MODELING AND SIMULATION OF SPARK IGNITION ENGINES

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MODELING AND SIMULATION OF SPARK IGNITIONENGINESYousef S.H. Najjar a & Abdullah M. Alturki aa Mechanical Engineering Department (Thermal) , King Abdulaziz University , Jeddah , S.APublished online: 25 Apr 2007.

To cite this article: Yousef S.H. Najjar & Abdullah M. Alturki (1996) MODELING AND SIMULATION OF SPARK IGNITION ENGINES,Fuel Science and Technology International, 14:8, 993-1018, DOI: 10.1080/08843759608947625

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FUEL SCIENCE & TECHNOLOGY INT'L., 14(8),993-1018 (1996)

MODELING AND SIMULATION OF SPARK IGNITION

ENGINES

Yousef S.H. Najjar and Abdullah M, Alturki

Mechanical Engineering Department (Thermal)

King Abdulaziz University, jeddan, SA

ABSTRACT

Modeling is important because it saves time, effort and cost needed for

engine development and prediction of performance, In this work, losses

due to imperfect construction oi the real engine, including progressive

combustion, valve timing and heat transfer have been modeled besides

engine friction. Hence, it becomes possible to convert the output of the

fuel-air cycle into net brake performance. Simulation of engine

performance was carried out by varying engine speed, compression ratio

and spark advance over wide range. Hence, it was possible to compare

the results with those from experiments on a single cylinder engine.

993

Copyright Cl:> 1996 by Marcel Dekker, Inc.

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994 NAJJAR AND ALTURKI

The model predictions were found to compare favourably with

experiment within 4.6% in power and 2.9% in SFC. The losses considered

in this work amount to about 14% of the fuel energy input.

INTRODUCTION

The best way to develop the techniques to enhance performance in

internal combustion engines, is to understand how to decrease losses.

Figure 1 shows a schematic diagram which explains why all the fuel

energy was not converted to work. The magnitude of some losses varies

with load or speed [11. Some of the losses would be different in

magnitude, for example, a rnulticytinder or a turbocharged engine; where

friction would be lower and fuel economy better, [21. There is some

arbitrariness in assigning losses, so the magnitudes shown in Fig. I should

not be taken very precisely. However, it suggests where the losses are

and Where effort should be exerted to improve the performance of the

engine.

Except the brake work, all other availability terms represent losses or

undesirable transfers from the system; hence decreasing terms

constitutes an improvement. These undesirable available energy transfer

and destruction terms fall into five categories [31: (I) combustion (2) heat

transfer, (3) exhaust to ambient, (4) fluid flow, (5) mechanical friction.

The combustion and exnaust losses are present in the ideal cycle models,

however, they are smaller than in the real engine [4J. The loss in

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SPARK IGNITION ENGINES

(1) Chemical energy of fuel (urp)

(2) Carnotcycle (Ist law limit): 'lear=1-TLITH

(3) Constantvol.cooling of productstznd law limit)

y-l(4) Ottoair standard cycle, '1 = I - (I/r )

. c

'1 = 100:l;

=74:l;

=52%

995

(5) Fuel-air cycletvariauon of properties & dissociation), '1La =45%

(6) Heat loss due to incomplete combustion ('1c=0.95) '1 = 40%

(7) Gross indicated actual enginetprogrossive combustion +

'Ii =08 ( '1La) = 36%s-,uc

".~u.~......"'

valve timing + heat transfer),

(8) Brake actual engine(pumping & rubbing friction), '1b='1m 'Ii

Automobile

Application

pumping

Ignition & Carburetion 0.173

0.188

(Accessory losses) Automobile transmission 0.137

power steering & alternator 0.12 I

Air conditioner O. 10

(9) Automobile engine efficiency 'Iauto = 10%

Fig. L Schematic diagram showing the effect of different losses, in the

automotive spark ignition engine, on efficiency.

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availability due to heat transfer, fluid flow, and mechanical friction are

real engine effects.

Refering to Fig. I the maximum output theoretically obtainable from a

certain quantity of fuel is approximately equal to the mechanical

equivalent of the internal energy of reaction urp hence efficiency would

be 100%, shown by level I. Assuming ambient temperature Ta = 300K

and the cornbuston temperature TH = 2900K, according to first law

analysis a completely reversible heat engine would produce theoretically

Carnot efficiency 'lear = 0.9, shown by level 2. According to the second

law analysis, the maximum amount of heat ranster that can be converted

to useful work is relatively less, hence the best we can hope to obtain

from constant volume cooling of combustion products is T)th = I - .tn

(TH/TL)/[(TH/TL)-I]=0.74 of the energy released by combustion 151. This

. is the upper limit set by the second law, as shown by level 3.

This second law efficiency could be obtained by using large number of

reversible infinitesimal engines. Hence, a more realistic cycle would be

. . r 1 . ..like the Otto cycle WIth T) = l-l/r . For typical compression ratios

Otto c

this comes to about 052 (level 4) assuming the working fluid as air with

constant thermodynamic properties whereas the processes are isentropic

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SPARK IGNITION ENGINES 997

compression and expansion and constant volume heat addition and

rejection. The value of such a cycle is to enable examining qualitatively

the influence of a number of variables on performance, because the

results differ a great deal from those of the actual engine. A more

convenient approximation to the real engine is the fuel-air cycle where

the reactants are assumed frozen during compression, wIlereas

combustion is complete witn T\c = 100% and products are in equilibrium.

Hence variation of specific heat and dissociation are taken into

consideration, however, the processes remain ideal. Typical efficiency of

such an ideal engine is about 0.45, as shown by level 5. Thus the losses

which can be ascribed to engine cycle amount to about 55% of urp. Most

of these losses are due to the irreversible combustion process, incomplete

expansion to ambient pressure and sensible exhaust heat [61.

Incomplete combustion causes thermal energy release to be less than the

chemical energy of the fuel hence, with combustion efficiency T\c = 0.95,

'"I = 0.4 as shown by level 6. This incomplete combustion results in the

formation of CO and UHC as pollutants. Imperfect construction of the

real engine including finite combustion rates, valve timing and throttling,

heat transfer to cylinder walls, and incomplete combustion, produce some

reduction from the ideal engine, represented by the fuel-air cycles about

20% [7] leaving the real engine with a gross indicated efficiency '"Ii = 036

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as shown by level 7. If the pumping and rubbing friction losses are

estimated by a mechanical efficiency of 30% then the brake efficiency flb

= 'li 'lm = 029 (level 13). The losses forming the difference between the

ideal engine and the actual measured values form the main SUbject of

investigation in this work. Tocomplete the picture, if the gasoline engine

is considered for automotive applications, the engine is grossly inefficient.

Only about 10% of the auto's energy input reaches the drive axle as

useful work. The accessory losses include pumping, ignition and

carburetion, automatic transmission, power steering and alternator, and

air conditioner [81, leaving final efficiency about 10% as shown by level 9.

EXPERIMENTAL FACILITY

A variable compression engine test rig was utilized in this work. The

engine is a single cylinder, four-stroke, water -cooled gasoline engine

which can be run on diesel The compression ratio can 00 varied between

S and I(\ by sliding the cylinder head in and out; the ignition timing can

be set between 300 and 10° BTDC. Displacement volume is 532 em3,

bore = 95 rnm. stroke = 32 mrn. length of the connecting rod = ISS mm,

port diameter is 30mm for both inlet and exhaust valves. Valve timing

is: ['10 344°, rvc 216°, EVO 144°, EVe = 16°. The rig comprises

instruments Which provide direct readout of brake power; torque; fuel,

air and coolant consumption or flow rate; besides exhaust and coolant

temperatures.

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The results either measued or calculated are tne brake power, air-fuel

ratio, specific fuel consumption, thermal efficiency, and exnaust

temperature. The properties of tlle fuel used is shown in table I.

MODELING AND SIMULATION

The ideal model used in this work is based on that of campell IS!.

However for the purpose of this work some modifications were done

namely fuel, compression ratio,spark advance,air mass fiw rate and heat

of reaction. In this ideal gas model, variation of thermodynamic

properties witll temperature for both reactants and products is

considered. Approximations are assumed to fit limited equilibrium

products to save computation time. Furthermore, compression and

expansion processesare isentropic.

The energy equation for the fuel-air rsidual gas charge is:

2

[ CPP _ I ]~ + [CR + ™ _ CPP].:!:2. _CR = 0CPM TM TS TS CPM TM

where CPM and CPP are constant pressure heat capacity (kJlkmol K) of

tile fuel air mixture and combustion products respectively.

Equation (1) may be solved for T1if tne difference between CPP and CPM

is ignored.

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1000

Property

NAJJAR AND ALTURKI

Table 1. Properties of gasoline

Gasoline

Formula CHZ.045

Relative molecularmass 100

Carbon/hydrogen mass ratio 5.37

Carbon, %by wt 35.444

Hydrogen, %by wt 14·550

Vapour pressure, kg/cmZ 0.7

Density, kg/ I 0.733

Net heat of combustion, kJ/kg. 43,705.5

Stoichiometric A/F mass ratio 14.Mo

Formula C7.12 H14.5O

Distillation

Initial boiling point, O( 33

10% recovery by Vol., °C 52

50% recovery by Vol., °C 30

90% recovery by Vol., O( 141

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T1~ CRTMCR - 1+TM!T5

(2)

1001

Tile energy equation for the combustion process can be written as:

Qv ~ r [N(I) {~ (T3) - ~ (T2)} I (3)

which can be conveniently solved by Newton-Raphson iterations,once we

have appropriate values for the product gas mole numbers, N(I) in Eq.

(3). Considering the general formula of fuel (CnHm) as a common

substitute for gasoline in thermodynamic analysis, assume the

correspondence between I values and product gases to be:-

with Yrepresenting moles 02/mole Cn Hm in the fuel/air mixture

CoHm + Y(02 + 3.76N2)

Hence NMO = 1+ 4.76 Y

Ymin ~ Ycc - n/4

NPO = m/4 + 4.76Y

NPO ~ (n + m/2) + 3.76Y

Urp ~ Hrp - RT (Np - Nr)

for Y > Ycc

for Ymin s y~ Ycc

(4)

(5)

Now the mole numbers and the value for QV required in Eq. (3) can be

set as follows:

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For Y 1 Ycc N( Il ~ 0.0, N(2) ~ n CM, N(3) ~ (m/2)CM, N(5)~3.76 Y CM,

and QV ~ -Urp NM/NMO

but for Ymin < Y < Ycc

N(l) ~ 2(Ycc-Y)CM, N(2) ~ (2Y-(n+m/2))CM, N(4)~0.0, N(5)~3.76 Y CM,

and QV ~ -(URP + 2 (Ycc-Y)(231400)NM/NMO

where the value of 231400 is the internal energy of dissociation of C02

(kJlKmol C02) and where

NM NXCM~--+

NMO NPO(6)

CM is a scale factor reducing the mole numbers to the proper size to fit

into engine.

Comparison of performance results of this model with experiment shows

a large discrepancy, which should be reduced by considering realistic

engine conditions, such as:

1) Progressive combustion process

2) Valve timing in the intake and exnaust processes

3) heat transfer

4) friction

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1. Progressive Combustion

1003

In tne fuel-air cycle instantaneous combustion is assumed. In the real

engine combustion occupies a finite time interval, as shown in fig. 2.

Ignition occurs before the piston reaches top dead center, and combustion

is not completed until the piston has moved beyond it.

In order to calculate the net work. done by gases between ignition and

the end of combustion, one needs to define where those two events occur

in the cycle in addition to the pressure-volume trace during combustion

[II. Hence,

DV VTDeDP = -P KB- + (p - P ) -- DN

V 3 2 V

relates the change in the cylinder pressure DP to the volume change DV

and the mass fracton of the gas ON that burns during the time interval

required for OV.

.If P and T are pressure and tempoature at ignition, the compression work

is [II

WCOtvlP = (NM + NX) CVR (T-T I) -1: [p + D: ] DV

and the expansion work. is

(8)

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1004

p

2

NAJJAR AND ALTURKI

Actual cycle

Isentrope through point b

Fuel , air cycle

Heat transfer lossExhaustbtow. downloss

vFig. 2 Actual cycle versus fuel_air cycle in S. I. engine

WEXP = r [p + DP ] DV + NP (u (Te) - u (T4)) (9)2 P P

Where Te = Pe VelR NP at the end of combustion.

2- Valve Timing: Intake and Exhaust Processes

Pistons move at finite speeds, which can become large; hence, their

motion exerts a controlling influence on engine performance.

The pressure change during the exhaust and intake strokes can be

expressed as Iollows:

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dp = K [RIm dM _~ dV ]dt r V dt V dt

(exhaust stroke)

(intake stroke) (10)

1005

where dM/dt depends on the now whether subsonic, choked or

supersonic.

In order to carry out cycle calculations that incorporate the detailed

treatment of the exhaust and intake processes, consider the real valve

timing and enective areas.

Exhaust valve: A = AOO !\SIN (n (Z-ZE)/(n-ZE)Il I / 3

intake valve: A = AOO lISIN (n (Z-ZI)/(n-ZO!lI/3

The work associated with the exhaust and intake strokes equals

(II)

(12)

where ~p denotes the change in pressure that accompanies the volume

change tN [l J.

3.Heat Transfer Process

Heat transfer affects engine performance, efficiency, and emissions.

Woschni 19J assumed a correction due to heat transfer. During intake,

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Table 2. Range of operating variables for the S.1. Engine

CR 6.00 7.00 8.00 10.00

SA 0.00 5.00 10.0 20.00

rpm 1250.0 1500.0 2000.0 2250.0

Table 3. Experimental data for the single cylinder S.1. engine

engine speedlrpm) 12500 1500.0 2000.0 2250.0

S.LE. power (l( IV) 530 6.30 370 3.40

sJ.c(g1k W h) 374.4 323-0 306.0 331.0

16.00

14.00

1200

~sc 10.00.,<l!3 8000

Q.

6.00

4.00

2.001000.00

ideo I

heat transfer

experiment

Iii Iii iii i I I i I I I IiI I1500.00 2000.00 2500.00

Engine speed. rpm

Fig.3: Variation of power with engine speedfor different modifications

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450.00

400.00 -

350.00s:3::<. 300.00o-

u 250.00LL

(fl

200.00

150.00

100.001000.00 1500.00 2000.00

Engine speed, rpm

experiment

f-iction

heat transfer

valve timing

progressivecombustion

ideal

2500.00

Fig.4: Variation of specific fuel consumption (g/kWh)with engine speed for different modifications

compression, and exhaust, He argued tnat tile average gas velocity should

be proportional to tile mean piston speed Sp' The average cylinder gas

velocity wwtm/s) determined for a four-stroke, water cooled, S.I. engine

is as follows 191

[VDISPTr ]

ww = CIS + C2 (P-p )P Pr Vr m

(13)

where P is tile instantaneous cylinder pressure; Pr, Vr, and Tr are the

working-fluid pressure, volume, and temperature at some reference

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45.00

40.00

c-35.00

>,u

.~ 30.00

.S!

<lJ

-025.00E~

<lJ0=f--

20.00

15.001000.00

~:y.;"o,/:/ -. \ proqressive

, r>:~.~~.COmbUSl<~n/ / / """ volve timing

:~~~ • heat transfer

:~ ~.,,,ion

/" • experiment•

II r-r-r-r-r-r-r-r-r-r-r-r-r-j

1500.00 2000.00 2500.00Engine speed, rpm

Fig.5: Variation of thermal efficiency with enginespeed for different modifications

Table 4. Variation in Power, SFC and efficiency due to

modifications on the ideal engine at design point

Engine with Power, k.W S.F.C. Ig/k.Wh ..n.X

ideal cycle 1354 199.74 41.24

pc 12.24 211.05 37.25

v.t 11.3 239.55 3442

h.t 1052 25702 32.04

iriction 9.1 2972 27.72

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SPARKIGNITION ENGINES 1009

1.20

1.00

~ 0.80~oQ.

o:i 0.60

0.40

CRSA

o.2a +nTTTTTTlrrTTTTTTTT'TTTTTTT'T'TTTT'T'TlrTTTTTT'nTTTTTT'T'Tl

0.00 0.50 1.00 1.50 200 2.50Non-dimentional variables (N, CR, SA)

Fig.6: Relative effect of operating variableson power

state, and Pm is the motored cylinder pressure at the same crank angles

as P. For the compression period CI = 2.23, C2 = 0.0.

For the combustion and expansion period C1= 2.23, C2 =3-24XIO-3,

Hence Woshni's correlation was finalized as:

( 14)

The area can be found by calculating burned gas-wetted area as a

function of radius based on spherical flame model [10] Total Wetted area

for cylinder head, piston and cylinder wall was estimated as

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1.10

~-_ .. SA

0.60 -r-r-rt j j j IIII i I I II r-r-r-r-r-r-r I It i i II j j 1111 i I III j j j ii' I Ii

000 0.50 1.00 1.50 200 2.50Non-dimentional variables (1'1, CR, SA)

1.00

0.70

~ 0.90o~

AUCIV:~ 0.80

w

Fiq.7: Relative effect of operating variabl eson specific fuel consumption

2Aw = 1.1466B ( 15)

The heat flux is

Q= Aw hc (Tg-TW) (16)

where Tw is the wall temperature assumed 400K and the working fluid

gas temperature assumed 1500K [9). Hence,

WNET = WE..XP - WCOMP + WLOOP - SUMQ (17)

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.~ ... expenmemt

1500.00 2000.00Engine speed, rpm

,:.1•

-f-rT""'-'-'-""'''''--'-rT""-,--,r-r-,,,-,..,--rr..-r-'l2500.00

9.00

10.00

800:;:sc

.: 7.00OJ

"00..

6.00

5.00

4.001000.00

Fig.8: Comparison of power from model withexperiment versus engine speed

where SUMQ = the summation of heat flux during the cycle.

Fig. 2 shows a comparison between the fuel-air cycle and the actual cycle

due to the previous three factors.

4. Friction

Friction mean eifective pressure ior several iour -stroke SI engines at

wide op",n throttle is given as a function of engine spe"'d [II J

FMEP = 0.97 + 015 (N/IOOO) + 0.05 (NIl000)2

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44000

400.00

L

~ 360.00<,0'

uu.: 320.00(J1

280.00

240.001000.00

•

1500.00 2000.00Engine speed.· rpm

• experirnemt

2500.00

Fig.9: Comparison of sfc from model withexperiment versus engine speed

Then friction po.....er is calculated from

FRP ; FMEP. VDISP. NIl20

DISCUSSION OF RESULTS

( Ig)

Parametric analysis of engine performance has been carried out. Hence

the wide variation of operating variables for both the experiment and the

model as shown in table 2. Thedesign point comprises N ; 2000 rpm, CR

; <') and SA ; lOoBTC. Experimental results obtained by varying "Ware

shown in table 3. Performance, in general, is graphically represented.

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Fig. 3 shows the variation of power with engine speed for different

modifications from the ideal engine namely progressive combustion,

valve timing, and heat transfer to get the indicated power for the real

engine. Friction is then subtracted to produce the brake power, which is

compared with the experimental results. The percent deviation from

experiment is 4.6%. Fig. 4 shows the variation of SFC with speed for

similar modifications as in the case of power. Figurs 5 shows the

variation in efficiency with speed for the different modifications. Tale 4

shows tne variation in efficiency along with power and sfc due to these

modifications at the design point. The trends for power, SFC and

efficiency are as expected. Plots for variation of power and SFC ....ith

other variables such as compression ratio CR and spark advance SA have

been cancelled in favour of brevity. However, their relative effects on

power and SFC are shown in the non-dimensional plottings of figures 6

and 7. It is clearly seen that speed has the highest whereas spark

advance the lowest relative effect on performance.

Figures I) and 9 compare the model predictions with experimental results

for power and src. The percentage deviation from the experiment, at the

design point, is about 4.6% in power and 2.9% in SFC.

CONCLUSIONS

1- Losses due to imperfect construction of the real engine, including

progressive combustion, valve timing and heat transfer have been

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modeled besides engine friction, to convert the output of the fuel

air cycle into brake performance.

2- Simulation of engine performance was carried out by varying

engine speed N, compression ratio CR, and spark advance over wide

range.

3- Experiments were done with a single cylinder engine over a wide

range of the above-mentioned operating variables.

4- The model compares favourably with experiment, with a deviation

around 46% in power and 2.9% in SFC.

5- The relative importance of the losses are generally in the following

sequence: friction, progressive combustion, valve timing and heat

transfer. These losses amount to about 14% of the fuel energy input

at the design point.

ACKNOWLEDGEMENTS

The autors would like thank Mr. O. Bashir and Mr. H. Abu Kayyas for

assistance during this research work, and Dr. M. Zaamout for producing

most of the drawings.

NOMENCLATURE

AOO wide open valve effective area for both valves, m2

B bore, m

CPM specific heat of the fuel-air mixture, kJ/kmol K.

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CPR specific heat of fuel, air plus residual gas mixture kJ/kmot K

CR compression ratio

DN the fraction of fuel-air mixture burned during (DZ)

DP increment in pressure during DZ, kPa

DW work done by the gas on the piston during DZ, k]

DZ crank angle increment, degree

FMEP friction mean effective pressure, kPa

FRP friction power, kW.

hc heat transfer coefficient, W/m 2 K

NM number of moles of fuel-air mixture in the engine at the start of

compression stroke, kmol

NMO number of moles of fuel-air mixture with I kmol fuel, kmol

Nr number of molesof reactants for stoichiometricmixture, kmol

NP actual number of moles of products in the engine,kmol.

NPO number of moles of products per I krnot of fuel, kmol

Np number of moles of products for stoichiomettric mixture, kmol

NX number of moles of residual gas, kmol

N(l) product gas mole number, kmol

N engine speed, rev /rnin

SA spark advance, degrees

SFC speciric fuel consumption, kg/k Wh

TM intake manifold temperature, K

T I mixture temperature at start of compression, K

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NAJJAR AND ALTURKI1016

Tg the working gas temperature, K

T5 residual gas temperature, K

VDISP displacementvolume, m3

U(X) tile internal enegy of the exhaust gas mixture, kJ

WCOMP work done on the gas during compression, kJ

WEXP work done on the gas during expansion, kJ

WLOOP work done on the gas during exhaust and intake, kJ

WNET net work output during the cycle, kJ

Y moles 0Z/mole fuel

To: Yfor stoichiometric mixture

Z crank angle at the start of combustion, radians.

ZED crank angle for exhaust valve opening before BDC, degree

ZE crank angle for ZED, radians.

zm crank angle for intake valve closing after BDC, degree

ZI crank angle for zm, radian.

ZI I crank angle at start of injection in C.I. engine

TJ thermal efficiency, :t

REFERENCES

1- Primus, R.J. and Flynn, P.F., "Diagnosing the real performance impact

of diesel engine design parameter variation", Proceedings of

International Symposium on Diagnostics and Modeling of

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Combustion in Reciprocating Engines, COMODIA 85, pp. 529-538,

Tokyo, September 4-6, 1985.

2- Foster, D.E., and Myers, P.S., "Heavy-duty diesel fuel economy",

Mechanical Engineering pp. 50-56, Dec. 1932

3- Heywood, [B, "Internal Combustion Engine Fundamentals", McGraw

Hill, New York., 19M.

4- Clarke, JM., "The thermodynamic cycle requirements for very high

rational efficiencies", Paper C53/76, Institution of Mechanical

Engineers, J. Mech. Engrg. Sci, 1974.

5- Campen, AS, "Thermodynamic Analysis of Combustion Engines",

john Willey & Sons, New York, 1979.

6- Ballaney, P.L., "Internal Combustion Engine", Khanna Publishers,

Delhi, 19&0.

7- Kerley, RV" and Thuston, K.W., "The indicated performance of Otto

cycle.engines·, SAE Transactions, Vol. 70, pp. 5-37, 1962.

8- Shupe, DS, "Automobile fuel economy", Mechanical Engineering, pp.

30-34, Dec. 1977

9- Woschni, G. "Universally applicable equation for the instantaneous

heat transfer coefficient in the internal combustion engine", SAE

paper 670931, SAE Transactions Vol. 76, 1967.

10- Poulos, S.G. and Heywood, lB., "The effect of chamber geometry on

spark ignition engine combustion", SAE paper 830334, SAE Trans.,

Vol. 92, 1983

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11- Barnes-Moss, H.W., "A cesignrs viewpoint in passenger car engines",

conference procedings, pp. 133-147, Institution or Mechanical

Engineers, London 1975.

RECEIVED: June IS, 1995

ACCEPTED: September 23, 1995

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Documents

MODELING AND SIMULATION OF SPARK IGNITION ENGINES