Energy 36 (2011) 3159e3169
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Modeling and experimental validation of a humidificationedehumidification desalination unit solar part K. Zhani a, H. Ben Bacha a, b, *, T. Damak c a
Laboratoire des Systèmes Electro-Mècaniques (LASEM), National Engineering School of Sfax, Sfax University, Tunisia College of Engineering in Alkharj, Alkharj University, P.O.Box 655, BP 655-11946 Alkahrj, Saudi Arabia c Unité de commande des Procédés Industriels, National Engineering School of Sfax, Sfax University, Tunisia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 September 2010 Received in revised form 29 January 2011 Accepted 2 March 2011 Available online 3 April 2011
This paper presents the modeling and the experimental validation of air and water solar collectors used in humidificationedehumidification (HDH) solar desalination unit. The solar desalination process is currently operating under the climatological conditions of Sfax (34 N, 10 E), Tunisia. To numerically simulate the air and water solar collectors, we have developed dynamic mathematical models of the solar collectors. The resulting distributed parametric systems of equations are transformed into a system of ordinary differential equations (ODEs) using the orthogonal collocation method (OCM). A comparison between numerical and experimental data was conducted. It was found that the two-temperature mathematical model describes more precisely the real behaviour of the water solar collector than the one-temperature mathematical model. It was also shown that the developed mathematical models are able to predict accurately the trends of the thermal characteristic of the water and air solar collectors. As a result, the proposed models can be used to size and test the behaviour of such a type of water and air solar collectors. 2011 Elsevier Ltd. All rights reserved.
Keywords: Solar collector Solar desalination Dynamic modeling Simulation Experimental validation
1. Introduction Over the past few decades, solar powered desalination systems based on humidification and dehumidification principles are becoming more popular throughout the world and only a handful of similar systems have been produced. These small-scale standalone desalination systems are much more versatile being able to be used in a variety of environments, relatively simple to design, less time to implement, low temperature demand, environmentally friendly systems and having smaller production cost. Creating a low cost sustainable desalination system would provide small, remote communities and sunny regions with the fresh water required to drink and to irrigate small areas of land allowing a range of crops to be farmed which could benefit the economy. According to literature review, there are many investigators who have developed and studied various standalone solar desalination systems using the humidification/dehumidification principle. The following is a summary of some of the literature studies. In 2010, Prakash Narayan et al. [1] conducted a comprehensive review of the state-of-the-art in solar-driven humidificatione * Corresponding author. College of Engineering in Alkharj, Alkharj University, P.O.Box 655, BP 655-11946 Alkahrj, Saudi Arabia. Tel.: þ966 506 678 408; fax: þ966 1 553 964. E-mail address:
[email protected] (H. Ben Bacha). 0360-5442/$ e see front matter 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.03.005
dehumidification (HDH) desalination units. The principal components of the HDH system are also reviewed and compared, including the humidifier, solar heaters, and dehumidifiers. Particular attention is given to solar air heaters, for which design data is limited; and direct air heating is compared to direct water heating in the cycle assessments. Alternative processes based on the HDH concept are also reviewed and compared. It was concluded that HDH technology has great promise for decentralized small-scale water production applications, although additional research and development is needed for improving system efficiency and reducing capital cost. In 2009, Adel M. Abdel Dayem and M. Fatouh [2] installed and tested a multi-effect HDH solar desalination system in Cairo. The system consists of two loops, a solar loop that can produce hot water and a water desalination loop to produce desalinated water. The solar loop is a thermosyphon water heater that consists of solar collectors with total surface area of 8.9 m2 connected to a storage tank. The desalination loop includes a feed tank that feeds hot salt water to a desalination chamber. A numerical simulation for the system was developed and validated with experimental measurements. Three systems were compared experimentally and numerically. It is found that the solar open system with natural circulation is more efficient regardless of practical difficulties where the closed system using an auxiliary heater has the highest distilled water production. In the same year, Soufari et al. [3] constructed a pilot unit with a capacity of 10 kg/h which was located at Iranian Research and
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Nomenclature A B b Cw Cpl di h l L I m M Pr Re T S Uw Uloss
area of water solar collector (m2) effective transmission absorption product (B ¼ sa) width of air solar collector (m) water specific heat (J/(kg K)) absorber plate mass thermal capacity (J/(kg K)) inner diameter of the condensation tower tube (m) heat transfer coefficient (J/(kg K)) width of water solar collector (m) length of solar collector (m) solar flux (W/m2) mass flow rate (kg/s) mass (kg) Prandtl number Reynolds number temperature (K) area of air solar collector (m2) overall energy loss from the water collector absorber to outside (W/(m2 K)) overall energy loss from the air collector absorber to outside (W/(m2 K))
Development Center for Chemical Industries (IRDCI), Karaj, Iran. This unit includes 28 m2 of flat plate water solar collector, a humidifier and a dehumidifier. The tests reveal that optimization before construction will result in better performance in practice. In 2004, Ben Amara et al. [4] designed and constructed a pilot solar desalination unit based on Multi-Effect Humidification/ Dehumidification (MEH) in Tunisia. The main parts of the fabricated unit consist of a heat equipment device (heat exchanger), a spray humidifier and a dehumidifier system. This equipment was used to simulate the seawater desalination process experimentally with an eight-stage air solar collector heating-humidifying system Since 1990, Ben Bacha et al. [5e7] published the main theoretical and experimental results developed on a prototype unit of 6 m2 of flat plate water solar collectors, also on two pilot desalination units, with 56 m2 and 37.5 m2 of water solar collectors located in Sfax, Tunisia. These solar desalination units are based on the Solar Multiple Condensation Evaporation Cycle principle (SMCEC). Both air and water solar collectors are the main components of a solar desalination unit and any improvement in their efficiency will have a direct bearing on the water production rate and the product cost [8]. The solar collectors that are used to heat water and/or air are expensive and can reach in some cases from 25 to 30% of the total desalination unit cost [9]. The amount of distillate water produced by the unit depends on the solar collector size. The performance of the collector depends mainly on the weather conditions, design and operating parameters. However, to estimate the optimum values of these parameters in different weather conditions using full experiments is costly and time-consuming. Therefore, the development of a simulation model offers a better alternative and has proven to be a powerful tool in the evaluation of the performance of the system. Based on literature studies on the HDH system, it can be noted that most of previous works have used either water or air solar collectors to supply the solar desalination unit with the needed thermal energy for evaporation. However, The solar desalination system, object of this work, differs from previously published works by the simultaneous using of air solar collector to heat air and water solar collector to heat water before humidification and thus in order to increase the thermal performance of the system. In
V x
velocity (m/s) coordinate in the flow direction (m)
Greek
a l m mp s s y
absorbance of the collector absorber surface thermal conductivity (W/m K) dynamic viscosity of water (Ns/m2) dynamic viscosity at the wall temperature (Ns/m2) transmittance StefaneBoltzman constant velocity of fluid (m/s)
Subscripts amb ambient co convection w water g global loss loss to ambient pl air absorber plate ab water absorber plate c collocation
addition to desalination field, solar collectors were used in various other domains such us heating, cooling and drying where several configurations of solar collectors have been developed. In literature, various designs of solar collectors with different shapes and dimensions were theoretically and experimentally studied [10e16]. Esen et al. [10] presented the results of an experimental investigation of a two-phase closed thermosyphon solar water heater. It was concluded that the working fluid had an effect on thermal performance of a two-phase thermosyphon solar collector. ElSebaii et al. [16] developed a transient mathematical model based on an analytical solution of the energy balance equations for a single pass flat plate solar air heater. The model was found to be able to predict the heater performance with good accuracy. The thermal performance of the heater was investigated by computer simulation for various black painted and selectively coated absorbers. It was found that the best performance was achieved using NieSn as a selective coating material. In three previous papers [17e19], we present the detail study of each unit components and the effect of different operating modes on fresh water production in steady state regime. The paper at hand deals with mathematical modeling in dynamic regime and experimental validation of the solar part of a water desalination unit based on the HDH principle. Its underlying objectives are as follows. To develop a dynamic mathematical model able to predict the thermal performance of the solar collectors. To present numerical and experimental data as an example of the validation process that has been carried out in order to assess the credibility of the numerical models.
2. System description Fig. 1 and Plate 1 show, respectively, a 3D view and a photograph of the solar desalination system. The principle of functioning of the unit consists of preheating sea or brackish water in the condensation tower by the latent heat of condensation. Then, the preheated water was heated in the water solar collectors and pulverized into the humidifier and the evaporation tower. Due to heat and mass
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Fig. 1. A 3D view of the solar desalination unit.
transfers between the hot water and the heated air stream in the humidifier in case of working in closed air loop and between the hot water and the ambient air stream in the evaporation tower in case of working in open air loop, the latter is loaded with moisture. To increase the surface of contact between air and water, and therefore to rise the rate of air humidification, packed bed is implanted in the tower of evaporation and the humidifier. The saturated moist air is then transported toward the tower of condensation where it enters in contact with a surface which its temperature is lower than the dew point of the air. The condensed water was collected from the bottom of the condensation tower, while the brine (the salty water exiting the evaporator and the humidifier) at the bottom of both the humidifier and evaporation tower will be either recycled and combined with the feed solution at the entry point or rejected in case of an increase of saltiness rates.
16 m2 of air solar collectors and 12 m2 of water solar ones. The air solar collector has 2 m length and 1 m width, and is formed by a single glass cover and an absorber. The absorbing aluminium material that traps the energy was constituted of 20 separated square channels with a thickness of 1 mm. The separating distance is 2 mm and each flow channel was 40 mm in width. The air gap between the absorber and the glass cover is 0.1 m. The rear and sides insulations were provided by polyurethane to reduce heat loss. A silicon sealant was used between the different components of the air solar collector to ensure insulation from the environment. The water solar collector device used by the present desalination prototype is of 2 m in length and 1 m in width. The water solar collector use a sheet-and-tube, in copper material, absorber with the tubes as an integral part of the sheet, the inner diameter of the tubes is 10 mm and the outer one is 12 mm.
Plate 1. A photograph of the desalination pilot unit.
3. Collectors design and instrumentation Solar energy collectors are heat exchangers that convert incoming solar energy to internal energy of the transport medium (air or water). The current solar desalination prototype employs
The measured variables in the experiments reported in this paper include inlet and outlet fluid (air and water) temperatures, ambient temperature and the solar irradiation incident on the field collector’s plane. The air and water solar collectors were instrumented with Pt100 thermistors with a sensibility of 0.3799 U/ C for measuring the outlet and the inlet fluid temperatures, ambient temperature and the temperature at the different collocation points
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The assumptions used in developing the mathematical model are listed below: the velocity of water is uniform, therefore the local state of water depends only on one side x, and the water temperature remains under 100 C point.
4.1.1. One-temperature mathematical model Since there are no mass or concentration changes, the system can be modeled solely from thermal energy balances. The thermal energy balance equations for the system formed by the absorber and water for a slice of the collector with a width of l, a length of dx and a surface of ds as shown in Fig. 4, is the next one: [The quantity of energy accumulated by the absorber and water masses] ¼ [(the quantity of energy received by a surface absorber element, dA and during a dt time) (the quantity of energy gained by water) (the overall Losses toward the outside)]. Mathematically this can be expressed as:
ðMCÞg Fig. 2. probes placement in the water solar collector.
(Fig. 2). The Pt 100, which measured the ambient temperature, was kept in a shelter to protect the sensor from direct sunlight. A pyranometer, with 1% accuracy and 12.29 mV/Wm2 sensibility, was used to measure the total solar irradiation placed in a horizontal plane adjacent to the collector. All sensors, which were calibrated before using to determine the probes sensibility, were connected to a data acquisition system (type Agilent 34970A). During experimentation, all the parameters were measured and recorded every 1 min for up to 420 min. All measurements started at 10:30 a.m. 4. Dynamic modeling 4.1. Water solar collector modeling The water solar collector can be viewed as a multivariable system with several input and output signals. Fig. 3 presents the water solar collector input/output diagram, this permits to visualize the different variables imposed by the outside middle as a function of time. It displays the external variables that would affect the water solar collector as the solar radiation, I (t), and ambient temperature, Tamb (t), and the collector input signals, namely the water flow rate, mw (t), and temperature, Twe (t), as well as the output signal which is the water temperature, Tws (t). Both I (t) and Tamb (t) are considered as perturbations seen their aleatory behaviour during the time. The plane solar collector can be described by two different models. The first model is formed by an equation to the partial derivatives. The second, be composed of two equations coupled to the partial derivatives binding the temperature of the fluid to the one of the absorber.
dA dTw ¼ I sv aab dtdA Qw Qlossabamb A
(1a)
With:
ðMCÞg ¼ Mw Cw þ Mab Cab Qw ¼ mw Cw dTw dt Qlossabamb ¼ Uw ðTab Tamb ÞdtdA The Eq. (1a) can be written as:
ðMCÞg
dA dTw ¼ I sv aab dtdA mw Cw dTw dt A Uw ðTab Tamb ÞdtdA
(1b)
It can be also further simplified as:
vTw 1 vTw mw x ¼ Tw þ f ðtÞ d vt vx
(1c)
With:
x ¼
ðMCÞg sv aab IðtÞ Cw þ Tamb ðtÞ ; d ¼ ; f ðtÞ ¼ Uw l Uw A Uw
4.1.2. Two-temperature mathematical model The essential detail of the two-temperature mathematical model is to consider that the temperature of water, Tw(t), is different of the one of the absorber, Tpl(t). The other assumptions admitted for the one-temperature mathematical model will be preserved for this second mathematical model. The thermal balances of the system formed by the absorber and water for a slice of the surface collector as shown in Fig. 5 are the following: For water element
Fig. 3. water solar collector input/output block diagram.
[(The quantity of energy accumulated by water)] ¼ [(The quantity of energy received by convection from the surface absorber element, dA and during dt time) (the quantity of energy gained by water during dt)]. Mathematically this can be expressed as:
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Fig. 4. Thermal energy balance of differential section of solar water collector (one-temperature case).
Mw Cw
dA dTw ¼ hcoabw ðTab Tw ÞdtdA mw Cw dTw dt A (2a)
It can be further simplified as:
vTw A Amw vTw ½hcoabw ðTab Tw Þ ¼ vt lMw vx Mw Cw
(2b)
physical parameters (flow rate, collector area, material and inclination angle of the collector). It should be noted that the fluid temperature and flow rate at the collector outlet are the two parameters with the most significant impact on the unit production as they are the input parameters of the distillation module. The distributed parameter character of these models requires the use of a reduction model method to obtain feasible approximation of the solution for the system behaviour. 4.2. Air solar collector modeling
For the absorber plate element [(The quantity of energy accumulated by the absorber’s mass)] ¼ [(The quantity of energy received by a surface absorber element, dA and during dt time) (the energy quantity lost toward the outside during dt time) (the quantity of energy transferred by convection toward air during dt)]. Mathematically this can be expressed as:
Mab Cab
dA dTab ¼ I sv aab dtdA Qlossabamb Qcoabw A
(3a)
With
Qcoabw ¼ hcoabw ðTab Tw ÞdtdA
Like the water solar collector, the air solar one can be viewed as a multivariable system with several input and output signals. Fig. 6 presents the air solar collector input/output diagram, this permit to visualize the different variables imposed by the outside middle as a function of time. It displays the external variables that would affect the air solar collector as the solar radiation, I (t), and ambient temperature, Tamb (t), and the collector input signals, namely the air flow rate, ma (t), and temperature, Tae (t), as well as the output signal which is the air temperature, Tas (t). Both I (t) and Tamb (t) are considered as perturbations seen their aleatory behaviour during the time. The assumptions used in developing the mathematical model are listed below:
(3b)
the velocity of air is uniform, therefore the local state of air depends only on one side x, and the area of the absorber, glass cover and air are considered equal.
The obtained mathematical model for the solar collector allows the determination, for variable solar intensity levels and ambient temperature, of the fluid instantaneous temperature at any point of the collector as a function of the command, geometrical and
The theoretical model employed for describing the behaviour of the collector that operates in dynamic regime is made using a thermal energy balances for the three collector components absorber plate, air and glass cover as presented in Fig. 3.
It can be further simplified as:
dTab AUw A ½f ðtÞ Tab þ ½hcoabw ðTw Tab Þ ¼ dt Mab Cab Mab Cab
Fig. 5. Thermal energy balance of differential section of solar water collector (two-temperature case).
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Mpl Cpl
dS dTpl ¼ I sv apl dtdSQlossplamb Qcopla Qradplv S
(5a)
It can be further simplified as:
dTpl S h I sv apl Uloss Tpl Tamb hcopla Tpl Ta ¼ dt Mpl Cpl i hradplv Tpl Tv
Fig. 6. Air solar collector input/output block diagram.
(5b) The thermal balances of the system formed by the absorber, air and the glass cover for a slice of the surface collector (Fig. 7) are the following: For an air element [(The quantity of energy accumulated by air)] ¼ [(The quantity of energy received by convection from the surface absorber element, dS and during dt time) þ (the quantity of energy received from the glass cover by convection and during dt time)] [the quantity of energy gained by air during dt]. Mathematically this can be expressed as:
Ma Ca
dS dTa ¼ hcopla Tpl Ta dtdS þ hcova ðTv Ta ÞdtdS S ma Ca dTa dt
For the glass cover element [(The quantity of energy accumulated by the glass cover’s mass)] ¼ [(The quantity of energy received by a surface glass cover element, dS and during dt time) þ (the quantity of energy transferred by radiation from the absorber toward the glass cover element during dt) (the quantity of energy transferred by convection toward air during dt) (the quantity of energy transferred by convection toward the ambient air during dt) (the quantity of energy transferred by radiation toward the ambient air during dt)]. Mathematically this can be expressed as:
Mv Cv
dS dTv ¼ I av dtdS þ Qradplv Qcova Qcovamb S Qradvamb
(4a) It can be further simplified as:
(6a)
It can be further simplified as:
i vTa S h Sma vTa hcopla Tpl Ta þ hcova ðTv Ta Þ ¼ vt bMa vx Ma Ca (4b)
dTv S h Iav þ hradplv Tpl Tv hcova ðTv Ta Þ ¼ dt Mv Cv i hcrvamb ðTv Tamb Þ
(6b)
With: For the absorber plate element
hcrvamb ¼ hcovamb þ hradvamb ;
[(The quantity of energy accumulated by the absorber’s mass)] ¼ [(The quantity of energy received by a surface absorber element, dS and during dt time) (the energy quantity lost toward the outside during dt time) (the quantity of energy transferred by convection toward air during dt) (the quantity of energy transferred by radiation toward the glass cover during dt)]. Mathematically this can be expressed as:
overall heat transfer coefficient toward outside The obtained mathematical models for the solar collectors allow the determination, for variable solar intensity levels and ambient temperature, of the fluid instantaneous temperature at any point of the collectors as a function of the command, geometrical and physical parameters (flow rate, collector area). It should be noted
Fig. 7. Thermal energy balance of differential section of solar air collector.
K. Zhani et al. / Energy 36 (2011) 3159e3169
that the fluid temperatures and flow rates at the collector outlet are the two parameters with the most significant impact on the unit production as they are the input parameters of the evaporation tower and the humidifier. The distributed parameter character of these models requires the use of a reduction model method to obtain feasible approximation of the solution for the system behaviour.
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Ordinary Differential Equations (ODE). On the other hand, the orthogonal collocation method (OCM) approximates the solution by a polynomial trial function, and the resulting set of ODE is often considerably smaller. Currently, the collocation method is very widely used in chemical and biotechnological engineering problems [23, 24]. 6.1. 6Formulation of the approximation method
5. Heat transfer coefficients Consider the following partial differential equation (PDE): For water solar collector The particular correlation to be used for calculating in tube heat transfer coefficients, hcoplw , depends upon the flow regime existing inside the tube e laminar or turbulent. For laminar flow Re < 2300
d 9 ! 0:0668Re Pr i = m 0:14 Lw 3:65 þ ¼ h d i0:66 ; mp di : 1 þ 0:04 Re Prð i Þ Lw 8
hcoplw
lw <
For turbulent flow Re > 2300
hcoplw ¼ 0:023
lw di
vT vT ¼ f x; t; T; ; . vt vx With:
i h t˛ 0; tf : time domain; tf < N x˛½x0 ; xl : spatial domain To study a collocation method in this model, the following approximation series is used for the variable T:
Tðx; tÞ ¼
0:8
Re
0:33
Pr
m mp
!0:14
For air solar collector The correlation for the convective heat transfer coefficient, hcopl-amb, with the speed of wind (Vwind) on the surface of the collector was suggested by Mc Adam [20] as:
hradplv ¼
2 þ T2 s Tpl v
Tpl þ Tv 1 1 þ 1
epl
N X
ci ðtÞ4i ðxÞ
The specific method applied is called orthogonal collocation due to certain orthogonality properties of the base functions fi. Due to technical reasons, the number of the base functions is given in the form of N þ 2. The points x0, and xNþ1, correspond to the initial and end points of the system. Consequently, the number of internal collocation points is N. By using the Lagrange interpolation polynomial, Lj, as a base function, the Eq. (8) can be written as follows:
Tðx; tÞ ¼
Nþ1 X
Lj ðxÞTj ðtÞ
j¼0
ev
The convective heat transfer coefficient between the absorber plate and air, hcopl-a, is given by:
with,
Lj ðxÞ ¼
Nþ1 Y i¼0
x xi xj xi
!
isj
Tj ðtÞ ¼ T x ¼ xj ; t xj ; ðj ¼ 0; 1; .; N þ 1Þ : the collacation points
lpl La ya 0:8 hcopla ¼ 0:0336 n La The radiation coefficient between the glass cover and ambient air is obtained from Nafey et al. [22]:
2 ðTv þ Tamb Þ hradvamb ¼ ev s Tv2 þ Tamb 6. Model approximation of the solar collectors The analytical solution of Eqs (1)e(6) is impossible and they must be discretized to obtain approximate, but still accurate, solutions. The method of finite differences has been used quite extensively in the past, but it usually requires a large number of discretization points and results in a correspondingly large set of
(8)
i¼1
hcoplamb ¼ 5:7 þ 3:8Vwind Many heat transfer coefficient expressions are available in literature. The radiative heat transfer coefficient between two parallel plates is obtained from Ong [21] as follows:
(7)
Fig. 8. Solar radiation measured during typical day in August.
(9)
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Fig. 11. Temporal variations of water solar collector temperature at the inlet, outlet and the four collocation points during a day.
Fig. 9. Ambient temperature measured during typical day in August.
With this method, the derivatives with respect to time and space are approximated as follows: Nþ1 X dTj ðtÞ vTðx; tÞ Lj ðxÞ ¼ dt vt j¼0 N þ1 X dLj ðxÞ vTðx; tÞ T ðtÞ ¼ dx j vx j¼0
(10) (11)
At the different collocation points, we can write:
vTðx; tÞ dTi ðtÞ ¼ vt x¼xi dt Nþ1 X vTðx; tÞ ¼ lij Tj ðtÞ vx x¼xi
(12)
a system of ODEs according to the time localized in every collocation point. The set of PDEs is transformed to the following set of ODE using the OCM with the boundary condition, Tw0 ¼ Tw ð0; tÞ ¼ Twe One-temperature mathematical model
2 0 1 3 Nþ1 X dTwi 14 mw x@ lij Twj li0 Twe A Twi þ f ðtÞ5 ¼ d dt j¼1
(14)
where i ¼ 1,2,3,.,N þ 1.
(13)
Two-temperature mathematical model
j¼0
With:
dLj ðxÞ lij ¼ dx x¼xi 6.2. Application of the OCM
dTabi AUloss A ½f ðtÞTabi þ ½hcoabw ðTabi Twi Þ ¼ Mab Cab dt Mab Cab
(15)
0 1 X dTwi A Amw @ Nþ1 ½hcoabw ðTabi Twi Þ l T þl Twe A ¼ dt lMw j¼1 ij wj i0 Mw Cw
6.2.1. Water solar collector By substituting the approximations presented earlier in the initial system formed by partial derivatives equations, we can get
where i ¼ 1,2,3,.,N þ 1.
Fig. 10. Comparison between experimental, predicted outlet temperatures with oneand two-temperature models.
Fig. 12. Comparison between numerical and experimental water collector outlet temperature.
(16)
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Fig. 13. Comparison between numerical and experimental temperature measurements at the fourth collocation point.
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Fig. 15. Comparison between numerical and experimental temperature measurements at the second collocation point temperature.
7. Results and discussion 6.2.2. Air solar collector The set of PDEs is transformed to the following set of ODE using the OCM with the boundary condition, Ta0 ¼ Ta ð0; tÞ ¼ Tae
dTvi S h I av þ hradplv Tpli Tvi hcova ðTvi Tai Þ ¼ Mv Cv dt i hcrvamb ðTvi Tamb Þ (17) dTpli S h I sv apl Uloss Tpli Tamb hcopla Tpli Tai ¼ dt Mpl Cpl i hradplv Tpli Tvi (18) i dTai S h hcopla Tpli Tai þ hcova ðTvi Tai Þ ¼ dt Ma Ca 0 1 X Sma @ Nþ1 (19) l T þ li0 Tae A bMa j ¼ 1 ij aj
Fig. 14. Comparison between numerical and experimental temperature measurements at the third collocation point.
The measured climatic conditions; solar radiation and ambient temperature for a typical day in august (summer time) at the city of Sfax, Tunisia are presented respectively in Figs. 8 and 9. As shown in Fig. 8, the chosen day is characterized by high fluctuation of solar radiation. All the following figures of this paragraph refer to these climatic conditions. To experimentally validate the developed mathematical models, the values of global solar radiation, ambient temperature, mass flow rates in the collectors and inlet fluid temperatures of the collectors were introduced to the simulation program as input data. 7.1. Experimental validation of water solar collector Fig. 10 presents a comparison between experimental, predicted outlet temperatures with one- and two-temperature mathematical models. It transpires from this figure that the two-temperature mathematical model describes more precisely the real behaviour of the water solar collector than the one-temperature mathematical model. It is also noticeable that the output of the mathematical model with one temperature is higher than the one of two temperatures. This result shows that it exist a thermal resistance between the absorber and the water. In order to compare experimental data with theoretical predictions, water solar collector temperatures; inlet, outlet and collocation points temperatures collector are plotted in Fig. 11 for
Fig. 16. Comparison between numerical and experimental temperature measurements at the first collocation point.
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K. Zhani et al. / Energy 36 (2011) 3159e3169 Table 1 The accuracy of the experimental results. Parameter
Average relative error ear (%)
Maximum absolute error emax ( C)
Minimum absolute error emin ( C)
Tas Tws Tc4 Tc3 Tc2 Tc1
7.574 3.407 5.981 4 6.527 7.022
7.928 9.100 7.572 7.792 8.599 8.537
3.95 102 2.78 102 7.62 103 5.14 102 3.05 102 2.76 103
With:emax ¼ maxjTexp ðiÞ Tsim ðiÞj, emin ¼ minjTexp ðiÞ Tsim ðiÞj, i ¼ 1, 2,.,k.
Fig. 17. Response of the collector outlet air temperature to natural fluctuation of solar radiation.
different experimental measurements. It is clear from Fig. 11 that the temporal variations of water solar collector temperatures have the same trends as solar radiation. One can also note that the measured water temperatures increase with increasing solar radiation and vice versa. Figs. 12e16 present the comparison between numerical and experimental temperature measurements, respectively, at the collector output, the fourth, the third, the second and the first collocation points. It is clear that the theoretical and experimental temperatures have the same trends. The gap between the theoretical and the experimental temperature values is because that the sensors are in contact with the exterior wall of the tube not emerged in water inside the tube. So, the measured temperature given by the sensor is that of the absorber one which is higher than water temperature. That is why the experimental temperature values are higher than the theoretical temperature ones. This would explain the gap between the theoretical and experimental measurements.
air solar collector leads to an increase in the thermal performance of the air solar collector and then the production of the solar desalination unit. But for low solar radiation intensity, the rapid response of the collector to solar fluctuations may be deficiency for solar desalination unit. Indeed, the air solar collector temperature drops quickly, resulting in condensation in the channels constituting the air solar collector absorber and a decrease in performance of the whole solar desalination process. This deficiency was experimentally verified by Ben Amara et al. [25]. Fig. 18 shows a comparison between the experimental and the theoretical values of air outlet temperature at the level of air solar collector. It is clear from this figure that the theoretical and experimental temperatures are in good concordance. It can be also noticed that the theoretical values are slightly superior to the measured ones. This may be due to the thermal loss that can be underestimated in our simulation model. 7.3. Experimental error Simple statistical analysis of the relative error between simulation and experimental measurements is included in Table 1. The accuracy of the experimental results may be calculated using the following definition:
3ar ð%Þ ¼ 7.2. Experimental validation of air solar collector Fig. 17 shows the response of the collector outlet temperature to natural fluctuation of solar radiation during daylight hours. In fact, it can be seen from this figure that when the solar radiation intensity presents a temporal fluctuation, a residual vacillation of the collector outlet temperature follows rapidly. Therefore, the collector presents a good response time to any climatic disturbance. For the high solar radiation intensity, the good response time of the
k jTexp ðiÞ Tsim ðiÞj 100 X Texp ðiÞ k i¼1
where Texp denotes the experimental data of T, while, Tsim and k are the theoretical prediction of T and the number of experimental measurements, respectively. The error analysis of the water solar collector temperatures shown in Figs. 12e16 and 18 is presented in Table 1. It is seen in this table that the agreement between experiment data and the results calculated from the theoretical prediction of the present device is fairly good. 8. Conclusion
Fig. 18. Comparison between numerical and experimental air collector outlet temperature.
This paper presents the modeling and the experimental validation of air and water solar collectors used in HDH solar desalination unit. To numerically simulate the solar collectors, we have developed dynamic mathematical models describing the behaviour of the solar collectors. The proposed mathematical models can be used to predict the thermal performances of solar collectors with good accuracy under the meteorological conditions and the variations of the entrance parameters. The experimental validation revealed that the numerical prediction of the solar collector temperatures e inlet, outlet and collocation points temperatures e was in good agreement with the experimental values measured by sensors installed on board the solar collectors. This proves the validity of the mathematical models established for the solar collectors and the effectiveness of the OCM used to solve them. In addition, the validated mathematical models would help in the development of a computer-based design and simulation software for such type of solar collectors.
K. Zhani et al. / Energy 36 (2011) 3159e3169
Acknowledgements The authors wish to express their deepest thanks and heartfelt appreciation to the Ministère de l’Enseignement Supérieur et de la Recherche Scientifique for its financial support and to the Agence Nationale de la Maîtrise de l’Energie (ANME) for the management of the project. It goes without saying that special thanks should be darted at the English teacher Mr. R.Romdhani
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