Simulationof Simple Abs System

7/30/2019 Simulationof Simple Abs System

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Simulation of a simple absorption refrigeration system

Khalid A. Joudi *, Ali H. Lafta

Department of Mechanical Engineering, College of Engineering, Baghdad University, Baghdad, Iraq

Received 5 June 2000; accepted 15 November 2000

Abstract

A steady state computer simulation model has been developed to predict the performance of an ab-

sorption refrigeration system using LiBrH2O as a working pair. The model is based on detailed mass and

energy balances and heat and mass transfer relationships for the cycle components. A computer program

has been developed to simulate the eect of various operating conditions on the performance of the in-

dividual components of the simulated system. These include an absorber, a generator, a condenser, an

evaporator and a liquid heat exchanger. A new model is introduced for representing the absorber. Si-

multaneous heat and mass transfer has been considered in the absorber, instead of heat transfer only as in

other works. The performance of absorber, generator, condenser and evaporator were simulated inde-

pendently. The whole system was then simulated as a working absorption cycle under various operatingconditions. Comparison between the present model results and manufacturer s data of the simulated system

showed excellent agreement. The present simulation results were compared qualitatively with other works

and were in very good general agreement. 2001 Published by Elsevier Science Ltd.

Keywords: Absorption system simulation; LiBr absorption system simulation; Absorption refrigeration system

simulation

1. Introduction

The absorption refrigeration system is one of the earliest methods of producing cold. It has

most commonly been used for refrigeration and air conditioning [1]. Theoretical and experimentalstudies of the performance of absorption refrigeration cycles, including those using LiBrH2O andNH3H2O as refrigerantabsorbent combinations, have already been reported by various authors.

Picher [2] tested a 1000 TR capacity LiBrH2O absorption refrigeration machine of a two shelltype. It was shown that the machine can operate with hot water at 80C and 120C, and it was

Energy Conversion and Management 42 (2001) 15751605

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* Corresponding author.

0196-8904/01/$ - see front matter

2001 Published by Elsevier Science Ltd.P I I : S0196- 8904( 00) 00155- 2


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Nomenclature

A surface area (m

2

)Bi Biot number Hcwds=KsocP specic heat capacity at constant pressure (kJ/kg C)D diameter (m)Ds mass diusivity of solution (m

2/s)Fc heat transfer correction factorFR ow ratio

g gravitational acceleration (9.81) (m/s2)Gz Graetz number xaso=Csdsh specic enthalpy (kJ/kg)

Dh heat of absorption hv hso 1 wo/w (kJ/kg)

hfg latent heat of vaporization (kJ/kg)H heat transfer coecient (kW/m2 C)k thermal conductivity (kW/m C]km mass transfer coecient (m/s)L length (m)Le Lewis number Ds=asoLp length of pass (m)_m mass ow rate (kg/s)

m, n numberMDC manufacturer design curve

N number of tubesNh number of tubes for one pass in horizontal directionNp number of tube passesNu Nusselt number HD=kNv number of tubes for one pass in vertical directionP pressure (kPa)Pr Prandtl number lcP=k_q heat ow per unit length (kW/m)Q total heat (kW)R thermal resistance (m2 C/kW)Re Reynolds number based on Di, 4 _m=pNDil

RF fouling factor (m2 C/kW)Sh Sherwood number kmds=DsT temperature (C)

DTm logarithmic mean temperature dierence (C)U overall heat transfer coecient (kW/m2 C)w mass fraction of water in solution (kg/kg)w average mass fraction (kg/kg)x coordinate along wall plate (m)X LiBr concentration, percent by weight in solution (%)

1576 K.A. Joudi, A.H. Lafta / Energy Conversion and Management 42 (2001) 15751605


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y coordinate perpendicular to wall plate (m)

Dy step size in y direction (m)

Greekc dimensionless mass fraction w wo=we Woc average dimensionless mass fractionC volume flow rate per wetted length _m=q (m2/s)ds solution lm thickness 3msoCs=g (m)g heat exchanger eectivenessh dimensionless temperature T To=Te Toh average dimensionless temperatureK dimensionless heat of absorption qsoDsDh=1 woksoC1l dynamic viscosity (Pa s)

m kinematic viscosity l=q (m2

/s)q density (kg/m3)r surface tension (N/m)/w derivative of h with respect to w at constant T, oh=ow (kJ/kg)a thermal diffusivity k=qcP (m

2/s)

Subscripts

1,2,... state points, or, sequence numbera absorber

av averagec condenser

cw cooling watere equilibrium, or evaporatorg generator

i interface, or (inside)i, j, k sequence indexia inside absorber tubes

ic inside condenser tubesie inside evaporator tubesig inside generator tubesn numbero entrance, or (outside)

oa outside absorber tubesoc outside evaporator tubes

og outside generator tubesp piper refrigerant

s solutionso solution properties at To and Xov vaporw wall

K.A. Joudi, A.H. Lafta / Energy Conversion and Management 42 (2001) 15751605 1577


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found that the cooling water connected in parallel to both absorber and condenser is more e-

cient than series connection. The coecient of performance (COP) was between 0.68 and 0.72.Waleed [3] developed a computer program to design heat exchangers for the generator, con-

denser and evaporator and to predict their performance for a 2 TR capacity lithium bromideabsorption machine under working conditions dierent from the design condition.

Eisa et al. [4] presented possible combinations of operating temperatures of the evaporator,condenser, absorber and generator and the concentration in the absorber and the generator up to

the crystallization limit. This determines the ow ratio and COP for any combination of tem-peratures. Flow ratio is dened as the ratio of the mass ow rate of the solution from the absorberto the mass ow rate of the refrigerant.

FR _ma

_mr1

Eisa et al. [5] conducted an experimental study to determine the eect of changes in operatingconditions in order to optimize the performance of the LiBrH2O absorption cooler. It was shown

that the most signicant parameter is the generator temperature. The higher the generator tem-perature, the higher is the COP. The ow ratio is also an important design and optimizing pa-rameter. An increase in ow ratio reduces the required generator temperature at the expense of a

reduction in the COP. Also, Eisa et al. [6] conducted more experiments on the same system of Ref.[5] to determine the eect on performance of operating the absorber and the condenser at dierent

temperatures. It was demonstrated that as the temperature dierence Tc Ta is increased, theCOP and the cooling capacity are decreased. Also, the COP is more sensitive to the absorber

temperature than to the condenser temperature.Mclinden and Klein [7] constructed a modular, steady state model for simulation of NH3H2O

absorption heat pumps. The model was based on detailed mass and energy balances and heat andmass transfer relationships for the components of the cycle and was applied to a prototype ab-sorption heat pump and compared with experimental data.

Grossman and Michelson [8] developed a modular computer simulation program for absorp-

tion systems, which makes it possible to simulate various cycle congurations. The program hasbeen tested on single and double stage absorption heat pumps and heat transformers with LiBrH2O and NH3H2O as the working uids. The results have been compared with experimental

data from tests of a LiBrH2O heat transformer with good agreement.The present study deals with a continuous absorption refrigeration LiBrH2O system. A steady

state simulation is based on mass balance and heat balance equations, as well as uid ow, heat

transfer and mass transfer correlations for each of the components. A new model is introduced forrepresenting the absorber. Simultaneous heat and mass transfer has been considered in the ab-

sorber instead of heat transfer only, in other works. The model was applied to an actual com-mercial absorption refrigeration plant manufactured by Mitsubishi-York, model ES-2A4-MWworking on LiBrH2O and using hot water as a heat source with a capacity of 211.1 kW re-

frigeration (60 TR) [9]. The computer model was used to simulate this system performance for avariety of operating conditions.

The simulated absorption refrigeration system consists of four basic components, an absorber,

a generator, a condenser and an evaporator, as shown schematically in Fig. 1. An economizer heatexchanger, normally placed between the absorber and the generator, makes the process more



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ecient without altering its basic operation. Low pressure water vapor from the evaporator isabsorbed in the absorber by the solution. The heat generated during the absorption process is

removed by cooling water. A pump circulates the weak solution, with a portion being sent to thegenerator through the solution heat exchanger. The other portion is mixed with the concentratedsolution returning from the generator through the heat exchanger to become an intermediate

solution, which returns to the absorber. In the generator, the solution coming from the absorber isboiled to release water vapor by heat addition, leaving behind a solution rich with LiBr, which isreturned to the absorber via a throttling valve to maintain the pressure dierential between thehigh and low sides of the system. In the condenser, the water vapor coming from the generator is

condensed to liquid. Then, it is passed via an expansion device to the evaporator pressure.

2. Mathematical model

The simulation procedure involves the casting of mathematical models for each componentmaking up the LiBrH2O absorption refrigeration system. The overall system performance maythen be evaluated by combining these models under the normal sequence of operation of the

simulated system. All components of the system were shell and tube exchangers of the counterow type.

Fig. 1. Schematic diagram of the simulated absorption refrigeration system.



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Several conditions and assumptions were incorporated in the model to simplify analysis

without abscuring the basic physical situation. These conditions and assumptions were as follows:

1. The system is simulated under steady state conditions. That is, the mass ow rate of water va-por generated in the generator is exactly the same as the rate of water vapor being absorbed inthe absorber.

2. The pressure drop in the pipes and vessels is negligible.

3. The heat losses from the generator to the surroundings and the heat gains to the evaporatorfrom the surroundings are negligible.

4. The expansion process of the expansion device is at constant enthalpy.

The heat transfer coecient of water for turbulent ow in smooth tubes was calculated ac-

cording to the correlation given by Dittius and Bolter [10]. The pool boiling heat transfer coecientused for pure water and aqueous solutions (LiBrH2O) was that given by Charters et al. [11]. The

condensation heat transfer coecient was evaluated using the Nusselt equation [10]. The evapo-ration heat transfer coecient employed was that by Lorenz and Yung [12] for lm evaporationoutside tubes. Water properties were derived from the Chemical Engineers Handbook [13], while

the thermodynamic properties of the LiBrH2O solution were obtained from Refs. [1,13].

2.1. Absorber

In the absorber, the LiBr solution is sprayed over horizontal tubes cooled by water owinginside. It absorbs the water vapor coming from the evaporator continuously and ows in a thin lm

around the tubes. Then, it is collected in the bottom of the lower shell. To give a description of the

heat and mass transport from a horizontal tube covered with a liquid lm, the following simpli-cation is made. The lm ow along one half of the tube is modeled as that along a vertical cooledwall with a length of half the tube circumference, which is a model suggested by Wassenaar [14,15].

A schematic representation of the model is shown in Fig. 2. On one side of the plate, a solution ofsubstance A (LiBr) in substance B (water) ows down as a thin laminar lm. At the liquidvaporinterface, the water vapor is absorbed and then transported into the bulk of the lm. The heat ofabsorption is released at the interface and transported through the lm and the wall to the cooling

medium (water). The cooling water ows on the other side of the plate in a direction perpendicularto the plane of the illustration (cross ow). Therefore, the cooling water temperatures may beassumed constant over the plate height, which is equivalent to assuming a constant circumferential

pipe temperature. The absorber model started with the following assumptions [14]:

1. The liquid is Newtonian and has constant physical properties. The values of the properties arebased on the liquid entry conditions.

2. The lm ow may be considered laminar and one dimensional.3. Momentum eects and shear stress at the interface are negligible.4. The absorbed mass ow is small relative to the lm mass ow.

5. At the interface, thermodynamic equilibrium exists between the vapor and liquid. The relationbetween surface temperature and mass fraction is linear with constant coecient at constantpressure.



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6. All the heat of absorption is released at the interface.

7. The liquid is a binary mixture and only one of the components is present in the vapor phase.8. There is no heat transfer from the liquid to vapor and no heat transfer because of radiation,

viscous dissipation, pressure gradients, concentration gradients or gravitational eects.

9. There is no diusion because of pressure gradients, temperature gradients or chemical reac-tions.

10. Diusion of heat and mass in the ow direction is negligible relative to the diusion perpendic-

ular to it.

Under the above assumptions, the equations of momentum, energy and diusion of mass and

their specic boundary conditions for this situation are represented in four dimensionless com-bined ordinary dierential equations [14,15]. These equations describe the average mass fractionof water in the solution w, the average solution temperature T, the heat transfer to the cooling

Fig. 2. Sketch of simplied geometry used in the absorber model.



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medium across the plate wall per unit width _qw, and the mass transfer of the water vapor to the

lm per unit width _mv in one innitesimal part of the lm with length dx as shown in Fig. 2. Forsimplication, these equations are written in dimensionless form, where they describe the change

of average mass fraction c, the average solution temperature h, heat transfer _qw, and mass transfer_mv with dimensionless length dGz. They are given in nal form as follows:

dc

dGz a1 h c 2

dh

dGz b1 h c ch hcw 3

d _qw

dGz ccP so _msTe Toh hcw 4

d _mv

dGz a _ms

we wo1 wo

1 h c 5

where

a Le

K

Nui 1

Sh

h i ; b 11

Nui 1

K Sh

h i ; c 11

Bi 1

Nuw

h iand h and c are the dimensionless temperature and mass fraction, respectively. Te is the equi-librium solution temperature for the solution at mass fraction wo at the chosen absorber (evap-orator) pressure. we is the equilibrium mass fraction of water in the solution for solution

temperature To at the chosen absorber pressure.To dene Te and we, the relation between the solution temperature and mass fraction is formed,

under assumption 5 above, by a linearization of the thermodynamic equilibrium equation of theLiBrH2O solution at a xed pressure. This equilibrium equation is expressed in the solutiontemperature Ts as a function of the LiBr concentration in the solution Xand the vapor pressure P

(or refrigerant temperature Tr), Ts fX;P or Ts fX; Tr [1]. The relation is

Ts C1w C2 6a

where

C1 21:8789 0:58527Tr 6b

C2 0:0436688 1:407Tr 6c

i.e., the Te and we values can be dened from Eq. (6) with the evaporator temperature as the

refrigerant temperature Tr as follows:

Te C1wo C2 7

and

we 1

C1To C2 8



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A good estimate for Nui, Nuw and Sh are the expressions found analytically by Ref. [14]. These

numbers are

Nui 2:67 9a

Nuw 1:6 9b

Sh 1

Le Gz

" ln 1

6Le Gz

p

r !#; Gz< Gz1 9c

Sh 1

Gz

ln2

Le

Gz

p

24Le

12p

; GzPGz1 9d

where

Gz1 p24Le

9e

Eqs. (2)(5) are solved numerically for a unit width of the plate by explicit nite dierences [16]and lead to

ci1 cidGz

a1 hi ci 10

hi1 hidGz

1 hi ci chi hcw 11

_qwi1

_qwi

dGz c cP so _msiTe

To

hi hcw 12

_msi1 _msidGz

a _msiwe wo1 wo

1 hi ci 13

for 16 i6 n n number of parts.In the solution, the length of the plate was divided into 40 equal parts. Each part is represented

by four combined ordinary dierential equations in terms of ci, hi, _qwi and _msi.Input variables for each part are: c, h, _q and _ms. The inputs of the rst part (i 1) are: c1 0,

h1 0, _qw1 0 and _ms1. The main outputs are: c2, h2, _qw2 and _ms2. Then, these are used as newinputs to the second part and so on to the end of the plate (c

n, h

n, _q

wnand _m

sn).

Thereafter, the following procedures are applied to determine the solution for the whole ab-

sorber length. Its geometry is described in Fig. 3.(1) The input conditions to the absorber are the mass ow rate _m9, temperature T9, and con-

centration X9 of the solution, as well as the evaporator temperature Te, cooling water temperature

inlet to the absorber T15 and mass ow rate of the cooling water _m15.(2) The simulated absorber consisted of multi-passes of tubes Np a (4 in this work) with pass

length Lp a (4.876 m). The four passes were simulated as one long pass with total tube length

equaling 4Lp a. This simplication eliminates the eect of added pressure drop due to directionchanges in the original 4 pass absorber. The added pressure is thought to be very small and does



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not aect the heat transfer and mass transfer calculations. The total length of each tube was

divided into 40 equal sections. Each of the 40 tube sections will have a length equivalent to a platewidth y as shown in Fig. 3

y 4Lp a

4014

(3) The solution starts with the rst horizontal row of tubes. The horizontal tubes are assumed

to be all in the same conditions, i.e., the simulation of one tube represents the situation of all tubes(number 1 Nh a) of that row. The input conditions for each pipe in this row are the mass ow

rate of the solution _ms per y width of the section, solution temperature To and mass fraction wo:

_ms _m9

Np aLp aNh a15

and

To T9 16

wo 1 X9

10017

Fig. 3. Schematic of the geometry of a cooled absorber lm: (a) front view section of the absorber tubes and (b) side

view section for the rst vertical row of the tubes.



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(4) Under the input conditions above, Eqs. (10)(13) can be applied to the rst tube (k 1) inthe rst vertical row at the rst section (j 1). The inputs start with c1 0, h1 0, _qw1 0 and_ms1 _ms. The main outputs are: cnk1, hn1 _qwn1 and _msn1. Then, they are used as new inputs to

the second tube (k 2) and (j 1) in the same vertical row as follows:

To new Tn1 hn1Te To To

wonew wn1 cn1we wo wo

_ms1 _msn1

_qw1 _qwn1

and start with h1 0, c1 0 and so on to the last tube (k Nv a). In this case, the output con-ditions are cnNv a , hnNv a , _qwnNv a and _msnNv a .

All the processes are taking place at constant cooling water temperature T15 j 1.(5) Similar results can be obtained for each of the other vertical rows of tubes at the same

section j 1 because the input conditions are the same for each vertical row (step (4)).Therefore, the rate of heat transfer to the cooling water and the mass ow rate of the solution forthe whole section are obtained by collecting the _qwnNv a and _msnNv a values for each vertical row, orthey can be expressed in the form:

_qwj Nh a _qwnNv a 18

_msj Nh a _msnNv a 19

for 16j6m:The cnNv a and hnNv a values that are obtained from step (5) are the same for the other vertical

rows at same section (j 1).(6) The same procedure as in steps (5) and (6) is repeated for (j 2; 3; . . . ; m) with a new

cooling water temperature at each section. This temperature can be obtained from the heat

balance around the cooling water circuit as follows:

Tj1 _qwj

_m15cPj Tj 20

(7) The total heat of the absorber and the total mass ow rate of solution leaving the absorber

are computed by collecting _qwj and _msj for all sections as follows:

Qa Xmj1

_qwj 21

_m2 Xmj1

_msj 22

The mass ow rate of the refrigerant that is absorbed in the absorber is

_m1 _mr _m2 _m9 23



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The cooling water temperature outlet from the absorber is

T16 Tm 24

The hnNv a and cnNv a values that are obtained from all sections (step (6)) along the absorberlength are converted to TnNv a and wnNv a values from:

TnNv a hnNv a Te To To 25

wnNv a cnNv a we wo wo 26

These values TnNv a and wnNv a are collected, and the average values as Tav and wav are ob-tained by a numerical integral method using Simpsons rule [16]. The temperature and concen-tration of the solution leaving the absorber T2 and X2 are

T2 Ta Tav 27

X2 Xa 1001 wav 28

2.2. The solution pump circuit

(a) Energy balance

Qp _m3h3 _m2h2 29

Qp is the mechanical energy required to pump the solution liquid, and it will be taken as zero in

the present work because its energy is very small compared with Qg.Thus,

_m3h3 _m2h2 30

_m3h3 _m4h4 _m8h8 31

_m9h9 _m8h8 _m7h7 32

h9 _m8h8 _m7h7

_m933

(b) Conservation of total mass

_m2 _m3 34

_m3 _m4 _m8 2 _m4 2 _m8 35

_m9 _m8 _m7 36

(c) Conservation of absorbate

_m2X2 _m3X3 37

From Eq. (34)

X2 X3 Xa 38



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_m3X3 _m4X4 _m8X8 39

Substituting Eq. (35) in Eq. (39) and eliminating _m3 provides

X3 X4 X8 Xa 40

_m9X9 _m8X8 _m7X7 41

Substituting Eqs. (34), (35) and (40) into Eq. (41) gives

_m9X9 12

_m2X2 _m7X7 42

Rearranging Eq. (42),

X9 1

2

_m2

m9X2

_m7

_m9X7 43

2.3. The solution heat exchanger

(a) The heat transfer processIt is expressed in terms of the eectiveness of the heat exchanger. The expression for the ef-

fectiveness is given as [10]

g T6 T7T6 T4

44


T7 T6 gT6 T4 45

(b) Energy balance_m4cP4T5 T4 _m6cP4T6 T7 46


T5 _m6cP6

_m4cP4T6 T7 T4 47

noting that _m4 _m5 1=2 _m2 and _m6 _m7

2.4. Generator

(a) Energy balance

Qg Qg1 _m6h6 _m10h10 _m5h5 48

or Qg may be expressed from the external circuit as Qg2

Qg Qg2 _m18cP18T18 T19 49

(b) Conservation of total mass

_m6 _m5 _m10 50

noting that _m10 _mr



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(c) Conservation of absorbate

_m5X5 _m6X6 51

Substituting Eq. (50) into Eq. (51) gives_m5X5 _m5 _m10X6 52

Rearranging Eq. (52) to obtain the ow ratio (FR)

FR _m5

_m10

X6

X6 X553

where X6 Xg.Thus,

FR Xg

Xg Xa54

(d) Heat transfer processThe generator is a shell and tube heat exchanger. It is assumed that the ow is counter ow

through multi-pass tubes. The heat transfer equation employed is [10],

Qg Qg3 UgAgDTm gFc 55

(e) Equilibrium equationThe generator pressure Pg is in equilibrium with the solution temperature in the generator

Tg T6 and its concentration Xg X6. The generator pressure equals the condenser pressure Pc.The condenser temperature is Tc T11, and its vapor pressure is Pc. Therefore, from the equi-librium equation of the LiBrH2O solution, the generator temperature Tg can be expressed as a

function of its concentration Xg and the condenser temperature Tc as follows [1]:Tg fTc;Xg 56

2.5. Condenser

(a) Energy balance

Qc Qc1 m11hfg11 57

or Qc may be expressed from the external circuit as Qc2

Qc Qc2 m16cP16T17 T16 58

(b) Heat transfer processThe refrigerant vapor entering the condenser is assumed to be saturated vapor at the condenser

temperature T11(Tc). So that

Qc Qc3 UcAcDTm c 59

2.6. Expansion device

h11 h12 hc 60

Note that _m11 _m12.



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2.7. Evaporator

(a) Energy balance

Qe Qe1 _m1h1 h12 61

but h11 h12.So,

Qe1 _m1h1 h11 62

noting that _m1 _m12.

Or Qe may be expressed from the external circuit as Qe2

Qe Qe2 m13cP13T13 T14 63

(b) Heat transfer process

In the evaporator, the water vapor is evaporated at the saturation temperature T1Te, thus

Qe Qe3 UeAeDTm e 64

2.8. The COP

The overall energy balance equation for the whole cycle will be

Qe Qg Qa Qc 0 65

The COP for the system is usually dened as

COP Qe

Qg 66

3. Computational model

The simulation of any absorption system means the representation of the actual behavior of thesystem mathematically. This process was done by casting mathematical models for each com-ponent making up the absorption refrigeration system. These components were an absorber, a

generator, an economizer (liquid to liquid heat exchanger), a condenser and an evaporator. Thesemodels were then combined and solved to give the required information about the temperature,

concentration and ow rate at each state point of the system and the heat quantities at eachcomponent as well as the performance of the system.

In the present work, a computer program was built to simulate the eect of various operatingconditions on the performance and output of the absorption refrigeration system.

3.1. Simulation of the solution heat exchanger and the absorber

Simulation of the solution heat exchanger and the absorber implies the determination of the

output conditions from the solution heat exchanger and the absorber block diagram for its inputconditions and physical dimensions of the absorber (Table 1). This is depicted in the information



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ow diagram in Fig. 4a. The simulation was accomplished by starting with initial values ofTa andXa as well as the input conditions as shown in Fig. 4a. Then T5 is computed from Eq. (47). Theinput conditions to the absorber, which are the parameters of the intermediate solution _m9, T9and X9, are then calculated. In the absorber, Ta, Xa, _mr and Qa are computed by applying Eqs.(2)(5) for the whole absorber length and solving them numerically by the nite dierence method[16]. The solution is represented in the seven steps described in Section 2. The new Ta and Xa are

Table 1

Design parameters of the absorber

Description Absorber Generator Condenser Evaporator

Inside diameter of tube (mm) 13.84 13.84 13.84 13.84Outside diameter of tube (mm) 15.87 15.87 15.87 15.87

Total number of tubes 484 200 121 256

Number of passes 4 2 1 4

Number of tubes per pass 121 100 121 64

Number of tubes in the vertical

direction per pass

11 10 11 8

Number of tubes in the horizontal

direction per pass

11 10 11 8

Length of the absorber (m) 4.876 4.876 4.876 4.876

Fouling factor (m2 C/kW) 8.6E06 8.6E06 8.6E06 8.6E06

Fig. 4. Information ow diagram of the system.



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compared with the initial reference values for a given accuracy. If the required accuracy is not

obtained, the new Ta and Xa are taken as new reference values, and the process is repeated. Theconvergence criterion was set equal to 0.0001. If the required accuracy is obtained, Ta, Xa, Qa, T16

and _mr are obtained as shown in Fig. 4a.

3.2. Simulation of the generator

This involves determination of conditions at the outlet from the generator block diagram for its

input conditions and for given values of the physical dimensions of the generator (Table 1). This isdepicted in the information ow diagram in Fig. 4b. The output data can be obtained by solving

two simultaneous nonlinear equations iteratively for two variables (Xg and T19) by using Powellsmethod [17], which is based on the classical NewtonRaphson technique. These equations arewritten in the form Q1i i 1; 2

Q11 Qg1 Qg2 67

Q12 Qg1 Qg3 68

Powells method deals with nonlinear equations as Fi and their variables xi to solve them si-multaneously. The simulation starts with an initial Xg and T19. Then, Q1i i 1; 2 values areobtained from Eqs. (67) and (68). The initial values of Xg and T19 are converted to xi (i 1; 2).

Also, Q1i i 1; 2 values are converted to Fi i 1; 2 values. The solution of Powells method

aim to reduce Fi towards zero, and it is said to converge when

P2i1F

2i

q6 106. If the required

accuracy is obtained Powells method will create new xi i 1; 2 values. These values are re-created to new Xg and T19. These values are taken as reference values, and the process is repeated

to nd Q1i. If the convergence is satised, the output conditions are obtained (Fig. 4b).

3.3. Simulation of the condenser

This implies the determination of the output data from the condenser block diagram for givenvalues of its physical dimensions (Table 1), and for its input data as shown in Fig. 4c. The outputdata can be obtained by solving the energy balance equations as two simultaneous nonlinear

equations iteratively for two variables (Tc and T17) by using Powells method. These equations arewritten in the form Q2i i 1; 2

Q21 Qc1 Qc2 69

Q22 Qc1 Qc3 70

The simulation starts with initial Tc and T17 values.

3.4. Simulation of the evaporator

This means determination of the output conditions from the evaporator block diagram for

given values of its physical dimensions (Table 1) and for the input conditions to it as shown in Fig.4d. The output data can be obtained by solving the energy balance equations as two simultaneous



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nonlinear equations iteratively for two variables (Te and T13) by using Powell's method. These

equations are written in the form Q3i i 1; 2

Q31 Qe1 Qe2 71

Q32 Qe1 Qe3 72

The simulation procedure is the same as that for the condenser and generator. The simulationstarts with initial Te and T13 values.

3.5. Simulation of the system

Simulation of the system essentially implies prediction of the heat transfer for each of thesystem components, the system COP, the conditions at all state points (Fig. 1) for the given

physical dimensions of the plant (Table 1), and for the input conditions to the system as shown inthe information ow diagram in Fig. 4. As discussed earlier, this necessitates determination of theoperating conditions for which the mass and energy balances for the whole system are satised,

together with the performance characteristics of the individual components. The simulationprocedures of Sections 3.13.4 can obviously be used to furnish these performance characteristics.

Consequently, system simulation needs an amalgamation of these component simulation proce-dures so that by using the aforementioned input information, the values of the desired output

variables are obtained. This is eected through the interlinking of variables which appear asoutput from one component and are used as input in the next component (Fig. 4). The problemessentially reduces to solving nonlinear Eqs. (67)(72) for the variables, Te, T13, Tc, T17, Xg, andT19. Variables Ta and Xa depend upon these variables, which are obtained numerically by a nite

dierence method as shown in Section 3.1.The simulation starts with reading input data and creates initial values of Te, T13, Tc, T17, Xg

and T19. First the iterative procedure is done in the solution heat exchanger and the absorber as

shown in the block diagram (Fig. 4a). If the required convergence is obtained, Xa, _mr, Qa and T16at the exit of the absorber and T5 at the inlet to the generator are determined. These are used as

input in the other components as shown in Fig. 4. Then, Q11, Q12, Q21, Q22, Q31 and Q32, re-spectively, are computed. These values are converted to Fi i 1; 6 values as shown in Table 2with their variables xi i 1; 6 values as shown in Table 2 with their variables xi i 1; 6. If therequired accuracy,

P6i1 F

2i

1=26 106, is not obtained, Powells method would create new

Table 2The nonlinear equations, which must be solved simultaneously and listed as Fi i 1; 6

Component name No. of equations in Powells

method

No. of equations in each

component

Reference equation

Generator F1 Q11 Qg1 Qg2 Eq. (67)F2 Q12 Qg1 Qg3 Eq. (68)

Generator F3 Q21 Qc1 Qc2 Eq. (69)F4 Q22 Qc1 Qc3 Eq. (70)

Evaporator F5 Q31 Qe1 Qe2 Eq. (71)F6 Q32 Qe1 Qe3 Eq. (72)



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xi i 1; 6 values. These values are taken as reference values, and the process is repeated to ndnew Fi i 1; 6 values. If the convergence is satised, Qa, Qc, Qg, Qe, COP and all informationfor each state point of Fig. 1 (temperatures, concentration, and ow rates) are obtained. More

comprehensive details about the simulation of the components and the system are given by Lafta[18].

4. Results and discussion

The computer model was used to simulate the systems performance for a variety of operatingconditions. As a reference point for evaluation of the eect of dierent parameters, a design

condition was selected which corresponds to the design point for the system. The design conditionis described in Table 3. The table lists, rst, the following input parameters:

1. Mass ow rate of the hot water and its inlet temperature, mass ow rate of the cooling water

and its inlet temperature and mass ow rate of the chilled water and its outlet temperature.2. Mass ow rate of weak solution leaving the solution pump from the absorber and the eective-

ness of the solution heat exchanger.

Next, the following calculated quantities are shown:

1. The temperature, mass ow rate and concentration at all the state points corresponding to Fig.1. The concentration is the LiBr concentration, percent by weight, in the solution.

2. The heat quantities in the evaporator, condenser, absorber and generator.

3. The COP.

Similar calculations were made for other selected sets of operating conditions.The performance characteristics of the individual components of the system are discussed rst

over a wide range of operating conditions, and then, the performance of the entire system isdiscussed. only typical results are presented for brevity.

4.1. Individual component performance

The performance of the absorber has been evaluated for various values of input conditions to

the absorber. The simulation included study of the eect of varying one of the input conditions(inlet cooling water temperature to the absorber T15, evaporator temperature Te and solution

concentration outlet from the generator Xg) while keeping the others constant.Fig. 5 shows the variation of the heat rejection to the cooling water Qa as a function of the inlet

cooling water temperature T15. The cooling water inlet temperature is varied from 24C to 34C as

possible operating limits in this gure and for a design value of Xg at 56%. Te was taken at 4C,6C, 8C and 12C, respectively. It can be seen that Qa decreases linearly as T15 is increased. Thevalues of Qa are higher at the higher evaporator temperature. This is because when T15Ta in-creases, the solution will absorb less refrigerant _mr, which keeps the solution concentration Xa at ahigher value [6]. Less refrigerant absorption means less heat liberation Qa to the cooling water [6]



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Table3

Designconditionsforthesimulatedsystem

Unit

Description

Value

Inputparameters

Evaporator

Massowrateofthechilledwater

10.0

8kg/s

Outletchilledwatertemperature

8C

Absorberandcondenser

Massowrateofthecoolingwater

20.1

kg/s

Inletcoolingwatertemperature

30C

Generator

Massowrateofthehotwater

14.1

kg/s

Inlethotwatertemperature

85C

Solutionpump

Massowrateofthesolution

8.0

3kg/s

Solutionheatexchanger

Eectivenessoftheheatexchanger

0.8

5

Statepoints(s

eeFig.

1)

Temperature(C)

Massowrate(kg/s)

Concentration(%)

Calculatedparameters

13

Chilledwater

inlettoevaporator

12

10.0

8

14

Chilledwater

outletfromevaporator

8

10.0

8

1

Vaporfromevaporatortoabsorber

5.7

0.0

89

2

Weaksolution

outletfromabsorber

33.1

8.0

3

54.6

3

Weaksolution

outletfromsolutionpump

33.1

8.0

3

54.6

4

Weaksolution

inlettosolutionheatexchanger

33.1

4.0

15

54.6

5

Weaksolution

inlettogenerator

66.5

3

4.0

15

54.6

6

Strongsolutio

noutletfromgenerator

74

3.9

26

56

18

Inlethotwate

rtogenerator

85

14.1

19

Outlethotwaterfromgenerator

80

14.1

7

Strongsolutio

noutletfromheatexchanger

39.1

7

3.9

26

56

8

Weaksolution

outletfromsolutionpump

33.1

4.0

15

54.6

9

Intermediates

olutioninlettoabsorber

36.1

7.9

4

55.2

10

Vaporfromgeneratortocondenser

38

0.0

89

11

Condensatefromcondensertoexpansiondevice

38

0.0

89

15

Inletcoolingw

atertoabsorber

30

20.1

16

Outletcooling

waterfromabsorber

33.3

9

20.1

17

Outletcooling

waterfromcondenser

36

20.1

Unit

Heatquantity

(kW)

Evaporator

211.1

Absorber

285

Generator

296.3

Condenser

221.7

COP

0:

71



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and vice versa. At a high Te, more refrigerant is absorbed [4], and Xa becomes lower. More re-frigerant absorption means more heat liberation to the cooling water.

Generator simulation includes the study of the eect of varying one of the input conditions,

such as inlet hot water temperature T18, the solution concentration at the outlet from the absorberXa and the condenser temperature Tc (or condenser pressure), on the performance while keepingother parameters constant.

Fig. 6 shows the variation of the heat supplied to the generator Qg as a function of T18 at a

design solution concentration Xa of 54.6% and three condenser temperatures. It can be seen fromthis gure that when T18 increases, Qg increases. The values of this parameter are higher at thelower Tc. The reason behind this behavior is that when T18 increases, the solution temperature Tgwill, of course, increase. Then, more refrigerant will be generated. This, in turn, causes an increasein the solution concentration Xg with LiBr, and then, Qg will increase as shown in Fig. 6. Animportant result in this gure is the limitation in the operating hot water temperature associated

with the condenser temperature. A condenser temperature of 34C allows a wide range of primehot water temperature (7595C), whereas this range is reduced to 10C (8595C) when the

condenser temperature becomes 44C. This can be attributed to the fact that the absorption cycleoperates when the generator concentration Xg is greater than the absorber concentration Xa to

generate refrigerant vapor [1]. Therefore, the minimum hot water temperature T18 to generaterefrigerant in the generator at a condenser temperature Tc of 34C is 75C (Tg 67:75C). Xg is55%, whereas Xa is 54.6%. The other values for T18 are obtained in a similar way at other con-denser temperatures.

The performance of the condenser includes study of the eect of varying one of the in-put conditions, such as refrigerant ow rate _mr and inlet cooling water temperature T16, on the

Fig. 5. Variation of the heat rejection with the inlet cooling water temperature.



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performance of the condenser while keeping other factors at constant values. Fig. 7 shows the

condenser heat rejection Qc to the cooling water as a function of the cooling water temperatureT16 for three refrigerant mass ow rates _mr. The heat rejection rate is almost insensitive within the

Fig. 6. Variation of the heat supplied to the generator with inlet hot water temperature.

Fig. 7. Variation of the heat rejection from the condenser with the inlet condenser cooling water temperature.



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cooling range of the illustration. However, the values of the heat rejection go up in steps with each_mr, as expected.

The evaporator performance is predicted by varying one of the input conditions, such as massow rate of the refrigerant _mr, condenser temperature Tc and outlet chilled water temperature T14,

while keeping others constant. Fig. 8 shows the variation of the cooling load Qe as a function ofthe outlet chilled water temperature T14 over the possible operating conditions for the chilledwater temperature from 5C to 15C and at three values of _mr and Tc. Qe increases slightly as T14is increased. The cooling load takes higher values at higher refrigerant ow rates and lower

condenser temperatures. The rate of increase of the cooling load with refrigerant ow rate in stepsis quite obvious, as they are directly related.

4.2. Overall system performance

The performance of the total system includes study of the eect of varying one of the input

conditions, such as inlet hot water temperature T18, inlet cooling water temperature to the ab-sorber T15 and outlet chilled water temperature T14, on the performance while keeping the othervariables in Table 3 constant.

The capacity of the system Qe is represented as a percentage of the nominal cooling capacity of211.1 kW (60 TR) in Fig. 9. This gure shows that when T18 is increased, the capacity increases

Fig. 8. Variation of the evaporator load with the outlet chilled water temperature.



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linearly. This trend is expected in the absorption refrigeration system [1]. The same trend wasobtained experimentally by Pichel [2] and theoretically by Waleed [3] for other conditions. LowerT15 values mean higher capacity. Also, Fig. 9 shows a comparison between the present theoretical

simulated system results and MDC. It can be seen that very good agreement is obtained betweenthe two. The percentage dierence between the two results was within 0.133.64%. The theoreticalpredictions show a much wider range in Figs. 916. The dashed lines are only extensions of the

computer prediction. The actual range of the system capacity is, of course, limited by the machinedesign limitations, which are limited by the capacity range given by the manufacturer designcurve. This is shown as solid lines in the computer output in the above illustrations.

Fig. 10 shows the variation of the COP of the system (Eq. (66)) with T18. The COP increaseswith T18 because of the increased cooling capacity. The values of COP are higher at the lower T15values. Eisa et al. [4] obtained a similar trend of variation of COP when Tg was increased atdierent Ta and Tc values. The system in Ref. [4] did not include a solution heat exchanger. Eisa

et al. [5] investigated the variation of COP with Tg experimentally for dierent Tc values. Theyobtained a similar trend of results as that presented here in Fig. 10. The manufacturer's COP(MDC) of the simulated system is plotted in Fig. 10 for comparison with the present theoretical

curve for COP. The percentage dierence in the results was within 0.441.65%.Cooling water is normally supplied to the absorber and condenser of an absorption system either

in parallel or in series. Figs. 11 and 12 show the variation of the capacity and the COP, respectively,

as a function ofT18 for cooling water in parallel and series. The inlet cooling water temperature inparallel to the absorber T15a and to the condenser T15c was 30C for both, while in series operation,only the inlet cooling water temperature to the absorber T15 is 30C. These gures show that the

capacity and COP are higher for the parallel cooling method, as would be expected, because of a

Fig. 9. Variation of the capacity with the inlet hot water temperature.



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lower condenser temperature in the parallel operation. Therefore, the performance improves.Pichel [2] presented experimental results of the capacity against T18 for series and parallel cooling.His results agree with the trend of results in Fig. 11 of the present work.

Fig. 11. Variation of the capacity with the inlet hot water temperature for cooling water in parallel and series.

Fig. 10. Variation of the COP with the inlet hot water temperature.



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Fig. 12. Variation of the COP with the inlet hot water temperature for cooling water in parallel and series.

Fig. 13. Variation of the capacity with the outlet chilled water temperature.



27/31

Fig. 13 shows that the capacity increases as T14 is increased, and higher values of T15 indicate

lower capacity. Pichel [2] presents experimental results of the refrigeration capacity on the same

Fig. 14. Variation of the COP with the outlet chilled water temperature.

Fig. 15. Variation of the capacity with the inlet cooling water temperature.



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coordinates as Fig. 13. The trend of that experimental data is the same as that in Fig. 13. MDC isincluded in this illustration for purposes of comparison between actual design data and the

present model results. It is clear that excellent agreement is obtained between them. The per-

centage dierence at T15 of 30C (which is the design value) in this comparison was less than 1%.Fig. 14 shows the system COP increasing as T14 is increased. The values of COP are higher at

lower T15. Eisa et al. [4] indicated that the COP increases as Te is increased, and that the best COP

is obtained when Ta and Tc are lower. Also, Eisa et al. [5] proved experimentally that the COPincreases as the evaporator temperature is increased. The results of Fig. 14 of the present modelare in agreement with the results of Refs. [4,5].

Fig. 15 shows the variation of the capacity as a function of T15. T18 was kept constant at 85C.The capacity decreases as T15 is increased and is higher at the higher values of T14 for the reasonsdiscussed earlier. Also, Fig. 15 illustrates a comparison between the present results and the MDCof the capacity variation with cooling water temperature. It can be seen that very good agreement

is obtained between them. The percentage dierence between the results was less than 1.65%.Fig. 16 shows the variation of COP with T15. The COP decreases when T15 takes higher values,

and higher values of T14 mean higher COP. Eisa et al. [4] showed that the COP decreases as theabsorber temperature Ta and condenser temperature Tc are increased. Also, Eisa et al. [5] have

found experimentally that the COP decreases as Ta and Tc are decreased. These results are inagreement with the present model results of Fig. 16.

The variation in the absorption cycle can now be represented on the equilibrium chart for the

LiBrH2O solution as shown in Fig. 17. The cycle is labeled with the same numbers for statepoints as those of Fig. 1. In Fig. 17a, T18 increases from 80C (state A) to 85C (state B) at avalue ofT15 of 30C and T14 of 8C. In Fig. 17b, T15 increases from 30C (state A) to 34C (state B)

Fig. 16. Variation of the COP with the inlet cooling water temperature.



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Fig. 17. Absorption refrigeration cycle on PXT diagram of LiBrH2O. (a) Eect of incresing T18 on the system

performance at constant T15 and T14. (b) Eect of increaing T15 on the system performance at constant T18 and T14. (c)

Eect of increaing T14 on the system performance at constant T18 and T15.



30/31

at a value ofT18 of 85C and T14 of 8C, while in Fig. 17c, T14 was changed from 8C (state A) to

10C (state B) at a T18 value of 85C and T15 30C. The above representation of the varia-tions in the absorption cycle gives a clear picture of the cycle variations with the parameters

discussed.

5. Conclusions

1. The simulation of the absorber and its representation with the present model was very success-ful. The validity of the simulation results was established by comparison with other works.

2. The simulation results of the overall system performance showed that the eects of varying sys-tem parameters in the simulation on system performance were typical of the LiBr absorptioncycle and gave quantitative as well as qualitative results.

3. Comparison between the present model results and the manufacturer's data showed excellentagreement.

References

[1] ASHRAE handbook, Fundamentals, ASHRAE, New York, 1985.

[2] Pichel W. Development of large capacity lithium bromide absorption refrigeration machine in USSR. ASHRAE J

1996:858.

[3] Waleed AF. Study of the eect of design parameters on a two ton lithium bromide absorption unit. MSc Thesis,

University of Technology, Baghdad, Iraq, 1983.

[4] Eisa MAR, Devotta S, Holland FA. Thermodynamic design data for absorption heat pump systems operating on

waterlithium bromide: Part I cooling. Appl Energy 1986;24:287301.

[5] Eisa MAR, Holland FA. A study of the operating parameters in a waterlithium bromide absorption cooler.

Energy Res 1986;10(2):13744.

[6] Eisa MAR, Diggory PJ, Holland FA. Experimental studies to determine the eect of dierences in absorber and

condenser temperatures on the performance of a waterlithium bromide absorption cooler. Energy Convers Mgmt

1987;27(2):2539.

[7] Mclinden MO, Klein SA. Steady-state modeling of absorption heat pumps with a comparison to experiments.

ASHRAE Trans Part-2B 1985;91:1793806.

[8] Grossman G, Michelson E. A modular computer simulation of absorption systems. ASHRAE Trans Part-2B

1985;91:180826.

[9] Catalogue for LiBr absorption chiller model ES-2A4.MW, 60 TR capacity. Mitsubishi Heavy Industries Ltd.,

Energy and Environment Research Center, Baghdad.

[10] Holman JP. Heat transfer, 8th ed. New York: McGraw-Hill; 1992.[11] Charters WWS, Megler VR, Chen WD, Wang YF. Atmospheric and sub-atmospheric boiling of H2O and LiBr

H2O solutions. Int J Refrig 1982;5(2):10714.

[12] Lorenz JJ, Yung D. A note on combined boiling and evaporation liquid lms horizontal tubes. Trans ASME,

J Heat Transf 1979;101:17880.

[13] Perry JH. Chemical engineers handbook, 3rd ed. New York: McGraw Hill; 1950.

[14] Wassenaar RH. A comparison of 4 absorber models. Internal Report K-176, Delft University of Technology,

Delft, Netherlands, 1992.

[15] Wassenaar RH. Falling lm absorption: a discussion on three types of model and on the data reduction of

absorption measurements. Proceedings of the 19th International Congress of Refrigeration, vol. IVa, Theme 4, 11R

Commission B1, 1995. p. 348.



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[16] Huliquist P. Numerical methods for engineering and computer scientists. New York: Addison Wesley; 1988.

[17] Rabinowitz P. Numerical methods for non-linear algebraic equations. London: Gordon & Breach; 1970.

[18] Lafta AH. Preliminary simulation of a simple absorption refrigeration system. MSc Thesis, Department of

Mechanical Engineering, University of Baghdad, Iraq, 1988.


Documents

Simulationof Simple Abs System