravity may play a significant role in this case.In the case of a 26°slope, condensation may initiate after an initial period; however, it produces more purified condensed water over time.In the case of a 15°slope, the process is even slower and produces less water.Since more water is being recovered in the case of 26°inclination, the rate of water production is 33.33% more efficient than 15 o and 35 o top surface inclination.In the subsequent analysis, we considered this case as the representative one.
It is important to mention that some earlier studies (Mohammad Hemmat, Esfandeh, and Toghraie (2021), Rahbar andEsfahani (2013), andRahbar, Esfahani, andFotouhi-Bafghi (2015)) showed the influence of the size of the solar still's thermoelectric cooling system (TEC) on the rate of freshwater production.The studies found that the use of TEC system enhances the effectiveness of solar water desalination upto 6.8%.In contrast, the present study shows the possibility of more water production enhancement (by 33%) by adjusting the top surface inclination.
In the following section, we incorporated the effect of surface wettability by modifying the contact angle-based boundary condition of the top surface.The inner wall of the top cover over the condenser section (of 26°inclined geometry) was divided into three different segments with alternately placed patches of different contact angles.Simulations have been done with such modified geometry, and results are discussed accordingly.

Temperature, vapour density and water volume fraction contour
Figure 4 shows the temperature and vapour density contour at a particular time instant for two different cases of solar still (modified and unmodified top surface).Here, the angle of inclination of the top surface is kept as 26°.In one case, the top surface over the condensing chamber is modified by incorporating different contact angle-based boundary conditions.In Figure 4(a) and (b), the temperature distribution is shown along the top glass cover, which was found to be uniform in case 4(a), whereas, in Figure 4(b), the lower surface temperature by 2.5 K was observed over the condensing chamber due to the surface modification.This low temperature of the modified surface indicates the possibility of an enhanced rate of condensation.In Figure 4(c) and (d), the profile of water vapor density was shown along a horizontal cross-sectional plane.In both cases, water vapor density was higher in the condensation chamber.In the case of a modified surface (Figure 4(d)), vapor density is found to be more than the unmodified one.Another crucial factor is the water volume fraction, which indicates how quickly condensation occurs.In the modified top surfaces of Figure 5(a) and (b), where a region of water volume fraction is visible, it denotes the presence of some condensed water in that zone independently of the unmodified top surface.After examining all of these factors, it was found that the condensation surface might be altered to increase efficiency, as in this case, the second slab was made hydrophobic.
Figure 5 shows the distribution of water volume fraction along the top surface and two vertical cross-sectional planes in both chambers.

Velocity contour and velocity vector profile
For understanding the hydrodynamics inside the solar still, the profile of velocity and velocity vectors was evaluated along the vertical cross-sectional plane and presented in Figure 6. Figure    6(a) shows the velocity contour, and 6(b) illustrates the profile of the velocity vector.Since the considered solar still is a closed system and there is no inlet or outlet, a free convection current is established inside the chamber.The velocity vector profile depicts the presence of swirling current generated due to the free convection.This free convective current is responsible for transferring heat inside the system.

Effect of variation of contact angle on condensing plate
To examine the impact of the contact angle of the top condensing plate on the rate of condensation, the area average water volume fraction on the condensing plate was determined.In Figure 7, it was observed that with the increase of hydrophilicity, area-averaged water volume fraction increases on the surface, indicating more condensation.A contact angle of 45 degrees has been found to be 15.7% more effective for condensation than those of 120 0 , and 150°.It is noteworthy to mention that a 45degree contact angle is generally observed on a normal glass surface.However, to achieve a contact angle greater than 120 0 , suitable surface modification along with a coating of silane type material can be adopted.

Effect of surface patterning of the top condensing plate
Results of the previous section indicated that surface wettability influences the rate of condensation.To further explore this phenomenon, a patterned surface was designed by dividing the top glass surface into four parts, as shown in Figure 1(e).A more significant part over the brine solution chamber was kept as a normal glass surface through which sunlight will enter to produce evaporation.The top surface over the condensing chamber is equally divided into three parts.The contact angle of the intermediate part was kept at 150 0 , whereas that of other parts has been kept at 45 0 .This arrangement provides the surface gradient of hydrophilicity and hydrophobicity.Such a patterned surface can be achieved by suitably coating with silane type of materials and necessary surface modifications.This type of surface is expected to influence the solar still's condensation rate.To analyze this effect, condensed water volume fraction on the condensing chamber was evaluated, and the mass of the collected water was determined at different time intervals.Figure 8 shows the temporal variation of condensed water mass at various surface modifications.It shows that only changes in surface wettability all over the condensing surface have little impact on the overall production rate (as shown in cases of 45 0 , 120 0 and 150 0 ).However, in the case of the patterned surface with alternate hydrophobic and hydrophilic strips, it was observed that more water was produced, making the overall process 12.8% more efficient.Thus, surface modification or patterning can be an excellent method to enhance the performance efficiency of a basin type of solar desalination unit.

Conclusion
In the present numerical study, the effects of geometry (top surface inclination) and the surface wettability of the condensation plate on the performance of a basin-type solar desalination unit was investigated.It was found that inclination angle and surface patterning significantly influence the overall production rate.It was observed that with the increase in the angle of inclination of the top surface, the production rate becomes faster due to the effect of gravity.However, at an intermediate inclination angle, the rate of water production is 33.33% more than 15 o and 35 o top surface inclination.Surface wettability or contact angle of the top surface has a significant influence on the rate of production of pure water.It was further proposed that if a patterned condensing surface with consecutive patches of hydrophilicity and hydrophobicity was used, the net production rate could be enhanced by 12.8%.Such a novel surface can be obtained by coating the condensing surface with suitable materials.Experimental validation of such predictions is kept as the future scope of our research.

Figure 2 .
Figure 2. Meshed geometry of a typical solar still along with detailed parameters.

Figure 3 .
Figure 3. Variation of mass of condensed water with time at a different angle of inclination of the top surface.
Figure4shows the temperature and vapour density contour at a particular time instant for two different cases of solar still (modified and unmodified top surface).Here, the angle of inclination of the top surface is kept as 26°.In one case, the top surface over the condensing chamber is modified by incorporating different contact angle-based boundary conditions.In Figure4(a) and (b), the temperature distribution is shown along the top glass cover, which was found to be uniform in case 4(a), whereas, in Figure4(b), the lower surface temperature by 2.5 K was observed over the condensing chamber due to the surface modification.This low temperature of the modified surface indicates the possibility of an enhanced rate of condensation.In Figure4(c) and (d), the profile of water vapor density was shown along a horizontal cross-sectional plane.In both cases, water vapor density was higher in the condensation chamber.In the case of a modified surface (Figure4(d)), vapor density is found to be more than the unmodified one.Another crucial factor is the water volume fraction, which indicates how quickly condensation occurs.In the modified top surfaces of Figure5(a) and (b), where a region of water volume fraction is visible, it denotes the presence of some condensed water in that zone independently of the unmodified top surface.After examining all of these factors, it was found that the condensation surface might be altered to increase efficiency, as in this case, the second slab was made hydrophobic.Figure5shows the distribution of water volume fraction along the top surface and two vertical cross-sectional planes in both chambers.Figure 5(a) represents the case with the modified surface, and Figure 5(b) shows the unmodified one.A comparison of the top contours shows the presence of more water in the case of the modified surface.The presence of more water in the brine chamber indicates a slower rate of evaporation in the unmodified case.

Figure 4 .
Figure 4. Temperature contour on the top glass surface without surface modification (a) and with surface modification (b).Vapour density contour along a horizontal cross-section plane in case of unmodified surface (c) and in case of modified surface (d).

Figure 5 .
Figure 5. Distribution of water volume fraction on the top glass surface and along two vertical cross-sectional planes in case of the modified top surface (a) and in case of the unmodified top surface (b).

Figure 7 .
Figure 7. Temporal variation of area-averaged water volume fraction at different contact angles of the top surface.

Figure 8 .
Figure 8. Variation of accumulated mass of condensed water with time at different modified condensation plate.