research article performance study of a four-bed silica

Research ArticlePerformance Study of a Four-Bed Silica Gel-Water AdsorptionChiller with the Passive Heat Recovery Scheme

Zhilong He,1 Xiaolin Wang,2 and Hui Tong Chua3

1 School of Energy and Power Engineering, Xi’an Jiaotong University, 28 Xianning West Road, Xi’an 710049, China2 School of Engineering & ICT, University of Tasmania, Hobart, TAS 7001, Australia3 School of Mechanical and Chemical Engineering, The University of Western Australia, 35 Stirling Highway,Crawley, WA 6009, Australia

Correspondence should be addressed to Xiaolin Wang; [email protected]

Received 23 August 2014; Accepted 19 October 2014

Academic Editor: Gongnan Xie

Copyright © 2015 Zhilong He et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Adsorption chiller technology is one of the effective means to convert waste thermal energy into effective cooling, whichsubstantially improves energy efficiency and lowers environmental pollution.This paper uses an improved lump-parameter designmodel to theoretically and experimentally evaluate the efficacy of the passive heat recovery scheme as applied to a four-bedadsorption chiller. Results show that the model can accurately track the experimental temporal system outlet temperatures. Theperformance predictions from this model compare favourably with experimental results. At rated temperature conditions and overa wide range of cycle times, both the cooling capacity and COP can be predicted to within 12.5%. The analyses indicate that themodel can be used confidently as a design tool for a four-bed adsorption chiller and the passive heat recovery scheme can effectivelyimprove the system performance.

1. Introduction

In the past three decades, silica gel-water adsorption chillershave been proven to be an economically viable and envi-ronmentally friendly technology that can effectively convertlow grade thermal energy to useful cooling [1–12]. In thestandard form, this genre of adsorption chillers can be drivenby any conceivable form of thermal energy with temperaturesabove 70∘C. By adopting a multibed and multistage design,the chiller can even be driven by 55∘C thermal energy andproduce reasonable cooling capacity at the expense of lowCOP [5, 9, 13, 14].

In order to improve the chiller performance, various tech-nologies have been diligently pursued. GBU mbH [12] andMayekawa Manufacturing Co. Ltd. applied the water circu-lation between the adsorber and desorber during switchingin their commercial adsorption chillers. Wang [15] and Quet al. [16] studied the combined heat and mass recovery inan adsorption cycle. Akahira et al. [17] investigated the effectof mass recovery on the chiller cooling capacity. Wang and

Chua [18] compared the passive heat recovery scheme andwater circulation scheme as applied to a standard two-bedadsorption chiller. They concluded that both heat recoveryschemes have the same efficacy in terms of performanceimprovement. However, in comparison to the water circu-lation scheme, the passive heat recovery scheme is muchsimpler in terms of the control systemdesign and it eliminatesthe need of water valves to save the hardware cost. Allthese technologies significantly improved the conversionefficiency for a standard two-bed adsorption chiller.However,all of them were oblivious to the opportunity of maximizingenthalpy extraction from the low grade waste heat source andthe issue of chilled water temperature fluctuation.

In the spirit of exploiting low gradewaste heat sources andimproving the energy conversion from waste heat to usefulcooling, Saha et al. [13] studied a multistage silica gel-wateradsorption chiller which could be operated by heat sourceswith temperatures as low as 55∘C at the expense of verylow COP. In the spirit of improving the energy conversionfrom waste heat to useful cooling, Chua et al. [14] proposed

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015, Article ID 634347, 10 pageshttp://dx.doi.org/10.1155/2015/634347

2 Mathematical Problems in Engineering

Condenser

EvaporatorChilled water inlet

Chilled water outlet

Bed 1 Bed 2 Bed 3 Bed 4

V5 V6 V7 V8 V9 V10 V11 V12

V13V14V15V16V17V18V19V20Hot water

GV1GV2 GV3 GV4

GV5GV6GV7GV7

V1 V2 V3 V4

Condenser outlet

To bed

To condenser

Bed outlet

FM

FM

FM

FM

Hot water inlet

Valve openValve closed

Coolingwaterinlet

Coolingwateroutlet

Figure 1: Schematic of a four-bed adsorption chiller adapted from [19].

a multibed regenerative adsorption scheme and demon-strated its efficacy theoretically. In comparison to a two-bed adsorption chiller, they aimed to maximize the energyextraction from low grade thermal energy thereby maxi-mizing the cooling capacity and concomitantly damp thechilled water outlet temperature fluctuation. Subsequentlythe four-bed adsorption chiller [5, 9, 19] was successfullyprototyped and validated the aforementioned virtues of four-bed chillers. However, the experimental study also revealedthe inadequacies of previous model [14] which significantlyoverestimates the chiller coefficient of performance (COP).Furthermore, the experimental temperatures at the beds andsystem outlets showed that there are a big room for heatrecovery from the hot water at system outlet.

The objective of this paper is to develop an improvedlump-parameter model to analyse the performance of a four-bed adsorption chiller with the passive heat recovery scheme.We will demonstrate that this model can accurately predictthe experimental temporal systemoutlet temperatures duringthe bed switching period. Specifically we will show that thesimulation results agree favourably with experimental dataover different operating conditions. Analyses show that themodel can be reliably used for chiller design.

2. Working Principle of a Four-BedAdsorption Chiller with Its PassiveHeat Recovery Scheme

The detailed operating scheme of the standard four-bedadsorption chiller is described in [14, 19, 20]. The four-bed

regenerative strategy is an extension from the standard two-bed chiller operation. Briefly in the standard two-bed chiller,adsorption cycles require two processes: heating-desorption-condensation and cooling-adsorption-evaporation. Theformer process requires energy to preheat the cold desorberand subsequently desorb water from the silica gel. The latterprocess demands energy removal from the precooling ofthe hot adsorber and the subsequent adsorption of watervapour onto silica gel. In the case of a four-bed chiller, oneadditional slave desorber and additional slave adsorber con-tribute to the desorption and adsorption processes, respec-tively. The operation of chiller is controlled so that a constantphase difference exists between the master and slave adsorb-ers and desorbers, respectively.The two processes in the oper-ation cycle become heating-slave desorption-master desorp-tion-condensation and cooling-slave adsorption-masteradsorption-evaporation. The hot water flows through themaster desorber and then into the slave desorber beforebeing purged. Similarly the cooling water enters the masteradsorber and then into the slave adsorber before returningto the cooling tower.

Figure 1 shows the schematic of a four-bed adsorptionchiller [19]. Bed 1 works as the master adsorber and bed 2the slave adsorber. Both adsorbers induce evaporation in theevaporator. Cooling water flows through bed 1 via valve 6and then into bed 2 via valve 1 to sustain the adsorption inboth beds. Meanwhile hot water flows through bed 3, whichacts as the master desorber, via valve 9 and then into bed 4,which acts as the slave desorber, via valve 3. Both desorbers

Mathematical Problems in Engineering 3

1 2

4 3

1 2

4 3

1 2

4 3

1 2

rejectioninput

Heating input

input

input

input

4 3

Passive heat recovery scheme

Standardscheme

Coolinginput

Coolinginput

Coolinginput

Coolinginput

Coolingrejection

Coolingrejection

Coolingrejection

Coolingrejection

Masteradsorber Slave

adsorber

Standardscheme

Heatinput

Heatrejection

Masterdesorber

Masterdesorber

Masterdesorber

Masteradsorber

Masteradsorber

Masteradsorber

Slavedesorber Master

desorberSlave

desorber

Slavedesorber

Slavedesorber

Slaveadsorber

Slaveadsorber

Slaveadsorber

Passive heatrecovery scheme

Normal operation Normal operation

Heating

Heating Heating

Heating

Heating

Switching process

Figure 2: Schematic of the passive heat recovery scheme.

are connected to the condenser, which condenses the vapourstemming from the two desorbers, and the condensate even-tually returns to the evaporator via a U-tube. This operatingphase ends when the master adsorber is nearly saturated andthe master desorber is sufficiently purged of water vapour. Inthe ensuing switching phase, bed 1 changes to a slave desorber,bed 2 to a master adsorber, bed 3 to a slave adsorber, and bed4 to a master desorber. Beds 2 and 4 are connected to theevaporator and condenser, respectively. During this period,due to the resident cooling water in the heat exchanger andits inherent thermal mass, bed 1 must be preheated. Similarlybed 3 must be precooled because of the resident hot waterand its inherent thermal mass. To prevent parasitic vapourmigration, beds 1 and 3 are isolated from both the evaporatorand condenser. The total energy input 𝑄input to the chillerincludes both the preheating energy 𝑄p-h during switchingperiod to preheat the cool desorber and energy input 𝑄hotinto both the master and slave desorbers during normaloperation to sustain the desorption.The total energy rejection𝑄rej comprises both the precooling energy 𝑄p-c to precoolthe hot adsorber and the energy rejection 𝑄

𝑐from both the

master and slave adsorbers during normal adsorption processto sustain the adsorption.

The passive heat recovery scheme has been described in[18, 19]. It aims to recover the energy 𝑄rec from the energy𝑄p-c to compensate for the energy𝑄p-h by always channellingthe water from the hot adsorber to the heat source andwater from the cool desorber to the cooling tower during theswitching period. Figure 2 schematically demonstrates thepassive heat recovery scheme. During the switching period,the cooling water upon passing through the hot adsorber

is heated and directed to the heat source instead of to thecooling tower by delaying the switching of valvesV16 andV19,respectively, as in Figure 1. Concomitantly, the incoming hotwater upon heating up the cool desorber is thereby cooledand directed to the cooling tower. This process terminateswhen the hot water outlet temperature equals the coolingwater outlet temperature.With this water circulation scheme,a portion of the otherwise rejected precooling energy 𝑄p-c isrecovered (𝑄rev) and returned to the heat source. Hence thepassive heat recovery scheme attenuates the energy input tothe chiller system and improves the COP.

3. Mathematical Modelling

The mathematical model is an improvement of our previousresearch work [14, 21]. The equations for adsorption beds areadapted from these two literatures and the equations for theconnection piping system are built based on the mass andenergy balance. The major assumptions are listed below.

(1) In the adsorbers and desorbers, the temperature of sil-ica gel, water and heat exchanger materials includingfins, tubes, and supporting frames are approximatedby a representative temperature.

(2) The cooling, heating, and chilled water in the heatexchanger tubes and connection pipes are discretizedinto a number of elements to capture the thermalwave propagation during the bed switching period.

(3) In the condenser, the tube bank surface is assumedto be able to hold a certain maximum amount of


condensate, 𝑀Maxref,cond. Beyond this the condensate

would flow into the evaporator via the U-tube.

(4) The system outlet is about 1m away from the beds’outlet according to the commercial adsorption chillerdesign.

3.1. Rate of Adsorption andDesorption. Therate of adsorptionor desorption is calculated by the linear driving force kineticequation:

𝑑𝑞

𝑑𝑡= 15

𝐷𝑠𝑜𝑒−𝐸𝑎/(𝑅𝑇)

𝑅2𝑝

(𝑞∗

− 𝑞) . (1)

All the coefficients were determined by Chihara andSuzuki [20] and 𝑞

∗ is available as a Henry’s law correlation[14] underpinned by manufacturer’s proprietary data [22]:

𝑞∗

= 𝐾𝑜exp(

−Δ𝐻ads𝑅𝑇

)𝑃, (2)

where𝐾𝑜= 2 × 10

−12 Pa−1 and Δ𝐻ads = 2.51 × 103 kJ/kg.

3.2. Energy Balance in the Adsorbers and Desorbers. Theenergy balance for the adsorber during its interaction withthe evaporator during normal operation can be described as

(𝑀sg𝑐V,sg +𝑀Hex𝑐V,Hex +𝑀sg𝑞bed,𝑖𝑐V𝑔)𝑑𝑇bed,𝑖

𝑑𝑡

= 𝑀sg𝑑𝑞bed,𝑖

𝑑𝑡

× {𝜁 [ℎ𝑔(𝑇evap) − ℎ

𝑔(𝑃evap, 𝑇bed,𝑖) + Δ𝐻ads]

+ (1 − 𝜁) Δ𝐻ads} − 𝑈𝑐

𝐴bed𝑁

𝑁

∑

𝑘=1

(𝑇bed,𝑖 − 𝑇𝑘,𝑖)

(3)

and the energy balance for the cooling water in the adsorberis expressed as

𝜌𝑓𝑐V𝑓

𝑉bed,𝑖

𝑁

𝑑𝑇𝑘,𝑖

𝑑𝑡

= ��cool [ℎ𝑓 (𝑇𝑘−1,𝑖) − ℎ𝑓(𝑇𝑘,𝑖)] + 𝑈

𝑐

𝐴bed,𝑖

𝑁(𝑇bed,𝑖 − 𝑇

𝑘,𝑖) ,

(4)

where 𝑖 represents an adsorber, 𝑖 = 1means master adsorberand 𝑖 = 2 means slave absorber, and 𝑘 represents the localelement ranging from 1 to𝑁.

The energy balance for the desorber during its interac-tionwith the condenser during normal operation is expressedas

(𝑀sg𝑐V,sg +𝑀Hex𝑐V,Hex +𝑀sg𝑞bed,𝑗𝑐V𝑔)𝑑𝑇bed,𝑗

𝑑𝑡

= 𝑀sg𝑑𝑞bed,𝑗

𝑑𝑡

× {𝜁 [ℎ𝑔(𝑇cond) − ℎ

𝑔(𝑃cond, 𝑇bed,𝑗) + Δ𝐻ads]

+ (1 − 𝜁) Δ𝐻ads} − 𝑈ℎ

𝐴bed,𝑗

𝑁

𝑁

∑

𝑘=1

(𝑇bed,𝑗 − 𝑇𝑘,𝑗)

(5)

and the energy balance for the hot water in the desorber isdescribed as

𝜌𝑓𝑐V𝑓

𝑉bed,𝑗

𝑁

𝑑𝑇𝑘,𝑗

𝑑𝑡

= ��hot [ℎ𝑓 (𝑇𝑘−1,𝑗) − ℎ𝑓(𝑇𝑘,𝑗)]

+ 𝑈ℎ

𝐴bed,𝑗

𝑁(𝑇bed,𝑗 − 𝑇

𝑘,𝑗) ,

(6)

where 𝜁 = 1 if 𝑞∗ > 𝑞 and 𝜁 = 0 if 𝑞∗ < 𝑞. 𝑗 represents adesorber. 𝑗 = 3meansmaster desorber and 𝑗 = 4means slavedesorber. 𝑘 represents the local element ranging from 1 to𝑁.

During the switching period, the slave adsorber and des-orber become themaster adsorber and desorber, respectively.Their energy balances are expressed in (3)–(6). At the sametime, the master adsorber becomes the slave desorber andthemaster desorber becomes the slave adsorber. Accordingly,the gas valves between the current slave desorber and con-denser and between the current slave adsorber and evapora-tor are shut and the volume inside those two adsorbent bedsis constant. For these two adsorbent beds, the energy balanceequation for the beds and the interacting fluids can be writtenas

(𝑀sg𝑐V,sg +𝑀Hex𝑐V,Hex +𝑀sg𝑞bed,𝑙𝑐V𝑔)𝑑𝑇bed,𝑙

𝑑𝑡

= −𝑈ℎ/𝑐

𝐴bed𝑁

𝑁

∑

𝑘=1

(𝑇bed,𝑙 − 𝑇𝑘,𝑙) ,

𝜌𝑓𝑐V𝑓

𝑉bed𝑁

𝑑𝑇𝑘,𝑙

𝑑𝑡

= ��cool/hot [ℎ𝑓 (𝑇𝑘−1,𝑙) − ℎ𝑓(𝑇𝑘,𝑙)]

+ 𝑈ℎ/𝑐

𝐴bed𝑁

(𝑇bed,𝑙 − 𝑇𝑘,𝑙) ,

(7)

where 𝑙 = 2 refers to the hot slave adsorber and 𝑙 = 4 to thecold slave desorber. 𝑘 ranges from 1 to𝑁.


The connecting pipes between the beds are utilised whenthe cooling (heating) fluid is directed from the master adsor-ber (desorber) to the slave adsorber (desorber). This thenimpacts on the temperature of the fluid in the slave adsorber(desorber), due to heat loss from the fluid while travellingthrough the pipes. The energy balances for the connectingpipes are expressed below:

𝜌𝑓

𝑉𝑓

𝑁tube𝑐V,𝑓

𝑑𝑇𝑘,𝑖/𝑗,𝑚

𝑑𝑡

= 𝛿��cool/hot [ℎ𝑓 (𝑇𝑘−1,𝑖/𝑗,𝑚) − ℎ𝑓(𝑇𝑘,𝑖/𝑗,𝑚

)]

+ ℏ𝐴𝑚,tube

𝑁tube(𝑇𝑚,𝑘

− 𝑇𝑘,𝑖/𝑗,𝑚

) ,

𝜌𝑚

𝑉𝑚

𝑁tube𝑐V,𝑚

𝑑𝑇𝑚,𝑘

𝑑𝑡

= ℏ𝑚,𝑓

𝐴𝑚,tube

𝑁tube(𝑇𝑘,𝑖/𝑗,𝑚

− 𝑇𝑚,𝑘

)

+ ℏ𝑚,air

𝐴air,tube

𝑁tube(𝑇air,𝑘 − 𝑇

𝑚,𝑘)

+ 𝑘𝑚(𝑇𝑚,𝑘−1

− 2𝑇𝑚,𝑘

+ 𝑇𝑚,𝑘+1

)𝑁𝐴cross,tube

𝐿,

(8)

where 𝛿 is defined as 𝛿 = 1 for connecting pipes betweenmas-ter adsorber and slave adsorber, and betweenmaster desorberand slave desorber; 𝛿 = 0 for connecting pipes between slaveadsorber and master desorber, and between slave desorberand master adsorber. The subscript 𝑚 highlights that we arereferring to the connecting pipes between beds, and 𝑘 rangesfrom𝑁 + 1 to𝑁 +𝑁tube.

The initial conditions for the adsorbers, desorbers, andconnecting pipes are expressed as follows.

For the adsorbers: 𝑇0,𝑖(0) = 𝑇

𝑘,𝑖(0) = 𝑇

incool, 𝑘 = 1 to 𝑁;

𝑇bed,𝑖(0) = 𝑇incool; 𝑞bed,𝑖(0) = 𝑞

inbed,𝑖; 𝑃evap(0) = 𝑃sat(𝑇

inchilled);

𝑇evap(0) = 𝑇inchilled.

For the desorbers: 𝑇0,𝑗(0) = 𝑇

𝑘,𝑗(0) = 𝑇

inhot, 𝑘 = 1 to 𝑁;

𝑇bed,𝑗(0) = 𝑇inhot; 𝑞bed,𝑗(0) = 𝑞

inbed,𝑗; 𝑃cond(0) = 𝑃sat(𝑇

incool);

𝑇cond(0) = 𝑇incool.

For the connecting pipes, 𝑇𝑘,𝑖,𝑚

(0) = 𝑇incool and 𝑇𝑘,𝑗,𝑚(0) =

𝑇inhot, 𝑘 = 𝑁 + 1 to 𝑁 + 𝑁tube. The corresponding piping

materials will have the same initial conditions as the watercontained therein.

The boundary conditions for the adsorbers and desorbersare expressed as follows.

During normal operation: for the master and slaveadsorbers: 𝑇

0,1(𝑡) = 𝑇

incool; 𝑇0,2(𝑡) = 𝑇

𝑁+𝑁tube ,1,𝑚(𝑡), and for

desorbers: 𝑇0,3(𝑡) = 𝑇

inhot; 𝑇0,4(𝑡) = 𝑇

𝑁+𝑁tube ,3,𝑚(𝑡).

During the switching operation, following from the nor-mal operation described immediately above: for the master

and slave adsorbers: 𝑇0,2(𝑡) = 𝑇

incool; 𝑇0,3(𝑡) = 𝑇

𝑁+𝑁tube ,2,𝑚(𝑡),

and for desorbers: 𝑇0,4(𝑡) = 𝑇

inhot; 𝑇0,1(𝑡) = 𝑇

𝑁+𝑁tube ,4,𝑚(𝑡).

The temperatures at the system outlet differ from thoseat the bed outlet due to the connection piping. The corre-sponding amount of resident water and piping material areseparately considered as lumped systems. For the standardoperation scheme, the temperatures at the system outlet canbe determined by

𝜌𝑓𝑉𝑓,cool𝑐V,𝑓

𝑑𝑇cool,out

𝑑𝑡

= ��cool [ℎ𝑓 (𝑇𝑁,2) − ℎ𝑓(𝑇cool,out)]

+ ℏ (𝑇pm,cool − 𝑇cool,out)𝐴pm,tube,

𝜌pm𝑉pm𝑐V,pm𝑑𝑇pm,cool

𝑑𝑡

= ℏpm,𝑓 (𝑇cool,out − 𝑇pm,cool)𝐴pm,tube

+ ℏpm,air (𝑇air − 𝑇pm,cool)𝐴air,tube,

𝜌𝑓𝑉𝑓,hot𝑐V,𝑓

𝑑𝑇hot,out

𝑑𝑡

= ��hot [ℎ𝑓 (𝑇𝑁,4) − ℎ𝑓(𝑇hot,out)]

+ ℏ (𝑇pm,hot − 𝑇hot,out)𝐴pm,tube,

𝜌pm𝑉pm𝑐V,pm𝑑𝑇pm,hot

𝑑𝑡

= ℏpm,𝑓 (𝑇hot,out − 𝑇pm,hot)𝐴pm,tube

+ ℏpm,air (𝑇air − 𝑇pm,hot)𝐴air,tube.

(9)

The initial conditions for the temperatures are 𝑇cool,out(0) =𝑇𝑚,cool(0) = 𝑇

incool, 𝑇hot,out(0) = 𝑇

𝑚,hot(0) = 𝑇inhot.

For the passive heat recovery scheme, the system outlettemperatures depend on the outlet temperatures at the slavedesorber and adsorber during the switching period. If 𝑇

𝑁,2≥

𝑇𝑁,4

then we assign 𝑇switch,cool = 𝑇𝑁,4

and 𝑇switch,hot = 𝑇𝑁,2

;if 𝑇𝑁,2

< 𝑇𝑁,4

then 𝑇switch,cool = 𝑇𝑁,2

and 𝑇switch,hot =

𝑇𝑁,4

. The system outlet temperatures can then be accordinglydetermined as

𝜌𝑓𝑉𝑓,cool𝑐V,𝑓

𝑑𝑇cool,out

𝑑𝑡

= ��cool [ℎ𝑓 (𝑇switch,cool) − ℎ𝑓(𝑇cool,out)]

+ ℏ (𝑇pm,cool − 𝑇cool,out)𝐴pm,tube


𝜌pm𝑉pm𝑐V,pm𝑑𝑇pm,cool

𝑑𝑡

= ℏ𝑚,𝑓

(𝑇cool,out − 𝑇pm,cool)𝐴pm,tube

+ ℏ𝑚,air (𝑇air − 𝑇pm,cool)𝐴air,tube

𝜌𝑓𝑉𝑓,hot𝑐V,𝑓

𝑑𝑇hot,out

𝑑𝑡

= ��hot [ℎ𝑓 (𝑇switch,hot) − ℎ𝑓(𝑇hot,out)]

+ ℏ (𝑇pm,hot − 𝑇hot,out)𝐴pm,tube.

𝜌pm𝑉pm𝑐V,pm𝑑𝑇pm,hot

𝑑𝑡

= ℏpm,𝑓 (𝑇hot,out − 𝑇pm,hot)𝐴pm,tube

+ ℏpm,air (𝑇air − 𝑇pm,hot)𝐴air.tube.

(10)

The initial conditions for the temperatures are similarlyassigned as 𝑇cool,out(0) = 𝑇

𝑚,cool(0) = 𝑇incool, 𝑇hot,out(0) =

𝑇𝑚,hot(0) = 𝑇

inhot.

3.3. Energy Balance for the Condenser. Theenergy balance forthe condenser and the cooling water inside the condenser isexpressed as

(𝑀ref,cond𝑐V𝑓 (𝑇cond) + 𝑀cond𝑐V,cond)𝑑𝑇cond𝑑𝑡

+∑𝜃𝑗ℎ𝑓(𝑇cond)𝑀sg

𝑑𝑞bed,𝑗

𝑑𝑡

= −∑𝑀sg𝑑𝑞bed,𝑗

𝑑𝑡[𝜁ℎ𝑔(𝑇cond) + (1 − 𝜁) ℎ

𝑔(𝑃cond, 𝑇bed,𝑗)

− (1 − 𝜁) (1 − 𝜃𝑗) ℎ𝑓(𝑇cond)]

− 𝑈cond𝐴cond𝑁2

𝑁2

∑

𝑘=1

(𝑇cond − 𝑇𝑘,cond) ,

𝜌𝑓𝑐V𝑓

𝑉cond𝑁2

𝑑𝑇𝑘,cond

𝑑𝑡

= ��cond [ℎ𝑓 (𝑇𝑘−1,cond) − ℎ𝑓(𝑇𝑘,cond)]

+ 𝑈cond𝐴cond𝑁2

(𝑇cond − 𝑇𝑘,cond) ,

(11)

where 𝜃𝑗is defined as

𝜃𝑗= 1 when 𝑀ref,cond < 𝑀

maxref,cond; 𝜃𝑗 = 1 when

𝑀ref,cond = 𝑀maxref,cond and 𝑑𝑞bed,𝑗/𝑑𝑡 > 0;

𝜃𝑗= 0 when𝑀ref,cond = 𝑀

maxref,cond and 𝑑𝑞bed,𝑗/𝑑𝑡 < 0.

The boundary and initial conditions are

𝑇0,cond (𝑡) = 𝑇

incool; 𝑇

𝑘,cond (0) = 𝑇incool, 𝑘 = 1 to 𝑁

2;

𝑇cond (0) = 𝑇incool; 𝑞bed,𝑗 (0) = 𝑞

inbed,𝑗;

𝑀ref,cond (0) = 𝑀maxref,cond.

(12)

3.4. Energy Balance for the Evaporator. The energy balancefor the evaporator and the chilled water inside the evaporatoris expressed as

(𝑀ref,evap𝑐V𝑓 +𝑀evap𝑐V,evap)𝑑𝑇evap

𝑑𝑡− ℎ𝑓(𝑇evap)

2

∑

𝑙=1

𝛾𝑙

𝑑𝑞bed,𝑙

𝑑𝑡

= − (1 − 𝜁) (1 − 𝜃) ℎ𝑓(𝑇cond)𝑀sg∑

𝑑𝑞bed,𝑗

𝑑𝑡

−𝑀sg∑𝑑𝑞bed,𝑖

𝑑𝑡[𝜁ℎ𝑔(𝑇evap) + (1 − 𝜁) ℎ

𝑔(𝑃evap, 𝑇bed,𝑖)]

− 𝑈chilled𝐴evap

𝑁1

𝑁1

∑

𝑘=1

(𝑇evap − 𝑇𝑘,evap) ,

𝜌𝑓𝑐V𝑓

𝑉evap

𝑁1

𝑑𝑇𝑘,evap

𝑑𝑡

= ��chilled [ℎ𝑓 (𝑇𝑘−1,evap) − ℎ𝑓(𝑇𝑘,evap)]

+ 𝑈chilled𝐴evap

𝑁1

(𝑇evap − 𝑇𝑘,evap) ,

(13)

where 𝛾 = 1 when the bed interacts with the evaporator and𝛾 = (1 − 𝜁)(1 − 𝜃) when the bed interacts with the condenser.The boundary and initial conditions are

𝑇0,evap (𝑡) = 𝑇

inchilled;

𝑇𝑘,evap (0) = 𝑇

inchilled, 𝑘 = 1 to 𝑁

1;

𝑇evap (0) = 𝑇inchilled; 𝑞bed,𝑗 (0) = 𝑞

inbed,𝑗;

𝑞bed,𝑖 (0) = 𝑞inbed,𝑖.

(14)

The cycle average cooling capacity 𝑄evap, energy input𝑄hot, and COP are, respectively, calculated as

𝑄evap = ��chilled𝑐V𝑓 ∫𝑡cycle

0

𝑇inchilled − 𝑇

outchilled

𝑡cycle𝑑𝑡,

𝑄hot = ��heat𝑐V𝑓 ∫𝑡cycle

0

𝑇inhot − 𝑇

outhot

𝑡cycle𝑑𝑡,

COP =𝑄evap

𝑄hot.

(15)


Table 1: Values for the parameters used in the present model.

𝐷so 2.54 × 10−4 m2/s𝐸𝑎

4.2 × 104 J/mol𝑅𝑝

1.7 × 10−4 m𝑈bed 1002W/m2

⋅K𝑈cond 5833W/m2

⋅K𝑈chilled 3028W/m2

⋅K𝐴bed 2.7m2

𝐴 cond 5.08m2

𝐴evap 3.53m2

𝐴 cham 7.1m2

𝑐𝑝,Al 905 J/kg⋅K𝑐𝑝,Cu 386 J/kg⋅K𝑐𝑝,sg 924 J/kg⋅K𝑀sg 36 kg𝑀bed 40 kg𝑀fin 21 kg𝑀cond 26 kg𝑀evap 13.6 kg𝑀water 57 kgℏ𝑚,air 10W/m2

⋅K𝑘𝑚

401W/m⋅K��cool 48 L/min��hot 48 L/min��cond 120 L/min��chilled 48 L/min

4. Results and Discussion

The investigations described herein are conducted on a four-bed adsorption chiller [19]. The values for the parametersused in the present model are furnished in Table 1. Thesimulation results are comparedwith the experimental resultsreported in our previous papers [9, 19] at the various workingconditions. The rated operating temperature conditions fol-low the convention stipulated in the ARI standard. The hotwater temperature is 85∘Cwhile the cooling and chilled watertemperatures are 29.4∘C and 12.2∘C, respectively.

The water temperatures at the outlets of the condenser,evaporator, and bed systems are commonly used to charac-terize the adsorption/desorption behaviour. Figure 3 showstypical temperature histories at the outlets of the four-bedadsorption chiller system with the passive heat recoveryat rated temperature conditions with a cycle time 320 s. Itcompares the predicted simulation results and experimentaldata published in our previous paper [19].The result indicatesthat our present simulation results exhibit a sufficiently goodagreement with the experimental data. Figure 4 presents thetemperature histories at the outlets of both condenser andevaporator. Again it displays a good agreement with theexperimental data. It is palpable that our model accuratelydescribes the workings of the passive heat recovery scheme.

Figures 5 and 6 show the system performance at differentcycle times, with simulations benchmarked against experi-mental data [9, 19]. Since the passive heat recovery scheme

15

25

35

45

55

65

75

85

95

0 100 200 300 400 500 600

Wat

er te

mpe

ratu

re (∘

C)

Time (s)

Hot water inlet

Hot water outlet

Cooling water inlet

Cooling water outlet

Figure 3: A comparison of the system temporal temperature profilesbetween experiment and simulations under passive heat recoveryscheme. —: experimental data; - - -: simulation results.

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500 600

Wat

er te

mpe

ratu

re (∘

C)

Time (s)

Condenser outlet

Condenser inlet

Chilled water inlet

Chilled water outlet

Figure 4: A comparison of temperature histories at condenserand evaporator outlets between experiment and simulations. —:experimental data; - - -: simulation results.

simply affects the hot water circulation external to the chillersystem, it does not affect the cooling capacity as shown inFigure 5, which is why only one set of cooling capacity curvesare presented. However, it substantially reduces the thermalenergy consumption at the hot water reservoir and hencemarkedly improves the system COP as presented in Fig-ure 6. At the rated condition where 𝑇out

chilled = 12.2∘C, 𝑇in

hot =

85∘C, 𝑇in

cool = 29.4∘C, and cycle time ranges from 120 s to

420 s which is the preferred cycle time for the four-bedadsorption chiller, the simulation can accurately predict thecooling capacity and COP to within 12.5%. This proves thatour kinetic model for the adsorption of water vapour isostensibly adequate to describe the boiling phenomenon atthe evaporator under the rated conditions and therefore forchiller design. Over all the cycle times, the passive heatrecovery scheme can boost the system COP by up to 25%.

The performance predictions at lower hot water tem-peratures are shown in Figures 7 and 8. Figure 7 depictsthe cooling capacity versus cycle time at the hot watertemperatures of 75∘C and 65∘C, respectively, which confirmsthat we can accurately predict the cooling capacity at the


1.0

2.0

3.0

4.0

5.0

6.0

7.0

50 100 150 200 250 300 350 400 450

Coo

ling

capa

city

(Rto

ns)

Cycle time (s)

Experimental data [19]Predicted cooling capacityExperimental data [9]

12.5% error bar

Figure 5: Predicted cooling capacity at ARI standard conditions(hot water temperature 85∘C, cooling water temperature 29.4∘C, andchilled water temperature 12.2∘C).

0.10

0.20

0.30

0.40

0.50

0.60

0.70

50 100 150 200 250 300 350 400 450

COP

Cycle time (s)

Predicted COP at standard schemePredicted COP at passive heat recovery schemeExperimental COP at passive heat recovery scheme [9]Experimental COP at standard scheme [19]

12.5% error bar

Figure 6: Predicted COP at ARI standard working conditions (hotwater temperature 85∘C, cooling water temperature 29.4∘C, andchilled water temperature 12.2∘C).

part-load conditions as well. However, with decreasing hotwater temperature, the prediction error gets slightly bigger.This is likely due to the idiosyncrasy of evaporator perfor-mance under off-rated conditions [23]. Figure 8 shows thefavourable predictive capability of our model for the COPat hot water temperatures of 75∘C and 65∘C, respectively. Ithighlights that the prediction error increases with decreasinghot water temperature. This may be due to our assumptionof a constant isosteric heat, which stems from the Tothisotherm fitting of the silica gel-water experimental data. Inreality, we believe the isosteric heat is actually dependent

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Coo

ling

capa

city

(Rto

ns)

Experimental cooling capacity at 75∘C

Predicted cooling capacity at 75∘C

Experimental cooling capacity at 65∘C

Predicted cooling capacity at 65∘C

50 100 150 200 250 300 350

Cycle time (s)

Figure 7: Predicted cooling capacity at hot water temperatures 75∘Cand65∘C, respectively (coolingwater temperature 29.4∘Cand chilledwater temperature 12.2∘C).

0.10

0.20

0.30

0.40

0.50

0.60

COP

Experimental COP with passive heat recovery at 75∘C

Predicted COP at 75∘C

Experimental COP with passive heat recovery at 65∘C

Predicted COP at 65∘C

50 100 150 200 250 300 350

Cycle time (s)

Figure 8: Predicted COP at hot water temperatures 75∘C and 65∘C,respectively (cooling water temperature 29.4∘C and chilled watertemperature 12.2∘C).

on the adsorption temperature but is currently hard to bedetermined quantitatively [24, 25].

5. Conclusions

A facile and reliable lump-parameter model for a four-bedadsorption chiller with the passive heat recovery has beendeveloped. Our predictive results compare favourably withexperimental results, over an assortment of operating condi-tions. The performance of a previously reported passive heat


recovery scheme, which substantially boosts the system COP,can also be favourably predicted by this lump-parametermodel. It is concluded that our improved lump-parametermodel adequately captures the characteristics of the four-bedadsorption chiller with the passive heat recovery scheme.Ourmodel will provide manufacturers with useful informationfor the design of four-bed adsorption chillers.

Nomenclature

𝐴: Heat transfer area (m2)COP: Coefficient of performance𝑐V: Specific heat capacity (J/kg⋅K)𝐷𝑠𝑜: Preexponent constant (m2/s)

𝐸𝑎: Activation energy of surface

diffusion (kJ/kg)ℎ: Enthalpy (J/kg)ℏ: Heat transfer coefficient (W/m2⋅K)𝑘: Thermal conductivity (W/m⋅K)𝑀: Mass (kg)𝑁: Number of discrete elements in the heat

exchanging tubes of the beds𝑁1: Number of discrete elements in the heat

exchanging tubes of the evaporator𝑁2: Number of discrete elements in the heat

exchanging tubes of the condenser𝑁tube: Number of discrete elements in the

connecting pipes𝑃: Pressure (Pa)𝑞: Fraction of refrigerant as adsorbed by

the adsorbent (kg/kg dry adsorbent)𝑞∗: Fraction of refrigerant which

can be adsorbed by the adsorbentunder saturation condition(kg/kg dry adsorbent)

𝑄evap: Cycle average cooling capacity (W)𝑅: Universal gas constant (J/mol⋅K)𝑅𝑝: Average radius of silica gel (m)

𝑡: Time (s)𝑡cycle: Cycle time (s)𝑇: Temperature (∘C)𝑈chilled: Heat transfer coefficient of

the evaporator (W/m2⋅K)𝑈cond: Heat transfer coefficient of

the condenser (W/m2⋅K)𝑈𝑐: Heat transfer coefficient of

the adsorber (W/m2⋅K)𝑈ℎ: Heat transfer coefficient of

the desorber (W/m2⋅K)𝑉: Internal volume of heat exchanger

tubes (m3)��: Flow rate (kg/s)Δ𝐻ads: Isosteric heat of adsorption (J/kg)𝛿: Flag that governs connecting

pipe transients𝜁: Flag that governs adsorber transients𝛾: Flag that governs evaporator transients𝜃: Flag that governs condenser transients𝜌: Density (kg/m3).

Superscripts/Subscripts

air: Airads: Adsorptionbed: Adsorption or desorption bedchilled: Chilled watercond: Condenser or condenser cooling watercool: Cooling water or bed cooling watercycle: Cycleevap: Evaporator or chilled water𝑓: Fluid (liquid water)𝑔: Gaseous waterhot: Hot water or heatingHex: Heat exchanger tube-fin assembly𝑖: Adsorberin: Inlet𝑗: Desorber𝑘: Discrete element𝑚: Metal tube or water in

the connecting pipespm,hot: Metal tube between desorber outlet

and system outletpm,cool: Metal tube between adsorber outlet

and system outletout: Outletp-a: Precoolingp-h: Preheatingrec: Recoveryref: Referencerej: Rejected energysat: Saturatedsg: Silica gel.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

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