Identification of Optimum Operational Parameter Levels for Plain Basin, Corrugated Basin and Compartmental Basin Solar Stills

This study aimed at optimizing or maximizing the distillate production in plain basin, corrugated basin and compartmental basin solar stills by integrating them with optimum level of the four operational parameters - Mass of Heat Storage Material, Basin Water Depth, Basin Cover Thickness and External Mirror Position. The efficiency of the parameters is not uniform and it differs from still to still due to variation in the structure of the basin. Further, the most efficient level in a parameter differs from still to still. A particular basin water depth which is highly productive in plain basin still may not suit well for corrugated or compartmental basin still. To find out the optimum parameter levels, the 4 operational parameters and the four levels of each parameter were combined as per L 16 orthogonal array and the distillate production under different combination of operational parameter levels were analyzed using S/N ratio analysis, mean response method, analysis of variance and regression analysis. The analysis revealed that the optimum mass of heat storage material was 16 kg in plain basin, 12 kg in corrugated basin and 10 kg in compartmental basin still. The efficiency of corrugated basin and compartmental basin solar stills was maximum at a lower basin water depth of 15 mm and 10 mm respectively. But plain basin still efficiency was maximum at a higher basin water depth of 20 mm. The optimum basin cover thickness was 4 mm in all the solar stills, in spite of a difference in the structure of the basin. In the same way, the distillate production was maximum when the external mirrors were positioned on the two sloping sides of the solar still (east and west direction). The expected production from the solar stills integrated with the optimum parameter levels was estimated using regression analysis

Keywords: Optimization, S/N Ratio, Mean Response, Regression Analysis, Taguchi Technique

Introduction
Clean potable water is the basic necessity for the survival and continuation of human race in this globe along with food and air. Providing safe drinking water to the people is emerging as a big challenge in underdeveloped and developing countries. Direct consumption of water available in lakes, ponds, rivers, sea and underground sources is not advisable because it may contain dissolved salts, heavy metals and harmful organism. But, pure and protected portable water can be produced from brackish and saline water through distillation and desalination. The existing desalination processes such as multistage flash evaporation, electro dialysis and reverse osmosis are energy intensive and costly. They depend on conventional energy sources (Hydrocarbon fuels) which produce negative impact on environment. The best alternative is solar distillation. It requires no extra energy other than solar radiation. It is cost free, pollution free and available in the site. It is suitable for remote arid and semi-arid zones where drinking water shortage is a major problem and solar radiation is high. The simplest form of solar distillation plant is a solar still. Solar stills are easy to fabricate and operate and their maintenance cost is also low. But the main drawback of solar distillation is that its initial investment cost is high and the productivity per unit area is low. To enhance the productivity of the solar still, various research works are being carried out till now. They improved the production capacity of the still by adopting different technologies under proper operational conditions. The productivity of as solar still is directly related to the area of the absorber plate of the still. The corrugated basin and fin increase the heat transfer rate from the basin to water. Further, the compartments in the basin reduce the volume of water held within each compartment and help the water to reach high temperature level. concluded that the distillate output of tubular solar still is inversely proportional to the water depth.
The basin cover plate receives the solar radiation and transmits it to the still. It also receives heat from the basin and transfer it to the atmosphere. During this process, it allows the vapour to condense and pass it to the collecting tray. Hence the cover plate should be efficient to allow the energy flow in both the direction for the efficient operation of the still. (Kalidasa Murugavel, 2008). Morad et al. (2015) found that increasing the basin glass cover thickness from 3 to 5 mm decreased system productivity from 1.63 to 1.36 L/m 2 .h for active solar still. Phadatare and Verma (2007) achieved enhancement of distillate output when 4 mm thick plexiglass was used at 2 cm depth brine. Abdulrahman Ghoneyem and Arif Heri (1997) concluded that a solar still with 3 mm thick glass cover plate produced 16.5 % more distillate than 6 mm thick glass cover. Kalidasa Murugavel (2008) conducted experimental study on window glass of different thickness and found that the transmittance was indirectly proportional to the thickness of the glass.
Reflectors increase the solar radiation receiving rate of the basin by reflecting additional solar radiation into the still. Internal and external mirrors increase the basin water temperature and enhance the productivity. Tanaka (2009) fabricated a basin type solar still with internal and external reflectors and the productivity increased by about 70 % to 100 %. Tanaka and Nakataka (2006) modified the basin type solar still with internal and external reflectors and the increase in distillate production was around 48 %. Tanaka Taguchi method is a statistical technique to identify the best parameter level among the different parameter levels available. This helps us to fabricate a Robust design solar still. Singh and Francis (2013) investigated the effect of water temperature and inclination angle in the performance of solar still with the help of Taguchi method and found water temperature as the most significant contributing factor. Verma et al. (2013) attempted to optimize the performance of a solar still using Taguchi method. They found water temperature as the most significant parameter and inclination angle of the glass cover as the least significant parameter. Gupta and Singh (2015) applied Taguchi method and concluded that water temperature and salt concentration were significant parameters and inclination angle and water depth were insignificant parameters in enhancing the performance of the solar still. Joe and Ramachandran (2017) fabricated a Robust design solar still by integrating all the best parameter levels identified by the Taguchi method and the distillate output collected was 95.54 % higher than the conventional still.
From the above literature study, we come to know that some modifications in the design of the still basin were introduced to improve the productivity. In addition to this, incorporation of some operational parameters in the stills also significantly increased the production. Without resorting to any heat source other than solar energy, the productivity was increased by incorporating some internal and external modifications. Spreading heat storage material and wick materials in the basin, maintaining optimum basin water depth, using appropriate basin cover material, thickness and inclination angle and fixing internal mirrors were some of the internal modifications introduced in the still. External modifications in the form of external mirrors to focus additional solar radiation was also made. In this study, an attempt was taken to maximize the productivity of the plain, corrugated and compartmental basin solar stills by incorporating them with heat storage material, regulating the basin water depth, varying the basin cover thickness and attaching and positioning the external mirrors. But the crux of the problem is this.
An operational parameter which is very productive in a particular basin type may not be as much effective in another basin type. There is difference in the contribution of heat storage material to distillate production in plain basin, corrugated basin and compartmental basin stills. Further, the efficiency of a parameter level is different at different stills, when the structure of the basin changes. A particular basin water depth which is very productive for plain basin may not suit well for corrugated and compartmental basin stills. So identification and integration of suitable parameters and parameter levels efficient for a still type is necessary. For this, we have to take into consideration not only the efficiency of parameters and parameter levels but also the basin type of the still. A solar still which is designed by incorporating the parameters and parameter levels which are efficient or optimum for the basin type is called as Robust design solar still and this will ensure maximum production. Identification of ideal parameter level suitable from solar still is done with the help of Taguchi method and regression technique.

Objective and Methodology Adopted
In this work, the productivity of the plain basin, corrugated basin and compartmental basin solar stills was to be improved by incorporating the stills with optimum (most efficient) levels of the four operational parameters. It was already proved that there is no single parameter level that can be used indiscriminately in different types of solar stills. So the focus of the present study was to select the best operational parameter level that yield maximum production in each solar still. The four parameters and the four parameter levels of each parameter which were considered for this study are summarized below conducted. To minimize the variation, each trial was repeated twice. The distillate collected from each trial was recorded and the collected data were analysed.
The following techniques were used to analyze the data a) S/N Ratio analysis -S/N ratio for each parameter level was calculated and the parameter level bearing the highest S/N ratio was identified as optimum parameter level b) Analysis of Variance -The analysis of variance was used to spot out the significant parameters among the different parameters taken for the study. The contribution of each parameter in determining the yield was also calculated.
c) Mean Response method -The average mean response value for each parameter level was calculated. Using these values, the average mean response graph was drawn. From the graph, we identified the optimum parameter levels.
The optimum response was also predicted.

d) Regression Analysis -The Regression equations for the 3 solar stills were
fitted. This helped to study the nature and degree of relationship between the dependent variable (Production) and independent variables (Parameters) and enabled to predict the output expected when the optimum parameter levels were incorporated in the solar still.

Experimental Setup
For conducting the experiments, 3 solar stills were fabricated. They were Still I -Plain basin solar still Still II-Corrugated basin solar still Still III-Compartmental basin solar still The solar stills were fabricated using 2 mm thick iron sheet. The length and width of the basins were 100 cm and 100 cm respectively. The height of the basin at the low end side was 31 cm and the height was 67 cm in the high end side. The stills were placed inside the wooden boxes and a gap of 1 cm was maintained between the still wall and the wooden box. The gap was filled by heat resistant materials to prevent loss of heat energy from the basin to the ambient. The stills were covered by glass covers and an inclination angle of 20 0 was maintained. The schematic diagram of solar still is given in Figure 1.

Fig.1 Schematic Diagram of Solar Still
In the plain basin, the entire 100 x 100 cm bottom basin plate was kept as plain surface and it was free from any basin liner modification. The entire basin area can hold the brine to be desalinated. The actual experimental setup of plain basin solar still is given in Figure 2.

Fig.2 Plain Basin Solar Still -Experimental Setup
In the corrugated basin, the bottom basin plate had corrugated arrangements. It had 4 pyramid like structures extending from one side of the basin wall to the other side of the wall. The length, width and height of each pyramid was 100 cm, 10 cm and 8 cm respectively. Between one pyramid and another there was plain surface of 12 cm x 100 cm.
Water to be desalinated was kept in the plain surface only that was in the 60 % of the basin area. The corrugated basin arrangement is shown in figure 3.

Fig.3 Corrugated Basin Solar Still -Experimental Setup
In the compartmental basin still, the bottom basin plate had 27 compartments. The length, width and height of 15 compartments were 20 x 12 x 8 cm respectively and the remaining 12 compartments were 20 x 10 x 8 cm respectively. Water to be desalinated was kept within the 27 compartments only (60 % of the basin area). The arrangement of compartments in compartmental basin is shown in figure 4.

Fig.4 Compartment Basin Solar Still -Experimental Setup
Since the experiments were to be conducted by varying the 4 operational parameters, the following additional arrangements were made Position IV-at the two sloping sides of the still (east and west side)

Result and Discussions
The experiments were conducted during the months of April and May 2019 in Tuticorin, Tamilndu. The experiments were started at 7 a.m. in the morning and continued upto 6 p.m. The distillate collected at the end of every one hour was measured and recorded. The measuring jar of 1000 ml capacity was used.

S/N Ratio Analysis
The signal to noise ratio (S/N ratio) is a statistic that combines mean and variance.
The objective in Taguchi method is to minimize the sensitivity of a quality characteristics to noise factors. This is achieved by selecting the factor levels corresponding to the maximum S/N ratios. In Table 2, S/N ratios for different parameter levels are given.   The optimum parameter levels differ from still to still. In parameter A (mass of heat storage material), the optimum mass for plain basin, corrugated basin and compartmental basin solar stills is 16 Kg, 12 Kg and 10 Kg respectively. In the plain basin still, the material is spread in the entire basin surface (1 m 2 area). So more basin material is required. In the corrugated basin still, the heat storage material is spread in the narrow gap of 12 cm x 100 cm between the two pyramid like structures. In the compartmental basin still, the material is to be spread within the narrow compartments only. In other words, the material spreading area is only 60 % of the basin surface area, in corrugated and compartmental basin solar stills. So the requirement of heat storage material is less. In parameter B (basin water depth), the optimum water depth is more in plain basin still, than in corrugated basin and compartmental basin stills. In plain basin, the surface area of the basin is wide. So maintaining uniform water depth was difficult. An attempt to reduce the water depth below a particular level resulted in the appearance of dry spots here and there because the surface area was slightly uneven. So maximum production was achieved only when the basin water depth was 20 mm. In corrugated basin solar still, the water to be desalinated is stored within a narrow strip of basin area (12 cm x 100 cm) . So there was not much difficulty in maintaining a lower water depth. The optimum basin water depth in corrugated basin still is lower than the optimum water depth of plain basin. In compartmental basin solar still, the water is stored within each compartment only. Since the water is stored within a small and enclosed area, it was feasible to keep the basin water at a very low level. The optimum basin water depth in compartmental basin still is the minimum (10 mm). In parameter C (basin cover thickness), the optimum thickness of the glass basin cover is 4 mm in all the 3 solar stills. The 4 mm thick glass cover proved to be the most efficient in many earlier studies also. In parameter D (position of external mirrors), the position IV (placing the mirrors on the two sloping sides of the still) is the best level in all the 3 solar stills because only in this position, the solar stills received the maximum solar radiation throughout the day.

Ranking of Parameters
S/N ration analysis helps us to identify the best parameter levels suitable for the 3 solar stills. Integration of these levels in the respective solar still maximizes the production.
Sometime, we may like to restrict ourself with those modification which are major contributors to production. One or two parameters may be the major contributors and the rest may be marginal performers. The delta value of a parameter shows the difference between the lowest and the highest S/N ration values in a parameter. Higher delta value is an indication that the incorporation of the best parameter level in that parameter brings maximum increase in production compared to other parameters with low delta value. The parameters are ranked on the basis of delta value. It guides us to choose the most contributing parameter in the midst of different parameters taken for the study. The inclusion of the parameter bearing the rank 1 must be given the top most priority and the inclusion of other parameters, may be as per the ranking order. In the case of low ranking parameters, we have to consider the cost involved and the returns expected. The uneconomic modification (parameters) may be dropped.
From the analysis of delta value we infer that placing external mirrors in position IV must be given the top most priority in all the 3 solar stills. The second priority must be for maintaining optimum water depth in the basin. If the third modification is to be incorporated, spreading heat storage material in the basin must be considered. Since the delta value for basin cover thickness (Parameter C) is the least, we have to analyse the cost and benefit of this modification in the parameter and decide accordingly.

Analysis of S/N Ratio using ANOVA
In this method, the S/N ratio is treated as response and the data is analysed using ANOVA method. This analysis helps as to identify the significant parameters and contribution of each parameter to total production.
We take H 0 = The operational parameters have no significant influence on production α= 0.05 The summary of ANOVA analysis for S/N Ratios is given in Table 3 (Refer Appendix II)

Analysis of Variance
The experimental findings are also analysed using the ANOVA technique

Significant Parameters
Analysis of variance helps to find out whether the parameters taken for the study, significantly influence the production or not. The summary of the findings of the analysis of variance is given in Table 4. (Refer Appendix III) The R-sq (adj) values for ANOVA analysis of plain basin, corrugated basin and compartmental basin solar stills show that the fitted model is a good fit of the data.
The following hypothesis is drawn.
Ho= The parameters have no significant influence on production α = 0.05 The calculated F values are greater than the table F values. So the null hypothesis is rejected. It is concluded that the parameters A, B, C and D significantly influence the distillate production in plain basin, corrugated basin and compartmental basin solar stills.

Contribution of Parameters
Analysis of variance also gives the percentage contribution of each parameter to total production in a solar still. The major contribution comes from parameter D To conclude, top most priority must be given for the identification and integration of the best external mirror positions in solar stills because this modification alone brings substantial increase in production. In addition to this, maintaining optimum basin water depth is important in corrugated basin still and compartmental basin still. The third priority may be for spreading optimum mass of heat storage material in the basin of corrugated and compartmental basin stills. Since the contributions of mass of heat storage material and basin water depth are equal, we cannot make a choice between the two.
Modifications in the basin cover thickness need not be given much importance in corrugated and compartmental basin stills because its contribution to production is not significant. Only in plain basin still, optimum basin cover thickness brings substantial improvement in production. The mean response value of a parameter level shows the average contribution of that level to distillate production. The parameter level that has the highest mean response value is considered as the best parameter level. The mean response values are summarized in Table 5.

Regression Analysis
When the experiments are conducted involving only quantitative factors, the nature of relationship between output (response) and input variables (Parameters) can be studied with the help of regression technique. This technique can be used to predict the output corresponding to an input or parameter level and thereby helps us to maximize the production process. In the present study, it is assumed that the response (y) is linearly related to more than one independent variables. So multiple regression model can be used to study this problem. Suppose, A, B, C and D are the four independent variables (Parameters), the regression model describing the relationship between output (response) and independent variables can be written as Y= + 1 + 2 + 3 + 4 Y= response (production) The following hypothesis are drawn Ho= 1 = 2 = 3 = 4 = 0 H1= ≠ 0 for atleast one variable The ANOVA computation for the regression equation are given in Table 6  After establishing that there is linear relationship between the dependent and independent variables, our next task is to identify the parameters that have significant linear relationship with distillate production. The regression coefficient of each parameter is tested with the help of t-test. When the calculated t-value is higher than the table t value (α=0.05), the parameter is said to have significant linear relationship with the dependent variable. The regression coefficients and their significant levels are summarized in Table 7 (Refer Appendix IV) The parameters A and D in plain basin still , parameter D in corrugated basin still and parameter A, B and D in compartmental basin still have significant linear relationship with the dependent variable.
A closer study of the regression coefficients help us to draw valuable inferences about the performance of the parameters at different levels and guide us to choose the most efficient parameter level. For the sake of mathematically studying the relationship between the dependent variable (distillate production) and the independent variables ( the parameters) , the four parameter levels are arranged in the ascending order, starting from the lower level to higher level and they are given the numerical values 1, 2, 3 and 4. The regression coefficient explains the nature and degree of relationship between the dependent and independent variable. The sign (positive or negative) of the regression coefficient and the significance level enable us to locate the optimum parameter level. The positive sign of the regression coefficient indicates that the selection of higher parameter level maximizes the production. The negative sign indicates that the choice must be a lower parameter level. Further, to pin-point the optimum parameter level, we have to take into consideration the significance level also. When the regression coefficient of a parameter is significant, the optimum parameter level is 4 when the regression coefficient has positive sign and 1 when it has negative sign. In case, the regression coefficient is not significant, the optimum parameter level may be 2 or 3. When the regression coefficient is not significant, but reasonably high, the optimum parameter level is 2 when the regression coefficient is negative and 3 when the coefficient is positive.
In plain basin solar still, the parameters A, B and D have positive regression coefficients. It is an indication that for maximizing production higher parameter levels ( So the optimum level for parameter C is 2.
To sum up, the optimum parameter levels for maximizing the production in plain basin solar stills are A4, B3, C2 and D4. In corrugated basin solar still, the identified optimum parameter levels are A2, B2, C2 and D4. For maximizing production in the compartmental basin solar still, the parameter levels A1, B1, C2 and D4 are to be incorporated.
The distillate production will be maximum or optimum, when the identified The above regression equations give the regression coefficient for each parameter level. The regression coefficients are tested using t-test to find out the significance level.
The complete list of regression coefficients, their calculated t-values and significance level are given in Appendix V.
The regression coefficient gives the contribution of each parameter level to production. Higher the regression coefficient, higher the contribution level. From the list, the most contributing parameter level in each parameter is identified and they are given in

Comparison of Production
The plain basin, corrugated basin and compartmental basin solar stills were modified in 16 different ways (16 different combination of parameters levels) and the average distillate production collected from the modified solar still were recorded by conducting the experiments. Then it was assumed that the above 3 solar stills were incorporated with the optimum parameters levels identified and the production expected from these solar stills were predicted (estimated). A comparison between the average production obtained from modified solar stills and production estimated from solar stills modified with optimum parameters level is given in figure 11.
The average production obtained from modified plain basin, corrugated basin and compartmental basin solar still was 3304, 3493 and 3629 ml/m 2 .day respectively. The estimated production when the above 3 solar stills were integrated with optimum parameter level was 6414, 7153 and 7629 ml/m 2 .day respectively and the increase in production predicted was 94 %, 105 % and 110 % respectively.
Stand alone triple basin solar desalination system with cover cooling and parabolic dish concentrator. Renewable energy, 90, 157-165.