In this article, a numerical

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1 ISESCO JOURNAL of Science and Technology Volume 10 - Number 17 - May 2014 (49-55) Abstract In this article, a numerical simulation model is presented to study the performance of a multistage solar capillary film distiller. The various phenomena of heat and mass transfers were considered to evaluate distillate production. In order to appreciate the developed model, numerical calculations were carried out to optimize various design parameters, namely the number of stages, the flow and temperature of brackish water and the Numerical Simulation of a Multilayer Stage Solar Capillary Film Distiller Moussa Zerrouki 1, Noureddine Settou 2, Yacine Marif 1, Mohammed Benhammou 1, and Mohammed Mustapha Belhadj 1 1 Research Unit on Renewable Energies in Saharan Environment (URERMS) P.O. Box 478, Center for the Development of Renewable Energies (CDER), 01000, Adrar, Algeria 2 Laboratory of Valorization and Promotion of Saharan Resources `VPRS University of Kasdi Merbah Ouargla, Algeria 1 Moussa.zerrouki@yahoo.fr cavity form factor inherent to the climate in Adrar, southern Algeria. Numerical results are also presented in this paper and show that the daily production of distillate increases in tandem with the increase in number of stages. However, the partial fraction of this production increase decreases inversely the addition of each new stage. Keywords: Capillary film, Numerical simulation, Production, Solar still, Stage. 1. Introduction The scarcity of drinking water caused by drought and at the same time by excessive exploitation of underground waters, is becoming a major threat to populations lives in many regions. Yet, sources of water with a certain salt content exist in the vicinity of many areas suffering from drinking water shortage. Solar distillation is considered not only as an economical and environment-friendly solution, but also as a real alternative to conventional fossil fuel energies. The works of Malik et al. [1] illustrate the considerable volume of research carried out to study conventional basin-type solar stills. To improve distillate production, several configurations were designed to enable the reuse of the latent heat of released evaporation (Cooper and Appleyard, R.S. Adhikari et al. [2], Ho-Ming Yeh et al. [3]). Other multi-effect distillers using capillary films were proposed by B. Bouchekima [4], and H. Tanaka [5]. For our part, we propose to study the effects of certain parameters such as the number of stages, the flow and feeding temperature of brackish water and the cavity form factor on the production of a multistage solar capillary film distiller (DIFICAP). For this purpose, we established an equation system governing the distiller s operation and the various coefficients of heat and mass exchange. A numerical simulation enabled us to obtain the results represented in the graphics, followed by analysis and discussion. 2. Modeling and Numerical Simulation The various flows of heat and mass transfers of a multistage capillary solar film distiller are illustrated in Figure 1. The prevailing environment temperature and the material and energy balances are obtained as follows: 49

2 Figure 1. Thermal processes of a multistage solar capillary film distiller 2.1 Energy balance of the glass cover (1) After development of all the terms, the assessment becomes: (2) The coefficients of heat transfer by radiation and convection can be calculated as [6, 7]. (3) (5) The sky temperature is estimated using the following formula: It is obvious that ambient temperature plays a key role in the distillation process. To calculate this temperature, we propose using the Parton and Logan formula [8]. 2.2 Result of first evaporator plate The thermal balance is: (6) (7) (4) (8) 50

3 (9) The coefficient of heat transfer by convection h c(p1,p2) can be written as [13]: (14) 2.3 Energy balance for J th plate (j=2 (n-1)): For each plate the thermal balance is given by: (10) Since the heat and mass transfers obey to the Chilton- Colburn analogy, the following correlation may be obtained [9]: (15) If we substitute the definition equations for Nu and Sh in Eq. (15), we can obtain (11) Using the same expressions (3) and (10), the preceding equation becomes simplified as: (16) By the transposition of these limits, the equation changes into (17) 2.4 Energy balance for n th plate (12) The last plate is considered as a simple condenser and the heat transfer assessment is expressed by: (13) Where Sc/Pr=Le and a/d m =Le, put n=1/3, Eq. (17) can be written as (18) The produced mass per surface unit of evaporation in the solar still is (19) Substituting the h (m(j,j+1)) of Eq. (18) in Eq. (19), we can obtain After developing formulation (13) using the same reasoning as for preceding ones we obtain: Although (20) (21) 51

4 The computing program is in FORTRAN90 write. Convergence is considered as attained when the relative error is inferior to A numerical approach using the Runge-Kutta-Fehlberg 4 method (5) was chosen to resolve the mathematical model obtained [10, 11], and resolve the system of first order differential equations. 3. Discussion and analysis of findings Calculations are carried out in the location of Adrar (geographical coordinates: latitude north, longitude 0.17 east, and altitude 264m), with a time difference of one hour [10] as from an initial moment t 0 =t sr (from sunrise) for each component of the distillers, and at an initial temperature. The standard day considered is 15 September, the inclination angle is set at 38, the wind speed is considered to be constant at 1.5 m/s, the flow rate of brackish water is fixed at 1kg/h except when studying the influence of flow on the daily production. The thermo-physical and geometrical properties of the component of the distiller are presented in the following table: Figure 2. Temperature evolution of the glass and the plates of a 5- stage distiller Figures 3 and 4 show the progression of daily production in cumulated distilled water and the mass flow at each respective stage. It is clear that the distillate s quantity decreases as it moves from one stage to the next. These results are in keeping with those obtained in other literature [4]. TABLE 1. Thermo-physical properties Parameters Symbols Glass Plate Density r Thermal l Conductivity Specific heat Absorptivity Cp a Figure 3. Evolution of cumulated flow of a 5-stage solar still Transitivity t Thickness e Emissivity Area A Figure 2 illustrates the evolution of the glass and plates temperature in a 5-stage solar still. It is noted that the curves are superimposed, and that the absorbing plate s temperature is higher while the last plate s temperature (a simple condenser) is neighboring ambient temperature. Figure 4. Evolution of mass flow of a 5 -stage distiller 52

5 The variation of the daily production in distillate as per number of stages is represented by Figure 5. We note that this production increased with the addition of each new stage. However, the fraction of increase drops inversely with the number of stages as is shown in Figure 6. This trend dictates the optimization of the number of stages in response to techno-economic considerations. Figure 7. Variation of the solar still s daily production as per flow rate of feed Number of stages Figure 5. Variation of daily production as per number of stages Number of stages Figure 6. Variation of fraction of increase in production as per number of stages The analysis of the curves in Figures 7 and 8 enabled us to note that the distillate s daily production is strongly influenced by the brackish water s feed rate. The production of a 5-stage solar still decreases from 17.5 kg/ day.m 2 to less than 12 kg/ day.m 2 when the flow increases by 1kg/h at 2.2 kg/h. On the other hand, this production is less influenced by variations in the temperature of the brackish water feeding the distiller. The distillate s quantity increases from kg/ day.m 2 to more than 18 kg/ day.m 2 when the brackish water s temperature increases from 30 C to 60 C. Figure 8. Variation of the solar still s production as per feeding water s temperature The influence of the form factor which is the link between the distance (evaporator-condenser) and cavity length L/d (pj,pj+1) is represented in Figure 9 which shows that distillate production increases when this distance varies in the opposite direction, although to a marginal extent. The curve indicates that this quantity drops from 15 kg/ day.m 2 to less than 13.5 kg/day.m 2 only when the distance decreases by 4 to 2.5 cm. Figure 9. Variation of the solar still s daily production as per form factor 53

6 Conclusion A numerical model was developed to measure the functioning of a multistage solar capillary film distiller. The model s viability is investigated in light of all the typical parameters inherent to the Adrar site in Algeria. Analysis of the results obtained during the numerical simulation of the effects of design and operation parameters enables us to draw the following conclusions: Distilled water production increased with the addition of each new stage. However, the fraction of increase drops inversely with the number of stages. The production of distilled water is influenced by the feeding rate, and to a lesser extent by the feed water s temperature and the form factor of the still cavity. References [1] M.A.S.Malik, G.N. Tiwari, A. Kumar et M.S. Sodha, Solar Distillation: a practical study of a range of stills and their optimum design, construction and performance, Pergamon Press, 1 st Edit, [2] R.S.Ashikari, Ashvini Kumar et G. D Sootha, Simulation Studies on a multi-stage stacked tray still, Solar Energy, Vol.54, N 5, pp , [3] Ho-Ming. Yeh & Chii-Dong Ho, Energy and mass balances in opentype multiple-effect solar distillers with air flow through the last effect, Energy, Vol. 24, pp , [4] Bachir Bouchekima, Bernad Gros, Ramdane Ouahes, Mostefa, Diboun, Etude théorique et application pratique du distillateur solaire à film capillaire, Éditions scientifiques et médicales Elsevier SAS, All rights reserved, [5] H. Tanaka et T. Nosoko et T. Nagata, A highly productive basin-typemultiple-effect coupled solar still, Desalination, 130 pp , [6] John Duffie & William. A Beckman, Solar engineering thermal processes, 3 rd edit, Library of Congress Cataloging, USA, [7] A. Bejan, Heat Transfer, Pergamon Press, 1 st Edit., USA [8] DC. Reicosky, L.J. Winkelman, J.M. Baker and DG. Baker, Accuracy of hourly air temperatures calculated from daily minima and maxima, Agricultural and Forest Meteorology, vol. 46, pp , [9] P.T. Tsilingiris, The application and experimental validation of a heat and mass transfer analogy for the prediction of mass transfer in solar distillation systems, Applied Thermal Engineering, Vol. 4, N 50, pp , [10] Zerrouki Moussa, Yacine Marif, Moustapha Belhadj and Noureddine Settou, Simulation et expérimentation d un distillateur solaire à film capillaire dans le sud Algérien, Annales des Sciences et Technologie (AST), Vol. 4, N 1, pp , [11] T.E Simos, A Runge-Kutta Fehlberg method with phase-lag of order infinity for initial-value problems with oscillating solution, Computers Math. Applic., 25, N 6, pp , [12] M. Capderou, Theoretical and experimental models, Solar atlas of Algeria (in French) Vol. 1 and 2, University Publications Department, Algeria,

7 Nomenclature a : A : Cp : d : g : G : h : h m : i : L : Le : Lv : m : m : (md) : Nu : Pr : Q : Ra : t : T : V : Greek symbols a : : e : l : r : s : t : u : Subscripts a : ah : f : Da : c : e : p : r : g : w : Thermal Diffusivity (m 2 /s) Area (m 2 ) Specific heat (J/kg. C) Distance (m) Gravity (m/s 2 ) Total radiation (w/m 2 ) Heat transfer coefficient (w/m 2 C) Mass transfer coefficient (m/s) Inclination angle ( ) Length (m) Lewis number Latent heat (J/kg) Mass (kg) Mass flow rate of brine (kg/m 2 ) Distillate mass flow (kg/m 2 ) Nusselt Number Prandtl Number Heat flow (w) Rayleigh Number Time (s) Temperature ( C) wind Speed (m/s) Absorption factor Emissivity factor Thickness (m) Thermal conductivity (w/m C) Density (kg/m 3 ) Boltzmann constant (w/m 2. C 4 ) Transmission factor Kinematic viscosity (m 2 /s) Ambient Humid air Feeding temperature Dry air Convection Evaporation Plate Radiation Glass Water 55