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Experimental investigation and mathematical modelling of a solid adsorption refrigeration systemB Ning Meia, Yingchun Xiea, Zhen Xua, Jian Sub,* a

College of Engineering, Ocean University of China, Qingdao 266071, People’s Republic of China b Nuclear Engineering Program, COPPE, Universidade Federal do Rio de Janeiro, CP 68509, Rio de Janeiro, 21945-970, Brazil

Abstract The objective of this work is to study the thermodynamic mechanism and performance of an engine exhaustpowered adsorption refrigeration system using CaCl2 as adsorbent and NH3 as refrigerant. A 6 kW nominal refrigerating capacity adsorption refrigerator was developed. The working performance of the refrigerator is presented. It is concluded that the refrigerating capacity at constant evaporating temperatures varies with the input heat into the generator, and the heat transfer affects strongly the mass transfer in the adsorbent, making it work in different mean generation and adsorption temperatures. A conventional test bed was developed for investigating the properties of CaCl2–NH3 adsorption/desorption unit tube. A mathematical model based on non-equilibrium thermodynamics was developed to describe the performances of the adsorption refrigerating system. D 2004 Elsevier Ltd. All rights reserved. Keywords: Adsorption refrigeration; Unit tube; Heat and mass transfer; Adsorption and desorption; Mathematical modelling; Experimental investigation

1. Introduction Due to increasing concerns with the environmental problems caused by CFCs and the huge energy consumed by conventional refrigeration systems, solid adsorption refrigeration systems driven by midB

Communicated by J.P. Hartnett and W.J. Minkowycz. * Corresponding author. Tel.: +55 21 2562 8448; fax: +55 21 2562 8444. E-mail addresses: [email protected] (N. Mei)8 [email protected] (J. Su).

0735-1933/$ - see front matter D 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2004.06.008

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and low-temperature heat sources have been developed as an economic and environmental friendly alternative [1–9]. Adsorption refrigeration systems have many advantages, such as quiet, cost effectiveness, simplicity in construction, cheap to maintain and, meanwhile, can be directly driven by a low-grade thermal energy such as engine exhaust and solar energy. Therefore, they can be widely used in fishery preservation, air-conditioning or ice-making fields, etc. A 6 kW nominal refrigerating capacity engine exhaust-powered adsorption refrigerator using CaCl2– NH3 pair was developed. The adsorption refrigerator can be used for both refrigeration and air conditioning purposes. The working performance of the refrigerator was investigated. An experimental test bed was built for the investigation of the heat and mass transfer behaviour in the desorption and adsorption processes of the adsorption refrigeration system by using a test unit tube. The adsorption rate of NH3 mainly depends on the temperature, pressure and the saturation level of the adsorbent. We developed a mathematical model for heat and mass transfer in a single tube bed in the adsorption refrigeration system based on the CaCl2–NH3 pair. The mathematical model consists of the energy conservation equation for porous medium in the bed, the adsorption equilibrium equation, the heat conduction equation for the tube wall, and the adsorption dynamics equation. Considering the high thermal conductivity and small thickness of the metallic tube wall, a lumped-capacity model is used to simplify the heat conduction equation for the tube wall. The energy equation for porous medium is solved by a second-order fully implicit finite difference method. A computer program is developed by implementing the numerical solution of the mathematical model.

2. Experimental study of a solid adsorption refrigeration system The construction and assembly of the adsorption refrigeration system performance test bed is illustrated in Fig. 1. The adsorber/generator unit consists of three groups of tube bank based on simple cycle. The evaporator consists of three spirally coiled tubes in a cylindrical vessel of salt water, whose temperature is maintained by an electrical heater, so that an electrical power meter can measure the evaporating temperature and nominal refrigerating capacity. The engine exhaust pipe is connected to the generator by a distribution valve, which can let only one group of the generator heated by engine exhaust

Fig. 1. The testing system of solid adsorption refrigerator. 1: Diesel engine; 2: dynamo meter; 3: distribution valve; 4: throttle; 5: pressure gauge; 6: relief valve; 7: generator; 8: check valve; 9: induction valve; 10: liquid pump; 11: vacuum pump; 12: condenser; 13: evaporator; 14 drain.

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Table 1 Specification of the diesel engine Parameter

Value

Bore Displacement Rated engine speed Rated engine output

180 mm 85.7 L 1000 rpm 1360 kW

while the others are cooled by water. The adsorbent is mixed with another inert material and treated by a special process to cope with the swelling of the CaCl2 grains. The machine has been operated for one cycle to obtain the final value of the adsorbent permeability. The rate of ammonia desorption from adsorbent is measured by a level gauge so that the desorption capacity of this refrigerator can be evaluated. The refrigerating capacity can be calculated by the following equation Z 1 m rdm ð1Þ W ¼ t 0 where m is the amount of adsorbed NH3 liquid, r is the latent heat of evaporation of NH3, t is the adsorption time, W is the refrigerating capacity. The refrigerator parameters and diesel engine specifications are shown in Tables 1 and 2. When the engine works at the nominal condition, it takes several minutes for 2.8 kg ammonia to release from the solid adsorbent, as shown in Fig. 2. The temporal history of NH3 desorption can be divided into three stages. In the first stage, NH3 is released slowly. It could be deduced that the heat from the engine exhaust is mainly used to increase the enthalpy of the solid adsorbent until the pressure in the generator is higher than that in the condenser. After that, NH3 is released rapidly through an endothermic reaction maintained by the heat input from engine exhaust and condensed in the condenser. In the final stage, NH3 is released slowly again at a higher temperature and pressure. At lower engine output, the amount of released NH3 drops down because of the lower input of engine exhaust heat flux. The refrigerating capacity is shown in Fig. 3. With constant adsorption pressure, that is, constant evaporation temperature of ammonia in the evaporator, the released ammonia adsorbs again by adsorbent, but the refrigerating capacity varies periodically. It could be deduced that the ratio of adsorption reaction is influenced by the saturation level of adsorbent; therefore, the refrigerating capacity keeps high at the beginning of the adsorption process when the state of adsorbent is far beyond its saturation state with ammonia, and then the ratio slows down when it tends to saturation. In its working period, desorption and adsorption seems independent if working conditions can be maintained for each Table 2 Parameters of the refrigerator Parameter

Value

Exhaust temperature Refrigerating capacity Size of unit tube Number of generator/adsorber Bank of unit tube

523–623 K 5–8 kW 1 m/ 0.025 m 3 52

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Fig. 2. Performance in the desorption process.

process. The refrigerating capacity, however, is controlled by desorption process, in which sufficient ammonia should be supplied to refrigeration.

3. Experimental study of a single tube adsorbent bed An experimental test bed was built for the investigation of the heat and mass transfer behaviour in desorption and adsorption processes of the adsorption refrigerating system by using a test unit tube, as

Fig. 3. Transient and Mean Refrigerating capabilities.

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Fig. 4. Schematic of the unit tube testing bed. 1: Delivery pipe; 2: adsorbent; 3: pressure gauge; 4: valve; 5: thermometer; 6: condenser/evaporator; 7: isolation vessel; 8: mixer; 9: outside thermocouple; 10: inside thermocouple; 11: middle thermocouple; 12: wall thermocouple; 13: steel shell.

shown in Fig. 4. The unit tube is a 1-m-long steel tube packed with adsorbent particles in a hollow cylinder. The parameters of the testing unit bed are given in Table 3. The unit tube is connected to a cylindrical condenser/evaporator, which is in a cylindrical vessel filled with water. By measuring the time history of the water temperature, the rate of ammonia released from or reabsorbed by the adsorbent during desorption and adsorption processes can be calculated. The reaction pressure in the unit tube was measured by a pressure gauge connected to the unit tube. When forced, uniform axial heat flux passes by the adsorption/desorption unit tube, the adsorbent is heated, and NH3 is released and diffused to the central cylinder hollow, which is then condensed in the condenser/evaporator. The behaviour of the unit tube in the desorption process is shown in Fig. 5. At the beginning, the temperatures on the two sides of the adsorbent increase linearly, and little NH3 is released from the adsorbent. When the temperature in the adsorbent is higher than 350 K, the temperature difference between the two sides of the adsorbent becomes larger and NH3 is released more rapidly. This indicates that the desorption reaction begins in this period, while the reaction heat is provided by the input heat and the temperature grades in the adsorbent become larger. In the final period, the temperature in the adsorbent tends to the same value while the desorption of NH3 stops. Cooling the unit tube, temperature and pressure in the adsorbent drop and NH3 can be readsorbed by the adsorbent when the pressure in the tube is lower than that in the evaporator. With constant adsorption pressure and sufficient cooling flow, the temperature on the inner wall of adsorbent drops while that of Table 3 Parameters of the testing unit tube Parameter

Value

Length Diameter Wall thickness Adsorbent charged Diameter of central void

1m 0.025 m 0.002 m 0.12 kg 0.005 m

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Fig. 5. The behaviour of the unit tube in the desorption process.

the outer wall almost keeps constant. The rate of NH3 readsorbed in the adsorbent is high at the beginning and decreases gradually as the adsorbent tends to the saturation level, as shown in Fig. 6.

4. Mathematical model of the adsorbent bed As observed earlier, the reactions of desorption and adsorption in an adsorption refrigerating system can bring NH3 from a lower temperature and pressure state into a higher temperature and pressure state.

Fig. 6. The behaviour of the unit tube in the adsorption process.

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A mathematical model for the desorption and adsorption processes is established by introducing the following simplifications of the physical problem: (1) desorption and adsorption reactions in the CaCl2–NH3 adsorbent are controlled by the mechanism of non-equilibrium thermodynamics; (2) mass diffusion in the porous media accords with Knudson’s diffusion; (3) NH3 is taken as an ideal gas; (4) the porous packed bed is uniform and has the same physical properties as the adsorbent; (5) thermal–physical properties are constant. 4.1. Energy equation BT ke B BT dX ¼ r þ qs qst qs cps þ X cpl Bt Br dt r Br

ð2Þ

where k is the thermal conductivity of CaCl2, c ps is the specific heat of CaCl2, c pl is the specific heat of NH3, X is the ratio of refrigerant weight to adsorbent weight, the power per unit mass released during the adsorption process, q st, is given by the Clausius-Clapeyron equation Blnp qst ¼ R ð3Þ Bð1=T Þ X 4.2. Mass transfer equation

e

Bqv BX ¼0 m qs Bt Bt

ð4Þ

where e is the ratio of porosity, q v is the density of ammonia gas and U s is the density of CaCl2. 4.3. Reaction kinetics equation According to Sokoda and Suziki [10], the adsorption rate is expressed as a function of the adsorption quantity X as, dX ¼ Ks Xeq X dt

ð5Þ

where X is the instantaneous adsorption quantity, K s is the overall mass transfer coefficient representing the mass transfer resistance in the adsorption process and consisted by internal and external resistences, Ks ¼

15D R2F

ð6Þ

where R F is the average diameter of adsorption particles, D is the mass transfer coefficient. Supposing that the adsorption molecules satisfy the Knudsen diffusion condition in the micro-channels of adsorption, the mass transfer coefficient can be determined as follows rﬃﬃﬃﬃﬃ T D ¼ 9700rF M

ð7Þ

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where T is the temperature of diffusion mass, M is the molecular weight of the adsorption substance, r F is the average radius of the micro-holes in the adsorption particles, given by 2VF 2eF ¼ ð8Þ rF ¼ St S t qF where V F is the volume of the hole, q F is the density of the particle, S t is the total surface area of the adsorption particle. 4.4. Tube wall equation The energy equation for the wall is written as mw c pw

BTw ¼ S o h fw Tf Tw S i h ws ðTw T Þ Bt

ð9Þ

where S o is the outer surface area of the single tube, S i is the inner surface area of the single tube, h fw is the heat transfer coefficient between the wall and the external heating or cooling fluid, h ws is the heat transfer coefficient between the wall and the adsorption particles. 4.5. Ideal gas equation of state ð10Þ

p ¼ qv RT 4.6. Initial conditions p ¼ po

for

T ðr; 0Þ ¼ T0

t¼0 for

t¼0

X ¼ X eq ðT0 ; p0 Þ for

t¼0

ð11Þ

4.7. Boundary conditions

BT ¼ 0 at Br

r ¼ R is

BX ¼ 0 at Bt

r ¼ R is

p ¼ pc

at

r ¼ Ris

ð12Þ

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and during the adsorption process T ¼ Te

at

BX ¼ 0 at Bt p ¼ pe

at

r ¼ Ris r ¼ Ris r ¼ Ris

ð13Þ

On the external boundary of the adsorption bed, the boundary conditions are given by ke

BT ¼ h ws ðTw T Þ; Br

p ¼ pc

at

at

r ¼ R os

r ¼ R os

ð14Þ

and during the adsorption process ke

BT ¼ h ws ðTw T Þ; Br

p ¼ pe

at

at

r ¼ R os

r ¼ R os

When desorbing, the desorbed ammonia is given by Z t dX qs dt m¼ dt 0 When adsorbing, the refrigerating capacity of the ammonia is given by Z 1 t dX W ¼ dt rqs t 0 dt

ð15Þ

ð16Þ

ð17Þ

Figs. 7 and 8 show the temperature distribution in the adsorption bed predicted by the numerical solution of the mathematical model. The temporal variations of temperature at several radial positions are shown in Fig. 7, while radial distributions of temperature at different times are shown in Fig. 8. The temperature gradient along the radial direction is due to the low thermal conductivity of the adsorption bed of CaCl2, usually 0.1–0.3 W/(mK). We can see that the maximum temperature difference across the adsorption bed may reach 30 8C, which decreases during the desorption process to around 10–30 8C. The temperature gradient is smaller during the adsorption process than during the desorption process. Fig. 9 shows the relative desorption ratio of ammonia as a function of time in the desorption process, which is strongly affected by the thermal conductivity of the adsorbent. It can be seen that when the thermal conductivity is increased from 0.1 W/(mK) to 5 W/(mK), the occurrence of desorption is delayed. However, the desorption period is reduced, being about 1/3 of the original period, which is

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Fig. 7. Temperature history in the adsorption bed.

helpful in reducing the period of the refrigeration cicle and increasing the average refrigerating capacity of the adsorption refrigeration system.

5. Conclusion In this paper, the performance of a solid adsorption refrigerator was studied, and the heat and mass transfer characteristics in the adsorbent bed during desorption and adsorption processes were investigated experimentally and numerically. As it is difficult to obtain the same parameters for experimental and numerical works, we can only compare relevant parameters. It is concluded that the refrigerating capacity at constant evaporating temperatures varies with the input heat into the generator,

Fig. 8. Radial distributions of temperature in the adsorption bed.

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Fig. 9. Relative ratio of adsorption as a function of time.

and the heat transfer affects strongly the mass transfer in the adsorbent, making it work in different mean generation and adsorption temperatures. The desorption reaction and its thermodynamic state can be controlled by input heat flux and heat and mass transfer properties of adsorbent. The engine exhaust temperature and the heat flux are the controllable parameters to the performance of a given adsorption refrigerating system. By increasing the exhaust temperature and the heat flux, the efficiency of the system can be improved. The increasing of thermal conductivity of the adsorbent is important to reduce the period of the refrigeration cicle and to increase the average refrigerating capacity of the adsorption refrigeration system. Acknowledgements The authors are grateful to the Science and Technology Agency of Qingdao, People’s Republic of China, the Brazilian National Research Council (MCT/CNPq) and the Ministry of Education of Brazil (MEC/CAPES) for the financial support during the realisation of the work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

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