Applied Energy 106 (2013) 232–242

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Applied Energy

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Mathematical modeling and experimental verification of an absorptionchiller including three dimensional temperature and concentrationdistributions

0306-2619/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.apenergy.2013.01.043

⇑ Corresponding author. Tel.: +61 450143123.E-mail address: jgaj@student.unimelb.edu.au (S. Jayasekara).

Saliya Jayasekara ⇑, Saman K. HalgamugeDepartment of Mechanical Engineering, The University of Melbourne, Parkville, Victoria, Australia

h i g h l i g h t s

" We modeled an absorption chilller including three-dimension heat and mass diffusion." We examined nonuniform concentration and temperature distributions in the solution." The simulation results are consistent with the experimental readings." The performance was analyzed against the cooling and firing water temperatures.

a r t i c l e i n f o

Article history:Received 23 February 2012Received in revised form 16 November 2012Accepted 16 January 2013Available online 27 February 2013

Keywords:DiffusionLiBr–H2OAbsorption chillerCCHP

a b s t r a c t

One of the main drawbacks in modeling absorption chillers is the lack of justified hypotheses of heat andmass diffusion in an annular flow on the outer surface of horizontal tubes. Heat and mass transfer indiffusion is a three-dimensional problem with vector characteristics. This paper introduces the character-ization of vapor–absorbent heat and mass transfer phenomena in three dimensional space to obtainsteady state simulation results for single effect LiBr–H2O absorption chillers.

It is thus possible for the first time to ascertain in the simulation that the heat and mass transfer char-acteristics are not uniform throughout the solution film. The diffusion boundary layer gradually becomesthicker towards the downstream tubes, which has previously been assumed but never confirmed in sim-ulations. The radial component of the concentration field exhibits a potential for determining an opti-mum film thickness which enhances the system performance. The ability to use the proposed modelwith various absorbents and different cooling capacities increases its applicability. The model also offersthe possibility to analyze different firing techniques at different temperatures. All the simulation resultsare consistent with the experimental data found in the literature.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Typically, centralized utility systems are associated with enor-mous heat loss in electricity production and non-trivial waste intransmission. Entrepreneurs, governments and policy makers arenow assessing the feasibility of in-house or island mode powergeneration techniques which recover waste heat. In-house powergeneration improves system performance while minimizing theloss of electricity in transmission and distribution. This also helpsto cut down energy costs and mitigate irreversible environmentalimpact on the biosphere. Decentralized power generation makesfor a better energy management system, allowing for the descend-ing levels of exergy required for generating electricity, cooling and

heating respectively. Combined Cooling Heating and Power (CCHP)system performance provides the management team with valuableinformation on pre-investment feasibility and also on short- andlong-term operation plans [1–3].

Absorption chillers represent a key stage in the use of lowexergy heat for cooling purposes in CCHP systems, instead of usingelectricity. The current energy market is competitive and volatiledue to underlying technical, economical and environmental issues.Computer simulation offers reliable information to exploit theseopportunities, and assess the influences of new approaches tonovel cycles. However, most of the mathematical models devel-oped are simple and imprecise [3–11]. A hypothesis that moreclosely matches real-world conditions is required for further devel-opments, such as could be offered by film hydrodynamics, an areathat clearly needs to be better understood in terms of mathemati-cal modeling of system physics.

Nomenclature

D mass diffusivity (m2 s�1)T temperature (�C)_m mass flow rate (kg s�1)

Cp specific heat capacity (J kg�1 K�1)P pressure (Pa)h specific enthalpy (kJ kg�1)_Q heat transfer rate (J s�1)g acceleration due to gravity (m s�2)u tangential velocity (m s�1)v radial velocity (m s�1)R tube external radius (m)r tube internal radius (m)K thermal conductivity (W m�1 K�1)�q heat transfer rate (J s�1)A surface area (m2)L tube length (m)

Greek lettersa thermal diffusivity (W m�1 K�1)v LiBr mass fractionh azimuth angle

q density (kg m�3)l viscosity (kg m�1 s�1)d film thickness (m)g generalized film thickness� generalized tube anglen generalized tube length

Subscriptsabs absorbercon condensercw cooling waterdsb desorberevp evaporatorrec recuperators saturatedsol solutionsti solution–tube interfacesvi solution–vapor interfacev vaporw water

S. Jayasekara, S.K. Halgamuge / Applied Energy 106 (2013) 232–242 233

1.1. Contribution

The main contribution of this paper is the characterization ofvapor–absorbent heat and mass transfer phenomena in three-dimensional space to obtain steady state simulation results for asingle effect LiBr–H2O absorption chiller, for the first time. Thisallows the simulation of non-uniform heat and mass transfer char-acteristics throughout the solution film. From this simulation, itbecomes possible to determine critical operational conditionsand parameters, such as tube surface wetting which degrades theperformance. This particular mechanism is difficult to analyze inpractice. One may use the model to determine the optimum filmthickness that avoids the surface wetting.

1.2. Outline of the paper

This paper presents a computer simulation of a single-effectLiBr–H2O absorption chiller. Section 2 presents an overview of thepast contributions with a brief introduction to the proposed methodand its importance. Section 3 describes proposed methodology,modeling of the absorption chiller, including three dimensionalconcentration and temperature distributions. Finally, Section 4gives the results and discussion of the study. The article concludeswith a brief summary.

2. Related work and proposed improvements

Numerous methodologies are adopted in the literature, ofwhich the following is a selective taxonomy.

2.1. Zero dimensional models

The vast majority of mathematical models of absorptionchillers, used for many simulation purposes (energy, commerce,environment, optimization, etc.), are based on zero-dimensionalanalysis, including most modular simulation software [5–7,12,13]like ABSIM, ASPEN and MODALICA. Each of the heat and masstransfer modules of the system (such as the absorber) is treatedas a control volume together with work, heat and mass transac-tions [8–10,14]. Inputs and outputs of the system modules have

clearly been defined to introduce energy balance in terms ofnumber of transfer unit (NTU), logarithmic mean temperaturedifference (LMTD), effectiveness (EFF) and/or closest approachtemperature (CAT), for steady and stable flow analysis [15]. Rele-vant equations describing the properties of fluids have also beenestablished. In the case of the absorber, these sets of linear alge-braic equations solve the final state of the solution’s bulk temper-ature, which is treated as saturated. Mass transfer characteristics ofthe unit are specified by the temperature, assuming equilibrium atthe liquid outlet and the vapor outlet [2,16,17]. Since the charac-teristic temperature and concentration (LiBr mass fraction) fieldsare ignored, the modeling is simple and imprecise.

2.2. One dimensional models

Many one-dimensional models found in the literature havewidely acknowledged that the diffusion of water vapor intoLiBr–H2O solution flows along vertical or inclined tubes and planes[15,18,19] due to gravity. The main objective of this study was todetermine the characteristic temperature and concentration flowfields due to differential heat and mass transfer along the directionof the solution flow. Temperature and concentration distributionsalong the tube or plate were established. Radial and circumferen-tial components have been neglected. In most studies, flow alonga vertical tube was simplified to resemble flow along a verticalplate. Mechanisms of heat and mass diffusion have been modeledby using heat and mass transfer coefficients determined from thedimensionless numbers of heat and mass transfer analogy. A setof non-linear ordinary differential equations were applied todescribe the local changes in the solution temperature and the con-centration due to heat and mass diffusion [20–22]. Even though,the bulk temperature and the concentration profiles have beenintroduced along the solution flow, the advantage over the zero-dimension model is small.

2.3. Two dimensional models

2.3.1. Circumference and radial distributionsThe combined heat and mass diffusion in LiBr–H2O flow

around horizontal tubes does not lend itself easily to mathematical

Fig. 1. Schematic diagram of the temperature (T) and LiBr mass fraction (v) profilesalong the tube radius.

Fig. 2. Schematic diagram of the diffusion boundary layer growth (vapor) along thesolution flow.

234 S. Jayasekara, S.K. Halgamuge / Applied Energy 106 (2013) 232–242

analysis. Most studies found in the literature have introduced theabsorption process in a laminar film flowing down an inclinedplane or vertical tube. Only a few studies have addressed the grav-ity flow of solution film on horizontal tubes [23–29]. The main useof this model is to determine the overall heat and mass transfercharacteristics of an annular flow over a horizontal tube in heatand mass exchangers, so the characteristic flow along the tubelength is neglected: only temperature and concentration fieldsalong radii and circumference have been considered. Heat andmass transfer relationships are extracted from the numerical pro-cedures based on the flow fundamentals and on the well-knownparameters of Reynolds, Prandtl and Schmidt numbers. This meth-od is limited for the solution flow over the entry tube set of thetube bank in the absorber/desorber. No corrections have been pro-posed for the characteristics of solution flow at an intermediate orlast tube (a tube with a predecessor tube). Therefore, only a minorpopulation of the entire tube bank is represented. However, thiscannot be considered as a two-dimension model for the entire heatand mass exchanger.

2.3.2. Circumference and longitudinal distributionsThe characteristic diffusion of heat and mass in solution film is

described by a set of ordinary differential equations on two-dimensional vector fields of temperature and concentration. Thediffusion equations, together with the energy conservation law,determine the circumferential and longitudinal components ofthe temperature and concentration fields by assuming that thethickness of the solution film is negligible compared to the otherdimensions within the system boundary. Such assumptions restrictthe necessity of analyzing solution velocity with characteristic heatand mass transfer along the radial direction. The main drawback ofthis procedure is the uniform concentration and temperature pro-files across the film thickness, which ignores the influence of pre-decessor tubes in determining the boundary value of the solutionflow entering into each tube row (except the first row). The resultsare directly affected by the Sherwood number and Schmidt num-ber, as the mechanism of heat and mass diffusion has been mod-eled by the dimensionless numbers of heat and mass transferanalogy [3,4,30,31]. The widely accepted boundary condition ofsaturated solution–vapor interface is used to solve the boundaryvalue problem [3,29,30]. This influences the concentration andtemperature at any given point in the solution film to be saturated.Thus, the results deviate from the exact distribution of flow fields.In order to overcome this deviation in final results, a pseudo-masstransfer skin has been introduced on the top surface of the solutionfilm [3,4]. Thus, the final concentration and temperature weredefined as the average between the saturated outermost skin andthe bottom layer, where no diffusion occurs, although obviously,no such real divide really exists between layers. The significanceof the model has been minimized by the neglected film thickness.

2.4. Three dimensional model

The diffusion of heat and mass across the solution film, and thediffusion boundary layer (vapor) growth along the solutionflow are schematically represented in Figs. 1 and 2 respectively.Anisotropic behavior of falling film diffusion on horizontal tubesdescribes a non-uniform distribution of temperature and concen-tration fields over effective film area. So, an iso-thermal or iso-concentration plane cannot be expected in reality. Hence thenecessity of finding a way to model the fact of heat and mass trans-fer phenomena on a fully developed three-dimensional flow field.The proposed method solves the momentum equation, as well asheat and mass transport equations, disclosing temperature andconcentration distribution in all three dimensions of the entireheat and mass exchanger. The three-dimensional temperature

and concentration fields can then appear mathematically in a setof second-order partial differential equations. The resulting differ-ential equations are then solved numerically. The flow of viscoussolution LiBr–H2O in a circular flow around the outer perimeterof a horizontal tube is simulated by solving the momentum andcontinuity equations with appropriate boundary conditions. Theresulting velocity components at every point are then used insolving the above diffusion equation for concentration and temper-ature field. Mass and energy conservations equations are used tocouple mass and energy transport equation during vapor absorp-tion process in the solution–vapor interface. Heat transfer equa-tions across the tube wall determine the boundary conditions forthe solution–tube interface of the film. Boundary layer heat trans-fer is used to determine the temperature of the water in the tube.

This method has imposed the necessity to integrate second-order partial differential equations at strictly specified boundaryconditions in every performed simulation. Disproportion in geo-metrical scale within the system boundary, with a large area ofheat/mass transfer and thin heat/mass transfer layers, causesthree-dimensional modeling complications. This fact has actuallylimited the practical importance of absorption unit models basedon a full three-dimensional heat and mass transfer analysis forcomplete heat and mass exchangers (such as absorbers), mainlydue to the imprecision and simplicity of the other methods.

2.5. The improvements over the previous methods

Many mathematical models have been developed for LiBr–H2Oabsorption cycles based on mass and energy balances, which

Fig. 4. Schematic diagram of the mathematical model structure.

S. Jayasekara, S.K. Halgamuge / Applied Energy 106 (2013) 232–242 235

neglect the vector characteristics of heat and mass transfer by dif-fusion [32–35]. Unlike in a zero-dimensional case, where saturatedproperties are used to determine the final values of the tempera-ture and the concentration, but the spatial variations in the solu-tion properties across the film thickness are ignored, diffusion isused to characterize the temperature and concentration fields inthe three dimensional space and account for the spatial variationsas well. However, there is limited number of studies incorporatingdiffusion into models in the literature. As mentioned above, mostof these models’ heat and mass transfer formulas were simplifiedwith the mass transfer coefficients determined from the dimen-sionless analogy’s mass transfer numbers. The two-dimensionalapproach does not describe the entire flow field within the systemboundary [3,4]. Its pseudo-utmost mass transfer skin aligns analyt-ical results with experimental readings by averaging the resultsbetween the initial and saturated value. In fact, no such layerexists. The proposed method can solve the three-dimensional dis-tribution of temperature and concentration fields in a series ofannular flow absorption processes over large number of horizontaltubes in columns, while remaining computationally economical.

3. Methodology

Fig. 3 shows a schematic of a single effect LiBr–H2O absorptionchiller, which consists of absorber, desorber, condenser, evapora-tor, recuperator and eductor. The entire cycle is performed byusing subunit models (e.g. condenser), which represent the math-ematical description of the physical process in each and every com-ponent of the system. These subunit models are equipped withthermo fluid behavioral correlations, such as heat and mass trans-fer equations and momentum equation. The main program (solver)calls the subunit models and links them with the system geometrymatrix and the control sequence with input information, as shownin Fig. 4. Each subunit model calls the respective property librarywhen invoked. The properties of the working fluid pair is takenfrom [36–42].

Fig. 3. Schematic diagram of a single effect LiBr–H2O absorption chiller.

3.1. Heat exchanger models

The spatial variation of temperature profiles of both heating andcooling fluids of the condenser, evaporator and the recuperator aredetermined by multi variable polynomials obtained by the differ-ential equations of heat transfer [43]:Z

T

_mCP dTDT

¼Z

AU dA; ð1Þ

where U is the overall heat transfer coefficient, and Dittus–Boelter’sequation with widely used correction factors is used to calculate thefluid–metal heat transfer coefficient. The Shah and Gungor–Winterton correlations were used to calculate the heat transfercoefficients of condensation and evaporation respectively [44–46].

The super-heated refrigerant vapor from the desorber deliversboth the sensible and latent heat to the cooling water counter cur-rent to the vapor flow in the condenser. Subsequently, the refriger-ant leaving the condenser may be at saturated or sub-cooled state.The net heat transfer rate through the condenser heat transfer sur-face area is given by:Z

Acond _Q ¼ _Q conð _m7; P2; T7; T14Þ

¼ _m13ðh15ðP15; T15Þ � h14ðP14; T14ÞÞ: ð2Þ

The refrigerant leaving the evaporator is assumed to be satu-rated and no super heating applied. Therefore, the net heat transferrate through the evaporator heat transfer surface area is given by:Z

Aevpd _Q ¼ _Qevpð _m8; P1; T8Þ

¼ _m11ðh11ðP11; T11Þ � h12ðP12; T12ÞÞ: ð3Þ

The energy recovered from the strong solution leaving thedesorber is delivered into the weak solution returning back tothe desorber. The net heat transfer rate through the recuperatorheat transfer surface area is given by:Z

Arecd _Q ¼ _Q recð _m4; _m3; T2; T4Þ ¼ _m4ðh4ðv4; T4Þ � h5ðv5; T5ÞÞ: ð4Þ

3.2. Heat and mass exchanger models, and the absorption chillerperformance

Heat and mass transfer rates for the absorber and the desorberare determined by solving set of ordinary differential equationsresulting from numerical approximation procedure from secondorder partial differential equations for the boundary value prob-lem. (detail description is given in Section 3.3). The net heat andmass transfer rates for the absorber are given by:

236 S. Jayasekara, S.K. Halgamuge / Applied Energy 106 (2013) 232–242

ZAabs

d _Q ¼ _Q absð _m6; _m10; _m13;v6; P1; T13Þ

¼ _m13ðh14ðP14; T14Þ � h13ðP13; T13ÞÞ; and ð5ÞZ

Aabsd _mv ¼ _mv:absð _m6; _m10; _m13;v6; P1; T13Þ ¼ _m10; ð6Þ

respectively. The net heat and mass transfer rates for the desorberare given by:Z

Adsbd _Q ¼ _Q dsbð _m3; _m7; _m16;v3; P2; T16Þ;

_Q dsb ¼ _m16ðh16ðP16; T16Þ � h17ðP17; T17ÞÞ; and ð7ÞZ

Adsbd _mv ¼ _mv:dsbð _m3; _m7; _m16;v3; P2; T16Þ ¼ _m7; ð8Þ

respectively. The temperature of the vapor generated in thedesorber is determined by the mean temperature of area integral,numerically:R

dsb TvdAAdsb

¼ T7ðP2; _m16; _m3; T3; T16;v3Þ: ð9Þ

The hydraulic energy balance of the solution pump includingthe isentropic efficiency (gis) of the compression, the electrome-chanical efficiency (gem) and the electricity power consumption(Psp) is:

Psp ¼_msol

gisgemqðT1;v1ÞðP2 � P1Þ: ð10Þ

The coefficient of performance (COP) for a thermally drivenabsorption chiller is defined as the cooling output divided by theheat input [8,9]:

COP ¼_Q evp

_Qdsb

: ð11Þ

3.3. Mathematical modeling of three dimension space of heat andmass exchangers

A film of liquid solution, composed of absorbent (LiBr) andabsorbate (H2O), flows downward by gravity outside a horizontal

Fig. 5. Schematic diagram of the tube bank arrange

tube. The falling film is cooled by cross-current water flow run-ning inside the tube. LiBr–H2O solution always remains in the li-quid phase, and the stagnant steam at low pressure is absorbedinto the solution. Fig. 5 shows the geometry of the problem andthe flow regimes on a representative absorber tube. The annularflow regime is divided into a flow pair by a vertical mirror plane.Identical solution flow in both regimes and relatively simplegeometry with a homogeneous vapor bath provide computa-tional simplicity. The radial distribution of the cooling watertemperature is assumed to be uniform except at the boundarylayer. The model equations are solved only for one side of theannular flow pair and the entire heat and mass exchanger isdeveloped symmetrically. The solution film thickness (d) is verysmall (1/40) compared to the radius (r) of the tube. Conse-quently, the curvature terms in the governing equations are neg-ligible, and the cylindrical coordinate system can be replaced bya rectangular coordinate system introduced on to the tube sur-face, assuming that the circumference distance (x) does notchange with regard to the radial distance (y) of the solution film.The cooling water flow direction (l) is cross-current to the solu-tion flow. Thus, the mathematical model of the absorber isdeveloped with following assumptions [3,4,26].

� Film flow is laminar.� Physical properties of the LiBr–H2O solution are constant within

the system boundary.� No viscous interaction between solution and vapor.� No slip between tube wall and the solution.� Negligible viscous dissipation.

The momentum and continuity equations [26,29] describing thefalling film solution over the horizontal tubes are:

�l @2u@y2 ¼ qg sin h; and ð12Þ

@u@xþ @v@y¼ 0; ð13Þ

respectively. The appropriate boundary conditions at the film sur-faces are: u = 0 at y = 0, and @u/@y = 0 at y = d. Consequently, the xand y directional velocity components can be derived as:

ment of a falling film horizontal tube absorber.

S. Jayasekara, S.K. Halgamuge / Applied Energy 106 (2013) 232–242 237

u ¼ qgl

sinxR

� �dy� 1

2y2

� �; and ð14Þ

v ¼ �qgy2

2l@d@x

sinxR

� �þ 1

Rd� y

3

� �cos

xR

� �� �; ð15Þ

respectively. Therefore, the solution film thickness d derived fromthe mass conservation is:

_msol ¼Z d

0quðyÞdy;

d ¼ 3l _ms

q2g sin xR

� �" #1

3

: ð16Þ

The derivative of film thickness d with respect to x is:

dddx¼ l _msolp3

9q2g

� 13 1

sin xR

� �13 tan x

R

� � : ð17Þ

Diffusion of water vapor into the strong aqueous LiBr solution ismodeled with the following assumptions [26,29]:

� Constant density, thermal conductivity and specific heatcapacity.� No pressure gradient.� Heat transfer to vapor phase is negligible.� Both fluids unmixed.

Heat and mass transfer equations for a differential control vol-ume of the annular film can be generalized as [26]:

u@T@xþ v @T

@y¼ a

@2T@y2 ; and ð18Þ

u@v@xþ v @v

@y¼ D

@2v@y2 ; ð19Þ

respectively. The two diffusion equations are coupled throughboundary conditions at the solution–vapor interface. Saturated va-por pressure prevails at the vapor–solution interface, such thatthe vapor concentration (derived from the mass transport equation)of the film at the interface is saturated at the interface temperature(derived from the energy transport equation) and pressure. Theother coupling is the energy balance in the interface.

The following relations for the temperature and the concentra-tion across the film thickness apply:

T ¼ Tsti þ ðTsvi � TstiÞyc; and ð20Þv ¼ vsti þ ðvsvi � vstiÞyj; ð21Þ

where the profile fitting factors c and j are determined by a set ofdata extracted from the exit temperature and concentration profilesacross the film of the predecessor tube.

(a) For the entry tubes facing the sprinklers (where, there are nopredecessor tubes), the LiBr solution is in thermodynamicequilibrium state with the inlet properties: Tsvi = Tsti, vsvi =vsti then, T = Tsti and v = vsti.

(b) At the solution–vapor interface, the LiBr solution is in its sat-uration state. Therefor, at the interface: T = Ts, v = vs at0 6 x 6 pr and y = d where, Ts = f(p,v), vs = f(p,T).

(c) The cooling water is cross-current to the solution flow. Thetube outer surface temperature is given in terms of coolingwater temperature and overall heat transfer coefficientderived from Eq. (26). At the wall it is impermeable, thusthe gradient of concentration is equal to zero: T = Tsti, @v/@y = 0 at y = 0 and 0 6 x 6 pr.

The change in enthalpy forms the vapor phase to solution state(heat of absorption) released at the solution–vapor interface. Thisgenerates the temperature gradient at the interface by thermalconduction. From the Fick’s law at 0 6 x 6 pr and y = d, the vapormass flux:

_mv ¼qDvs

@v@y

: ð22Þ

Therefore, the heat flux produced by the absorption process is:

_qsvi ¼ _mvhv � _mv@hsol _msol

@ _mw; where _mv ¼ D _mw;

_qsvi ¼ _mv hv � hsol þ v @hsol

@v

� : ð23Þ

Consequently, the heat flux across the solution–vapor interface ð _qÞcan be determined by:

_qsvi ¼ KsoldTdy

� svi

: ð24Þ

The entire heat flux from the solution film, comprising the heatof absorption and the sensible heat of solution, is determined bythe temperature gradient of the film at the solution–tube interface(radial distribution). Thus, the heat flux across the solution–tubeinterface into the cooling water ð _qÞ is:

_qsti ¼ KsoldTdy

� sti: ð25Þ

Therefore, the temperature of the solution–tube interface is:

Tsti ¼ _qsti=U þ Tcw;

U ¼ 1R

hcwr þRlnðR=rÞ

Ktube

; ð26Þ

where hcw is the water side convective heat transfer coefficient.The linear heat flux density across the semi-circular tube wall to

the cooling water ð�qÞ is:

�q ¼Z pr

0

_qstiðxÞdx: ð27Þ

Therefore, the energy balance of the cooling water flowing insidethe tube:

�q ¼ _mcwCpdTcw

dl; ð28Þ

dTcw

dl¼

�q_mcwCp

:

3.3.1. Solution methodologyThe coordinate transformation is:

e ¼ xpR

; ð29Þ

g ¼ yd; and ð30Þ

n ¼ lL: ð31Þ

Therefore, the transformed governing equations are:

u ¼ qgd2

lsinðpeÞ g� 1

2g2

� �; ð32Þ

v ¼ �qgd2g2

2lr1p@d@e

sinðpeÞ þ d 1� g3

� �cosðpeÞ

� �; ð33Þ

Table 1Input data for the YORK-YIA 6C4 absorption chiller [48].

Node Value

Steam pressure at desorber (kPa) 111.71Cooling water pressure (kPa) 250Chilled water pressure (kPa) 250Cooling water temperature at absorber inlet (�C) 29.4Chilled water temperature at evaporator inlet (�C) 11Chilled water temperature at evaporator exit (�C) 6.67Cooling water mass flow rate (kg/s) 117Chilled water mass flow rate (kg/s) 78.3

238 S. Jayasekara, S.K. Halgamuge / Applied Energy 106 (2013) 232–242

@T@e¼ g

dddde� prv

du

� �@T@gþ pra

ud2

� @2T@g2 ; and ð34Þ

@v@e¼ g

dddde� prv

du

� �@v@gþ prD

ud2

� @2v@g2 : ð35Þ

Similarly, the variation of film thickness and its derivative are:

d ¼ 3l _ms

q2g sinðpeÞ

� �13

; ð36Þ

ddde¼ l _msp3

9q2g

� 13 1

sinðpeÞ13 tanðpeÞ

: ð37Þ

The boundary conditions are:

(a) T = Tsti + (Tsvi � Tsti)(gd)c, v = vsti + (vsvi � vsti)(gd)j, for theentry tubes: Tsvi = Tsti and chisvi = vsti

(b) T = Ts, v = vs at 0 6 e 6 1 and g = 1(c) T ¼ Tsti;

@v@g ¼ 0 at 0 6 e 6 1 and g ¼ 0

The Fick’s law at 0 6 e 6 1 and g = 1 is:

_mv ¼qDdvs

@v@g

: ð38Þ

The temperature gradient across the solution film at solution–vaporinterface becomes:

@T@g

� sv i

¼_qsvidKsol

: ð39Þ

The energy balance of the cooling water flowing inside the tubebecomes:

�q ¼Z 1

0

_qstiðeÞde; ð40Þ

dTcw

dn¼ L

�q_mcwCp

: ð41Þ

4. Results and discussion

The proposed mathematical model for a LiBr–H2O absorptionchiller is a novel approach to uncover the heat and mass transfer

Table 2Dimensions and specifications of the YORK-YIA 6C4 absorption chiller [49].

Component Fouling factor Specification

Absorber .008 323 numbers of 90/10 CuNi bare tubGenerator .008 121 numbers of 90/10 CuNi bare tubCondenser .008 83 numbers of 90/10 CuNi bare tubeEvaporator – 312 numbers of 90/10 CuNi bare tubRecuperator – 154 numbers of 90/10 CuNi bare tub

phenomena in the absorber in three-dimensional space [47]. Thissimulation model can also be used for characteristic studies onannular flow over horizontal tubes in LiBr falling film absorbersto reveal the heat and mass transfer relations with dimensionlessnumbers. Most of the published literature considers only theuppermost tube, facing fresh solution coming from the sprinklersat uniform temperature and concentration (see Fig. 5) [26].

The proposed mathematical model calculates the thermal per-formance of the system in a steady state. The system’s performanceis experimentally verified in both modes, as a chiller and as a heatpump. Simulation of the chiller was performed using a setting sim-ilar to the available experimental data shown in Table 1. This wasacquired from the technical documentation in the operating andmaintenance guide of LiBr–H2O absorption chiller instruction man-ual for the industrial absorption chiller YORK-YIA 6C4 [48]. Thisembraced a complete set of data on operating temperatures, con-centrations and working pressures to address the preferred operat-ing condition of the entire chiller. The system geometryparameters are depicted in Table 2, which was acquired from thetechnical documentation for parts renewal [49]. Simulation as aheat pump, the system has the same input and the geometry datasupplied in [4]. Comparison of simulations with experimentalresults are presented in Tables 3 and 4 respectively.

Both the simulation results largely agree with the experimentaldata. The discrepancy between the experimental and simulationresults is due to various reasons: measurement errors, errors intro-duced in fitting equations to all extensive and intensive propertiesof fluids etc. These deviations are clearly addressed by the authorsof the papers where the property tables and equations were ex-tracted [36,37,39–42]. Other sources of errors are the assumptionsused: for example, constant specific heat capacity and the ne-glected error in numerical integrations.

For the LiBr concentration profiles in Fig. 6, it can be seen that themajority of vapor diffusion takes place in a thin layer near the solu-tion–vapor interface, and subsequently diffuses slowly into thesolution film. As the flow continues towards the flow downstream,the vapor diffuses up to the tube wall, implying a parabolic decay inthe concentration plot across the film. Fig. 7 describes the averagetemperature contour at each tube exit. Generalized film thickness(g) from 0 to 1 denotes the locations between tube wall and thesolution–vapor interface, respectively. It should be noted fromFig. 7, that the average temperature profile across the flow upstreamexhibits a parabolic growth, due to a distinct heat effect associatedwith absorption and sub-cooling. In the flow downstream where thesub-cooling effect is minimal, the dominant heat of absorption isresponsible for the linear behavior of the temperature plot. It canbe concluded that heat transfer is greater in the upstream flow,which is also reflected in the solution–vapor interface concentrationprofile as shown in Fig. 8.

The solution–vapor and solution–tube interfaces’ LiBr massfraction of the thin solution film is depicted in Fig. 8. The results(Fig. 12) suggest that the absorption is more rapid at the general-ized tube angle e = 0.5 (h = p/2), where the film is thinning thanat the bottom of the tube. It is also noted that the higher rate ofchange in mass fraction in the upper stream tubes are indicativeof a predominant diffusion mass transfer. Thus the average LiBr

e bank (19 columns � 17 rows), 6.8 m length 17.6 mm bore and 0.71 mm thicke bank (11 columns � 11 rows), 6.8 m length, 17.3 mm bore and 0.89 mm thickbank, 6.8 m length, 25.4 mm bore and 0.89 mm thick

e bank, 6.8 m length, 17.6 mm bore and 0.71 mm thicke bank, 5.6 m length, 10 mm bore and 1.2 mm thick

Table 3Experimental verification with the YORK-YIA 6C4 absorption chiller [48].

Parameter Experimentalresults

Simulationresults

Deviation(%)

Absorber pressure (kPa) 0.853 0.850 �0.35Generator pressure (kPa) 6.31 6.4 1.4Refrigerant mass flow rate

(kg/s)0.63 0.64 2.5

LiBr concentration fromeductor (%)

59.8 59.87 0.134

LiBr concentration fromabsorber (%)

57.7 58.1 0.713

LiBr concentration fromdesorber (%)

61.8 62.09 0.47

Solution temperature fromeductor (�C)

43.67 42.38 �2.94

Solution temperature fromabsorber (�C)

36.72 35.88 �2.28

Solution temperature fromdesorber (�C)

88.89 90.62 1.95

Cooling water dischargetemperature (�C)

36.63 35.58 �2.8

Chilled water dischargetemperature (�C)

6.67 6.85 2.1

Steam mass flow rate (kg/s) 0.907 0.917 1.9Cooling load (kW) 1455 1464.2 2.35Circulation ratio 15.1 14.8 �1.98COP 0.68 0.707 1.17

Table 4Experimental verification with the absorption heat pump of Sun and Fu [4].

Parameter Experimentalresults

Simulationresults

Deviation(%)

Absorber pressure (kPa) 0.803 0.800 �0.375Generator pressure (kPa) 6.163 6.100 �1.02Refregerent mass flow rate

(kg/s)0.33 0.331 0.44

LiBr concentration fromeductor (%)

60.7 59.89 �1.33

LiBr concentration fromabsorber (%)

58.1 57.78 �0.534

LiBr concentration fromdesorber (%)

63.3 62.52 �1.233

Solution temperature fromeductor (�C)

45.1 42.24 �1.9

Solution temperature fromabsorber (�C)

33.9 33.54 �0.259

Solution temperature todesorber (�C)

57.3 56.8 �0.82

Vapor temperature fromdesorber (�C)

86.7 85.4 �1.5

Hot water dischargetemperature (�C)

95.2 92.91 �2.4

Cooling water dischargetemperature (�C)

33.3 34.9 5.01

Chilled water dischargetemperature (�C)

6.4 6.75 5.48

Cooling load (kW) 759 741.2 �2.37COP 0.68 0.67 �1.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.57

0.575

0.58

0.585

0.59

0.595

0.6

0.605

LiBr

mas

s fra

ctio

n ( χ

)

Generalized film thickness (η)

i=1 i=2

i=3i=4

i=16i=17

i-Tube number

Fig. 6. Simulated profiles of LiBr mass fraction (averaged over the length of thetube) across the film thickness at tube angle h = p and considering each tube in asingle column in the horizontal tube absorber; absorption pressure: 0.85 kPa, inletsolution LiBr mass fraction: 59.87%, cooling water inlet temperature: 29.4 �C(absorber geometry data is presented in Table 2).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 130

32

34

36

38

40

42

Generalized film thickness (η)

(erutarep

metmliF

o)

C

i=1i=2

i=3i=4

i=17

i-Tube number

i=16

Fig. 7. Simulated temperature (averaged over the length of the tube) profiles acrossthe film thickness at tube angle h = p and considering each tube in a single columnin the horizontal tube absorber; absorption pressure: 0.85 kPa, inlet solutiontemperature: 42.38 �C, cooling water inlet temperature: 29.4 �C (absorber geometrydata is presented in Table 2).

S. Jayasekara, S.K. Halgamuge / Applied Energy 106 (2013) 232–242 239

mass fraction is exponentially decaying from the upper tube and isrelated to the fact that the vapor absorption slows down on thedownstream tubes at a low cooling rate. Thus the diffusion bound-ary layer develops slowly and composes a wet tube surface as thegeneralized tube angle (e) advances (Fig. 8). Contrariwise, the solu-tion–tube interface’s mass faction decays slowly while increasingthe gradient. In absorbers of practical interest, the size of the filmthickness is not expected to form a vapor boundary layer in thesolution–tube interface. From Eq. (16), it is evident that the thick-ness is directly proportional to the mass flow rate. Therefore, it is

indicated that, there exist an optimum mass flow rate which canavoid the tube surface wetting and maximize the chiller perfor-mance. The LiBr concentration of solution film is a function of filmthickness and the effective tube length. The average LiBr mass frac-tion at a given cross section area can be obtained by integrating theconcentration profile across and along the film thickness. The re-sults suggest that the overall heat and mass fluxes are non-uniformthroughout the solution film.

The solution–vapor interface temperature shown in Fig. 9 canbe described by the heat of absorption and the heat of sensiblecooling of the hot solution. Solution flow dynamics are attributedto the wave formation of temperature and concentration profilesdue to the stagnation effect of the stream-wise velocity componentclose to the tube angles h = 0 and h = p. So the temperature changesdue to the varying thermal resistance which is governed by thefilm thickness. The average solution–vapor interface temperaturedecays faster in the flow upper stream and then gradually dropstowards the downstream. Minimum temperature differencebetween the solution and the tube surface is called the pinch pointdifference, which is of practical interest in determining the totalheat transfer area. In addition, the hot solution comes into contactwith the relatively cool tube surface at the entrance of the absor-ber. This causes a rapid drop in the solution–tube interface temper-ature at the upstream flow of the solution as shown in Fig. 9. Thelocal fluctuation in solution–tube interface temperature is directlyproportional to the heat flux across the tube wall. It is clear that the

0 0.20.4

0.6 0.81

0 2 4 6 8 10 12 14 16 18

0.560.5650.57

0.5750.58

0.5850.59

0.5950.6

0.605

Generalized tube angle (ε) and the tube number

LiBr

mas

s fra

ctio

n (χ

)

Solution-tube interface

Solution-vapor interface

Fig. 8. Simulated profiles of LiBr mass fraction in the solution-vapor and the solution–tube interfaces of the solution film flowing over a single tube-column in the horizontaltube absorber; absorption pressure: 0.85 kPa, inlet solution LiBr mass fraction: 59.87%, cooling water inlet temperature: 29.4 �C (absorber geometry data is presented inTable 2).

0 0.20.40.60.81

0 2 4 6 8 10 12 14 16 1828

30

32

34

36

38

40

42

44

Generalized tube angle (ε) and the tube number

(erutarep

metmliF

o C)

Solution-tube interface

Solution-vapor interface

Fig. 9. Simulated temperature profiles in the solution-vapor and the solution–tube interfaces of the solution film flowing over a single tube-column in the horizontal tubeabsorber; absorption pressure: 0.85 kPa, inlet solution temperature: 42.38 �C, cooling water inlet temperature: 29.4 �C (absorber geometry data is presented in Table 2).

240 S. Jayasekara, S.K. Halgamuge / Applied Energy 106 (2013) 232–242

increased heat fluxes, due to thin film thickness at the tube anglesof p/2, can be attributed to the wavy temperature profile.

Cooling water flowing inside the tube removes the heat ofabsorption and the heat of sub-cooling of the hot solution film. Thisinevitably causes the ascending spatial wall temperature in thecoolant stream-wise, in both the solution and the cooling wateras shown in Fig. 9. Eventually, the rate of absorption is reducedat the increased water temperature. The average concentrationand temperature along the tube length and across the film thick-ness at the azimuth angle of p of last tube determine the state ofthe solution leaving the absorber.

The coefficient of performance (COP) of the chiller is a functionof the difference between the vapor concentration of strong solu-tion and that of the weak solution. The greater the difference thehigher the COP is. The vapor concentration of the strong solutionleaving the desorber depends on the solution temperature andthe condensing pressure of the refrigerant (governed by the firingtemperature and the condenser cooling temperature respectively).Similarly, the concentration of the weak solution depends on theevaporation pressure and the solution temperature leaving theabsorber (governed by the chilling temperature and the coolingwater temperature respectively). Therefore the COP is directly pro-portional to the difference between the firing temperature and thecooling temperature. At the minimum firing temperature of thedesorber, the vapor concentration of the strong solution reachesthe concentration of the weak solution, making the difference

between concentrations smaller and the circulation losses exces-sive, leading to a low COP. The concentrations of both the solutionsleaving separately from the desorber and the absorber are not atthe saturated or equilibrium state (assumed as saturated in [3,4])due to the non-uniform distribution of concentration across thefilm thickness as shown in Fig. 6. The cooling capacity of the chilleris determined by the latent heat of the refrigerant at the evaporatorpressure and the liquid refrigerant (water) flow through the evap-orator (no super heating applied).

Figs. 10 and 11 illustrate the characteristic thermal performanceobtained from the simulation performed on a large number of dis-crete input and output data. For both cases, the geometry and thechilled water temperature are fixed. Both characteristics presenttypical thermal performance of the LiBr–H2O absorption chillersat different levels of hot water and cooling water inlet temperature[9,50]. The COP rises rapidly to a maximum with ascending firingtemperature from a low value. with a further increase of hot watertemperature, the COP peaks before decline. This can clearly be seenat low cooling water temperatures, as shown in Fig. 13. The declinein COP at the higher desorber temperature is a result of unexpectedrefrigerant mass flow combined with super heating in the con-denser and the loss of exergy in the desorber. The reduction ofeffective condensing area, due to the vapor sub-cooling togetherwith the accelerated refrigerant mass flow rate, results in theelevated condenser pressure, which increases the vapor concentra-tion of the strong solution. Similarly, the COP decreases with

2426

2830

3234 70 80 90 100 110 120 130

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Hot water temperature (oC)

Cooling water temperature ( oC)

Coe

ffici

ent o

f per

form

ance

(CO

P)

Fig. 10. Simulated behavior of the COP; chilled water temperature: 6.85 �C, chilledwater mass flow rate: 78.3 kg/s, cooling water mass flow rate: 117 kg/s, hot watermass flow rate: 35 kg/s (chiller geometry data is presented in Table 2).

2426

2830

3234

70 80 90 100 110 120 130

0

50

100

150

Perc

enta

ge c

oolin

g ca

paci

ty (%

)

Hot water temperature (oC)

Fig. 11. Simulated behavior of the percentage cooling load; chiller rated capacity:1450 kW, chilled water temperature: 6.85 �C, chilled water mass flow rate: 78.3 kg/s, cooling water mass flow rate: 117 kg/s, hot water mass flow rate: 35 kg/s (chillergeometry data is presented in Table 2).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.5945

0.595

0.5955

0.596

0.5965

0.597

0.5975

0.598

0.5985

0.599

LiBr

mas

s fra

ctio

n (χ

)

Generalized tube angle (ε)

Solution-tube interface

Solution-vapor interface

Fig. 12. Simulated profile of LiBr mass fraction (averaged over the length of thetube) in the solution-vapor and the solution–tube interfaces of the solution filmflowing over the first semi circular tube in the horizontal tube absorber; absorptionpressure: 0.85 kPa, inlet solution LiBr mass fraction: 59.87%, cooling water inlettemperature: 29.4 �C.

70 80 90 100 110 120 1300.62

0.64

0.66

0.68

0.7

0.72

0.74

Hot water temperature (oC)

)PO

C(ecna

mr ofr epf ot nei ciff eoC

Fig. 13. Simulated behavior of the COP at the cooling water temperature of 24 �C;chilled water temperature: 6.85 �C, chilled water mass flow rate: 78.3 kg/s, coolingwater mass flow rate: 117 kg/s, hot water mass flow rate: 35 kg/s, COP peaks at121 �C (chiller geometry data is presented in Table 2).

S. Jayasekara, S.K. Halgamuge / Applied Energy 106 (2013) 232–242 241

increasing cooling water temperature, which is associated with anincreased condenser pressure, leading to a higher vapor concentra-tion in the strong solution. In addition, the temperature rise ofcooling water decreases the vapor concentration of weak solutionleaving the absorber. This also leads to a lower COP. Although,the COP increases slowly from the rated value to a peak withincreasing hot water temperature, maintaining the rated refriger-ant flow rate (the rated capacity) increases the COP beyond the val-ues depicted in Fig. 10.

The percentage cooling capacity increases rapidly with increas-ing firing temperature and decreasing cooling temperature, asshown in Fig. 11 due to the fact that more water evaporates fromthe solution at low pressure and high temperature. Similarly, theIncrease in COP, increases the percentage cooling capacity withascending hot water temperature and descending cooling watertemperature.

5. Conclusion

A mathematical model of a LiBr–H2O absorption chiller wasdeveloped, considering the three-dimensional vector characteris-tics of heat and mass distributions. Performance simulation wascarried out for two different cycles, representing the modes as achiller and as a heat pump. The simulation results agree closelywith experimental data in both cases. We anticipate that the modelis capable to accommodate different geometries and differentworking fluids. Three-dimensional heat and mass transfer phe-nomena in the absorber reveals a greater change in concentrationand temperature fields across the film thickness. This would deter-mine the state of the inhomogeneous solution at any point within

242 S. Jayasekara, S.K. Halgamuge / Applied Energy 106 (2013) 232–242

the solution film. The effect of fundamental flow parameters onheat and mass transfer can also be investigated through the aver-age Sherwood and Nusselt numbers. These can help to establisha new set of correlations for the entire tube bank or to extendthe correlations of entry row proposed by Babadi and Farhanieh[26]. The model appears to hold considerable promise to solvesome questions which are difficult to analyze in practice withthe thin nature of the solution film. The concentration flow fieldacross the film thickness revealed by this study, points to the needfor an optimized film thickness for non-wetted tube surface. Theabsorber performance decreases when the diffusion boundarylayer penetrates to the solution–tube interface where, no non-destructive measuring is possible. The system’s response againstthe superheated refrigerant leaving the evaporator and pump mod-ulation with the ejector can also be studied. The change of the COP,when the system is fired by hot water as well as by steam fromsame energy source can also be determined. This could aid thepre-investment feasibility analysis for poly-generation projects.

Acknowledgement

This work was supported by the ID-Seed Funding Scheme pro-vided by the Melbourne Energy Institute of the University ofMelbourne.

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