The influence of heat exchanger parameters on the optimum cycle time of adsorption chillers

Applied Thermal Engineering 29 (2009) 2708–2717

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

The influence of heat exchanger parameters on the optimum cycle time of adsorption chillers Takahiko Miyazaki *, Atsushi Akisawa Institute of Symbiotic Science and Technology, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei-shi, Tokyo 184-8588, Japan

a r t i c l e

i n f o

Article history: Received 1 September 2008 Accepted 6 January 2009 Available online 20 January 2009 Keywords: Adsorption chiller Cooling capacity Optimization Coefficient of performance Silica gel

a b s t r a c t The research investigated the influences of heat exchanger parameters, such as heat capacity and NTU, on the optimum performance of a single-stage adsorption chiller. Silica gel–water pair was chosen as the adsorbent–adsorbate combination so that low temperature heat source under than 100 °C could be utilized as the driving force. The mathematical model of the adsorption chiller using dimensionless parameters was developed and a global optimization method called the particle swarm optimization was applied in the simulation to obtain the optimum cycle time. The results showed that the smaller heat capacity heat exchanger improved both the maximum specific cooling capacity (SCC) and the COP. While, the larger NTU of the adsorbent bed resulted in the decrease of the COP due to the short cycle time although the maximum SCC was enhanced. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Adsorption chillers are environmentally friendly because they employ natural refrigerant. In addition, the adsorption chillers can enhance the efficiency of energy systems if they are driven by waste heat or by renewable energy. Because of the increased attention to the ozone layer depletion and the global warming, the adsorption refrigeration has been intensively studied for the past few decades. The major adsorbent–adsorbate pairs for air conditioning purposes are zeolite–water, activated carbon–ammonia, silica gel– water and so on. Among them, silica gel–water is a suitable and useful pair for most of the applications under than 100 °C. There are examples of the commercialized adsorption chillers using silica gel–water pair with the driving temperature of as low as 70 °C in Japan [1]. The minimization of the size per cooling capacity and the increase of the coefficient of performance (COP) as well as the reduction of the production cost are, however, necessary to make the adsorption chillers competitive in the market. To improve the cooling performance and/or to lower the driving temperature, some variations of adsorption refrigeration cycles have been proposed such as heat and mass recovery cycles [2,3], multi-stage cycles [4,5], multi-bed cycles [6–8]. It was presented that these advanced cycles would achieve better performances compared with that of the conventional two-bed, single-stage adsorption chiller. On the other hand, additional adsorbent beds

* Corresponding author. Tel./fax: +81 42 388 7282. E-mail address: [email protected] (T. Miyazaki). 1359-4311/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2009.01.005

and heat exchangers of the advanced cycles could result in the increase of production cost and the enlargement of chiller size. The two-bed, single-stage adsorption chiller is the basic configuration of the adsorption chiller that produces continuous cooling effect. The influences of the heat exchanger design and the operating conditions on the performance of the adsorption chiller have been investigated experimentally and numerically. Cho and Kim [9] studied a silica gel–water adsorption chiller with the driving temperature at 85 °C using a simulation model validated by the comparison with experimental data. The effects of the overall thermal conductance (UA value) on the cooling capacity and on the cycle time were presented. Saha et al. [10] and Boelman et al. [11] analyzed the performance of the waste heat driven adsorption chiller by simulation and experiment. A commercially available adsorption chiller was used for the experiment, and the mathematical model was developed to simulate their adsorption chiller. They showed that the cooling capacity was maximized at the adsorption time of around 300 s, and the COP was increased with the longer adsorption time. Chua et al. [12] also studied the effects of the adsorption time as well as the switching time on the cooling capacity and on the COP. They developed the transient distributedparameter model, which gave better agreement with the experimental data compared with the lumped-parameter model. It was shown that the cooling capacity was high at the adsorption time between 300 and 600 s. It was also observed that the cooling capacity was maximized at the switching time of 35 s. From the viewpoint of the physical design of the adsorption chiller, it is also important to study the effects of heat exchanger parameters on the performance. The optimization of the design of a zeolite–water adsorption heat pump was performed by van

T. Miyazaki, A. Akisawa / Applied Thermal Engineering 29 (2009) 2708–2717

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Nomenclature A C C* cp CC COP D Ea DHad DHev km _ m M N NTU Ps R Rs SCC t T U

heat transfer area, m2 water content of the adsorbent, kg kg1 water content at the adsorption equilibrium, kg kg1 specific heat, J kg1 K1 cooling capacity, W coefficient of performance surface diffusivity, m2 s1 activation energy, J mol1 adsorption heat, J kg1 latent heat of refrigerant, J kg1 overall mass transfer coefficient, s1 mass flow rate, kg s1 mass, kg the number of the adsorbent beds   UA the number of heat transfer units ¼ mc _ p vapor pressure, Pa universal gas constant, J mol1 K1 average radius of the adsorbent, m specific cooling capacity, W/kg time, s temperature, K overall heat transfer coefficient, W m2 K1

Greek letters a heat capacity ratio b latent to sensible heat ratio c enthalpy ratio  heat exchanger effectiveness k latent heat ratio

Benthen et al. [13]. The effects of some heat exchanger parameters such as the heat transfer area and the heat capacity were analyzed and the average power of the system was increased by the optimization. The influence of the heat transfer coefficient of the adsorber was also studied. It was shown that the average power was increased and the cycle time was shortened by the enhancement of the heat transfer coefficient. Cacciola et al. [14] studied the influence of the heat capacity ratio, which was defined as the ratio of the heat capacity of the adsorber’s metallic part to the heat capacity of the adsorbent, on the COP and on the specific power. The results showed that the COP and the specific power decreased with the increase in the heat capacity ratio. Saha et al. [8] chose the overall thermal conductance, which was equal to the UA value, and the adsorbent-to-adsorber inert material heat capacitance ratio, which was the inverse of the heat capacity ratio used by Cacciola et al., as parameters for the investigation of a three-bed adsorption chiller. They elucidated the influences of these parameters on the performance, and concluded that the overall performance of the chiller could be improved by increasing the heat capacitance ratio, but there was not much benefit in going higher values than that used in current, commercialized machines. Alam et al. [15,16] investigated the effects of the heat exchanger design on the performance of the silica gel–water adsorption chiller. The optimum switching frequency was presented by parametric analyses. Following Alam et al., Voyiatzis et al. [17] analyzed the effects of heat exchanger design and switching frequency on the performance of their novel adsorption chiller using a similar technique. Cerkvenik and Ziegler [18] used another technique for the optimization of adsorption heat pump cycles in terms of COP and heat exchange area. They showed the relation between the maximum COP and the required heat exchange area with taking into consideration the effect of cyclic operation.

l n

x h

s /

mass ratio mass flow ratio switching frequency dimensionless temperature dimensionless time dimensionless water content

Superscripts a adsorption process d desorption process Subscripts b adsorbent bed c condenser ca cooling water for the adsorbent bed cc cooling water for the condenser ch chilled water e evaporator h hot water hc half cycle i inlet m metallic part of the heat exchanger o outlet s silica gel rw refrigerant in liquid phase rv refrigerant in gas phase w heat transfer medium

Most of the precedent researches were based on parametric runs of chosen parameters. It is usual, however, that several parameters depend on others, such as adsorption time and switching time, and multiple variables have to be optimized at the same time. Therefore, our study uses a global optimization method called the particle swarm optimization (PSO), which controls all variables simultaneously to search the optimum point. The main purpose of our research is to maximize the specific cooling capacity (SCC) of the silica gel–water adsorption chiller by optimizing the heat exchanger design and the operating conditions. In addition to that, we intend to obtain design guidelines of the adsorption chiller, which is independent of the chiller size in terms of cooling capacity. For these purposes, the lumped-parameter model of a commercial-based adsorption chiller is modified to represent the equations using dimensionless parameters. By the dimensionless form of the mathematical model, the influence of the adsorbent mass can be eliminated and the model gives a consistent SCC and COP irrespective of the adsorbent mass. Then, the influence of the dimensionless parameters of heat exchanger design is discussed from the viewpoint of the optimum cycle time, the maximum specific cooling capacity, and the COP. 2. The mechanism of the adsorption chiller and the cycle time allocation 2.1. The mechanism of the adsorption chiller The components and the operation of the adsorption chiller are illustrated in Fig. 1. The chiller consists of two adsorbent beds, a condenser, and an evaporator. In Fig. 1a, the adsorbent bed 1 is in the desorption process, and the adsorbent bed 2 is in the adsorption process. In the adsorption process, the refrigerant evaporates

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Fig. 1. The schematics of the two-bed, single-stage adsorption chiller.

in the evaporator, which causes the cooling due to the removal of heat from the chilled water. The refrigerant vapor is adsorbed by the adsorbent with the release of the adsorption heat. The adsorption heat has to be eliminated from the adsorbent bed by the cooling water to maintain the relative pressure in the adsorbent bed at a high level. In parallel with the adsorption process in an adsorbent bed, the desorption process is carried out in the other bed. The adsorbent bed in the desorption process is heated by the hot water and releases the refrigerant stored in the adsorbent. The refrigerant is transferred to the condenser, and it turns into the liquid phase by the discharge of the condensation heat to the cooling water. Then, the refrigerant liquid travels to the evaporator through the U-shape pipe or the expansion valve with reducing its pressure. To generate continuous cooling effect, two adsorbent beds alternately execute the adsorption process. Before the adsorbent beds change the processes, the switching process is usually carried out to make the pressure in the adsorbent beds closer to the connection targets. During the switching process, sensible heating and cooling of the adsorbent beds are carried out. As shown in Fig. 1b, the adsorbent bed 1, which completed the desorption process, is cooled down by the cooling water, and the adsorbent bed 2, which completed the adsorption process, is heated up by the hot water. There is no refrigerant transfer during the switching process. 2.2. The time allocation of the adsorption and switching processes The cycle time allocation is illustrated by the time chart shown in Fig. 2. The cycle consists of four operational modes. The time length of the modes A and C is called the adsorption time, and that of the modes B and D is called the switching time. The sum of the time lengths of the four operational modes can be called the cycle time. The adsorption time obviously affects the cooling performance of the adsorption chiller because the cooling effect is obtained during the adsorption process.

Fig. 2. The time chart of the adsorption chiller operation.

The cooling effect gradually diminishes as the adsorption process progresses because the water content of the adsorbent approaches the equilibrium. The switching time is also influential on the performance of the adsorption chiller because of the following reasons. First of all, there is no cooling effect during the switching process. Therefore, the excess switching time reduces the average cooling capacity of the cycle. Second, short switching time depresses the heat exchange performance of the adsorbent bed due to the large temperature difference between the adsorbent bed and the heat transfer medium at the beginning of the adsorption process. Finally, if the switching time is too short, the reversed refrigerant flow will occur from the condenser to the adsorbent bed, or from the adsorbent bed to the evaporator. 2.3. The theoretical adsorption cycle and the theoretical COP Fig. 3 shows the theoretical adsorption cycle on a P–T diagram. During the desorption and adsorption processes, the water content of the adsorbent changes under constant pressure (a?b and c?d). While, the role of the switching process is the sensible heating and cooling, and it is shown as pressure and temperature change under constant water content (b ?c and d?a). The practical cycle of the adsorption chiller can approach to the theoretical cycle when the adsorption time is sufficient to achieve the minimum and the maximum water contents given at b and d, and the switching time is appropriate for temperature changes from b to c and from d to a. Provided that there is no heat recovery processes, a theoretical COP of the adsorption cycle can be defined as the ratio of the latent cooling energy of refrigerant to the sum of the heat input during the switching and the desorption processes. Therefore,

Ms DHev ðC max  C min Þ M s DHad ðC max  C min Þ þ M s cps ð1 þ ab ÞðT h  T ca Þ k ¼ 1 þ ð1 þ ab Þð1=bÞ

COPth ¼

ð1Þ

where Ms is the mass of the adsorbent, and cps is the specific heat of the adsorbent. Cmax and Cmin are the maximum and the minimum water contents, respectively. Th and Tca represent the temperatures of the driving heat source that is the hot water to the desorber and of the coolant that is the cooling water to the adsorber, respectively. DHev and D Had are the latent heat of the refrigerant and the adsorption heat of the adsorbent, respectively. ab, b and k are the heat

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Fig. 3. The theoretical adsorption cycle on a P–T diagram.

Table 1 The definitions of the dimensionless parameters. Parameter

Definition

Meaning

Source

Heat capacity ratio Refrigerant heat capacity ratio Latent to sensible heat ratio Enthalpy ratio

a ¼ MMms ccpm ps arw = cprw/cps

The ratio of the heat capacity of the metallic part of the heat exchanger to that of the adsorbent The ratio of the heat capacity of the liquid refrigerant to that of the adsorbent

[23] [23]

The ratio of the adsorption heat of the ideal adsorption process to the heat required for the maximum temperature change of the adsorbent The ratio of the enthalpy of the refrigerant liquid at temperature T to the adsorption heat

[23]

Heat exchanger effectiveness Latent heat ratio

 = 1  eNTU

The heat exchanger effectiveness in case of

k ¼ DDHHeadv

The ratio of the latent heat of the refrigerant to the adsorption heat

[23]

Mass ratio

l ¼ MMrws

The ratio of the mass of the refrigerant liquid to that of the adsorbent

[25]

Mass flow ratio

n¼

The ratio of the mass flow rate of the reference heat exchanger to that of the hot water

[25]

The ratio of the heat capacity of the adsorbent to that of the heat transfer medium during the half cycle time

[23]

Switching frequency

max C min Þ b ¼ DHcadpsðC ðT h T ca Þ

T c ¼ cDprw Had

_ ref m _h m

x¼

M s cps _ h cpw t hc m

capacity ratio of the adsorbent bed, the latent to sensible heat ratio, and the latent heat ratio, the definitions of which are given in Table 1. It is obvious from Eq. (1) that larger ab and smaller b are responsible for lower theoretical COP.

3. The mathematical model of the adsorption chiller The temperature variations of the heat exchangers were predicted by the lumped-parameters model. The model was based on the following assumptions.  The temperature and pressure distributions in the heat exchangers are uniform.  The refrigerant can be uniformly adsorbed by the adsorbent.  The heat exchangers are well-insulated, and there is no heat loss to the surroundings.

3.1. Energy balance and mass balance equations The energy balance equations of the adsorbent bed, condenser, and evaporator are given in Eqs. (2)–(5) as below:

cpmin cpmax

!0

– [24]

  dT d b _ h cpw ðT h;i  T h;o Þ M s cps þ Ms cprw C db þ M b;m cpb;m ¼m dt   dC d þ DHad  cprw T db M s b dt   dT ab a _ ca cpw ðT ca;i  T ca;o Þ ¼m Ms cps þ M s cprw C b þ Mb;m cpb;m dt   dC a þ DHad  cprw T ab Ms b dt dT c _ cc cpw ðT cc;i  T cc;o Þ ¼m ðM c;rw cprw þ Mc;m cpc;m Þ dt d dC  ðDHev  cprw T c ÞMs b dt a dC b þ cprw T e M s dt dT e _ ¼ mch cpw ðT ch;i  T ch;o Þ ðM e;rw cprw þ Me;m cpe;m Þ dt a dC  ½DHev  cprw ðT c  T e ÞM s b dt

ð2Þ

ð3Þ

ð4Þ

ð5Þ

where T represents temperature in Kelvin, and C represents water _ and cp are mass in kg, mass flow rate in content in kg/kg. M, m, kg/s, and specific heat in J/kg K, respectively. The superscripts a

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and d indicate adsorption and desorption, respectively. The denotations of the subscripts are given in the nomenclature. The mass balance of the refrigerant can be expressed by Eq. (6) after neglecting the mass of the refrigerant in the gas phase. a

d

dM c;rw dM e;rw dC b dC b þ þ Ms þ dt dt dt dt

! ¼0

ð6Þ

We assumed that the amount of the refrigerant liquid in the evaporator could be constant by controlling the mass flow rate from the condenser to the evaporator. Therefore, (dMe,rw/dt) equals zero. 3.2. The adsorption rate and the adsorption equilibrium The adsorption rate of the silica gel–water combination was modeled by Sakoda and Suzuki [19] as

dC ¼ km ðC   CÞ dt

ð7Þ

The overall mass transfer coefficient, km, was estimated by Eqs. (8) and (9).

km ¼

15D

ð8Þ

R2s

  Ea D ¼ D0 exp  RT

ð9Þ

where D represents the surface diffusivity. D0 is a constant, and is given as 2.54  104 m2/s. Ea represents the activation energy of surface diffusion, and is given as 4.20  104 J/mol. R is the universal gas constant and equals 8.314 J/mol K. The water content at the adsorption equilibrium, C*, is predicted by Eq. (10), which gives an approximation curve of the adsorption equilibrium of type A silica gel [20].

0:8½Ps ðT rv Þ=Ps ðT b Þ C ¼ 1 þ 0:5½Ps ðT rv Þ=Ps ðT b Þ 

ð10Þ

where Ps(T) represents the vapor pressure at temperature T. 3.3. Performance indices The average cooling capacity, CC, of the cycle and the COP are given in Eqs. (11) and (12).

CC ¼

_ ch cpw m

R thc 0

ðT ch;i  T ch;o Þdt thc

R _ ch cpw 0thc ðT ch;i  T ch;o Þdt m COP ¼ R _ h cpw 0thc ðT h;i  T h;o Þdt m

ð11Þ ð12Þ

where thc denotes the half cycle time. The specific cooling capacity, SCC, is defined as the average cooling capacity per unit mass of the adsorbent, as given in Eq. (13).

CC SCC ¼ Ms N

ð13Þ

where N represents the number of adsorbent beds. In our case, N = 2. 3.4. Validity of the mathematical model The model has been used for the prediction of the performance of the silica gel–water adsorption chiller. Saha et al. compared the heat balances of the heat exchangers between the calculated results by a similar mathematical model and the experimental results of the three-stage adsorption chiller [4].

They revealed that the differences between the calculation and the experiment were by 5% for both the evaporator and the condenser, by 7% for the adsorber, and by 15% for the desorber. Alam et al. also examined the validity of the model [21]. They observed that the outlet temperatures of the heat transfer media from the adsorbent beds differed by 15% between the calculation and the experiment at the beginning of the cycle. The temperature variations, however, qualitatively matched. Miyazaki et al. [22] compared the SCC and the COP between the simulation and the experiment for their adsorption chiller. It was shown that the simulation results and the experimental results showed the same tendency in terms of the SCC and the COP. In addition, the differences between the simulation and the experimental results were within 10% for both the SCC and the COP. The difference between the simulation and the experiment could be due to the heat losses from the casings of the heat exchangers and the pipes to the surroundings. We, therefore, concluded that the model was acceptable for the qualitative analysis of the performance. 3.5. Modified equations using dimensionless parameters Eqs. (2)–(7) were rewritten using dimensionless parameters listed in Table 1. In addition, the dimensionless temperature, the dimensionless water content, and the dimensionless time were defined by Eqs. (14)–(16), respectively.

T  T ca T h  T ca C  C min /¼ C max  C min t s¼ t hc h¼

ð14Þ ð15Þ ð16Þ

The maximum and the minimum water contents, Cmax and Cmin, were determined by the adsorption equilibrium corresponding to the relative pressure of Ps(Tcc)/Ps(Th) for the minimum and to the relative pressure of Ps(Tch,o)/Ps(Tca) for the maximum. Then, the dimensionless water content, /, represents a normalized value of the water content between the theoretical maximum and the minimum, while the water content, C, represents the mass ratio of adsorbed water to a dry adsorbent. Using Eqs. (2)–(7), (14)–(16) yields:

dhdb h ð1  cb Þb d/db ¼ ð1  hdb Þ þ ds xpb pb ds dhab nca ca a ð1  cb Þb d/ab ¼ h þ ds xpb b pb ds dhc ncc cc ðk  cc Þb d/db ce b d/ab ¼ ðhcc;i  hc Þ  þ ds xp c pc ds pc ds dhe nch ch ðk  cc þ ce Þb d/ab ¼ ðh  h Þ  ds xpe ch;i e pe ! ds a d dlc d/b d/b ¼ ðC max  C min Þ þ ds ds ds d/b ¼ jð/  /b Þ ds

ð17Þ ð18Þ ð19Þ ð20Þ ð21Þ ð22Þ

where pb = 1 + ab + arwCb, pc = ac + arwlc, and pe = ae + arwle. j represents the multiplication of the overall mass transfer coefficient and the half cycle time, kmthc. By the dimensionless form of the mathematical model, the influence of the adsorbent mass can be eliminated from the performance indices, namely, the SCC and the COP. Specifically, the SCC and the COP are constant under fixed heat capacity ratio, NTU, and switching frequency even if the adsorbent mass is varied.

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4. The optimization method

Table 3 The nominal operating conditions.

The adsorption time, the switching time and the mass flow rate of the chilled water were optimized using the particle swarm optimization (PSO) [26]. The mass flow rate of the chilled water was a variable to control the average outlet temperature of the chilled water. The SCC was optimized under the constraint of the average outlet temperature of the chilled water. The PSO is a technique categorized in metaheuristics. It can find a quasi-optimal solution by iterative calculations, and it is useful to optimize the model with non-linear calculations for engineering purposes. The algorithm of the PSO starts the search for the optimum solution with randomly distributed particles within a range preset. Each particle holds the values of the variables, which are the adsorption time, the switching time and the chilled water mass flow rate, as well as the objective function value that is the sum of the SCC and a penalty value. Then, the particles update the values of the variables by sharing information on the best value achieved so far with other particles. Finally, all the particles hold the optimum solution after the updating for generations. In our case, the optimum solution was found within 3000 generations using 20 particles. The particles in a 3-dimensional space will be visualized in the next chapter.

Adsorbent beds Hot water inlet temperature Hot water mass flow rate Cooling water inlet temperature Mass flow ratio of the cooling water

Th,i _h m Tca,i nca

85 °C 1.0 kg/s 30 °C 1.0

Condenser Cooling water inlet temperature Mass flow ratio

Tcc,i ncc

30 °C 1.2

Tch,i Tch,o

14 °C 9 °C

5. Results and discussion

The maximum SCC Optimum solutions Adsorption time Switching time Mass flow ratio of the chilled water (nch) COP at the maximum SCC

5.1. The maximum SCC at the basic heat exchanger design The heat exchanger parameters of the basic design, the nominal operating conditions, and the thermal properties of water and silica gel are given in Tables 2–4. The basic design followed the commercial adsorption chiller used by Boelman et al. [11]. The value of the heat capacity ratio of the adsorbent bed, ab, is based on a finand-tube type heat exchanger. The NTU values and the mass flow rates of the heat transfer media give UA values of heat exchangers as 4.34 kW/K, 12.0 kW/K, and 4.33 kW/K for the adsorbent beds, the condenser, and the evaporator, respectively. 5.1.1. The results of the PSO and the optimum solution The search of the optimum solution was performed within the range from 100 s to 1000 s for the adsorption time and from 10 s to 100 s for the switching time. The optimum solution at the nominal operating conditions with the basic heat exchanger design is summarized in Table 5. Fig. 4a shows all particles that satisfied the constraint in a 3-dimensional space. The optimum combination of the adsorption time and the switching time was 453 s and 40 s as the particles that hold these values achieved the highest SCC. The sectional views at the switching time of 40 s and at the adsorption time of 453 s are given in Fig. 4b and c, respectively, to show the optimum point clearly. Table 2 The basic heat exchanger design. Adsorbent beds Silica gel mass Heat capacity ratio Number of heat transfer units Condenser Heat capacity ratio Number of heat transfer units Mass ratio Evaporator Heat capacity ratio Number of heat transfer units Mass ratio

Ms

ab NTUb

ac NTUc

lc ae NTUe

le

47 kg 1.8 1.0 0.22 2.3 0.5 0.11 1.7 0.5

Evaporator Chilled water inlet temperature Chilled water outlet temperature a

a

Average over the cycle time.

Table 4 The thermal properties of water and silica gel. Specific heat of water Specific heat of silica gel Latent heat of water Adsorption heat of silica gel

4180 924 2.5  106 2.8  106

J/kg K J/kg K J/kg J/kg

Table 5 The optimum solution at the basic heat exchanger design. 135.4 W/kg 453 s 40 s 0.59 0.58

To confirm the optimum obtained by the PSO, parametric runs of simulation were carried out and the results are also depicted in Fig. 4b and c. The particles that satisfied the constraint were on the curves obtained by the parametric runs, which means that the PSO searched the optimum solution on the curved surface that gave SCC as a function of the adsorption time and the switching time. It was also observed that the SCC increased rapidly to the maximum and decreased moderately from the maximum with the increase of the adsorption time. While, the slope around the optimum was gentle with the increase of the switching time. 5.1.2. The effect of the adsorption time on the water content Because the water content of adsorbent was strongly connected with the adsorption time, the variations of water content with dimensionless time were compared between the optimum solution case and non-optimum solution cases. The solutions A and B depicted in Fig. 4b were chosen as representatives of the non-optimum solution cases, and the variations of water content during the adsorption and desorption processes are illustrated in Fig. 5. The theoretical maximum and minimum water contents were predicted from the P–T diagram, and are also shown in Fig. 5 as the lines at 0.19 kg/kg and at 0.057 kg/kg, respectively. The results showed that the water content at the end of the adsorption process was much lower than the theoretical maximum water content in the optimum solution case. With prolonged adsorption time, such as given in the solution B, higher water content could be achieved at the end of the adsorption process, and cumulative cooling energy would be increased. As the desorption progresses faster than the adsorption due to higher adsorbent temperature, the energy input for desorption becomes minimal before the adsorption process is in saturation. Hence, the longer adsorption time results in the higher COP as long as the adsorbent is capable of adsorbing refrigerant. The COP approaches to the theoretical

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(a)The particles in a 3-dimensional space 150

150 The optimum (135.4 W/kg)

Plane A

The optimum (135.4 W/kg)

140 130

130

120

Solution A (129.1 W/kg)

110 100

Solution B (123.0 W/kg)

90 80

60 100

200

300

400

500

600

700

120

Solution C (131.8 W/kg)

110 100

Solution D (132.5 W/kg)

90 80

Parametric run of simulation Particles of the PSO

70

SCC [W/kg]

SCC [W/kg]

Plane B

140

Parametric run of simulation Particles of the PSO

70

800

900 1000

60 10

20

30

40

50

60

70

80

90

Adsorption time [s]

Switching time [s]

(b)The particles on the plane A

(c)The particles on the plane B

100

Fig. 4. The particles and the optimum solution.

tion time should be much shorter compared with that to achieve the theoretical COP because average cooling capacity over the cycle time would decrease with longer adsorption time. In contrast to the adsorption process, the water content at the end of the desorption process was sufficiently close to the theoretical minimum water content. The reason can be explained by the difference of mass transfer speed in adsorption and desorption. The mass transfer coefficient in the desorption process is larger than that in the adsorption process because of higher adsorbent temperature. Therefore, the adsorbent can desorb the refrigerant up to the theoretical minimum with relatively short time.

0.20

Water content, C [kg/kg]

0.18

The optimum Solution A Solution B

Theoretical maximum

0.16 0.14 Adsorption

0.12 0.10 0.08 0.06 0.04

Theoretical minimum

0.02 0.00 0.0

Desorption

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Dimensionless time, τ Fig. 5. The variations of the water content with dimensionless time for the optimum solution (adsorption time = 453 s), the solution A (adsorption time = 309 s), and the solution B (adsorption time = 783 s).

COP given in Eq. (1) by the adsorption time with infinity because the water contents approach to the theoretical maximum and the minimum. In terms of the SCC maximization, however, the adsorp-

5.1.3. The effect of the switching time on the adsorbent bed temperature The variations of the adsorbent bed temperature of the optimum solution case and non-optimum solution cases are compared in Fig. 6. The non-optimum solutions are the solutions C and D in Fig. 4c, where the switching times are 18 s and 66 s, respectively, with the adsorption time of 453 s. During the switching process, the adsorbent beds are sensibly heated or cooled under the constant water contents. Theoretically, the adsorbent bed pressures should equal the condenser and the

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T. Miyazaki, A. Akisawa / Applied Thermal Engineering 29 (2009) 2708–2717

800

90 80

Desorption

70

700

Sensible cooling

Theoretical end of sensible heating

60 50

Theoretical end of sensible cooling

40 30 20 0.0

Adsorption

0.1

0.2

0.4

0.5

0.6

0.7

0.8

0.9

500 400 300 Th = 75ºC Th = 85ºC Th = 95ºC

200 100

Sensible heating

0.3

600

0 0.6

1.0

0.8

1.0

Dimensionless time, τ

evaporator pressures at the end of the sensible heating and cooling processes, respectively. In this respect, the theoretical end of the sensible heating and that of the sensible cooling can be determined by the combination of the water content after adsorption process and the condenser pressure, and by the combination of the water content after desorption process and the evaporator pressure, respectively. The temperatures at these theoretical ends are also given in Fig. 6. The results revealed that the bed temperatures at the end of the switching process (s = 1.0) in the optimum solution case were closest to the theoretical end temperatures among the three solutions shown in Fig. 6. In case of the solution C, the bed temperatures were still far from the theoretical ends, which would cause inefficient adsorption and desorption in the beginning of the adsorption process. In case of the solution D, the bed temperature exceeded the theoretical ends, and the cooling effect would be depressed by the over-cooling/heating. 5.2. The influence of the operating conditions The optimum half cycle times at different hot water temperatures and at different mass flow rates of the heat transfer media to the adsorbent beds were investigated. When mass flow rate was varied, the NTU of the adsorbent beds was also changed so that the UA value of the adsorbent beds kept constant. The NTU is inversely proportional to the mass flow rate under the constant UA value. Fig. 7 shows the optimum half cycle time with the variation of the mass flow rate. The length of the optimum switching time was about 8–9% of the half cycle time for every optimum solution. The optimum half cycle time was decreased with the larger mass flow rates because the larger mass flow rates could produce higher cooling power. The higher hot water temperature also caused the increased cooling power, which resulted in the shorter optimum half cycle time at the hot water temperature of 95 °C. The maximum SCC and the COP at the maximum SCC are depicted in Fig. 8. The maximum SCC was magnified by the larger mass flow rate and the higher hot water temperature because of the increased cooling power. Contrary to the effect of the mass flow rate on the maximum SCC, the COP was declined when the mass flow rate was increased. This is because of the shorter half cycle time at the larger mass flow rate. As discussed in the previous section, the longer cycle time causes the better COP. In addition to that, the heat exchanger effectiveness of the adsorbent beds deteriorated by the decrease in the NTU with the increase in the mass flow rate, which was another reason of lower COP with larger mass flow rates.

1.4

1.6

1.8

Fig. 7. The influence of the mass flow rate of the heat transfer media to the adsorbent bed on the optimum half cycle time.

200 180 SCC

160 140

SCC [W/kg]

Fig. 6. The variations of the bed temperature with dimensionless time for the optimum solution (switching time = 40 s), the solution C (switching time = 18 s), and the solution D (switching time = 66 s).

1.2

Mass flow rate [kg/s]

0.8

120 100 80

Th = 75ºC Th = 85ºC Th = 95ºC

60 40

0.7

COP [-]

The optimum Solution C Solution D

Half cycle time [s]

Bed temperature, Tb [ºC]

100

0.6

20 COP

0 0.6

0.8

1.0

1.2

1.4

1.6

0.5 1.8

Mass flow rate [kg/s] Fig. 8. The effect of the mass flow rate on the maximum SCC and the COP.

It was also found that the effect of the hot water temperature on the COP was insignificant. The reason was that the improvement of the SCC by the higher hot water temperature was curtailed by the shorter cycle time. 5.3. The influence of the heat exchanger parameters on the optimum solution Parametric studies on the heat capacity ratio and on the NTU of the adsorbent beds were carried out to investigate the effects of the heat exchanger parameters on the optimum solution. The optimization was run for each calculation case. 5.3.1. The effect of the heat capacity ratio of the adsorbent beds The effect of the heat capacity ratio of the adsorbent beds on the optimum cycle time is depicted in Fig. 9. The optimum adsorption time and the optimum switching time are shown as a stacked bar chart, and the height of the stacked bar represents the optimum half cycle time. The larger the heat capacity ratio was, the longer the optimum half cycle time was. The large heat capacity ratio means the excessive heat capacity of the heat exchanger material compared with that of the adsorbent. Therefore, the half cycle time had to be prolonged to heat or to cool the heat exchanger material in the case of the large heat capacity ratio. Fig. 10 shows the maximum SCC and the COP at the maximum SCC. Both the maximum SCC and the COP decreased with the in-

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T. Miyazaki, A. Akisawa / Applied Thermal Engineering 29 (2009) 2708–2717

600

700 Adsorption time Switching time

400 300 200 100 0

Adsorption time Switching time

600

Half cycle time [s]

Half cycle time [s]

500

500 400 300 200 100

1.4

1.6

1.8

2.0

2.2

0

2.4

0.6

0.8

1.0

Heat capacity ratio, αb

1.2

1.4

1.6

NTU

Fig. 9. The effect of the heat capacity ratio of the adsorbent beds on the optimum cycle time.

Fig. 11. The effect of the NTU of the adsorbent beds on the optimum cycle time.

140

140

120

100

SCC COP

80

0.7

60

COP [-]

SCC [W/kg]

120

0.6

40

100

SCC COP

80

0.7

60

0.6

40 0.5

20

0.5

20 0

SCC [W/kg]

160

COP [-]

160

0

1.4

1.6

1.8

2.0

2.2

2.4

0.4

Heat capacity ratio, αb Fig. 10. The effect of the heat capacity ratio of the adsorbent beds on the maximum SCC and the COP.

crease in the heat capacity ratio. The insufficient cooling of the adsorbent bed due to the excess heat capacity would be a reason of the lower SCC in the case of the larger heat capacity ratio. In addition to that, the excess heat capacity was responsible for the ineffective heating during the desorption process. That caused the deterioration of the COP at the larger heat capacity ratio. Similar observations on the effect of the heat capacity ratio are presented by Cacciola et al. [14] and by Saha et al. [8]. Compared with their results, however, the influence of the heat capacity ratio was slightly mitigated due to the optimization of the cycle time in our observations. It implied that disadvantage in performance with larger heat capacity ratio could be compensated by the optimization of cycle time in some degree. 5.3.2. The effect of the number of the heat transfer units The optimum cycle time is shown in Fig. 11. The NTU directly affects the heat exchanger effectiveness, , defined in Table 1. Therefore, the larger NTU improved the heat exchange process between the adsorbent beds and the heat transfer media, which resulted in the shorter half cycle time with the larger NTU. The maximum SCC and the COP are shown in Fig. 12. The enhanced heat exchanger effectiveness improved the sensible heating and cooling in terms of temperature efficiency. Therefore, the higher maximum SCC could be obtained by the shorter cycle time with the increase of NTU. On the other hand, because the heat input was large at the early stages of sensible heating and desorption processes, the short adsorption time had a negative effect on the COP as shown in Fig. 12.

0.6

0.4 0.8

1.0

1.2

1.4

1.6

NTU Fig. 12. The effect of the NTU of the adsorbent beds on the maximum SCC and the COP.

6. Conclusions The research investigated the influences of the operating conditions and the heat exchanger parameters on the optimum performances of the single-stage adsorption chiller. The findings of the study are listed below.  The optimum half cycle time was shortened by the larger mass flow rate and the higher hot water temperature because of the increased cooling power. The COP was decreased with the larger mass flow rate, which was attributed to the shorter cycle time as well as to the decreased heat exchanger effectiveness.  The diminution of the heat capacity ratio of the adsorbent beds enhanced both the maximum SCC and the COP. The optimum cycle time of the smaller heat capacity ratio was shorter.  The large NTU amplified the maximum SCC because of the improved heat exchanger effectiveness. The COP at the maximum SCC was, however, reduced with the larger NTU because of the shorter cycle time.

Acknowledgements The research was supported by Grant-in-Aid for Scientific Research, Grant-in-Aid for Young Scientists (B), Ministry of Education, Culture, Sports, Science and Technology.

T. Miyazaki, A. Akisawa / Applied Thermal Engineering 29 (2009) 2708–2717

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