water adsorption chiller performance

Applied Energy 89 (2012) 142–149

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Physical and operating conditions effects on silica gel/water adsorption chiller performance Ahmed R.M. Rezk, Raya K. Al-Dadah ⇑ Department of Mechanical Engineering, University of Birmingham, Birmingham, Edgbaston B15 2TT, United Kingdom

a r t i c l e

i n f o

Article history: Received 5 July 2010 Received in revised form 5 October 2010 Accepted 19 November 2010 Available online 1 February 2011 Keywords: Adsorption chiller Silica gel/water Empirical simulation

a b s t r a c t Adsorption refrigeration systems are commercially developed due to the need of replacing the conventional systems which utilise environmentally harmful refrigerants and consume high grade electrical power. This paper presents the key equations necessary for developing a novel empirical lumped analytical simulation model for commercial 450 kW two-bed silica gel/water adsorption chiller incorporating mass and heat recovery schemes. The adsorption chiller governing equations were solved using MATLABÒ platform integrated with REFPROPÒ to determine the working fluids thermo-physical properties. The simulation model predicted the chiller performance within acceptable tolerance and hence it was used as an evaluation and optimisation tool. The simulation model was used for investigating the effect of changing fin spacing on chiller performance where changing fin spacing from its design value to minimum permissible value increased chiller cooling capacity by 3.0% but decreased the COP by 2.3%. Furthermore, the effect of generation temperature lift on chiller performance and the feasibility of using it as a load control tool will be discussed. Genetic Algorithm optimisation tool was used to determine the optimum cycle time corresponding to maximum cooling capacity, where using the new cycle time increased the chiller cooling capacity by 8.3%. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Heat powered adsorption cooling systems are becoming increasingly considered for applications where cooling is required and low grade heat (temperature as low as 55 °C) is available. Applications for such systems include combined cooling, heating and power (CCHP) system employed in many industrial and commercial applications [1] and sustainable building climatisation using solar energy as heat source [2,3]. Adsorption cooling systems is a promising solution for more environmentally friendly system [4]. In an adsorption cooling system, a solid adsorbent that has high affinity to the refrigerant is used to move the refrigerant from the evaporator pressure to the condenser pressure by means of adsorption effect during adsorbent bed cooling followed by desorption effect during heating. During the last few decades, several adsorbing materials were investigated including silica gel/water, zeolite/water and activated carbon or activated carbon fibres/ammonia, methanol, ethanol or R134a. For water chilling applications, silica gel/water adsorption pair has the advantages of the excellent physical and thermal properties of water (high latent heat of evaporation, high thermal conductivity, low viscosity, ⇑ Corresponding author. Tel.: +44 (0) 121 4143513. E-mail address: [email protected] (R.K. Al-Dadah). 0306-2619/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2010.11.021

thermally stable in wide range of operating temperature and the compatibility with wide range of materials) and good adsorbing properties of silica gel (high adsorption/desorption rate, low generation heat and low generation temperature). Silica gel/water adsorption pair can be classified as the best adsorption pair for chilling applications and activated carbon/R134a is the best for refrigeration applications, with the main drawback of R134a is its global warming potential [5]. Adsorption refrigeration systems modelling is a primary tool for design and optimisation of these machines [6]. There are many modelling techniques which were used to simulate the adsorption refrigeration systems such as lumped-parameter simulation technique [7–10], lumped analytical simulation technique [11– 21], dynamic simulation technique [22–25] and distributedparameter simulation technique [26]. Object oriented simulation tool such as MODELICA was also used by Schicktanz and Núñez [27] to simulate the adsorption refrigeration units. All these simulation techniques present the overall heat transfer coefficient for adsorbent beds, evaporator and condenser as constant values. That limits the prediction capability of the effect of any physical change on the adsorption chiller performance, especially the adsorbent bed. This paper presents the key equations to develop a novel empirical lumped analytical simulation model for a commercial 450 kW two-bed silica gel/water adsorption water chiller. The

A.R.M. Rezk, R.K. Al-Dadah / Applied Energy 89 (2012) 142–149

chiller utilises heat and mass recovery schemes. The importance of such type of simulation technique is highlighted by investigating the influence of fin configuration on chiller performance. Operating conditions significantly affect adsorption chiller performance. One of the most important operating conditions is the operating temperatures [28–31]. The time required for different operating modes (adsorption/desorption, mass recovery and heat recovery) also influences chiller performance [32–34]. However, most of the currently published work on the effect of operating conditions are based on parametric runs of chosen parameters and the need for using a global optimisation technique to obtain the optimum parameters is essential [12]. Genetic Algorithm (GA) one of the robust population-based global optimisation tools was used to determine the global optimum parameters. GA repeatedly modifies a population of individual solutions using three rules namely; selection, crossover and mutation. Over successive generations, the population evolves toward an optimal solution. GA has the advantage over standard optimisation algorithms of the ability to solve a variety of problems of discontinuous, non differentiable, stochastic, or highly nonlinear objective functions. This paper aims at studying the influence of operating temperatures on chiller performance and the feasibility of using regeneration temperature lift as a control tool. Also the effect of cycle time for different operating modes (ads/des, mass recovery and heat recovery) on chiller performance, and the use of GA to determine the optimum cycle time using the cooling capacity as an objective function will be described.

143

structed from externally enhanced high efficiency finned copper tubes (GEWA-B)Ò. 3. Simulation model The simulation model of the adsorption system was constructed from four sub-models describing the performance of evaporator, condenser, adsorber and desorber. The four sub-models were linked together taking into account the various operating modes. Eqs. (1)–(3) present the energy balance equations for adsorbent bed, evaporator and condenser respectively, where the adsorbent, adsorbate and heat exchanger metal are assumed to be momentarily at the same temperature. Eq. (4) presents the refrigerant mass balance in the evaporator taking into account no flow condition in case of heat and mass recovery.

ðfMbedw C w ðT bed Þ þ M sg wsg Cpref ðT bed Þ þ Msg C sg þ M bedmet C bedmet ÞdT bed =dt ¼ ð1  fÞ

n¼N Xbed

dUAbedn  LMTDbed þ ð/  @Þ½cfhg ðT Hex Þ

n¼1

 hg ðPHex ; T bed Þg þ ð1  cÞfhg ðPHex ; T Hex Þ  hg ðPbed ; T bed ÞgMsg dwsg =dt þ /Msg DHsg dwsg =dt

ð1Þ

bCpref ;f ðT ev ap ÞMref ;ev ap þ C ev apmet M ev apmet cdT ev ap =dt ¼ UAev ap  LMTDev ap þ /½href ;ev ap;in  href ;ev ap;out Msg dwsg =dt þ dEpump =dt

2. System description Fig. 1 shows a schematic diagram of the simulated two-bed adsorption chiller and Table 1 shows the various operating modes of the chiller. Each adsorbent bed is connected to the evaporator or condenser by flap valves operated by the pressure difference between heat exchangers during adsorbing or desorbing respectively. On the other hand, the flow of cooling and heating water through the heat exchangers at different operating modes is controlled by 12 pneumatic valves. Physically, the adsorbent bed heat exchanger is constructed from plain copper tubes with aluminium rectangular fins and silica gel granules are packed to fill the gaps between fins. The evaporator and condenser are shell and tube heat exchangers where the refrigerant flows on the shell side and the secondary fluid (water) flows inside the tubes. The condenser heat exchanger is constructed from plain copper tubes while the evaporator is con-

ð2Þ

bCpref ;l ðT cond ÞMref ;cond þ C condmet M condmet cdT cond =dt ¼ UAcond  LMTDcond þ /½ðhref ;cond;l  href ;cond;g Þ þ Cpref ðT cond  T bed ÞM sg dwsg =dt dMref ;f ;ev ap =dt ¼ /  M sg ðdwdes =dt þ dwads =dtÞ

ð3Þ ð4Þ

where M (kg), C (kJ kg1 K1), Cp (kJ kg1 K1), T (K), LMTD (K), P 1 (kPa), h (kJ kg1), w (kgw kgsg ), DHads (J kg1) and t (s) are the mass, specific heat, specific heat at constant pressure, temperature, log mean temperature difference, pressure, specific enthalpy, uptake value, isosteric heat of adsorption, and time respectively. The subscripts bed, evap and cond refer to adsorbent bed (ads/des), evaporator and condenser condition respectively and w, sg, ref and met refer to water, silica gel, refrigerant and metal respectively. Subscripts g,

Fig. 1. Diagram for simulated two-bed cycle adsorption heat pump.

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Table 1 Chiller cyclic operation modes and valving. Mode

B-A

B-B

V-AE

V-AC

V-BE

V-BC

BP

V1

V2

V3

V4

V5

V6

V7

V8

V9

V10

V11

V12

A – ads/des B – mass recovery C – heat recovery D – ads/des E – mass recovery F – heat recovery

HW NF CW CW NF CW

CW NF CW HW NF CW

X X X O X X

O X O X X X

O X O X X X

X X X O X X

X O X X O X

O X X X X X

X X X O X X

O X X X X X

X X X O X X

X X O X X X

X X O O X X

O X X X X O

X O X O O O

O O O X O X

X X X X X O

X O O X O O

X O X X O X

HW = hot water, CW = cooling water, NF = no flow, X = close, O = open.

f, refer to fluid vapour and liquid condition respectively and Hex refers to the heat exchanger that interconnect with the adsorbent bed. A group of flags (f, /, @, c) were used to enable or disable some of the equation terms based on the operating mode as shown in Table 2. The rate of adsorption was evaluated using linear driving force kinetic model (LDF), where water vapour can reach all silica gel granules and the inter-particle mass transfer resistance can be neglected.

dw ¼ ð15Dso =R2p Þ expðEa =RTÞðw  wÞ dt

ð5Þ

where Rp (m), Dso (m2 s1), Ea (J mol1), R (J mol1 K1) and w⁄ 1

(kgw kgsg ) are particles radius, pre-experimental constant, activation energy, universal gas constant and equilibrium uptake respectively. Adsorption isotherms describe the amount of refrigerant that should be contained in the adsorbent pores at equilibrium conditions. There are many correlations that have been used to calculate the adsorption isotherms for different types of adsorbent materials. Freundlich model which was modified by Saha et al. [11] to give more precise fitting of the experimental data for silica gel/water pair was used to determine the adsorption isotherms. Eqs. (6)– (8) present the modified Freundlich model and all constants are furnished in Table 3.

Table 3 Parameters value of the simulation model. Constant

Value

Constant

Value

Constant

Value

A0 A1 A2 A3

6.5314 0.72452E1 0.23951E3 0.25493E6

B0 B1 B2 B3

15.587 0.15915 0.50612E3 0.53290E6

Dso Ea Rp DHads

3.625E3 4.2E4 0.16E3 2.939E6

The interface thermal contact resistance between two different materials depends on contact area, voids area, filling material and thermal conductivity for both materials [35]. Contact thermal resistance between zeolit granules and heat exchanger metal surface was experimentally investigated by Zhu and Wang [36]. Due to the negligible effect (1.5% difference in contact resistance value) of the difference in thermal conductivity of silica gel (0.198 W/mK) and zeolite (0.097 W/mK) on the contact thermal resistance [35], Eqs. (11)–(13), were used in the model. These equations are polynomial expressions with minimum R-squared value of 0.986 for the thermal contact resistance measured by Zhu and Wang [36] for three different zeolite granules sizes 50, 100 and 200 mesh corresponding to 0.297, 0.149 and 0.074 mm respectively.

Rcontact;#50 ¼ 0:0013T 2bed  0:1773T bed þ 8:6221

ð11Þ

ð6Þ

Rcontact;#100 ¼ 0:0012T 2bed  0:1624T bed þ 7:6785

ð12Þ

A3 T 3ads

ð7Þ

Rcontact;#200 ¼ 0:0008T 2bed  0:1214T bed þ 6:422

ð13Þ

BðT ads Þ ¼ B0 þ B1 T ads þ B2 T 2ads þ B3 T 3ads

ð8Þ

w ¼ AðT ads Þ½Psat ðT ref Þ=Psat ðT ads ÞBðT ads Þ AðT ads Þ ¼ A0 þ A1 T ads þ

A2 T 2ads

þ

where A0–3 and B0–3 are constants. Eqs. (9) and (10) present the methodology of evaluating incremental overall conductance of the adsorbent bed (dUAbed) and the overall conductance of evaporator and condenser heat exchanger respectively (UAevap-cond) based on different thermal resistance R. Simulation model governing equations are solved using MATLABÒ platform using ODE45 solver to compile the differential equations simultaneously and materials thermo-physical properties are evaluated by REFPROPÒ software. More detailed description of calculating the heat transfer thermal resistance can be found in [5].

dUAbed ¼ 1=Rw;bed þ Rtube;bed þ Ro;bed

ð9Þ

UAev apcond ¼ 1=Rw;ev apcond þ Rtube;ev apcond þ Rref ;ev apcond

ð10Þ

Table 2 Simulation model switching flags. Mode

Flag f

Flag /

Flag @

Flag c

ads – evaporation des – condensation Mass recovery Heat recovery

0 0 1 0

1 1 0 0

1 0 1 1

1 0 0 0

3.1. Performance indicators To evaluate adsorbent bed thermal performance two performance parameters were used; namely heat capacity ratio HCR and number of transfer unit NTU. HCR is the ratio between the thermal capacity of silica gel to that of the adsorbent bed metal, Eq. (14). Higher HCR means higher heat absorbed by silica gel compared to metal that directly enhances chiller COP. NTU is a dimensionless parameter whose magnitude influences adsorbent bed heat transfer performance, Eq (15). It is noteworthy to mention that enhancement of HCR and NTU improve adsorbent bed overall performance.

HCR ¼ M sg C sg =Mmet C met

ð14Þ

_ wCw NTU ¼ UAbed =m

ð15Þ

To evaluate adsorption chiller overall performance four indicators are used; namely cooling capacity ‘Qevap’ Eq. (16), heating load ‘Qheat’ Eq. (17), coefficient of performance ‘COP’ Eq. (18), Carnot coefficient of performance ‘COPcarnot’ Eq. (19) and chiller efficiency ‘g’ Eq. (20).

Q ev ap ¼

Z 0

t cycle

_ chw C w ðT chw;in  T chw;out Þdt m

 t cycle

ð16Þ

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Q heat ¼

 t cycle _ hw C w ðT hw;in  T hw;out Þdt tcycle m

Z

ð17Þ

0

COP ¼ Q ev ap =Q heat

ð18Þ

  COP Carnot ¼ ½ðT ads  T des Þ T des   ½T ev ap ðT ads  T ev ap Þ

ð19Þ

gchiller ¼ COP=COPCarnot

ð20Þ

_ (kg s1) presents secondary fluid mass flow rate and subwhere m scripts chw, hw refer to chilled water and hot water respectively.

load and cooling capacity are also presented. It is known that the predicted value of thermal simulation model can be accepted if the absolute average percent deviation is below 30%, [37]. Table 4, and Fig. 2, indicate clearly the good agreement between the model and experimental results. Table 5 presents the absolute average percent deviation for average cooling, heating and chilled water outlet temperature in addition to cooling capacity, heating power and COP for additional experimental runs. It can be seen that the maximum absolute percent deviation calculated based on steady state cycle is 17.8%.

4. The effect of fin spacing on adsorption chiller performance

Fig. 2, compares the predicted chilled, cooling and heating water outlet temperatures and their actual analogous values which were supplied by the manufacturer based on the same average inlet conditions. Table 4 presents the average percent deviation (APD) and absolute average percent deviation (ABS-PD) for cooling, heating and chilled water outlet temperatures for the test results shown in Fig. 2. The deviation between the predicted COP, heating

To improve heat and mass transfer performance in the adsorbent bed the following factors need to be considered: (1) Improving the overall heat transfer coefficient U and heat transfer area A in order to improve the overall conductance of the adsorbent bed UA significantly affect the heat transfer performance and the adsorption kinetics. (2) Increasing the fins height increases the silica gel thickness over heat exchanger tubes and decreases adsorbent bed permeability. (3) Changing the fins configuration affects the metal mass of the adsorbent bed, which affects the overall performance of the adsorption chiller. The simulation model was used to investigate the effect of fin spacing on the performance of adsorption chiller with the amount of silica gel kept constant and operating temperature of 11, 29.5 and 88.5 °C for chilled, cooling and heating water respectively and ads/des, mass recovery and heat recovery time of 430, 30 and 20 s respectively. As fin spacing changed, fin configuration (height and/or width) changed in order to accommodate the same amount of silica gel, Fig. 3a. It was observed that changing the fin width does not affect bed HCR or NTU in case of heating and cooling, Fig. 3b, 4a and b respectively. Therefore fin height was kept constant and fin width varied to keep the mass of silica gel constant without affecting the bed permeability. Decreasing fin spacing results in increasing the number of fins which will increase bed NTU but reduces its HCR due to increasing the surface area and the mass of metal in the bed. Increasing the adsorbent bed heat transfer performance by means of fin spacing reduction enhances the adsorption kinetics and hence chiller cooling capacity, Fig. 5. In contrast, the reduction in the bed HCR increases chiller heating capacity to heat up the increased metal mass, Fig. 5, these trends confirmed by Cacciola and Restuccia [25,38]. However, the rate of cooling capacity increase is lower than the rate of heating capacity increase which causes chiller COP to decrease by reducing fin spacing. To sum up, changing fin spacing from design value to minimum permissible value can in-

Water Outlet Temperatures [ºC]

3.2. Chiller simulation model results

100 90 80 Tchwi_Mod Tchwo_Pred Tcwi_Mod Tcwo_Pred Thwo_Pred Thwi_Act Thwo_Act Tcwi_Mod Tcwo_Act Tchwi_Act Tchwo_Act Thwi_Mod

70 60 50 40 30 20 10 0

0

240

480

720

960

1200

1440

1680

1920

Cycle Time [S] Fig. 2. Comparison between predicted data and actual data.

Table 4 Simulation model deviation mchw = 1180 L/min).

analysis

(mhw = 1100 L/min,

mcw = 4000 L/min,

Term

APD (%)

ABS-PD (%)

Term

APD (%)

ABS-PD (%)

Thw,o Tcw,o Tchw,o

1.6 1.1 16.5

2.4 3.4 16.5

Qevap Qheat COP

12.9 10.9 2.8

12.9 10.9 2.7

Table 5 Simulation model deviation analysis at one steady state cycle. Term

RUN-1

RUN-2

RUN-3

RUN-4

Unit

mhw mcw mchw

1100 4000 1180

1100 4000 1180

1100 4000 1180

2200 4000 1320

L/min L/min L/min

Thw,i,av Tcw,i,av Tchw,i,av

88.6 29.5 11.1

89.0 29.4 11.1

88.8 29.4 11.1

88.2 29.2 11.1

°C °C °C

Deviation analysis (actual o/p temperature and ABS-PD) 79.7 1.6 80.1 Thw,o Tcw,o 33.4 0.9 33.4 Tchw,o 5.8 12.3 5.7 Qheat 650 10.3 654 Qcool 439 13.1 446 COP 0.68 3.7 0.68

1.5 0.8 13.1 9.9 13.6 3.9

79.9 33.3 5.7 652 444 0.68

1.6 1.0 13.3 9.9 13.5 3.8

83.3 33.6 5.8 704 487 0.69

0.9 0.0 15.7 10.6 17.8 7.8

°C °C °C °C °C °C

and and and and and and

% % % % % %

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A.R.M. Rezk, R.K. Al-Dadah / Applied Energy 89 (2012) 142–149

Fig. 3. Fin height and HCR versus fin configuration.

Heating Capacity Cooling Capacity Chiller COP

700

0.75 0.70

650

0.65

600

0.60

550

0.55

500

0.50

450

0.45

400

0.40

350

0.35

300

0.30 2.2

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Fin Spacing Ratio [ -]

Chiller Cooling Capacity [kW]

750

Chiller COP [ -]

Chiller Cooling and Heating Capacity [ kW ]

Fig. 4. Bed NTU versus fin configuration (a) bed heating and (b) bed cooling.

550 500 450 400 350 300 250 200 150 100 50 0

Tcw_in = 25.0 Tcw_in = 30.0 Tcw_in = 35.0 Tcw_in = 40.0 Experiments

470 460 450 440 430 420 59.1 59.2 59.3 59.4 59.5 59.6 59.7

20

25

30

35

40

45

50

55

60

65

70

75

80

Generation Temperature Lift [ K ] Fig. 6. The effect of generation temperature lift on chiller cooling capacity.

Fig. 5. The effect of fin spacing on chiller performance.

crease the chiller specific cooling capacity by 3%, but decrease chiller COP by 2.3% due to the increase of heating capacity by 5.4%.

5. Operating temperatures Operating temperatures influence adsorption chiller performance. Lowering cooling water inlet temperature not only in-

creases cooling capacity, but also enhances adsorption chiller COP, due to the significant increase in adsorption rate. Increasing heating water temperature also enhances chiller cooling capacity due to enhancing desorption rate. The difference between the heating water temperature and the cooling water temperature is termed as the generation temperature lift [11]. Fig. 6 presents the change in chiller cooling capacity versus generation temperature lift at various cooling water inlet temperatures at fixed ads/

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A.R.M. Rezk, R.K. Al-Dadah / Applied Energy 89 (2012) 142–149

1.0

0.8

Chiller COP [ -]

1.0

Tcw_in = 25.0 Tcw_in = 30.0 Tcw_in = 35.0 Tcw_in = 40.0 Experiments

0.9

0.9 0.8

0.7

0.7

0.6

0.6

0.5

0.5 0.80

0.4

0.4

0.75 0.70

0.3

0.3

0.65

0.2

0.60 59.1 59.2 59.3 59.4 59.5 59.6 59.7

0.1 20

25

30

35

40

45

50

55

60

65

70

75

80

Generation Temperature Lift [ K ]

(a)

0.2 0.1 20

25

30

35

40

45

50

55

60

65

70

75

80

Generation Temperature Lift [ K ]

(b)

Fig. 7. The effects of generation temperature lift on chiller (a) COP and (b) efficiency.

des, mass recovery and heat recovery times. As the generation temperature lift increases chiller cooling capacity increases. Fig. 7 presents the variation in chiller COP and chiller efficiency versus generation temperature lift. It can be seen that at low cooling water temperature, the chiller COP and efficiency decrease with increasing the generation temperature lift over the tested range. However, at higher cooling water temperature (Tcw > 30 °C), the chiller COP initially increases to a certain point and then remains relatively constant with increasing the generation temperature lift. On the other hand, the chiller efficiency after reaching maximum point decreases with increasing the generation temperature lift. The decrease in chiller efficiency at low generation temperature lift and high cooling water temperature is due to the insufficient refrigerant circulation required to generate the cooling power. On the other hand, the decrease in chiller efficiency at high temperature lift is due to the increase in heat losses [21]. Chiller COP and efficiency behaviours encourage using generation temperature lift as a load control tool. For example, at cooling water temperature of 35 °C, the chiller cooling capacity increased almost linearly (from 180 to 342 kW) with increasing the generation temperature lift (from 40 to 65 K). The reduction in chiller COP (from 0.63 to 0.60) and efficiency (from 0.68 to 0.52) are relatively small.

6. Cycle time During the physical adsorption process, the solid adsorbent adsorbs the refrigerant from the evaporator container to develop a cooling effect by means of refrigerant evaporation. The heat generated due to the adsorption process is removed to sustain the adsorption process and maintain the cooling effect. However for specific adsorption time, the rate of adsorption decreases with increasing the amount of refrigerant adsorbed until the bed becomes saturated with refrigerant. Hence the cooling effect reduces with increasing the adsorption time. The adsorbent bed is regenerated by heating and the desorbed refrigerant is condensed and passed back to the evaporator to repeat the aforementioned process. As the adsorption time increase, the heating load decreases and hot water outlet temperature approaches the inlet temperature. This will increase the COP but decrease the cooling capacity. Continuous cooling is achieved by using two beds, where one bed is connected to the evaporator in adsorption mode and the other bed to the condenser in desorption mode. Before reversing adsorption and desorption modes sufficient time period is required

to preheat/precool the adsorption/desorption beds to avoid premature connection between the hot bed and evaporator which results in momentary desorption of adsorbed refrigerant and undesirable reduction in instantaneous cooling capacity. In the simulated adsorption chiller the switching period is divided into mass and heat recovery periods. It is noteworthy that during switching period there is no interconnection between adsorbent beds and evaporator/condenser where no cooling effect can be achieved anymore. As a result, appropriate switching time can improve the cooling capacity and COP of the adsorption chiller. Fig. 8 presents the effect of changing ads/des and mass recovery time periods simultaneously on chiller cooling capacity for different heat recovery times using constant operating temperature given in Section 4. It is observed that as ads/des time period increases, chiller cooling capacity increases sharply, reaches a maximum at certain time and then decreases gradually. Within the investigated range, it was observed that the cooling capacity at maximum point in Fig. 8a–c produces 6.1% and 0.4% higher and 5.7% lower values compared to the reference operating times given in Section 4. GA is used to calculate the optimum values for ads/des, heat recovery and mass recovery times that achieve the maximum cooling capacity, which is the optimisation objective function. GA is a subclass of evolutionary algorithms that based on the natural selection processes that drive the biological evolution. The algorithm starts the first iteration with initial random population for each parameter to get a set of individuals (Npopulation  Nparameter). This population is used for calculating the corresponding objective function values. A new generation is then developed to be used as a new population in next iteration using a selection function based on three rules named; elite selection, crossover and mutation. The individuals that achieved the best objective function values in the current generation and granted to survive to the next generation are elite individuals. Crossover enables the algorithm to extract the best individuals and recombine them into potential superior individuals using a specified crossover fraction. The mutation rule replaces the remaining population with randomly selected new ones. Crossover fraction of 1 does not enhance the solution where the new generation is just a new combination of the initial population. However, crossover fraction of zero gets the new generation based on mutation only which diverge the solution. GA is applied to determine global optimum operating times within a specific range that could include the optimum combination that maximize the cooling capacity. The range of times used

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Fig. 8. The effect of ads/des and mass recovery time period on chiller cooling capacity (a) theat

were 250–450 s for ads/des time period, 10–50 s for mass and heat recovery time periods. The number of population for each individual parameter is selected to be 20 while the number of elite count is 2, the crossover fraction is 0.8 and the rest of individuals are managed by mutation rule. These were recommended by Mathwork GA ManualÒ [39]. After 30 iterations the GA solver stopped, where no more improvement in the solution in terms of objective function value, average diversity and best, worst and mean score. The determined optimum ads/des, mass recovery and heat recovery time period values are 345, 12 and 14 s respectively. Chiller cooling capacity at the new cycle time increased by 8.3% and COP reduced from 0.66 to 0.60 compared to their analogues values while chiller working at reference operating cycle times.

7. Conclusions The presented simulation model predicted the performance of commercial 450 kW adsorption water chiller with good accuracy. The model is a global model that has the ability to investigate the effect of various physical parameters on the performance of the adsorption chiller. This advantage is highlighted by investigating the effect of fin spacing on chiller performance, where chiller cooling capacity increases by 3% by reducing fin spacing from its design value to the minimum permissible value. Chiller operation conditions such as operating temperature and cycle time directly influence chiller performance. Operating temperature can be used as a load control tool to mange chiller operation in case of part load with high efficiency. Cycle time can be used to improve chiller performance to get more cooling and GA is used to determine the global optimum cycle time corresponding

recovery

= 20 s, (b) theat

recovery

= 60 s, (c) theat

recovery

= 100 s.

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