Modelling and performance study of a continuous adsorption refrigeration system driven by parabolic trough solar collector

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Solar Energy 83 (2009) 850–861 www.elsevier.com/locate/solener

Modelling and performance study of a continuous adsorption refrigeration system driven by parabolic trough solar collector A. El Fadar a,*, A. Mimet a, M. Pe´rez-Garcı´a b a

Energetics Laboratory, Sciences Faculty, Abdelmalek Essaadi University, BP 2121, 93000 Tetouan, Morocco b Dpto. de Fı´sica Aplicada, Universidad de Almerı´a, Spain Received 26 May 2008; received in revised form 26 November 2008; accepted 3 December 2008 Available online 29 December 2008 Communicated by: Associated editor Ruzhu Wang

Abstract This article suggests a numerical study of a continuous adsorption refrigeration system consisting of two adsorbent beds and powered by parabolic trough solar collector (PTC). Activated carbon as adsorbent and ammonia as refrigerant are selected. A predictive model accounting for heat balance in the solar collector components and instantaneous heat and mass transfer in adsorbent bed is presented. The validity of the theoretical model has been tested by comparison with experimental data of the temperature evolution within the adsorber during isosteric heating phase. A good agreement is obtained. The system performance is assessed in terms of specific cooling power (SCP), refrigeration cycle COP (COPcycle) and solar coefficient of performance (COPs), which were evaluated by a cycle simulation computer program. The temperature, pressure and adsorbed mass profiles in the two adsorbers have been shown. The influences of some important operating and design parameters on the system performance have been analyzed. The study has put in evidence the ability of such a system to achieve a promising performance and to overcome the intermittence of the adsorption refrigeration systems driven by solar energy. Under the climatic conditions of daily solar radiation being about 14 MJ per 0.8 m2 (17.5 MJ/m2) and operating conditions of evaporating temperature, Tev = 0 °C, condensing temperature, Tcon = 30 °C and heat source temperature of 100 °C, the results indicate that the system could achieve a SCP of the order of 104 W/kg, a refrigeration cycle COP of 0.43, and it could produce a daily useful cooling of 2515 kJ per 0.8 m2 of collector area, while its gross solar COP could reach 0.18. Ó 2009 Elsevier Ltd. All rights reserved. Keywords: Parabolic trough collector; Adsorption; Refrigeration; Activated carbon/ammonia; Continuous cycle; Simulation

1. Introduction In recent years, considerable attention has been paid to adsorption refrigeration systems, which are regarded as environmentally friendly alternatives to conventional vapour compression refrigeration systems, since they can use refrigerants that do not contribute to ozone layer depletion and global warming. In addition, the adsorption sys*

Corresponding author. Tel.: +212 66280523; fax: +212 39 99 45 00. E-mail address: [email protected] (A.E. Fadar).

0038-092X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2008.12.003

tems have the benefits of simpler control, no vibration and lower operation costs, if compared with mechanical vapour compression systems and, in comparison with the absorption systems, they do not need a solution pump or rectifier for the refrigerant, do not present corrosion problems due to the working pairs normally used, they are less sensitive to shocks and to the installation position (Wang et al., 2006) and they could be operated with no-moving parts (Wang et al., 2002). Furthermore, refrigeration as a solar energy application is particularly attractive because of (i) the non-dependence on conventional power and (ii)

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Nomenclature surface/cross-sectional area (m2) concentration ratio specific heat (J kg1 K1) inner diameter of the metal heat transfer tube (m) outer diameter of the metal heat transfer tube/ Do internal diameter of adsorbent bed (m) inner diameter of the receiver tube (m) di outer diameter of the receiver tube (m) do collector heat removal factor FR F0 collector efficiency factor H specific enthalpy of ammonia (J kg1) h heat transfer coefficient (W m2 K1) heat transfer coefficient between the receiver and hfr the fluid flowing within receiver I direct solar radiation on aperture (W m2) collector length (m) Lc reactor length (m) Lr L(Tev) latent heat of ammonia at evaporation temperature (J kg1) m mass (kg) adsorbed mass of ammonia on a layer of actima vated carbon (kg) mass flow rate of water (kg s1) m_ f P pressure (bar = 105 Pa) cooling production (J) Qc q mass flow rate of ammonia (kg s1) inner radius of the metal heat transfer tube (m) Ri inner radius of adsorbent bed (m) Ro external radius of adsorbent bed (m) R1 r radial coordinate (m) T temperature (K) temperature at start of regeneration (K) Tg1 temperature at the end of desorption process Tg2 (K) t time (s) cycle time (s) tcycle overall heat loss coefficient from the receiver UL (W m2 K1) u specific internal energy (J kg1) V volume (m3) W width of aperture (m) x adsorbed mass of ammonia per unit mass of adsorbent (kg kg1) A C Cp Di

the near coincidence of peak cooling loads with the solar energy availability. Despite their advantages, the adsorption refrigeration systems present some drawbacks, such as low COP, low SCP, high weight and high cost. So, in order to overcome these inconveniences, various approaches have been under-

Greek symbols DHads latent heat of adsorption (J kg1) Dx adsorption capacity difference between adsorption and desorption phases (kg kg1) e bed porosity g collector efficiency optical efficiency go h volume fraction of the adsorbed phase k thermal conductivity (W m1 K1) q density (kg m3) Subscripts a adsorbate, adsorbed ads adsorption amb ambient c collector con condensation, condenser e equivalent ev evaporation, evaporator f fluid (water) g gas gl global heat heating in inlet fluid l liquid (ammonia) max maximum met metal min minimum out outlet fluid r receiver s solid sat saturation st storage tank Abbreviations AC activated carbon COP coefficient of performance COPcycle cycle coefficient of performance COPS solar coefficient of performance HTF heat transfer fluid HWST hot water storage tank PTC parabolic trough collector SCP specific cooling power (W kg1)

taken, such as improvement of heat and mass transfer in adsorbent beds, enhancement of the adsorption properties of the working pairs, design and study of different kind of cycles and improvement of regenerative heat and mass transfer between beds. However, the widespread use of the adsorption refrigeration systems is still limited by the

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technical and economic constraints. For this reason, the research activities in this field are still increasing to overcome these problems. During recent decades, several solar adsorption refrigeration units were successfully tested with different combinations of adsorbents and adsorbates. The most studied pairs in this field are activated carbon/ammonia, activated carbon/methanol, zeolite/water and silica gel/water. These investigations include the research on ice-making and congelation purposes (Tchernev, 1978; Pons and Guilleminot, 1986; Grenier et al., 1988; Critoph, 1994; Sumathy and Zhongfu, 1999; Wang et al., 2000; Boubakri et al., 2000; Buchter et al., 2003; Hildbrand et al., 2004; Li et al., 2004; Khattab, 2004), refrigeration for food and vaccine storage (Critoph, 1999; Anyanwu and Ezekwe, 2003; Lemmini and Errougani, 2005; Gonza´lez and Rodrı´guez, 2007) and air-conditioning applications (Wang, 2001; Saha et al., 2001; Lu et al., 2003). The literature shows that most of these systems were intermittent, in which adsorption and cooling production can only be achieved during nights. On the other hand, the solar collector/adsorber is one of the most important elements of any solar adsorption refrigeration system that needs more investigations. Indeed, several reports have mentioned its importance, i.e. the low thermal conductivities and poor porosity characteristics of adsorbents have as effect, the bulky collector/generator/adsorber component and, thus, its excessive heating capacity, leading to rather low thermal COP (Anyanwu, 2003). The adsorptive systems’ development is still limited by the adsorber-solar collector component cost (Leite et al., 2004) and recently, it has been reported that a potential barrier to the commercialization of the solar adsorption refrigeration systems is large collector costs (Baker and Kaftanog˘lu, 2007). Nevertheless, collector costs can be reduced by increasing the adsorption cycle’s COP or decreasing the operating temperature of the collector (Baker, 2007). In this context, parabolic trough collectors (PTCs) seem to be a reasonable alternative, since they could achieve a high cycle’s COP due to their high efficiency. They are the most developed and deployed type of solar concentrators (Badrana and Eck, 2006) and their technology is the most verified-solar technology through deployment and construction testing (Price and Hassani, 2002). They have been used in various applications, such as steam generation (Kalogirou, 1996; Zarza et al., 2004), seawater desalination (Kalogirou, 1998), hot water production (Kalogirou and Lloyd, 1992; Valan Arasu and Sornakumar, 2007), etc. Moreover, Bird and Drost (1982) have recommended that the PTC concept should receive the highest priority for commercial development for low temperature (65–177 °C) solar process heat applications. Even so, most of the studies conducted on the solar adsorption cooling systems have been achieved with either flat plate or evacuated tube collectors, whereas little attention has been devoted to concentrating collectors, in particular the PTCs.

This paper presents the study of a novel system in an attempt to overcome the intermittent character of solar adsorption refrigeration systems, and test the applicability of PTC to these systems with the aim to improve their performance. Thus, a numerical investigation is performed to describe a two-bed continuous adsorption refrigeration cycle. A parametric analysis is carried out to evaluate some optimal design and operating values of the system. 2. System description and working principle A schematic diagram of the proposed two-bed continuous adsorption refrigeration system is shown in Fig. 1. It consists of a solar concentrator (PTC), a heating water tank, a cooling water tank, a condenser, an evaporator, tank of ammonia, refrigerant valves, circulating pump and two cylindrical adsorbers containing the activated carbon-ammonia, and so on. The receiver, which is placed along the focal line of the concentrator, consists of a stainless steel tube covered by a glass envelope for reducing thermal heat losses that can take place by radiation and convection. On the other hand, the adsorbent bed in each adsorber is coated with a layer of insulation material; it is heated up and cooled down by means of a stainless steel tube inserted in the adsorbent. Water from the hot water storage tank (HWST) is pumped through the receiver where it is heated and then flows back into the HWST. The heat gained by the PTC from the solar radiation is accumulated in HWST. Hot water from the storage tank is then used for heating the two adsorbers. Note that the HWST temperature, taken as a heat source temperature, changes through the day, however it could be controlled by a differential thermostat controller. For producing cold continuously, the adsorbers have to be operated out-of-phase, i.e. when one adsorber is being heated up and then desorbs refrigerant into the condenser under high temperature and high pressure (saturation pressure at the temperature of the condenser), the other adsorber is cooled down and adsorbs refrigerant vapour from the evaporator under low temperature and low pressure (saturation pressure at the temperature of the evaporator). The hot water temperature in tank increases through the day and when it reaches the required value that is capable to generate desorption of refrigerant, the HWST is connected to the adsorber (1) to be heated up, and desorption of ammonia from the adsorbent occurs. The desorbed refrigerant is condensed in the condenser and then the liquid ammonia flows to the evaporator via a flow control valve. During the same period, the other adsorber (2) is cooled down from the cooling water tank. As the adsorbent bed temperature decreases, the vapour pressure is lowered down. When this pressure reaches the evaporation pressure (the saturated vapour pressure of the refrigerant), the adsorber (2) and evaporator are connected, and the refrigerant is evaporated within the evaporator and then adsorbed into the adsorbent. Consequently the cooling effect is produced in the surrounding space.

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a

Cold water tank

Adsorber 1 PTC

Differential thermostat

Heat storage tank

3 4

Flow meter

1

2

Adsorber 2 Pump

Heat transfer fluid loop Refrigerant path

7

b

6

5

Layer of AC

dr

Ro r r+dr R1

Fig. 1. (a) Schematic diagram of the solar powered continuous adsorption refrigeration system: 1. condenser; 2. ammonia tank; 3. expansion valve; 4. evaporator (b) longitudinal and cross sections of one adsorber; 5. adsorbent; 6. metal of heat exchanger; 7. shell (insulation material).

It is noteworthy to mention that, in order to enhance the system performance, the heat and mass transfer channels in adsorbers (1) and (2) can be connected with each other, at the switch time, to recover heat and mass. These processes are not included in this work. 3. Mathematical formalism 3.1. Model assumptions The main model assumptions adopted in this work are as follows: 1. The pressure is uniform inside the adsorbent bed. 2. The adsorbent bed is considered as a continuous medium and the conduction heat transfer in the medium can be characterised by an equivalent thermal conductivity, ke. 3. The adsorption/desorption process is an isobaric process. 4. The porous medium properties have a cylindrical symmetry. 5. All phases are continuously in thermal, mechanical and chemical local equilibrium. 6. The heat transfer is radial and the convection heat transfer due to the radial mass transfer is neglected.

7. The HTF temperature is uniform. 8. The condenser and evaporator are ideal, i.e. Tev and Tcon are constant during the isobaric phases. 9. The two adsorbers have identical thermo-physical, structural and geometrical characteristics. 10. The gaseous phase behaves as an ideal gas. 3.2. Model equations Considering the assumptions stated above, a one-dimensional transient model based on combined heat and mass transfer and the thermodynamics of the adsorption process in adsorbent bed, and on energy balance of the PTC and heat storage tank is developed. The model equations are expressed in the following sections. 3.2.1. Thermal analysis of collector 1. PTC modelling The thermal efficiency of a parabolic trough collector is defined as the ratio of the useful energy produced over any time period to the beam radiation incident on the collector aperture over the same period. Under steady state conditions, it can be calculated from the ‘Hottel–Whillier–Bliss’ equation: g ¼ F R go 

F R U L ðT in  T amb Þ C I

ð1Þ

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where UL is solar collector heat loss coefficient, Tin is the temperature of the fluid entering the collector, Tamb is the ambient temperature and go is the optical efficiency. The concentration ratio (C) describes the characteristics of the concentrating solar collector. It is defined as the ratio of the collector aperture area Ac to the receiver area Ar. W pd o

C¼

ð2Þ

FR is the collector heat removal factor. Its value depends on the geometry of the collector and operating conditions: FR ¼

m_ f C pf ½1  expðAr U L F 0 =m_ f C pf Þ Ar U L

ð3Þ

0

F is collector efficiency factor which is given by: F0 ¼

1 UL

1=U L do þ hfd; or d i þ 2k ln ddoi r

ð4Þ

Furthermore, the instantaneous collector efficiency can also be expressed, in function of the temperature gain acquired in the collector, by the following expression: g¼

m_ f C pf ðT out  T in Þ IWLc

ð5Þ

Tout is the temperature of the fluid leaving the collector. From Eqs. (1) and (5), we can calculate at each instant Tout versus Tin. 2. Hot water storage tank modelling The storage tank temperature is evaluated with the aid of the energy balance equation in the tank: ðM st C pf þ M met C pmet Þ

dT st ¼ m_ f C pf ðT out  T in Þ þ UAst ðT amb  T st Þ dt

ð6Þ

where Cpf,, Mst, and Tst are, respectively, the specific heat, mass and temperature of water in the storage tank. Cpmet is the specific heat of the storage tank metal, and Mmet is its mass, while (UAst) is loss coefficient-area product of the storage tank. In the right side of Eq. (6), the first term designates the thermal input from the parabolic trough collector. We can also determine the heat quantity Qst that could be stored in the tank without any heat removal during the day from the start point (sunrise) to the final point, when the tank water reaches its maximum temperature. It is given by the following equation: Qst ¼ M st C pf ðT st; max  T st; i Þ

ð7Þ

where Tst, i and Tst, max are, respectively, the initial temperature and maximum temperature reached by hot water in the tank. 3.2.2. Heat and mass transfer equations in the adsorbent bed 1. Mass conservation equation The mass conservation of ammonia in the control volume of the bed (a layer with radial coordinate r and thickness dr) yields:

@ @q ½2pr dr Lr ððe  hÞqg þ hqa Þ ¼ qðr;tÞ  qðr þ dr;tÞ ¼  dr @t @r

ð8Þ

where q is the ammonia flow rate within the layer of adsorbent bed. 2. Energy balance equation @ ½2pr dr Lr ðð1  eÞqs us þ ðe  hÞqg ug @t þ hqa ua Þ þ qðr þ dr;tÞH g ðT ðr þ drÞ;pÞ  qðr;tÞH g ðT ðrÞ;pÞ  2  @ T 1 @T þ ð9Þ ¼ 2prke drLr @r2 r @r where

H g ðT Þ ¼ H a ðT Þ þ DH ads

ð10Þ

Hg(T) and Ha(T) are the specific enthalpies of ammonia at gaseous phase, and adsorbed phase, respectively. The latent heat of adsorption DHads is calculated by applying the Clausius–Clapeyron equation (Teng et al., 1997):   2 @ ln P ð11Þ DH ads ¼ RT @T x where R is the gas constant of the adsorbate; x is the adsorbed mass of refrigerant per unit of adsorbent mass (kg/kg), which is a function of the temperature (T) and pressure (P) of adsorbent bed. It is estimated from the Dubinin–Astakhov (D–A) equation (Dubinin and Astakhov, 1971).  n   P sat Þ ð12Þ x ¼ W 0 ql ðT Þ exp DðT ln P where ql is the density of liquid adsorbate; Wo is the total volume of the micropores accessible to the vapor; D is the coefficient of affinity and n is a characteristic parameter of the adsorption pair. For the pair used in this work, the numerical values of Wo, D and n are given in (Mimet, 1991), which are found to be 0.456  103 m3/kg, 0.53  104 Kn and 1.49, respectively. 3. Combined heat and mass transfer equation in the porous medium The heat and mass transfer equation in the porous medium is obtained by combining the energy balance and mass conservation equations, i.e. Eqs. (8) and (9): h i @T ð1  eÞqs C ps þ ðe  hÞqg C pg þ hqa C pa @t  2  @ T 1 @T @ p þ ððe  hÞqg Þ þ ¼ ke @r2 r @r @t qg    1 p @ma ð13Þ þ þ DH ads @t 2pr dr Lr qa 3.2.3. Boundary and initial conditions To complete the mathematical formulation of the model, the initial and boundary conditions are reported as below:

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 Initial conditions T 1 ðt ¼ 0Þ ¼ T ads ¼ T min and P 1 ðt ¼ 0Þ ¼ P ev ¼ P sat ðT ev Þ for adsorber 1. T 2 ðt ¼ 0Þ ¼ T g2 ¼ T max and P 2 ðt ¼ 0Þ ¼ P con ¼ P sat ðT con Þ for adsorber 2.  Pressure boundary conditions (for both adsorbers): P ðtÞ ¼ P ev=con ; when connected to the evaporator/ condenser.  Temperature boundary conditions (for both adsorbers) r ¼ Ri r ¼ R1

  @T ¼ hgl ðT HTF  T Þ @r r¼Ri   @T ¼0 @r r¼R1  ke

ð14Þ Fig. 2. Climatic data used in the simulation.

ð15Þ

hgl is the global heat transfer coefficient between the HTF and the adsorbent bed. The corresponding thermal resistance Rgl is written as follows: " # lnðDo =Di Þ 1 1 Rgl ¼ 1=2pLr þ Di þ Do ð16Þ kmet hi 2 h e 2 The equivalent thermal conductivity of adsorbent bed ke and the heat transfer coefficient between the bed and metallic tube he were obtained from experimental results (Mimet, 1991). The heat transfer coefficient between the HTF and the metallic tube, hi is calculated with the aid of Dittus–Boelter correlation (Zhu, 1989) for smooth tubes as follows: n hi ¼ 0:023R0:8 e Pr

ð17Þ

where n is a constant. For heating process n = 0.3, while n = 0.4 for cooling process. Besides, the thermodynamic equilibrium properties of the adsorbent/adsorbate are taken from the literature: activated carbon (CHEMVIRON, 1988), ammonia gas (Institut International de froid, 1981) and adsorbed ammonia (Mahamane, 1989), while climatic data that we used in the simulation correspond to the case of a clear type day of July, measured in Tetouan (35°350 N 5°230 W), Morocco (Aroudam, 1992). The hourly diffuse radiation has been calculated from the hourly global radiation, using a correlation available in the literature (Aroudam et al., 1992). The climatic data are reported in Fig. 2. The other input data to the simulation program are shown in Table 1. 3.3. Performance analysis The assessment parameters of the performance of the adsorption refrigerating system considered in this study are the refrigeration cycle COP (COPcycle), the solar coefficient of performance (COPs) and the specific cooling power

(SCP). These parameters are defined by the following formulas: (1) The cycle COP is expressed as: COPcycle ¼

Qc Qabs

ð18Þ

where Qc is the cooling production at the evaporator during adsorption cycle. It is equal to the refrigerant latent heat of evaporation minus the sensible heat to cool down the refrigerant from the condensation temperature to the evaporation temperature:   Z T con C pl dT ð19Þ Qc ¼ mAC D x LðT ev Þ  T ev

Qabs is the heat supplied to the adsorber, namely, the input heat required to heat up (i) the metallic tube of heat exchanger (Q1), (ii) the adsorbent (Q2), (iii) the ammonia (Q3), and (iv) the heat necessary to desorb the differential amount of ammonia (Q4). Qabs ¼ Q1 þ Q2 þ Q3 þ Q4 Z Tg 2 mmet C pmet dT Q1 ¼ Q2 ¼ Q3 ¼ Q4 ¼

T ads Z Tg 2 Tads Z Tg 2 Tads Z Tg 2 T g1

ð20Þ ð21Þ

mAC C pAC dT

ð22Þ

mAC xðT ; P ÞC pl dT Z Tg 2 dx dT mAC hd dx ¼ mAC hd dT T g1

ð23Þ ð24Þ

where hd is heat of desorption, while x(T,P) is the adsorption capacity at T and P. (2) The gross solar coefficient of performance is defined as the ratio between the cooling production and the incident solar energy on the surface of solar collector during the whole day, it is expressed as follows:

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Table 1 Main input data used in the simulation. Symbol

Parameter

Value

Unit

Collector components C Cpmet Cpw do e FR Lc UL W go qmet qw

Concentration ratio Specific heat capacity of the metal Specific heat capacity of water Outer diameter of the receiver tube Tank thickness Collector heat removal factor Collector length Overall heat loss coefficient from the receiver Aperture width of the collector Optical efficiency Density of the metal Density of water

17 0.46 4.196 0.015 0.003 0.90 1.00 8.00 0.80 0.70 7850 974.10

– kJ kg1 K1 kJ kg1 K1 m m – m W m2 K1 m – kg m3 kg m3

Geometric and thermophysical characteristics of adsorber Specific heat of adsorbent Cps Do Inner diameter of adsorbent bed Heat transfer coefficient between the bed and metallic tube he Lr Reactor length Latent heat of ammonia at evaporation temperature (0 °C) L(Tev) s Thickness of the metal heat transfer tube e Porosity of adsorbent bed Equivalent thermal conductivity of adsorbent ke qs Density of adsorbent

0.836 0.04 33.45 0.50 1262.40 0.002 0.71 0.431 500

kJ kg1 °C1 m W m2 K1 m kJ kg1 m – W m1 K1 kg m3

Operating conditions m_ f Tads Tcon Tev vHTF

0.01 297.15 303.15 273.15 0.10

kg s1 K K K m s1

Qc A IðtÞdt sunrise c

COPS ¼ R sunset

Water mass flow rate in the solar collector piping Adsorption temperature Condensing temperature Evaporating temperature Velocity of heat transfer fluid

ð25Þ

(3) The SCP is defined as the ratio between the cooling production and the cycle time per unit of adsorbent mass: SCP ¼

Qc tcycle :mAC

ð26Þ

4. Numerical solution First, Eqs. (1)–(6) are combined in one Eq., and the outlet fluid temperature Tout and the storage tank temperature Tst at any each time are determined by numerical integration of the time derivative. For solving the differential equations related to the adsorbent bed, a numerical method based on both the finite differences technique and a fully implicit scheme is used. The discretized equations are solved using the Tri-Diagonal Matrix Algorithm (TDMA) and the nonlinearity of the equations is solved by iterative techniques. A computer program written in FORTRAN and based on this numerical scheme has been developed in order to simulate the behaviour of the adsorption cooling system.

5. Experimental validation In order to validate the model of heat and mass transfer within the adsorbent, a tubular reactor with a double stainless steel envelope heat exchanger has been used. The inner diameter and length of this reactor were taken to be equal to 53 mm and 250 mm, respectively. Each reactor cover has in its centre a hole, allowing the inlet or outlet of the ammonia gas. The temperature of the thermostat used in the experiment ranged between 20 and 250 °C. The reactor was packed with 274 g of activated carbon particles having a mean diameter of 2 mm; it was heated at isosteric phase by means of thermal oil, which circulates along the 4 mm thickness of the inter-envelope space with a flow rate of 1.5 l/min. It is noted that the AC used in the experience is BPL 4*10 from CHEMVIRON firm (CHEMVIRON, 1988). The experimental set-up employed was described in detail in a previous work (Mimet, 1991). In Fig. 3, we have reported the experimental and model results; this figure depicts the time evolution of predicted and experimental temperatures at three different radial positions inside the reactor (positions 2, 3, and 6). The temperatures were measured using six thermocouples placed in different points listed in Table 2. The comparison between these values shows a good agreement. Therefore, the onedimensional model of heat and mass transfer within the

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adsorbent bed is validated in the isosteric heating phase. However, it is not enough to ensure that the model is valid to describe the full cycle.

formance, such as heat source temperature, and adsorbent bed thickness, are investigated. The simulation results are shown graphically.

6. Results and discussion

6.1. Collector optimization

In this section, a numerical investigation is conducted under the operating and design conditions listed above. The effects of some important parameters on system per-

The effect of mass flow rate on outlet fluid temperature is depicted in Fig. 4. It can be seen that the outlet fluid temperature reduces with an increase in the mass flow rate. The influence of mass flow rate is more pronounced for small values (less than 0.005 kg/s). Under the condition of water mass flow rate in the solar collector piping of 0.01 kg/s, Fig. 5 represents the daily variation of mean water temperature in the heat storage tank (Tst) with different storage tank volumes (Vst). It is observed that Tst increases with a decrease in Vst. From the real climatic data used in the simulation, it can be seen that, with an appropriate choice of storage tank size, tank temperature could satisfy the system from the solar collector for long period of time (roughly between 11:00 and 18:00), i.e. during this period, the tank could provide the adsorbers with the required heating temperature in the range 70100 °C. Under the same condition of water mass flow rate (0.01 kg/s), Fig. 6 shows the effect of the heat storage tank size on both maximum temperature that could be reached in the tank and heat stored in this tank (Qst). The latter is defined as the heat that could be stored in the tank without any heat removal during the day from the start point (sunrise) to the final point, when the tank water reaches its maximum temperature. As expected, the greater the storage tank size the less the maximum temperature of storage tank and the more the heat stored in the tank. It can also be observed that, the optimal size for storage tank would be in the range between 0.02 and 0.05 m3.

Fig. 3. Comparison of the predicted transient temperature distributions with experimental data.

Table 2 Thermocouples positions within the cylindrical adsorber. Thermocouple number, i Radial position, ri (cm) Axial position, zi (cm)

Fig. 4. Effect of mass (Vst = 0.015 m3).

1 0.00 6.00

2 0.00 12.00

3 1.5 12.00

4 2.65 12.00

flow rate on outlet

5 0.00 18.00

6 1.00 18.00

fluid temperature

Fig. 5. Daily variation of mean water-temperature in the storage tank with different tank volumes.

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6.2. Temperature, pressure, and adsorbed mass within the adsorber The heat storage tank temperature (heat source temperature) changes through the day due to the climatic conditions. However, it can be controlled by means of a differential thermostat controller. Thus, the profiles of temperature, pressure, and adsorbed mass in the adsorber are represented, with the working conditions of heat source temperature of 100 °C to generate desorption process, while cooling water temperature is taken as 32 °C to generate adsorption process. Fig. 7 depicts the temperature variation of both adsorbers. It can be observed that, before attainment of thermal equilibrium, there is a significant gradient of temperature

between the layers of adsorbent (activated carbon) in each adsorber. This equilibrium has been reached in adsorber (2) being at cooling-adsorption process for about 30 min, while this lasts roughly 35 min, for the adsorber (1) being at heating-desorption process. Indeed, the speed of temperature variation within the adsorber is an assessment criterion of the heat transfer performance in adsorbent. Fig. 8 shows the Du¨hring diagram of the adsorption refrigeration cycle simulated from the current formalism. In this figure, the temperature refers to the average temperature of all layers of the adsorbent bed. The various processes of a complete cycle are: pre-heating process (1–2), desorption process (2–3), pre-cooling process (3–4), and adsorption process (4–1). The variation of adsorbed mass of adsorbate (ammonia) in the two adsorbent beds is plotted in Fig. 9, it corresponds to the computed values during the processes of isos-

Fig. 6. Variation of maximum tank temperature and heat stored in the tank with storage tank volume.

Fig. 8. Du¨hring diagram of the simulated adsorption refrigeration cycle (R1 = 40 mm; Theat = 100 °C).

Fig. 7. Temperature variation for the two adsorbers with time; Layer 1: r = 20.2 mm; Layer 2: r = 29.8 mm; Layer 3: r = 39.8 mm (R1 = 40 mm; Theat = 100 °C).

Fig. 9. Adsorbed mass variation during isosteric heating-desorption process for adsorber 1 and isosteric cooling-adsorption process for adsorber 2 (R1 = 40 mm; Theat = 100 °C).

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teric heating and desorption for adsorber 1, and isosteric cooling and adsorption for adsorber 2. 6.3. Thickness of adsorbent bed

Fig. 10. Influence of the adsorbent bed thickness on SCP and on COPcycle (Theat = 100 °C).

Fig. 11. Variation of daily cooling capacity and COPs with adsorbent bed thickness (Theat = 100 °C).

In this part, the simulated results have been obtained at Tev = 0 °C, while the heat source temperature and cooling water temperature were taken to be 100 and 32 °C, respectively. The other working conditions are the same as shown in Table 1. The radial thickness of adsorbent bed is an important parameter for system optimization, its influence on specific cooling power (SCP) and refrigeration cycle COP (COPcycle), for values in the range 10–90 mm, is depicted in Fig. 10. It can be seen that the COPcycle remains almost constant when the adsorbent thickness increases. Although a larger thickness of adsorbent means that the cycled refrigerant mass will increase, leading to an increase in the COPconsumed by the adsorber cycle, the heat energy components increases as well (except the heat input to the metal tube), this then would penalize the system performance. On the contrary, the SCP of the adsorption system is very sensitive to the adsorbent thickness variation, i.e., the system is compact with small values of bed thickness. This tendency results because, with a high thickness (high adsorbent mass) the thermal resistance increases. Consequently, the heat exchange rate during the cycle process is reduced contributing to a longer cycle time. As result, a reduction in the SCP. It is evident that, values greater than 40 mm are not recommended. Fig. 11 depicts the variation of daily cooling production and COPs with adsorbent bed thickness. It can be seen that, under a daily direct solar radiation of 14 MJ per 0.8 m2 of collector area (17.5 MJ/m2), the COPs and cooling capacity reduce from 0.18 to 0.082, and from 2515 to 1152 kJ per day and per 0.8 m2 of collector area, respectively, when the bed thickness ranges from 10 to 90 mm. This is because; with higher values of bed thickness the cycle time becomes relatively longer. Therefore, the number of cycles that could be achieved during the collection period from solar energy is reduced. As result, smaller values of daily cooling production and COPs are obtained. 6.4. Heat source temperature

Fig. 12. Effect of the heat source temperature on SCP and on COPcycle (R1 = 40 mm).

In this part, the working conditions are the same as cited in Section 6.3, while the adsorbent bed thickness (R1  Ro) is fixed at 20 mm. Fig. 12 illustrates the simulation results of the influence of heat source temperature (Theat) on the system performance, in the range 60–120 °C. It can be seen that both COPcycle and SCP increase with an increase in Theat. The increase in the driven temperature leads to an increase in the generation temperature, therefore, the cycled mass amount of refrigerant will increase. Hence, the cooling effect will also increase. As result, the COPcycle and SCP will increase. The shortness of the total cycle time,

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Fig. 13. Variation of daily cooling capacity and COPs with heat source temperature (R1 = 40 mm).

caused by the increase of the driven temperature, could also contribute to the improvement of the SCP. However, beyond a certain value of Theat (90–100 °C), the COPcycle remains almost stable. This tendency reflects the fact that the most amount of refrigerant is desorbed at this temperature, and beyond this optimal value, the energy consumed by the adsorber increases only the sensible heat of its components. Fig. 13 describes the variations of daily cooling capacity and gross solar COP with heat source temperature. It can be observed from this figure that both COPs and cooling capacity increase with an increase in Theat, they rise from 0.025 to 0.22, and from 356 to 3030 kJ per day and per 0.8 m2 of collector area, respectively, when the heat source temperature is increased from 60 to 120 °C. The reason is that, at higher heat source temperature, on one hand, the amount of refrigerant circulated increases; on the other hand, the cycle time becomes shorter, resulting in an increase of the number of cycles that could be completed. Consequently, an increase of both daily cooling capacity and COPs is observed. 7. Conclusions The aim of the current work was to present a novel system, in which the solar parabolic trough collector has been introduced to the adsorption refrigeration purpose in order to achieve continuous cycles using two adsorbent beds. A theoretical model based on the heat and mass transfer in the adsorbent, and on the heat balance equations in the collector components has been developed. A computational program was developed in order to simulate the behaviour of the solar adsorption refrigeration system and to optimize its performance. The results shown are logical and coherent with expectations. Through the analysis of the prediction results, a number of conclusions can be drawn as follows:

1. It was found that the variation of the adsorbent bed thickness affects the specific cooling power more than the cycle COP. On the other hand, it was put in evidence that the increase in the heat source temperature would result in an increase in cycle COP, solar COP and specific cooling power. 2. Within the ranges of investigation, simulation results show that the values of optimal performance are obtained at heat source temperatures between 80 and 100 °C, with small radial bed thickness (10–30 mm) and in the range 15–30 m3 for hot water storage tank. 3. Due to its high efficiency, the parabolic trough collector could make possible the achievement of continuous operation of the adsorption system, when combined with the needed components (two beds, hot and cold storage tanks). The obtained results demonstrated the possibility to produce cooling for a long period in a sunny day and, hence to overcome the intermittent character of solar adsorption refrigeration systems. This achievement could be an efficient way of the application of solar energy.

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