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Dynamic simulation of an ammonia-waterabsorption refrigeration system

Weihua Cai1, Mihir Sen2 and Samuel Paolucci3

Department of Aerospace and Mechanical Engineering

University of Notre Dame, Notre Dame, IN 46556

July 1, 2010

Abstract

A dynamic model of a single-effect absorption refrigeration cycle has been developed. Mod-eling of the cycle performance requires thermodynamic properties which are obtained fromequations of state for refrigerant-absorbent mixtures. The transient response of the absorp-tion refrigeration cycle is investigated using mass, momentum and energy balances for the

different parts of the system. Some design and operation parameters that affect the cycleperformance are identified.

Keywords: absorption-refrigeration, ammonia-water, dynamics, equation of state

1 Introduction

A typical single-effect absorption refrigeration cycle consists of four basic components, an

evaporator, an absorber, a generator and a condenser, as shown in the schematic of Fig. 1.

The cooling cycle starts at the evaporator, where liquefied refrigerant boils and takes some

heat away with it from the evaporator, which produces the cold desired in the refrigerated

space. The refrigerant vapor releases its latent heat as it is absorbed by an liquid absorbent

in the absorber. It is necessary to separate the refrigerant from the absorbent, and this is

done in the generator. A pump drives the solution into the generator which is heated by a

heat source (e.g. steam, hot water, direct firing, solar cell). The solution is heated and the

refrigerant vapor driven out of it. Part of the solution is throttled back into the absorber.1Currently at Caterpiller, e-mail: [email protected] author, e-mail: [email protected]: [email protected]

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A solution heat exchanger, normally located between the absorber and the generator, makes

the process more efficient without changing its basic operation. Subsequently, the condenser

cools the refrigerant vapor back into the liquid state. The cycle continues after the refrigerant

goes through an expansion valve.

There have been some papers published on the steady-state and dynamic simulations of

absorption refrigeration systems. A computer code ABSIM has been developed for steady-

state simulation of absorption systems in a flexible and modular form (Grossman and Zaltash,

2001). It has been employed by many users for performing cycle evaluations, testing control

strategies, and preliminary design optimization. Detailed distributed models of absorption

heat pumps using H2O/NH3 have been developed (Butz, 1989). Step change response of the

system has been investigated. In an advanced energy storage system using H2O/LiBr as the

working fluid (Xu et al., 2007b,a), dynamic models of the operation have been developed, and

the simulation results predicted the dynamic characteristics and performance of the system.

An object-oriented dynamic modeling library named ABSML has been designed (Fu et al.,

2006). Different absorption chiller models, including single-effect, double-effect, LiBr/H2O

and H2O/NH3 systems, have been successfully developed in the library. Simulation results on

transient behavior and during startup and shutdown show good match between experimental

data and simulations. Numerical simulation have been carried out to predict the transient

operating characteristics and performance of an absorption heat pump using H2O/LiBr to

recover waste heat (Jeonga et al., 1998). The simulation of absorption and refrigeration

systems is very helpful for understanding and evaluating the system as well as for system

design, operation and control, and device design or selection in detail (Lucas et al., 2007;

Sohel and Dawoud, 2006; Donate et al., 2006; Lucas et al., 2004; Atmaca et al., 2002; Vargas

et al., 1998; Yang and Guo, 1987).

Modeling the cycle performance requires thermodynamic properties. However, very

few papers utilize equations of state to obtain the thermodynamic properties. Yokozeki

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(Yokozeki, 2005) is the first to perform the steady state modeling of an absorption-refrigeration

cycle using equations of state to calculate thermodynamic properties. In the present work we

develop a dynamical model for a single-stage absorption refrigeration cycle, where all ther-

modynamic properties have been consistently obtained from equations of state for mixtures.

The aim of this work is to study the effects of thermodynamic properties on the steady state

performance and dynamic response of an absorption refrigeration cycle. The modeling and

calculations are carried out for an ammonia-water system for which good data are available.

2 Dynamic modeling

2.1 Governing equations

Fig. 1 shows a schematic of the absorption refrigeration cycle. The principal components

of a conventional absorption refrigeration system are generator, condenser, evaporator, and

absorber. In the present study, some assumptions are made in developing the dynamic

modeling. In the lumped-parameter approach, each component is characterized by a single

temperature, pressure, and concentration. The flow in the pipes is assumed to be one-

dimensional, and no diffusion of heat occurs in the flow direction. In addition, there is no

heat loss from generator to the surroundings nor heat gain by the evaporator from the sur-

roundings, and the expansion process in the valve is assumed to occur at constant enthalpy.

We write the coupled governing equations for the complete absorption refrigeration cycle

by examining the balances of mass, energy, and momentum for the different components in

the cycle. We take Mi(t) to correspond to the mass within component i, and mi(t) the mass

flow rate between components, as labeled in Fig. 1. Subsequently, the overall mass balances

for each component are given by

dMCdt

= m1 m2 , (1)dME

dt= m3 m4 , (2)

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dMAdt

= m4 + m10 m5 , (3)dMG

dt= m7 m8 m1 (4)

m2 = m3 , (5)

m5 = m6 = m7 , (6)

m8 = m9 = m10 . (7)

Here we take Ci(t) to be the mass fraction of the absorbent coming out of a component.

Subsequently, we have the following absorbent mass balances

d

dt(MACA) = m10C10 m5C5 , (8)

d

dt(MGCG) = m7C7 m8C8 , (9)

C5 = C6 = C7 = CA , (10)

C8 = C9 = C10 = CG . (11)

The momentum equations between the components are given by

dm1dt

+1

2f1

m1|m1|1A1D1

=A1L1

(PG PC) , (12)dm2

dt+

1

2f2

m2|m2|2A2D2

=A2L2 PC P

iV1 , (13)

1

21

1

2A2V1m2|m2| = PiV1 PoV1 , (14)

dm3dt

+1

2f3

m3|m3|3A3D3

=A3L3

PoV1 PE

, (15)

dm4dt

+1

2f4

m4|m4|4A4D4

=A4L4

(PE PA) , (16)dm5

dt+

1

2f5

m5|m5|5A5D5

=A5L5

PA PiP

, (17)

P = PoP PiP , (18)dm6

dt+ 1

2f6

m6|m6|6A6D6

= A6

L6(PoP PG) , (19)

dm9dt

+1

2f9

m9|m9|9A9D9

=A9L9

PG PiV2

, (20)

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1

22

1

9A2V2m9|m9| = PiV2 PoV2 , (21)

dm10dt

+1

2f10

m10|m10|10A10D10

=A10L10

PoV2 PA

, (22)

where fi is the pipe friction factor (a single correlation relating pipe friction loss to Reynolds

number and surface roughness for laminar, transitional and turbulent flow alike is used

(Churchill, 1977)), i is the expansion valve friction factor, Li and Di are pipe length and

diameter respectively, Ai is the pipe cross-sectional area, and AVi is the smallest cross-

sectional area of the expansion valve, i is the density, and Pi is the pressure. The superscripts

i and o stand for the inlet and outlet of a component, respectively.

The performance of a pump, which is the prime mover that increases the pressure of the

solution, is given by empirically-determined characteristic curves. This can be conveniently

represented as a low order polynomial

P = PoP PiP = a1 + a2m5 + a3m25, (23)

where a1, a2 and a3 are parameters determined from the manufacturers technical data. For

the current study, we assume that they are constant.

Letting hi(t) be the specific enthalpy, the energy balances for the components are given

by

d

dt(MChC) = m1h1 m2h2 QC , (24)

d

dt(MEhE) = m3h3 m4h4 + QE , (25)

d

dt(MAhA) = m4h4 + m10h10 m5h5 QA , (26)

d

dt(MGhG) = m7h7 m8h8 m1h1 + QG , (27)

Qx

= m7h7

m6h6 = m8h8

m9h9 , (28)

m6h6 = m5h5 + WP , (29)

h2 = h3 , (30)

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h9 = h10 , (31)

where Qi = FiUiTi, Fi the total heat transfer area, Ui is the overall heat transfer coefficient,

Ti = TiTi,, Ti is the temperature of the component, Ti, is the temperature surroundingthe component, and WP is from Eq. (73). Note that convective heat losses have been

neglected in the above model.

The above equations are complemented by an equation of state (EOS)

P = P(T , V , x) , (32)

where V = V /n is the molar volume, V is the total volume, x xr = nr/n is the molefraction of the refrigerant, n = nr + na is the total number of moles, and nr and na are the

number of moles of the refrigerant and absorbent respectively. In addition, we note that the

total mass M is given by

M = V , (33)

where is the total density given by

=1

V[xMr + (1 x)Ma] , (34)

where Mr and Ma are the molecular masses of the refrigerant and absorbent respectively.Lastly, the mass fraction y of the absorbent is given by

y =Ma(1 x)

xMr + (1 x)Ma . (35)

Note that

x = Ma(1

y)

yMr + (1 y)Ma . (36)

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2.2 Equation of state

The theoretical performance of a vapor-absorption refrigeration cycle can be determined

once the equation of state is given. A generic Redlich-Kwong (RK) EOS (Yokozeki, 2005)

for the mixture is

P =RT

V b a

V(V + b), (37)

where R is the universal gas constant.

For a pure specie i, parameters ai and bi are given as

ai = 0.42748R2T2ci

Pcii , bi = 0.08664

RTciPci

, (38)

where Tci and Pci are the critical temperature and pressure, and

i =3

j=0

j

TciT T

Tci

j. (39)

The subscripts are 1 for NH3 and 2 for H2O. The critical parameters and EOS constants of

the pure refrigerant and absorbent are shown in Table 1.

For the mixture, the following rules are used

a = ij

xixj

aiaj [1 gij(T)kij] , (40)

b =i

j

xixjbi + bj

2(1 nij) , (41)

where

gij = 1 + cijT , (42)

cij = cji, cii = 0 , (43)

kij =lijlji(xi + xj)

ljixi + lijxj, kii = 0 , (44)

and where cij = cji, lij = lji, and nij = nji are empirical interaction parameters given in

Table 2.

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The enthalpy h is a thermodynamically derived variable given by

h =

k

C0pkxkdT h , (45)

where

h = RT2

V

ZT

V

dV

VRT(Z 1) , (46)

and

Z = P V /RT (47)

is the compressibility. The ideal gas heat capacity at constant pressure for each component

is modeled as a polynomial

C0p = C0 + C1T + C2T2 + C3T

3 , (48)

where the coefficients are given in Table 3.

3 Results and discussion

3.1 Steady state

Let mr denote the refrigerant mass flow rate, and ms the solution mass flow rate, and r the

mass flow rate recirculation factor. After a sufficiently long time the system relaxes to the

following steady state

m1 = m2 = m3 = m4 = mr , (49)

m5 = m6 = m7 = ms , (50)

m8 = m9 = m10 = ms mr , (51)

r msmr

= yG

yG yA , (52)

mr|mr| = 2 1A2

1D1

f1L1(PG PC) , (53)

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= 22A

2

2D2

f2L2(PC PiV1) , (54)

= 22A

2

V1

1(PiV1 PoV1) , (55)

= 23A

2

3D3

f3L3(PoV1 PE) , (56)

= 2 4A2

4D4f4L4

(PE PA) , (57)

ms|ms| = 2 5A2

5D5

f5L5(PA PiP) , (58)

= 26A

2

6D6

f6L6(PoP PG) , (59)

P = PoP PiP , (60)

ms mr = 2 9A2

9D9

f9L9(PG PiV2) , (61)

= 2 9A2

V2

2(PiV2 PoV2) , (62)

= 210A

2

10D10

f10L10(PoV2 PA) , (63)

QC/mr = (h1 h2) , (64)

QE/mr = (h4 h3) , (65)

QA/mr = h4 + (r 1)h10 rh5 , (66)

QG/mr = h1

rh7 + (r

1)h8 , (67)

Qx/mr = r(h7 h6) = (r 1)(h8 h9) , (68)

WP/mr = r(h6 h5) , (69)

h2 = h3 , (70)

h9 = h10 . (71)

Substituting Eqs. (68) and (69) into Eq. (67) gives

QG/mr = h1 + (r 1)h10 rh5 WP/mr . (72)

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The pump power is given by

WP = m5P/5 . (73)

To calculate the coefficient of performance (COP), we make following assumptions: (1)

the condition at Point 4 in Fig. 1 (exit of evaporator) is that of a saturated vapor; (2) the

condition at Point 2 (exit of condenser) is that of a saturated liquid; (3) the condition at Point

1 (inlet to condenser) is a superheated state; (4) the condition at Point 10 (solution inlet to

the absorber) is a solution bubble point. The first step is to obtain PC and PE as saturated

vapor pressures of a pure refrigerant at given temperatures of TC and TE. Then, given the

pipe geometry and expansion valve specifics, the refrigerant flow rate mr is obtained from

Eqs. (54)(56). The pressures PG and PA are obtained from Eqs. (53) and (57). Using a

method, such as flash calculation (Yokozeki, 2005; Ness and Abbott, 1982), xG, xA, VG and

VA are obtained at the given temperatures TG and TA and pressures PG and PA. Given the

constants a1, a2 and a3 from eq. (23), m5 is first calculated from Eqs. (58)(60), and then

the mass circulation ratio r can be calculated. The thermodynamic properties at point 10

are determined using the bubble-point T-method (Yokozeki, 2005; Ness and Abbott, 1982).

Enthalpies at other points are obtained from the equation of state with known T , P , V and

x. Now it can be readily shown that the COP for the steady state cycle operation is given

by

COP =QE

QG + WP=

h4 h3h1 + (r 1)h10 rh5 . (74)

To calculate the COP, we make the following assumptions: (1) the condition at Point 4

in Fig. 1 (exit of evaporator) is a pure refrigerant dew point with T = TE; (2) the condition

at Point 2 is a refrigerant bubble point and there is no subcooled (saturated) liquid; (3) the

condition at Point 1 (inlet to condenser) is a superheated state of a pure refrigerant with

T = TG; (4) the condition at Point 10 (solution inlet to the absorber) is a solutions bubble

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point specified with the absorber pressure PA and a solution concentration of the generator

CG.

Taking TG = 100C, TC = 40

C, TA = 30C, TE = 10

C, and assuming mr = 1 kg/s

without loss of generality, the performance of the absorption refrigeration cycle is shown in

Table 4. For the NH3/H2O pair, the calculated performance agrees with that of (Yokozeki,

2005). Keeping other temperatures constant, the COP decreases nearly linearly as the

temperature of the generator or absorber increases, as shown in Figs. 2 and 3. The decrease

in COP means that, in the present example, the generators heat-input increases while the

evaporator heat (at a fixed temperature) is constant.

However, the mass-flow-rate ratio r behaves in opposite trends between the generator and

absorber and in a highly non-linear fashion, as shown in Figs. 4 and 5. The steep increase

in r at low TG or high TA can be easily understood. The decrease of temperature difference

between TG and TA results in a smaller solubility difference between xG and xA. As a result,

the mass flow rate ratio r increases steeply, which can be seen in Eq. (52).

3.2 Dynamic response under step change

Now we study the dynamics of the NH3/H2O pair. Initially, the absorption refrigeration

cycle is at steady state operation with TG = 100

C, TC = 40

C, TA = 30

C, TE = 10

C.

The bulk concentration and temperature of a mixture determine its pressure. A step change

is introduced by increasing the pressure rise P across the pump by one percent. As a

result, the mass flow rate m5 quickly increases, as shown in Fig. 6. It is seen that the system

quickly reaches a new steady state. But as the flow rate increase, the frictional loss also

increases. The combined result of pressure force and friction results in an overshoot of the

flow rate. When more solution flows into the generator, more heat is gained from the high-

temperature source, which explains the evolution ofQG in Fig. 7. As more solution flows into

the generator, more refrigerant m4 is generated, as shown in Fig. 8. When more refrigerant

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is generated, more heat is gained from the refrigerated space, which explains the increase

of QE in Fig. 9. The evolution of the COP is shown in Fig. 10. This can be explained

by the evolution of QE and QG. Both QE and QG increase while more heat goes into the

evaporator.

4 Conclusions

A lumped-parameter dynamic model has been developed for a absorption refrigeration cycle.

All thermodynamic properties have been consistently calculated based on an equation of state

for mixtures. We have successfully demonstrated the usefulness of the EOS model for the

absorption refrigeration cycle process. We have shown that the coefficient of performance of

the cycle increases when the generator temperature or absorber temperature decreases.

The dynamical response to a step change is also investigated. The system quickly reaches

a steady state given the operation parameters for this specific example. The increase of pump

pressure rise results in an increase in the system performance. The instantaneous flow rate,

heat rates, and COP are also observed to oscillate in time before reaching steady state.

Acknowledgment

The authors thank the U.S. Department of Energy for support of this work, and Mr. G.

Puliti and Drs. J.F. Brennecke, E.J. Maginn and M. Stadtherr for discussions.

References

I. Atmaca, A. Yigit, and M. Kilic. The effect of input temperatures on the absorber pa-

rameters. International Communications in Heat and Mass Transfer, 29(8):11771186,

2002.

D. Butz. Dynamic behaviour of an absorption heat pump. International Journal of Refrig-

eration, 12(4):204212, 1989.

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S.W. Churchill. Friction-factor equation spans all fluid-flow regimes. Chemical Engineering,

84(24):9192, 1977.

M. Donate, L. Rodriguez, A. De Lucas, and J.F. Rodriguez. Thermodynamic evaluation of

new absorbent mixtures of lithium bromide and organic salts for absorption refrigeration

machines. International journal of refrigeration, 29(1):3035, 2006.

D.G. Fu, G. Poncia, and Z. Lu. Implementation of an object-oriented dynamic modeling

library for absorption refrigeration systems. Applied Thermal Engineering, 26(2-3):217

225, 2006.

G. Grossman and A. Zaltash. ABSIM - modular simulation of advanced absorption systems.

International Journal of Refrigeration, 24(6):531543, 2001.

S. Jeonga, B.H. Kangb, and S.W. Karngb. Dynamic simulation of an absorption heat pump

for recovering low grade waste heat. Applied Thermal Engineering, 18(1-2):112, 1998.

A. De Lucas, M. Donate, C. Molero, J. Villasenor, and J.F. Rodriguez. Performance evalu-

ation and simulation of a new absorbent for an absorption refrigeration system. Interna-

tional Journal of Refrigeration, 27(4):324330, 2004.

A. De Lucas, M. Donate, and J.F. Rodriguez. Absorption of water vapor into new working

fluids for absorption refrigeration systems. Industrial & Engineering Chemistry Research,

46:345350, 2007.

H.C. Van Ness and M.M. Abbott. Classical Thermodynamics of Non-Electrolyte Solutions

with Applications to Phase Equilibria. McGraw-Hill, New York, 1982.

Y.U. Paulechka, G.J. Kabo, A.V. Blokhin, O.A. Vydrov, J.W. Magee, and M. Frenkel.

Thermodynamic properties of 1-butyl-3-methylimidazolium hexafluorophosphate in the

ideal gas state. J. Chem. Eng. Data, 48:457462, 2003.

13


14/25

R.C. Reid, J. Prausnitz, and B.E. Poling. The Properties of Gases & Liquids. McGraw-Hill,

New York, 4 edition, 1987.

M.B. Shiflett and A. Yokozeki. Absorption cycle utilizing ionic liquid as working fluid. In

US Patent 20060197053A1. 2006.

M.I. Sohel and B. Dawoud. Dynamic modelling and simulation of a gravity-assisted so-

lution pump of a novel ammonia-water absorption refrigeration unit. Applied Thermal

Engineering, 26(7):688699, 2006.

J.V.C. Vargas, I. Horuz, T.M.S. Callander, J.S. Fleming, and J.A.R. Parise. Simulation of

the transient response of heat driven refrigerators with continuous temperature control.

International Journal of Refrigeration, 21(8):648660, 1998.

S.M. Xu, L. Zhang, C.H. Xu, J. Liang, and R. Du. Numerical simulation of an advanced en-

ergy storage system using H2O-LiBr as working fluid, Part 1: System design and modeling.

International Journal of Refrigeration, 30(2):354363, 2007a.

S.M. Xu, L. Zhang, C.H. Xu, J. Liang, and R. Du. Numerical simulation of an advanced

energy storage system using H2O-LiBr as working fluid, Part 2: System simulation and

analysis. International Journal of Refrigeration, 30(2):364376, 2007b.

W.-J. Yang and K.H. Guo. Solar-assisted lithium-bromide absorption cooling systems. In

Proceedings of the NATO Advanced Study Institute, pages 409423, 1987.

A. Yokozeki. Theoretical performances of various refrigerant-absorbent pairs in a vapor-

absorption refrigeration cycle by the use of equations of state. Applied Energy, 80:383399,

2005.

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A

C

V

E

C G

A

P

Heat exchanger

Q

Q

RefrigerantQx

Solution

2

3

4

1

8

10

9

7

6

5

A: Absorber E: Evaporator G: Generator

QE

Refrigerated space

QG

Hightemperature source

1

Wp2V

C: Condenser

V : Valves1,2 P: Pump

Figure 1: Schematic of absorption refrigeration cycle.

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340 360 380 400 420 4400.5

0.55

0.6

0.65

0.7

0.75

TG

COP

Figure 2: COP vs. generator temperature.

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290 295 300 305 310 315 320 3250.58

0.6

0.62

0.64

0.66

0.68

0.7

Figure 3: COP vs. absorber temperature.

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340 360 380 400 420 4401

2

3

4

5

6

7

8

9

TG

r

Figure 4: Mass flow rate ratio vs. generator temperature.

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290 295 300 305 310 315 320 3251

2

3

4

5

6

7

TA

r

Figure 5: Mass flow rate ratio vs. absorber temperature.

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0 20 40 60 80 1000.5

1

1.5

2

2.5

t (s)

Flow

rate

m5

(kg/s)

Figure 6: Response of mass flow rate of weak solution for step change.

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1 20 40 60 80 1005.0408

5.0408

5.0409

5.0409

5.041

5.0411

5.0411

5.0412

5.0412x 10

5

t (s)

QG

(J/s)

Figure 7: Heat transfer rate at generator for step change.

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1 20 40 60 80 100

0.2912

0.2913

0.2914

0.2915

0.2916

0.2917

t (s)

Flow

rate

m1

(kg/s)

Figure 8: Response of mass flow rate of refrigerant for step change.

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1 20 40 60 80 1003.234

3.2345

3.235

3.2355

3.236

3.2365

3.237x 10

5

t (s)

QE

(J/s)

Figure 9: Heat transfer rate at evaporator for step change.

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1 20 40 60 80 1000.6416

0.6417

0.6418

0.6419

0.642

0.6421

t (s)

COP

Figure 10: Coefficient of performance for step change.

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6. combustion in ic engines

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