Improving the performance of solar still using vibratory harmonic effect

Desalination 251 (2010) 3–11

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Desalination j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d e s a l

Review

Improving the performance of solar still using vibratory harmonic effect Khaled M.S. Eldalil 1 Mech. Eng. Dept., Tanta Univ., Tanta, Egypt

a r t i c l e

i n f o

Article history: Received 4 September 2009 Received in revised form 6 October 2009 Accepted 8 October 2009 Available online 7 November 2009 Keywords: Distillation Solar still Vibratory harmonic motion Nocturnal production

a b s t r a c t A new concept of active vibratory solar still is presented in this study. A flexible packed stretched media installed in the bottom of the basin to increase the efficiency of the still is applied. The flexible packed media is formed from stretched helical coiled copper wires, which are considered as a good media for heat absorbing and transferring and as a simple thermal storage system. Also, a vibrator (resonator) is installed in the middle of the system structure. The target of using the vibrator is to generate forced vibration to excite the flexible packed media to break the boundary layer and surface tension of the saline water and improve convective heat transfer, and also to excite the condensed polycarbonate glass cover to assist the condensed droplets to slide down before it becomes bigger and possibly falls down in the basin, thus increasing the water vaporization and condensation. Experimental and theoretical analysis including system dynamic modeling coupled with the exciting vibrator is presented and the condition of maximum excitation of the absorbing added media is determined. The performance is compared with the conventional solar stills (CSS). The governing equations including the flexible packed media, the harmonic vibratory excitation, and the energy storage are presented. The vibratory excitation effect is accounted by two new parameters the ‘vibratory performance gain and the ‘vibratory power effect’. The productivity due to added backed helical wires is found to be 3.4 l/m2 day, with an efficiency of about 35%, and the productivity with vibration is increased to be 5.8 l/m2 day and the average daily efficiency is about 60%. The nocturnal production ranges from 38% to 57%. © 2009 Elsevier B.V. All rights reserved.

Contents 1. 2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental work . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Solar still station configurations . . . . . . . . . . . . . . . . . . 2.2. Experimental measurement procedure . . . . . . . . . . . . . . . 3. Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Thermal analysis of the helical wires without vibration . . . . . . . 3.2. The vibrator-system modeling . . . . . . . . . . . . . . . . . . . 3.3. Preliminary vibratory thermal analysis of the helical wire packing layer 3.4. Production rate and economics . . . . . . . . . . . . . . . . . . 3.5. The developed proposed performance parameters . . . . . . . . . 3.5.1. The vibratory performance gain (VPG) . . . . . . . . . . . 3.5.2. Vibratory power effect (VPE) . . . . . . . . . . . . . . . 3.5.3. The vibratory power-insolation ratio (VPIR) . . . . . . . . 4. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Effect of the flexible packing (helical wires) . . . . . . . . . . . . 4.2. Effect of the harmonic excitation of the system . . . . . . . . . . . 4.3. Effect of the thermal storage . . . . . . . . . . . . . . . . . . . . 5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

E-mail address: [email protected]. R&D Consultant, Egypt and Saudi Arabian.

0011-9164/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2009.10.004

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K.M.S. Eldalil / Desalination 251 (2010) 3–11

1. Introduction It is well known that water problems, which are either the lack of it or pollution, have become very large in many areas of our planet, especially in deserts, in traditionally dry regions and in modem industrial areas. Moreover, remote areas or islands with low population, where fresh water supply by means of transport is expensive, face the problem of water shortage every day. However, it is for those areas that installation and operation of solar stills seem to be a promising and the most appropriate way to deal with their water problem. In addition, the process includes the use of clean and abundant energy which is friendly to the environment, and concurrence of periods of high sunshine with high water demand. Numerous studies on solar stills of various designs to increase its productivities and efficiencies have been carried out theoretically and experimentally. These studies include the determination of the dependence of the productivity on weather, the design and operation parameters [1]. Solar stills are classified into two groups in terms of energy supply: passive and active. The passive solar stills are conventional solar stills (CSS) which use the solar energy falling on the basin effective area as the only source of thermal energy. However, in the active solar still, extra thermal energy is given to the passive solar still for faster evaporation, and hence increasing productivity. Increasing the productivity of the solar stills attracts many investigators, several techniques are tried and tested in order to satisfy this main target. A technique of floating sponge [2], as an absorbing media is used to increase the conduction heat transfer of the brine water and hence accelerate the evaporation rate. A modified type of wick type solar still based on the good capillarity of a jute wick is studied by ALKarafhouli et al. [3], this type is simply a conventional solar still provided with a blackened jute wick floated with a polystyrene sheet. Results showed that the floating-wick type solar still gives higher productivity but it cannot resist contamination. Minasian et al. [4] developed the floating-wick type by increasing the cooling effect of the condensing cover. This technique is modified by Tiwari et al. [7] and E1-Bahi and Inan [8], who added one or more outside condensing chambers to magnify the condensing effect, and found that the daily production was increased by 70%. In case of using double glass condenser covers, E1Bahi and Inan [9] and Fatani and Zaki [10], found that the efficiency increased from 37% to more than 69% especially when the condenser cover cooled down. A multiple effect solar stills have been studied by Tanaka et al. [5,6], who constructed and tested vertical two and three-effect-type stills by recycling the condensing heat to increase the total amount of distillate and its efficiency. They developed it by adding a heat-pipe solar collector and the still is predicted to produce distilled water with efficiency increased factor of 1.2–1.6. Mink et al. developed this technique by adding an air blown still [10]; they estimated the effect on the still productivity and found it very promising for enhancing the thermal efficiency, and thus a further increase in the productivity per unit area. Active solar distillation on the other hand is considered the second type of technique used to increase the productivity and efficiency of CSS. Prasad et al. [11] and Phadatare et al. [12] found that when feeding the thermal energy into the basin from an external source, it can increase the evaporating surface temperature and can lead to the increase of the nocturnal production. The first study on nocturnal production was reported by Malik and Tran [13]. Voropoulos et al. [14] used hot water tank underneath the absorbing surface working as energy storage tank, they found that the nocturnal production is increased relatively with the total production by 60% [15–17]. Zeinab et al. [18] presented a new active technique by using a rotating shaft installed close to the basin water surface to break the boundary layer of the basin water surface together with adding packed thermal layer. The packed layer is installed in the bottom of the basin to increase the efficiency of the still; it is formed from glass balls which are considered a simple thermal storage system. They found that the

efficiency of the modified solar desalination system using packed layer was increased by 5–7.5%, and by 2.5–5.5% for the modified one using a rotating shaft. For improving the solar still performance new approaches are highly welcome. An attempt to improve the performance of solar still should include an investigation on the performance of new design configurations. To the best of our knowledge, a vibratory excited flexible packed stretched media installed in the basin has not been investigated. The objective of this study is to investigate the performance enhancement of a solar still coupled with vibratory excited flexible packed stretched media in two modes of operation. The first mode includes the operation of the still with a flexible packed stretched layer which is installed in the bottom of the basin. For the aim of comparison; in the second mode a vibratory harmonic excitation is applied together with the first mode. In this respect, the article is concerned mainly with the system productivity to evaluate the effect of the proposed concept on improving the performance of the solar stills and also, the effect on the nocturnal production. We can summarize the technique in the following notes: 1- Installing flexible packed media (stretched helical coiled copper wires) on the bottom of the basin submerged in the brine water. 2- Applying forced vibration of very low power to excite the modified absorbing media. 3- Increasing the stored energy capacity by increasing the water depth and using good isolation. 4- Improving the collection process of the condensation. 2. Experimental work 2.1. Solar still station configurations This active solar still is designed and built in the southern desert area of Saudi Arabia (Wadi El-dwaser, 21.5° latitude and 44° longitude), in the year 2006 to supply distillate water to a battery service center in a large farm. It uses the underground water as a brine, which is lifted from deep wells. The system has a double-sloped cover of 30° inclination with a horizontal and total effective area of 2.064 m2. It is made from coated steel sheets and angles. Fig. 1 shows a schematic drawing of the solar still, equipped with basin level control valve, which is included inside a closed tank. The transparent cover is made from polycarbonate composite sheets of 4 mm thickness partitioned to six segments, three on each side. A tight sealing of the inside enclosure is attained by using a silicon rubber paste with galvanized bolts for all connections of top cover and basin parts. The basin total height is 70 mm and it has two troughs, one on each side for collecting the distillate, then transferring it to the outside collecting vessels, which are tightly closed and located at shaded spots in the way of natural air ventilation stream. Helical copper wires are stretched over the basin bottom, as shown in Fig. 2. The coil mean diameter is 25 mm and the wire diameter is 1.5 mm, they are blackened as the basin bottom. The average depth of the brine water in the basin is 60 mm, and the total average water mass is about 80 kg. The vibrator is located at the center of the base bottom as shown in Fig. 1. It is composed of a rotating disk driven by an ac motor, and as shown in Fig. 3, the disk has an unbalanced mass of 30 g, located at a radius of 40 mm. The motor speed is 1800 rpm, so the frequency of the vibration is 30 Hz and the maximum exciting force is about 21N. The vibration is directed mainly to the vertical direction by using unidirectional elastic supports (rubber constrained layer) underneath the four columns which are carrying the system. The power consumed by the vibrator is about 60W, so that the daily electric consumption is about 1.44 kWh. The basin outside surface is covered by two layers of foiled glasswool with a total thickness of 40 mm and rested on wooden plates with

K.M.S. Eldalil / Desalination 251 (2010) 3–11

5

Fig. 1. Active solar still configurations.

a thickness of 25 mm. The solar still is directed to the north–south direction. The design parameters of the system are: -

Effective black area of basin is 2.064 m2. Net helical coil wire surface area is 4.75 m2. Coil has a diameter of 25 mm. Copper wire has a diameter of 1.5 mm. Density of wire material (copper) is 8890 kg/m3. The double-sloped angle is 30° horizontally.

- The basin height is 70 mm. - The isolation thickness of wool glass is 40 mm with a thermal conductivity of Kw g = 0.038 W/mK. Wood thickness is 25 mm with a thermal conductivity of 0.04 W/mK. - Vibrator frequency is 30 Hz. - Exciting force is 20 N. - Mass of the station is 150 kg. - Mass of brine water is 80 kg. - Mass of helical coiled wires is 6.55 kg. - Density of polycarbonate glass sheet is 900 kg/m3.

Fig. 2. Basin and stretched helical coiled wires.

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K.M.S. Eldalil / Desalination 251 (2010) 3–11

cover, brine water, and helical wire backed layer. Solar insolation average power W/m2.

Is

The performance of the modified solar still with helical wires is evaluated by the ratio of the energy utilized in water vaporization for daily distillate water productivity (Wd1, l/m2) to the total input solar energy (Is, W/m2) as follows: ηw =

Wd1 ρd Ld Is × 12 × 3600 × 1000

ð6Þ

where:

ρd Ld

Fig. 3. Vibrator configuration.

distillate density kg/m3 distillate latent heat = 2.34 MJ/kg.

2.2. Experimental measurement procedure The measurements of the productivities, with and without vibration, of the proposed solar still station are done in the first three weeks by running the vibrator day by day in order to have a two consecutive day record at the same climatic conditions, for evaluating the vibratory harmonic effect. These two days (19th and 20th of September 2006) are found to have the same climatic conditions. The starting measuring time begins at 6 am and the ending measuring time is at 6 am of the second day, so the quantity of distillate water is measured at time hours of 12 pm, 18 pm, 12 0.0 am and 6 am. The solar irradiation distribution is calculated on the 20th day of September 2006 [19] and [20], for autumn sunny day and the total solar insolation is found to be 22.43 MJ/m2 day. 3. Governing equations 3.1. Thermal analysis of the helical wires without vibration The helical wires are used to assist the desalination process during the sunrise and after the sunset. The target of using it is to increase the distillate water productivity per day. The thermal equations of the helical wires are derived with no vibration and neglecting losses as [18]: qw1 = mw Cpw

∂Tw1 ∂t

= Aw Is ðατÞw + Ab Is ðατÞb qw2 = mw Cpw = mw Cpw

3.2. The vibrator-system modeling The aim of the system modeling from the theory of vibration point of view is to determine the dynamic parameters of the system elastic components, such that elastic foundation supports, the helical wires, and polycarbonate transparent glass sheets which magnify the transmissibility of the excitation. The system dynamically is modeled through two steps, the first step is the vibratory excitation and foundation support-system modeling; the second step is the systemhelical coiled wires and system-glass sheet modeling. The first modeling is based on the excitation effect of the vibratory harmonic forced motion on the system structure and foundation supports. The second modeling is based on the vibration transmissibility principle. The system modeling diagram is shown in Fig. 4. Considering the system and foundation supports as spring mass system constrained to move in the vertical direction and excited by a rotating unbalanced mass (m). As in reference [21] in details, the unbalance is represented by an eccentric mass m with eccentricity e that is rotating with angular velocity ω. Letting y be the displacement of the nonrotating mass (M−m), where

ð1Þ during sunlight

∂Tw2 ∂t ∂Tw1 ∂T + mb Cpb b ∂t ∂t

ð2Þ ð3Þ

after sunset :

ð4Þ

The total solar radiation will be qt = qg + qb + qw = Is × 12 × 3600

ð5Þ

where: Subscripts w and b denote helical wires packing and brine water, respectively. Cpw and Cpb Specific heat of helical wires and brine water, respectively. mw and mb Masses of the helical wires and brine water, respectively. Aw and Ab Surface areas of helical wires and brine water, respectively. (ατ)w and (ατ)b Absorptivity and transmissivity of the helical wires and brine water respectively. Total solar insolation per day MJ/m2 day. qt qg, qb, qw Total solar irradiation absorbed by polycarbonate glass

Fig. 4. System dynamic modeling.

K.M.S. Eldalil / Desalination 251 (2010) 3–11

M is the mass of the whole moving mass. From the static equilibrium position, the displacement of m is: ð7Þ

y + sin ωv t: Applying Newton's 2nd law of motion in y direction: d2 ðy + e sinωv tÞ = kf y−cf y˙ ðM−mÞÿ + m dt 2

7

cf crf Elastic foundation critical damping coefficient = 2Mωnf, Nm/s.

ζf

The damping ratio of the foundation =

crf

The excitation transmissibility of the helical coiled wires can be evaluated by the transmissibility dimensionless equation as follows [21]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2  1 + 2ζw ωωv

ð8Þ

nw

X = Y = sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi = TRw   2 2 h i

ωv ωv 2 + 2ζw ω 1− ω

where:

nw

M−m kf cf ωv M m e

Nonrotating mass The elastic foundation stiffness, N/m The elastic foundation damping coefficient, N s/m The frequency of the vibrator, rad/s The mass of the structure, kg The unbalance mass of the vibrator, kg The radius of the unbalance mass center of gravity, 0.04 m.

Differentiating Eq. (8) twice: ðM−mÞÿ + m ðM−mÞÿ +

dð y˙ + eωv ðsinωv tÞ = kf y−cf y˙ dt

2 mðÿ−eωv

cos ωv tÞ = kf y−cf y: ˙

ð9Þ ð10Þ

nw

where: X TRw ωnw kw cw ζw crw

The displacement amplitude of the helical wires, m Transmissibility ratio for helical wires pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi The natural frequency of the helical wires = kw = M rad/s The stiffness of the helical wires, N/m The damping coefficient of helical wires, N s/m The damping ratio of the helical wires = cr/crw Helical wire packing critical damping coefficient, N s/m.

Then the helical wire excitation displacement amplitude can be obtained as follows:  2 me ωωv

This can be arranged to:

nf

2

Mÿ + cf y˙ + kf y = ðmeωv sin ωv tÞ:

ð11Þ

X=

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2  1 + 2ζw ωωv nw

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi:   2 2 h i   2 2 h i

ωv ωv 2 ωv ωv 2 1− ω M 1− ω + 2ζw ω + 2ζf ω nw

The solution of the differential Eq. (11) consists of two parts, the complementary function, which is the solution of the homogeneous equation, and the particular integral. The complementary function, in this case, is a damped free vibration. The particular solution to the preceding equation is a steady-state oscillation of the frequency ω as that of the excitation. In our case where the steady-state solution part is considered, we can assume the particular solution to be of the form:

ð17Þ

nw

nf

nf

ð18Þ And for glass covers, the excited displacement amplitude will be evaluated by the same transmissibility equation as follows: ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s  2  1 + 2ζg ωωv ng

ð12Þ

y = Y sinðωv t–φÞ

where: Y is the amplitude and φ the phase shift of the displacement with respect to the exciting force. The amplitude and phase shift are found by substituting equation (12) in the differential Eq. (11), then we can obtain the following: 2

meωv Y = qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðk−Mω2v Þ2 + ðcf ωv Þ2

ffi = TRg Z = Y = sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 2 h i

ωv ωv 2 + 2ζg ω 1− ω ng

ng

where: Z is the displacement amplitude of the glass covers, and the suffix (g) denotes the glass covers. Similarly, the glass covers displacement amplitude Z is found as:

ð13Þ

 2 me ωωv nf

2

meωv Y = rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2ffi k 2 c M M −ω2v + Mf ωv

ð14Þ

ð19Þ

Z=

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2  1 + 2ζg ωωv ng

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 2 h i2   2 2 h i2

1− ωωv M 1− ωωv + 2ζg ωωv + 2ζf ωωv ng

ng

nf

nf

ð20Þ meω2v Y = qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c ffi f M ðωnf −ω2v Þ2 + M ωv 2 Y=

ð15Þ

meðωv =ωnf Þ2 ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 2   ωv ωv 2 M 1− ω + 2ζf ω nf

ð16Þ

nf

where:

Y ωnf

rffiffiffiffiffi The system displacement amplitude, m k The natural frequency of the system-foundation = , rad/s M

where g denoting to polycarbonate glass cover. There were different phase angles between the vibrator harmonic and the excited parts of the system; it had no effect on our application. Eqs. (17) and (19) represent the transmissibility of the vibration to the helical wires packed layer and polycarbonate glass cover. They indicate that the maximum exciting displacement will occur, when the damping coefficients of the foundation supports (ζf) and the excited elements (ζw and ζg) are very small and almost the same. And also, when the natural frequencies of these parts (ωnf, ωnw and ωng) are very close to the vibrator harmonic frequency (ωv) or may be equal to it. So, sharpening of resonance will occur [21]. This case will be very close to the resonance of the system, but due to the lower excitation power with respect to the system stiffness, no damage is expected. The amplitude

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K.M.S. Eldalil / Desalination 251 (2010) 3–11

displacements of the helical wires and polycarbonate glass covers will be calculated using Eqs. (18) and (20). The polycarbonate glass sheets can stand strongly to the excited displacement without breaking like glass. This is due to its high elasticity and its very low damping coefficient. Neglecting the higher order values of ζf, ζw, and ζg because of their very small values, then the peak of the transmissibility will occur when [22]. ωv = ωnf =

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1−2ζnf ; similarly ωv = ωnw = 1−2ζnw and ωv = ωng = 1−2ζng :

ð21Þ The vibrating helical wires will induce traveling harmonic waves in the brine water in the normal direction of the helical wires motion [23]; these traveling waves have a value depending on the vortex shedding in the wake of the helical wires. Evaluating the relative velocity between brine water and helical wires will be getting more complex; so, we will consider only the wire velocity, which can be calculated as a root mean square value of the peak velocity (Vwm) as: X X Vwm = ωw × pffiffiffi = ωv pffiffiffi : 2 2

ð22Þ

The helical wire velocity is a function of the harmonic excitation frequency, and it will magnify the part of forced convection of heat transfer in the energy balance process when working with the vibrator.

Fig. 5. Typical variation of transmitted motion ratios of helical wires and polycarbonate cover, and Reynolds number with a variation of frequency ratios.

parameters are maximum at a resonance mode of frequency ratio equal to 1.0. The efficiency of the still with helical wire packing layer when vibratory harmonic effect is applied ηvw is expressed by the ratio of the energy utilized for water productivity (Wd2) vaporization to the net input energy that as: ηvw =

Wd2 ρd Ld Is × 12 × 3600 × 1000

ð26Þ

3.3. Preliminary vibratory thermal analysis of the helical wire packing layer The helical wire packing layer is considered as a regularly shaped wire matrix (porous media) and when excited by the vibratory harmonic motion a forced convection heat transfer process will exist with the surrounded brine water; it can be modeled as indicated in details by the author in reference [24]. The modified Nusselt number can be calculated from the combined free-forced convection model [24], as follows: ffiffiffiffiffi ap 5 Pr

Nu = CRe

b

× Gr

ð23Þ

where: Wd2 is the daily yield of distillate when vibratory harmonic effect is applied, l/m2 day. 3.4. Production rate and economics Using external source of energy to assist and activate the vaporization process will lead to estimate the economics of the production rates per unit energy (or specific production) l/kWh. It is found to be as follows:

where: a, b, and C Constants depending on helical wires shape, surface temperature, and layer arrangement (parallel or perpendicular). Grashof number Gr Prantl number Pr Modified Reynolds number ranging from 800 to 104. Re The convective heat transfer coefficient can be obtained as follows: hcw =

Nu Ks 2Dw

Wd2 : Pv × 24

It is found to be equal to 8.06 l/kWh for the whole vibratory daily yield, and 3.33 l/kWh when considering only the increased yield due to vibratory effect. So, the cost of power needed for producing 1 l of distillate (specific cost), is equal to the inverse of the specific production multiplied by the price of the unit energy, as follows:

ð24Þ specific cost =

where: hcw Dw Ks

specific production rate =

Pv × 24 ×A Wd2

where: A is the cost of 1 kWh, which is about 0.04$/kWh. The specific cost is found to be about 0.005$/l in case of considering the whole vibratory daily yield which is equal to 5.8 l/m2 day.

Heat transfer coefficient. Helical wire equivalent diameter m Brine water thermal conductivity J/h m °C.

3.5. The developed proposed performance parameters Modified Reynolds number is as follows: Re = ρb

Vwm μb

ð25Þ

where: suffix (b) denotes brine water. A typical variation of the transmitted motions of the helical wire packing layer and polycarbonate cover and associated Reynolds number with varying of the frequency ratios is shown in Fig. 5; the

In this section, we will define some of the proposed parameters that can describe the relations between the increase (gain) in the daily yield distillate and the consumed energy which is utilized in the vibratory harmonic operation. - The vibratory performance gain (VPG), dimensionless - Vibratory power effect (VPE), dimensionless - The vibratory power–insolation ratio (VPIR).

K.M.S. Eldalil / Desalination 251 (2010) 3–11

Fig. 6. The vibratory power effect with respect to the increasing yield ratio at a vibratory power ratio (VPR) of 0.0575.

3.5.1. The vibratory performance gain (VPG) The average vibratory harmonic effect may be expressed by “vibratory performance gain (VPG)a” is a dimensionless parameter which evaluates the ratio between the energy that is utilized in the gain of the daily yield of distillate due to vibratory harmonic effect to the energy which is consumed by the vibrator (Pv) in 24h; it can be obtained as follows: ðVPGÞa =

ðWd2 −Wd1 Þρd Ld Pv × 24 × 3600

ð27Þ

where The vibrator specific motor power, W/m2 Pv (Wd2 − Wd1) The increase in the daily yield of distillate due to vibratory harmonic effect, l/m2 day. The value of the VPG is found to be more than 1; it means that the increase in the daily yield due to the harmonic effect extracts more energy from the source (thermal storage) than that consumed by the vibrator, so, there is an additional energy added to the power consumed by the vibrator which is converted to thermal power in the energy balance process. This additional energy comes from the thermal storage which is part of the total insolation. Hence, the vibratory effect works as a catalytic agent to assist the heat transfer process, and hence increasing the rate of vaporization. Also, it assists the condensed droplets on the polycarbonate covers to slide down easy by breaking the surface tension before it grows up and possibly gets lost. The VPG may be calculated as the average value either per day or for each specific period of the day, so it may be expressed as follows: ðVPGÞΔt =

ðΔWd Þρd Ld : Pv × Δt × 3600

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Fig. 8. Comparison of productivities over a period span of 6 h for helical packed wires with and without vibration.

3.5.2. Vibratory power effect (VPE) Also we can define another dimensionless parameter called the “vibratory power effect (VPE)” as follows:

VPE =

Pv × 24 × 3600

VPE =

Pv

Is × 12 × 3600 Is





ðWd2 −Wd1 Þρd Ld × 100 Wd1 ρd Ld

ð29Þ

ðWd2 −Wd1 Þ × 100 2Wd1

 where: Is is the average insolation power over 12 h and equals to 520 W. 3.5.3. The vibratory power-insolation ratio (VPIR) ΔWd × 100 VPE = VPIR  2Wd1

ð30Þ

where: VPIR is the vibratory power ratio = 0.0575.

VPE = 0:0575 ×

2Wd1 × 100: ΔWd

ð31Þ

This parameter has a value ranging between 100 for no any gain and zero for infinite gain. As shown in Fig. 6, its value was found to be about 20.35, i.e. within the gain limit. The gain limit means that the increased yield is more than the amount that can obtained by the vibratory energy.

ð28Þ

Fig. 7. Effect of packed helical wires on the accumulated productivity in comparison with normalized values of Refs. [7,10], and [18].

Fig. 9. Comparison of accumulated productivities with and without vibration.

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K.M.S. Eldalil / Desalination 251 (2010) 3–11

Fig. 10. Daily yield of distillate and efficiency for 3 weeks. Fig. 13. Solar insolation distribution and production rate performance PRP.

values of [7] and [10]. The total daily yield of distillate reached a value of 3.4 l/m2, with an efficiency of 35%, as shown in Fig. 10. The peak of production rate (productivity) over a period interval of 6h occurred at time hour 18 (6 pm), as shown in Fig. 8. 4.2. Effect of the harmonic excitation of the system

Fig. 11. Vibratory performance gain (VPG) and its average.

The effect of modified absorbing surface coupled with harmonically excited vibration on the productivity (production rate) over an interval period of 6 h, is shown in Fig. 8. There is a significant increase from 1.3 l/ (m2 6 h) to 2.2 l/(m2 6 h) with an increasing ratio of 69%, while the accumulated productivity is shown in Fig. 9 which indicates that the total daily yield of distillate is increased from 3.4 l/m2 to 5.8 l/m2 by an increasing ratio of 72%. The peak value of the productivity (production rate) occurred at time hour 24 (at midnight), due to the effect of excitation for utilizing the stored thermal energy. Fig. 10 shows the average daily yield of distillate and efficiency throughout three weeks. The “vibratory performance gain (VPG)” which is defined by Eq. (27) is shown in Fig. 11; there is a peak value of 3.5 at time hour 24 (12am at midnight) and has a daily average value of 2.17. The figure indicates that the value of VPG is started from zero at the beginning of the solar time hour (6 am) and increased gradually by a constant rate until it reaches its peak at time hour 24 (12am at midnight). This happened due to the excitation of thermal storage which increases the nocturnal production. 4.3. Effect of the thermal storage

Fig. 12. Solar insolation distribution and productivity.

4. Experimental results 4.1. Effect of the flexible packing (helical wires) The accumulated productivity of the solar still with modified helical packed wires is shown in Fig. 7; there is a significant increase when compared with the normalized values of CSS of reference [18] by a ratio of about 35%. The figure gives different comparisons with other normalized

The effect of thermal storage in the basin brine water and helical packed wires on the nocturnal production is shown in Fig. 12 with daily distribution of solar insolation on the 20th day of September 2006 in the Wadi Eldwaser area. It is shown that the daily nocturnal production is 1.4 l/m2 with a percentage of 41% of the total yield when operating without vibration and increased to a value of 2.9 l/m2 with a percentage of 50% when operating with vibration. The maximum productivities (production rate) are found at time hour 18 (6 pm) for the helical packed wires and at time 24 (12 am) when working with vibration, so that the vibratory excitation extends the nocturnal production period by 6 h, as shown in Fig. 13. The percentage of nocturnal production for three weeks with vibration is shown in Fig. 14; its value is ranged from 37% to 50%. 5. Conclusion A new concept is used in the present work, based on modifying the absorbing surface media by installing stretched helical coiled wires in

K.M.S. Eldalil / Desalination 251 (2010) 3–11

Fig. 14. Nocturnal production ratio.

the basin of the solar still, and this packed layer has a good performance effect when it is excited harmonically. A dynamic model is derived in order to determine the dynamic values of the system component parameters that maximize the excitation transmissibility which is required for each part (helical wires and glass cover). The excitation of the helical wires is found to have a good effect on the performance of the modified solar still, due to increasing Nusselt number. This is magnifying the overall heat transfer coefficient. Also it increases the condensate on the vibrating polycarbonate glass covers. The daily total yield of distillate of the still with added helical wires is found to be 3.8 l/m2 with an efficiency of 35% and increased with vibration to 5.8 l/m2 with an efficiency of 60%. The increasing percentage due to the vibratory excitation effect is found to be 72%. The daily total production of the still with helical wires is found to be 35% more than the value of CSS and when vibration is applied this ratio increases to 132%. The effect of vibration is defined by two new parameters, the first is ‘vibratory performance gain’, it was found that its value varies over a day period to be of average value of 2.17 and peak value of 3.5 at time hour 24 (12 am midnight). The second parameter is ‘vibratory power effect’, it was found that its value to be about 20.35. The results showed that using this concept is very promising for developing basin-type solar stills with very low investment costs. References [1] M.A.S. Malik, G.N. Tiwari, A. Kumar, M. Sodha, Solar Distillation, Pergamon Press, Oxford, 1982 pp. 58–71.

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