International Journal of Heat and Mass Transfer 63 (2013) 171–182

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Towards an optimal performance of adsorption chillers: Reallocationof adsorption/desorption cycle times

0017-9310/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.03.076

⇑ Corresponding author at: Advanced Graduate Program in Global Strategy forGreen Asia, Interdisciplinary Graduate School of Engineering Sciences, KyushuUniversity, Kasuga-koen 6-1, Kasuga-shi, Fukuoka 816-8580, Japan. Tel.: +81 92 5837903; fax: +81 92 583 8909.

E-mail address: saha.baran.bidyut.213@m.kyushu-u.ac.jp (B.B. Saha).

I.I. El-Sharkawy a, H. AbdelMeguid a, B.B. Saha b,c,⇑a Mechanical Power Engineering Department, Faculty of Engineering, Mansoura University, El-Mansoura 35516, Egyptb Advanced Graduate Program in Global Strategy for Green Asia, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen 6-1, Kasuga-shi,Fukuoka 816-8580, Japanc International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Fukuoka 819-0395, Japan

a r t i c l e i n f o

Article history:Received 13 December 2012Received in revised form 29 March 2013Accepted 29 March 2013

Keywords:AdsorptionCoolingCOPOptimizationSilica gelWater

a b s t r a c t

This paper presents a theoretical investigation of the effect of adsorption/desorption times allocation onthe performance of adsorption chillers. The ratio between the duration of adsorption and desorptionmodes is varied to optimize the system performance. Herein, (f) stands for the ratio between durationof desorption and adsorption modes of the adsorption cooling cycle. Employing a two-bed silica gel/waterbased adsorption chiller, theoretical results show that the system performance in terms of cooling capac-ity and COP is improved by reducing the ratio (f). However, percentage of improvement depends on thesystem design and its operating conditions. It is also found that, for each cycle time, there is an optimalvalue of (f) that maximizes the system performance.

Theoretical results show that for a half cycle time of 350 s, switching time of 35 s and f of 0.8, the sys-tem delivers continues cooling using only two sorption reactors and minimizes fluctuations in chilledwater outlet temperature.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The world energy demand increases due to the growth of pop-ulation and enhanced economic activities. However, non-renew-able energy resources such as fossil fuels are limited andeventually, one day, it will run out. Renewable energy including,solar, wind and biomass can provide a practical solution for theshortage of conventional energy resources. For instance, solar en-ergy has many attractive features and can be used in many appli-cations such as solar heating, cooling and power generation. Solarcooling systems are proven renewable energy technologies andattractive alternative to produce useful cooling from solar energy.Thermally driven adsorption cooling systems are considered tobe sustainable cooling systems as these systems can be poweredby solar energy or waste heat sources. The main features of thesesystems are; (i) they are powered by clean and renewable energy(solar) or waste heat. Utilization of waste heat to produce usefulcooling instead of releasing it to the ambient could contribute inthe reduction of global worming and thermal pollution [1–3], (ii)

they use natural or alternative refrigerants such as water, metha-nol and ethanol which have no harmful effects on the environment,and (iii) they also have no moving parts and require significantlysmall electricity usage.

From the above mentioned perspectives, extensive research ef-forts have been conducted to improve the system performance interms of COP and cooling capacity. Using of proper adsorbent/refrigerant pair is essential for improving the system performance[4–11]. Operating conditions have a significant effect on the per-formance of adsorption chillers. Effect of the inlet conditions(temperature and flow rates) of heating/cooling fluid on the sys-tem performance are discussed by a sizable number of research-ers [12–18]. Adsorption/desorption and switching times are alsocrucial parameters affecting the system performance. Durationof adsorption and desorption modes is usually considered to beequal. A recent attention to the effect of desorption/adsorptiontime ratio on the system performance have been considered byseveral researchers where the desorption process is carried outfaster than the adsorption process [19,20]. Glaznev, and Aristov[20] experimentally studied the temporal evolution of isobaricadsorption uptake for a monolayer of loose adsorbent grains lo-cated on a metal plate. The study conducted on Fuji silica/waterpair. The results showed that, the desorption process carriedout faster than adsorption process by a factor of 2.2–3.5, hence,for the best performance of the adsorption cooling cycle the

Nomenclature

A0 coefficient in Eq. (2) (kg kg�1)A1 coefficient in Eq. (2) (kg kg�1 K�1)A2 coefficient in Eq. (2) (kg kg�1 K�2)A3 coefficient in Eq. (2) (kg kg�1 K�3)B0 coefficient in Eq. (3) (�)B1 coefficient in Eq. (3) (K�1)B2 coefficient in Eq. (3) (K�2)B3 coefficient in Eq. (3) (K�3)COP coefficient of performance (�)Cp specific heat capacity (kJ kg�1 K�1)Ds surface diffusivity (m2 s�1)Dso pre-exponential constant (m2 s�1)Ea activation energy (J mol�1)f the ratio of desorption time to adsorption time (�)F0 geometric parameter used in LDF model (�)M mass (kg)_m mass flow rate (kg s�1)

P equilibrium pressure (kPa)Ps saturation pressure (kPa)Qst isosteric heat of adsorption (kJ kg�1)Ru universal gas constant (kJ kmol�1 K�1)

Rp radius of adsorbent particle (m)T temperature (K)t time (s)W adsorption equilibrium uptake (kg kg�1)W instantaneous adsorption uptake (kg kg�1)UA overall heat transfer coefficient-area product (W K�1)Subscriptsads

adsorbent/adsorptionbed adsorber/desorber reactorc condenser cooling waterchill chilled watercond condensercw cooling waterdes desorptionevap evaporatorhw hot waterin inlet conditionmetal metalout outlet conditionref refrigerant

172 I.I. El-Sharkawy et al. / International Journal of Heat and Mass Transfer 63 (2013) 171–182

optimal adsorption/desorption times allocation should be opti-mized. Aristov et al. [21] studied the temporal evolution of qua-si-isobaric adsorption/desorption curves for simple bedconfiguration of n layers of loose Fuji silica RD grains, typicallyn = 1,2,3,4 and 8, located on a heat transfer metal support. Theyused fast temperature drop or jump techniques within a temper-ature range suitable for adsorption cooling applications. Theyfound that under certain conditions the kinetics of isobaricadsorption/desorption is invariant with respect to the ratio be-tween heat transfer surface and adsorbent mass. A new cycletime allocation for enhancing the performance of two-bedadsorption chillers was proposed [22]. The authors assumed thatthe duration of adsorption phase (presents half-cycle time) equalssum of desorption, pre-cooling and pre-heating times (present thesecond half-cycle time). The proposed allocation showed animprovement on the system performance in terms of coolingcapacity and COP. The intermittent cooling cycle with variableadsorption/desorption duration at fixed total cycle time wasinvestigated [19]. The actual performance of LiNO3/silica KSK(SWS-9L) was tested in a single bed adsorption chiller with spe-cial emphasis on the optimization of the relative duration ofadsorption and desorption phases to maximize the COP and thecooling capacity of the cycle. The authors concluded that the sys-tem performance could be improved by shortening desorptiontime compared to that of adsorption phase. Influence of cycletime and the relative duration of adsorption/desorption phasesusing a single bed. AQSOA-FAM-Z02/water based adsorption chil-ler was also experimentally investigated [23]. The composite sor-bent of LiNO3/vermiculite, SWS-9V was proposed to operate atlow regeneration temperature (<70 �C) and was also tested by alab-scale adsorption chiller [24]. The optimization results illus-trated that the optimal cycle performance, for given operatingconditions, are strongly dependent on the cycle time and the rel-ative duration (R) of the isobaric adsorption and desorption times.For high driving temperature (90 �C), the system achieved theoptimal performance at cycle time = 1200 s when the adsorptionduration is 7 times longer than the desorption one, which corre-sponding to f = 0.14. While, at low driving temperature (68 �C),the optimal performance were obtained at cycle time = 1800 s,

protracting the duration of the desorption time at the expensesof the adsorption one (f = 1.33).

The present study aims to investigate of the optimum adsorp-tion/desorption time allocation for enhancing the performance ofadsorption chillers. Duration of adsorption and desorption modesare varied to optimize the system performance. Two-bed silicagel/water based adsorption chiller is used in this study.

2. System description

Fig. 1(a) shows a schematic diagram of two-bed adsorptionchillers. As can be seen from Fig. 1(a), the system comprises fourheat exchangers namely a condenser, an evaporator and two sorp-tion (adsorber/desorber) reactors. In the presented adsorption sys-tem, two refrigerant valves were placed between the evaporatorand the adsorber/desorber reactor and another pair of refrigerantvalves installed between the condenser and the sorption reactorsto control the refrigerant flow throughout the system. The evapo-rator and condenser are connected together through a bended tubeto keep a pressure difference between both of them. The systemoperation consists of four modes namely, A, B, C and D, respectively[16]. In Mode A, valves V2 and V3 are opened whilst V1 and V4 areclosed (see Fig. 1a). Refrigerant evaporates at evaporator pressureextracting the cooling load from chilled water and flows to Bed1through V2. Refrigerant vapor is then adsorbed at Bed1 at whichcooling water removes generated heat of adsorption. On the otherhand, Bed2 is heated up using hot water at which desorbed refrig-erant is released and flows to the condenser through V3. Refriger-ant vapor is then condensed and moves to the evaporator througha bended tube. Heat of condensation is removed using coolingwater. In this mode, Bed1 and Bed2 are, respectively, in adsorptionand desorption processes. The system is then switched to Mode Bwhere all valves are closed. Bed1 is in pre-heating mode andheated up by hot water whilst Bed2 is in pre-cooling mode andcooled down using cooling water. Modes C and D are exactly theopposite of modes A and B. Fig. 1(b) shows the thermodynamicprocesses of adsorption cooling cycle. The cycle composes four pro-cesses namely, adsorption, pre-hating, desorption and pre-cooling

( ), ,( )P cw cw out cw inmc T T−

Cooling water in

Cooling water out

Hot water out

Hot water in

Bed2 Bed1

V4 V2

V3 V1

Chilled water in

Chilled water out

Liquid refrigerant

Cooling water in

Cooling water out

( ), ,( )P chill chill in chill outmc T T−

( ), ,( )P hw hw in hw outmc T T−.

( ), ,( )P c c out c inmc T T−

( )ads st

dwQ

dt( )ads st

dwQ

dt

Condenser

Evaporator

.

.

.

5 15 25 35 45 55 65 75 85 95

Pre

ssur

e

Temperature [oC]

0.01

0.02

0.040.15 0.071.03.0 0.2

AdsorptionEvaporator

pressure

DesorptionCondenserpressure

Condenser

Evaporator

(a)

(b)

Fig. 1. (a) Schematic diagram of two-bed adsorption chiller. (b). Thermodynamic processes of basic adsorption cooling cycle using silica gel-water pair.

I.I. El-Sharkawy et al. / International Journal of Heat and Mass Transfer 63 (2013) 171–182 173

processes. A detailed description of adsorption cooling cycle can befound elsewhere [6,8,16].

In the present study, theoretical calculations have been con-ducted based on a two-bed adsorption cooling system proposedby Saha et al. [15]. The system performance has been investi-gated experimentally by Boelman et al. [25] and theoreticallyby Chua et al. [26]. Physical design parameters of evaporator,condenser and sorption heat exchangers are furnished inTable 2.

3. Mathematical modeling

3.1. Adsorption isotherms and kinetics

Adsorption isotherms of the RD type silica-gel/water pair is esti-mated by using the modified Freundlich equation [15] (S-B-K equa-tion) as given by Eq. (1) below;

W ¼ AðTsÞPsðTwÞPsðTsÞ

� �BðTsÞ

ð1Þ

174 I.I. El-Sharkawy et al. / International Journal of Heat and Mass Transfer 63 (2013) 171–182

where;

AðTsÞ ¼ Ao þ A1Ts þ A2T2s þ A3T3

s ð2Þ

BðTsÞ ¼ Bo þ B1Ts þ B2T2s þ B3T3

s ð3Þ

In the above mentioned equations, A(Ts) and B(Ts) are functions ofthe adsorbent temperatures where Ao � A3 and Bo � B3 are constantsgiven in Table 1.

The linear driving force model (Eq. (4)) is used to estimate theadsorption rate of silica gel/water pair.

dwdt¼ 15Ds

R2p

ðW �wÞ ð4Þ

Ds ¼ Dso exp � Ea

RuT

� �ð5Þ

where Ds is the surface diffusivity, Dso stands for the a pre-exponen-tial constant. Ea is the activation energy and Ru is for the universalgas constant (see Table 1).

3.2. Energy balance of adsorber/desorber reactors

Lumped parameter model is used to describe the energy bal-ance of the adsorber/desorber reactors where both adsorbent andthe heat exchanger metals are assumed to have the same temper-ature. Eq. (6) below describes the energy balance of the adsorberexchanger during adsorption process,

ðMcP;M þMref cp;ref þMmetalcp;metalÞdTdt

¼ /Madsdwdt

� �ðQ stÞ � ð _mcPÞcwðTcw;out � Tcw;inÞ ð6Þ

where the flag / = 0 during switching and / = 1 during adsorptioncycle operation. In Eq. (6), the left hand side presents the changeof the internal energy of adsorption reactor including heat exchan-ger metal, adsorbent and refrigerant. The first term of the right handside presents the heat realised due to adsorption process whilst the

Table 2Values adopted in the cycle simulation [15].

Symbols Value

Mads (kg) 47ð _mcpÞhw=cw (kW) Heating: 5.36 Cooling: 6.36

ðMcpÞcondðkJÞ 24.280 � 0.386 + 20 � 4.186ðMcpÞevapðkJÞ 12.450 � 0.386 + 50 � 4.186

ðUAÞbedðW � K�1Þ 4241.38

ðUAÞcondðW � K�1Þ 15349.80

ðUAÞevapðW � K�1Þ 4884.90

Table 1Numerical values of parameters used in Eqs. (1)–(5) [15].

Parameter Value

A0 (kg kg�1) �6.5314A1 (kg kg�1 K�1) 0.072452A2 (kg kg�1 K�2) �0.23951 � 10�3

A3 (kg kg�1 K�3) 0.25493 � 10�6

B0 (�) �15.587B1 (K�1) 0.15915B2 (K�2) �0.50612 � 10�3

B3 (K�3) 0.5329 � 10�6

Dso (m2 s�1) 2.54 � 10�4

Ea (J mol�1) 4.2 � 104

Rp (m) 1.74 � 10�4

second term stands for the heat rejected to the ambient by coolingwater (see Fig. 1a).

The log mean temperature difference (LMTD) method is used toestimate the outlet temperature of cooling fluids as given by Eq. (7)below;

Tcw;out ¼ Tbed þ ðTcw;in � TbedÞ exp�ðUAÞbed

ð _mcpÞcw

� �ð7Þ

Energy balance of desorber reactor (during desorption process) canbe described by Eq. (8) where the flag / = 0 and / = 1 during switch-ing and desorption processes, respectively.

ðMcP;M þMref cp;ref þMmetalcp;metalÞdTdt

¼ /Madsdwdt

� �ðQstÞ � ð _mcPÞhwðThw;out � Thw;inÞ ð8Þ

Similar to Eq. (6), the left hand side of Eq. (8) shows the change ininternal energy of the desorber reactor. The first term of the righthand side presents heat extracted due to desorption phenomenonwhilst the second term is the heat added to sorption bed from hotwater.

The exit temperature of the outlet hot water can be estimatedusing the equation given below;

Thw out ¼ Tbed þ ðThw;in � TbedÞ exp�ðUAÞbed

ð _mcpÞhw

� �ð9Þ

3.3. Condenser and evaporator energy balance

The energy balance equations for the condenser and evaporatorcan be expressed by Eqs. (10) and (11), respectively. Numerical val-ues of the flag / are similar to that given in Eqs. (6) and (8).

ðMcPÞconddTcond

dt¼ / hfg Mads

dwdes

dt

� �� ð _mcPÞcðTc;out � Tc;inÞ ð10Þ

ðMcpÞevapdTevap

dt¼ �/hfg Mads

dwads

dt

� �� ð _mcPÞchillðTchill;out

� Tchill;inÞ ð11Þ

Employing the LMTD approach, the outlet temperature of the con-denser and evaporator heat exchangers are given by Eqs. (12) and(13), respectively.

Tc;out ¼ Tcond þ ðTc;in � TcondÞ exp�ðUAÞcond

ð _mcpÞc

� �ð12Þ

Tchill;out ¼ Tevap þ ðTchill;in � TevapÞ exp�ðUAÞevap

ð _mcpÞchill

� �ð13Þ

3.4. Mass balance

The mass balance equation for of the adsorption cooling systemcan be expressed by;

dMref

dt¼ �Mads

dwads

dtþ dwdes

dt

� �ð14Þ

3.5. System performance

Performance of thermally driven adsorption chillers in terms ofcooling capacity and COP is calculated using the followingrelations;

Qcyclechill ¼

R tcycle0 ð _mcPÞchillðTchill;in � Tchill;outÞdt

tcycleð15Þ

I.I. El-Sharkawy et al. / International Journal of Heat and Mass Transfer 63 (2013) 171–182 175

COP ¼R tcycle

0 ð _mcPÞchillðTchill;in � Tchill;outÞdtR tcycle0 ð _mcPÞhwðThw;in � Thw;outÞdt

ð16Þ

Here tcycle denotes the total cycle time.

4. The proposed cycle time allocation

As adsorption cooling cycle is composed of four batch operatedprocesses; adsorption, pre-heating, desorption and pre-cooling, thecycle time can be estimated using the following relation;

tcycle ¼ tpre�heating þ tdesorption þ tpre�cooling þ tadsorption ð17Þ

In conventional adsorption cooling cycle, adsorption and desorptionprocesses are equal in time duration. However, it is proven thatkinetics of desorption is faster than that of adsorption [19,20].Accordingly, desorption time is proposed to be shorter than thatof adsorption and the ratio between them is defined as (f). There-fore, Eq. (17) can be written as;

tcycle ¼ 2tpre�heating=pre�cooling þ ð1þ f Þ � tadsorption ð18Þ

The present simulation aims to investigate the optimal values forboth (f) and switching time that maximize the system performance.

5. Simulation and optimization procedure

The developed mathematical model which is described in Sec-tion 3, is coded and solved by the MATLAB function ode15s. For

Fig. 2. The combination of adsorption time and desorption time at d

Table 3Rated operating conditions.

Hot water inlet Cooling water inlet

Temperature (�C) Flow rate (kg s�1) Temperature (�C) Flow

85.7 1.28 31.1 (1.5

optimization procedure, Nondominated Sorting Genetic Algo-rithm-version II (NSGA-II) was employed. NSGA-II is a multi-objec-tive genetic algorithm developed by Deb et al. [27] and Deb andSundar [28]. The NSGA is an evolutionary algorithm from the fieldof Evolutionary Computation. There are two versions of the algo-rithm, the classical NSGA and the updated and currently canonicalform NSGA-II. Deb provides in depth coverage of Evolutionary Mul-tiple Objective Optimization algorithms in [29], including a de-tailed description of the algorithm. NSGA-II is used to estimatethe optimal adsorption/desorption and switching times for two-bed silica gel/water based adsorption chillers that maximize bothcooling capacity and COP.

It is found that the system COP increases with the increase ofadsorption/desorption time and the effect of switching time ismarginal. For this reason, a single objective optimization procedurewas carried out to maximize the cooling capacity only with thesame decision variables.

To investigate the effect of the desorption/adsorption time ratio(f), at different half cycle times and different switching times onthe system performance (cooling capacity and COP), the simulationprocess is carried out in imbricate three for-loops, the first one isfor different half cycle times, the second covers a wide range ofswitching times (tpre_heating = tpre-cooling starting from 20 s to 100 swith increment of 5 s) and the last loop is for the (f).

For both specified cycle time and switching time the simulationis conducted for f varied from 0.1 to 1.0 with an increment of 0.05.For each value of f, the adsorption time and desorption time is esti-mated according to Eqs. (17) and (18). The resulting combination

ifferent f values for cycle time = 700 s and switching time = 35 s.

Chilled water inlet

rate (ads + cond) (kg s�1) Temperature (�C) Flow rate (kg s�1)

2 + 1.37) 14.8 0.7

10

2030

40

50

300 400 500 600 700 800 900 1000

11

11.5

12

12.5

13

13.5

14

14.5

switching time [s]Adsorption/Desorption time [s]

Coo

ling

cap

acit

y [k

W]

20 25 30 35 40 45

250300

350400

14.58

14.59

14.6

14.61

14.62

14.63

14.64

switching time [s]Adsorption/

Desorption time [s]

Coo

ling

cap

acit

y [k

W]

(a)

(b)

(c)

1020

3040

50

200400

600800

10000.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

switching time [s]Adsorption/Desorption time [s]

COP

Fig. 3. (a) COP versus adsorption/desorption and switching times for optimal system performance at assorted operating conditions for conventional adsorption chiller. (b).Cooling capacity versus adsorption/desorption and switching times for optimal cooling capacity at assorted operating conditions for conventional adsorption chiller. (c).Adsorption/desorption and switching times for optimal cooling capacity at assorted operating conditions for conventional adsorption chiller.

176 I.I. El-Sharkawy et al. / International Journal of Heat and Mass Transfer 63 (2013) 171–182

I.I. El-Sharkawy et al. / International Journal of Heat and Mass Transfer 63 (2013) 171–182 177

of adsorption and desorption times at different f values for bothspecified cycle time (700 s) and switching time (35 s) is shown inFig. 2 as a representative example. For each cycle time, the simula-tion process was run 323 times for different combination ofswitching times and f values.

6. Results and discussion

Optimization technique is used to estimate the optimal valuesof adsorption/desorption and switching times that maximize bothcooling capacity and COP for conventional adsorption chiller. Chil-ler specifications adapted on the simulation are presented on Ta-ble 2 while the operating conditions are given in Table 3. Effectof adsorption/desorption and switching times on COP is presented

f = t

Swit

chin

g ti

me

[s]

13.51312.5

13.5

13

12.5

1212

11109

0.1 0.2 0.3 0.4 0.520

30

40

50

60

70

80

90

100

f = t

Swit

chin

g ti

me

[s]

0.4070.4

050.4025

0.4

0.3975

0.3950.3925

0.39

0.38

0.37

0.360.34

0.1 0.2 0.3 0.4 0.520

30

40

50

60

70

80

90

100

(a)

(b)

Fig. 4. (a) A contour plot of cooling capacity of the assorted adsorption chiller versus (f) aadsorption chiller versus (f) and switching time. Half cycle time = 350 s.

in Fig. 3(a), it is obvious that the system COP increases with the in-crease of adsorption/desorption time whilst the effect of switchingtime is marginal. Fig. 3(b) shows a plot of the optimal values ofadsorption/desorption and switching times versus the coolingcapacity. As can be seen from Fig. 3(b), the cooling capacity reachesits maxima at adsorption/desorption and switching times of 315and 35 s, respectively. It is worthy to mention here that, the shortcycle times are not appear on Fig. 3(b) because the optimal COPcould not be achieved at this region. Meaning that, both COP andcooling capacity cannot be maximized together at short cycletimes. As the cycle COP increases with the increase of cycle time,optimization procedure has been carried out to optimize the cool-ing capacity only. The results are presented in Fig. 3(c). It is clearfrom this figure that, the maximum value of cooling capacity is

Des/t

Ads

14.7

14.6

14.5

14.4

14.3

14.2

14.1

14

14.7514.714

.614.514

.414.314

.214.114

0.6 0.7 0.8 0.9 1

Des/t

Ads

0.40.40250.4050.40750.41

0.41250.415

0.4175

0.415

0.41250.4

1

5

0.6 0.7 0.8 0.9 1

nd switching time. Half cycle time = 350 s. (b). A contour plot of COP of the assorted

178 I.I. El-Sharkawy et al. / International Journal of Heat and Mass Transfer 63 (2013) 171–182

about 14.63 where the half cycle time ranges between 300 and350 s which corresponding to a COP of about 0.42.

A contour plot of cooling capacity of the assorted adsorptionchiller relating (f) and switching time is presented in Fig. 4(a).The half cycle time is 350 s whilst (f) is varied between 0.1 and1. It is clear from Fig. 4(a) that, the maximum adsorption capacityis achieved at (f) of about 0.85 and switching time of about 35 s.Fig. 4(b) shows the contour plot relating COP, (f) and switchingtime. It can be seen that, the COP also reaches its maxima atf = 0.85. Fig. 5(a) and (b) shows respectively plots of cooling capac-ity and COP versus (f) and switching time for a half cycle time of450 s. One can notice that, the maximum cooling capacity isachieved within region bounded by 0.85 < f < 0.9 and switching

f =

Swit

chin

g ti

me

[s] 13.713.613.5

1312.51211.5

10.5

0.1 0.2 0.3 0.4 0.520

30

40

50

60

70

80

90

100

f = t

Swit

chin

g ti

me

[s]

0.454

0.447

0.44

0.4330.426

0.4050.384

0.1 0.2 0.3 0.4 0.520

30

40

50

60

70

80

90

100

(a)

(b)

Fig. 5. (a) A contour plot of cooling capacity of the assorted adsorption chiller versus (f) aadsorption chiller versus (f) and switching time. Half cycle time = 450 s.

time ranges from 30 to 35 s. It is obvious from Fig. 5(b) that theCOP reaches its maximum value at (f) of about 0.45 whilst the in-crease in COP after that is marginal.

The cooling capacity and COP are investigated in the same man-ner for relatively long half cycle time, typically 600 s, and theoret-ical results are presented in Fig. 6(a) and (b). It is obvious that, themaximum value of cooling capacity is achieved within the range0.85 < f < 0.95, and switching time varied between 30 s and 50 swithout significant effect of the change in switching time. It canbe also noticed that, the COP reaches its maxima at f = 0.4, howeverthere is a marginal change at higher values of (f).

Fig. 7 shows plot of cooling capacity and COP versus half cycletime for adsorption cooling system working at conventional and

tDes

/tAds

14.614.5

14.414.3

14.214.1

1413.9

13.8

13.7

14.6514.614

.514.414

.314.214

.11413.913

.8

0.6 0.7 0.8 0.9 1

Des/t

Ads

0.4540.447

0.6 0.7 0.8 0.9 1

nd switching time. Half cycle time = 450 s. (b). A contour plot of COP of the assorted

f = tDes

/tAds

Swit

chin

g ti

me

[s]

13.913.8

13.713.6

13.513.4

13.3

13.9

13.8

13.7

13.613

.513.4

13.3

13.2

13.1

1312.51211.5

1110

9

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 120

30

40

50

60

70

80

90

100

f = tDes

/tAds

Swit

chin

g ti

me

[s]

0.49

0.49

0.495

0.5

0.495

0.49

0.485

0.48

0.460.44

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 120

30

40

50

60

70

80

90

100

(a)

(b)

Fig. 6. (a) A contour plot of cooling capacity of the assorted adsorption chiller versus (f) and switching time. Half cycle time = 600 s. (b). A contour plot of COP of the assortedadsorption chiller versus (f), and switching time. Half cycle time = 600 s.

I.I. El-Sharkawy et al. / International Journal of Heat and Mass Transfer 63 (2013) 171–182 179

the new cycle time allocations. The cooling capacity and COP fornew cycle is estimated at the optimal values of (f) and switchingtime. It can be seen from Fig. 7 that, the cooling capacity increaseswith the increase of half cycle time until reaches its maxima at halfcycle time between 350 s and 450 s. It is also obvious that, there isan improvement on both cooling capacity and COP using the newcycle time allocation.

7. Case study of a cycle time allocation

To assure that the evaporator is always connected with one ofsorption reactors for less fluctuations of the chilled water outlet

temperature, a new cycle time allocation is proposed and pre-sented in Fig. 8. Herein, the half cycle time is considered to be350 s as a case study where the values of (f) and switching timefor this arrangement are considered to be 0.8 and 35 s, respec-tively. Fig. 9 shows the temporal history of the system heatexchangers, namely adsorber/desorber reactors, evaporator andcondenser. The system is working at the new cycle time allocationthat presented in Fig. 8 and the following operating conditions;Th = 85.7 �C, Tc = 31.1 �C and Tchill,in = 14.8 �C. Chilled water outlettemperatures for adsorption chiller working at conventional andnew cycle time allocation are shown in Fig. 10. It can be seen fromFig. 10 that, the fluctuations of the chilled water outlet tempera-ture is significantly reduced by using the new cycle time

CO

P

Coo

ling

capa

city

[kW

]

Half time Cycle [s]

Fig. 7. Cooling capacity and COP versus half cycle time for adsorption coolingsystem working at conventional and new cycle time allocations.

180 I.I. El-Sharkawy et al. / International Journal of Heat and Mass Transfer 63 (2013) 171–182

allocations. This is due to continues connection of the evaporatorwith the adsorber reactor. The results of this case study agree withthe results obtained by Miyazaki et al. [22].

Pre-h Desorption Pre-c

P

Bed1

Bed 2

0 35 315 350

0 350

Adsorption

Evaporator

0 350

Connected to Bed 2

Fig. 8. The case study of cycle time allocation at; half cycle time = 350 s; f = 0.8 and

Tem

pera

ture

[o C

]

T

Eva

Co

Fig. 9. Temperatures of the system heat excha

8. Results verification

The results of this paper agree well with the results and conclu-sions obtained by Miyazaki et al. [22]. The reason for this agree-ment is that both work use the same specifications of adsorptionchiller, which has been proposed by Saha et al. [15]. However,the time allocation in the present work is considered to be moregeneric and general in which the duration of adsorption phase isnot required to be the half of total cycle time as illustrated inFig. 2. A case study of cycle time allocation is presented herein toconsolidate our results and findings.

Glaznev and Aristov [20] measured adsorption and desorptionkinetics for Fuji RD type silica gel considering the adsorbent andheat exchanger as an integrated unit. They found that the desorp-tion phase (for monolayer) is about 2–3 times faster than that ofthe adsorption phase. However, results of the present study showthat value of f (desorption time/adsorption time) between 0.8and 0.9 is sufficient to optimize the system performance. In ouropinion, the reason for this difference owing to the system hard-ware including the configurations of adsorber/desorber heatexchangers, condenser and evaporator, mass of adsorbents andfluxes of heat transfer fluid, etc. Cooling and heating response of

Pre-c re-h

700

665 385 700

Adsorption

Desorption

700

Connected to Bed 1

switching time of 35 s. Pre-c: Pre-cooling process. Pre-h: Pre-heating Process.

ime [s]

porator

ndenser

Desorber

Adsorber

ngers using the new cycle time allocation.

Fig. 10. Chilled water outlet temperatures for adsorption chiller working at conventional and new cycle time allocations.

I.I. El-Sharkawy et al. / International Journal of Heat and Mass Transfer 63 (2013) 171–182 181

adsorber/desorber heat exchanger affects significantly the adsorp-tion/desorption dynamics of adsorbent.

Sapienza et al. [24] experimentally tested the composite sor-bent SWS-9V at high driving temperature (90 �C) and cycle timeof 1200 s and the optimal value of f was found to be 0.14. While,at low driving temperature (68 �C) and cycle time of 1800 s the ra-tio f had an optimal value of 1.33. These results assert that for thesame system and the same adsorbent but with different drivingtemperature and cycle time there is a wide range of the optimal va-lue of f depending on the system working conditions.

It is worthy to mention that, the optimal values of f obtained inthis study are based on the isotherms, kinetics, system specifica-tions which are presented in Tables 1 and 2, and a similar studyis necessary for any particular chiller unit or different adsorbent-refrigerant pair.

9. Conclusion

Performance of silica gel/water based adsorption chiller hasbeen investigated. NSGA-II optimization technique is used to esti-mate the optimal values of adsorption/desorption and switchingtimes that maximize both cooling capacity and COP for conven-tional adsorption chiller. The results show that the system COP in-creases with the increase of adsorption/desorption time whilst theeffect of switching time is marginal, and the cooling capacityreaches its maxima at adsorption/desorption and switching timesof 315 and 35 s, respectively, for the presented system. Optimiza-tion procedure has been carried out to optimize the cooling capac-ity only, and the results illustrate that the maximum value ofcooling capacity is about 14.63 kW where the half cycle timeranges between 300 and 350 s which corresponding to a COP ofabout 0.42.

Effect of the ratio between desorption and adsorption times (f)on the system performance in terms of COP and cooling capacityhas been studied. Theoretical results show that, the system perfor-mance is improved when (f) is less than unity regardless the cycletime. It is also found that, for each cycle time, there is an optimalvalue of (f) that maximize the system performance. According to

the results of the present study, at a half cycle time of 350s, themaximum adsorption capacity is achieved at f = 0.85 and switchingtime of 35 s whilst maximum cooling capacity is achieved withinregion bounded by 0.85 < f < 0.9 and switching time ranges from30 to 35 s at half cycle time of 450 s. This study also presents a cy-cle time allocation that achieves continues cooling using two sorp-tion reactors only. Employing the proposed cycle time allocation,the fluctuations of the chilled water outlet temperature is signifi-cantly reduced.

The results obtained from this work accord with the facts con-cluded by Miyazaki et al. [22], Aristov et al. [19], Sapienza et al.[24], Glaznev, and Aristov [20], Aristov et al. [21], that the optimalvalue of the ratio f that gives the best performance of the cycle de-pends strongly on the system configurations, physical dimensions,number of adsorbent beds, the adsorbent, cycle times, driving heatsource temperature and so on. Moreover, for the same system theoptimal value of f has a wide range according to the system work-ing conditions and designated cycle times.

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