2004 appl therm eng zervas e. correlations between cycle to cycle variations and combustion...

7/30/2019 2004 Appl Therm Eng Zervas E. Correlations Between Cycle to Cycle Variations and Combustion Parameters of a

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Correlations between cycle-to-cycle variations

and combustion parameters of a spark ignition engine

Efthimios Zervas *

Ecole des Mines de Nantes - Departement des Systemes, Energetiques et Environnement, 4, rue Alfred Kastler,

44307 Nantes, France

Received 4 October 2003; accepted 21 February 2004

Available online 25 March 2004

Abstract

The coefficient of covariation (COV) of the in-cylinder pressure is determined on each crank angle of a

number of cycles, in the case of a natural gas feed SI engine operating under lean conditions. The resulting

curve of COV versus crank angle is explored. Its shape is independent of the experimental conditions and it

is always the same for all the experimental points used. Three points of this curve show particular interest,

as they correspond to the combustion beginning, combustion end and the point where the mass burned

fraction is 50% (half combustion duration). The hypothesis concerning the combustion limits is proved bythe comparison of the COV curves of fired and motored cycles and by the determination of the combustion

beginning and end using different methods. The hypothesis of the half combustion duration point is verified

from a burn rate analysis of the cycle. The integral of the COV curve in the combustion region is proposed

as a criterion of the cyclic dispersion quantification. The integrals of the first and second combustion

periods are explored as a function of the engine operating parameters.

2004 Elsevier Ltd. All rights reserved.

Keywords: Cyclic variability; Combustion limits; Ignition delay; Spark advance; Volumetric efficiency; Fuel/air ratio

1. Introduction

The phenomenon of cycle-by-cycle variation is widely known in the case of spark ignitionengines. Even under constant conditions, consecutive cycles are not exactly the same; combustionprocess does not progress in the same way, resulting a different in-cylinder pressure curve. The

* Present address: Renault, 1, Allee Cornuel, Lardy 91510, France. Tel.: +33-1-69-27-84-87; fax: +33-1-69-27-82-92.

E-mail address: [email protected] (E. Zervas).

1359-4311/$ - see front matter

2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.applthermaleng.2004.02.008

Applied Thermal Engineering 24 (2004) 20732081

www.elsevier.com/locate/apthermeng
http://mail%20to:%[email protected]/http://mail%20to:%[email protected]/


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reasons of these cyclic variations are the differences of turbulence within the cylinder from cycle to

cycle, the non-homogeneous air/fuel mixture, and the bad mixture of the exhaust gas residualswith the unburned charge, especially in the vicinity of the spark plug [13]. The initial stages of

combustion play an important role on the later flame development [4], thus small differences at thekernel formation may produce significant in-cylinder pressure variations. The disappearance ofcycle-to-cycle variations can lead to a fuel economy up to 6% [5], but a total elimination of thisphenomenon is not desirable, for reasons of engine management systems and knock control [3].

Cycle-to-cycle variations are directly linked with variations in output torque, which directlyinfluences the vehicle driveability [2].

Engines with transparent parts and laser beams for the measurement of the flame position and

fluctuations can be used to determine cycle-to-cycle variations [6]. But the most frequently em-ployed methods are based on the in-cylinder pressure measurements [2,3]. Several definitions are

proposed for the quantification of cyclic dispersion: the maximum pressure, the crank angle of thispressure, the maximum pressure rise and its crank angle, the IMEP, the 01%, 010%, 050% and

090% burn durations are widely used [2,3]. The mean values of these parameters, their standarddeviation or the coefficient of covariation, COV (also named relative standard deviation, RSD,which is defined as the standard deviation over the mean value) are commonly used to determine

cyclic dispersions [2,3]. Other models, including the entire pressure/time history of the cycle, arealso proposed [7,8].

In this work, the coefficient of covariation (COV) of the in-cylinder pressure is calculated on

each crank angle for a wide number of experimental points. The corresponding curve, which hasthe same shape for every experimental point, is explored and discussed. Three points of this curveare of particular interest, as they correspond to the combustion beginning, combustion end, and

the point where the mass burned fraction x is 50%, or the net heat release curve dQ presents its

maximum value. The integral of the COV curve in the area of combustion is proposed for thequantification of the cyclic variability phenomenon.

2. Experimental section

The engine used in this work is a Lister Peter TS1, one-cylinder, four stroke cycle Diesel engine,

adapted for natural gas feed by adding a spark plug, and coupled with an electric engine toregulate its speed at 1500 rpm. More characteristics are: stroke 8.78 cm, bore 9.52 cm, dis-placement 625 cm3, compression ratio 11.87. The collected data are: crank angle position,spark current, inlet and in-cylinder pressure (frequency used 18 kHz). Other measurements are:temperature of intake air, exhaust gas and engine oil, engine power, spark advance, intake air and

natural gas mass flow, intake air hygrometry, exhaust gas concentration (CO, CO2, O2, HC andNOx).

A first set of experimental points is used for the study of spark advance (SA), throttle opening

(expressed as volumetric efficiency, VE) and fuel/air equivalence ratio influence U. For the studyof SA influence, 9 points are used at 10, 12.5, 15, 17.5, 20, 22.5, 25, 27.5 and 30 ca (VE 0.5 andU 0:75); for the study of VE influence 7 points at 0.33, 0.40, 0.45, 0.50, 0.55, 0.60 and 0.66(SA 20 ca and U 0:75) and for the U influence, 7 points at 0.6, 0.65, 0.7, 0.75, 0.8, 0.75, 0.9(SA 20 ca and VE 0.5). An additional set of 17 points, covering the empty spaces of the three

2074 E. Zervas / Applied Thermal Engineering 24 (2004) 20732081


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dimension matrix formed from the above three parameters is also used. For each experimental

point, the data of 200 individual cycles are acquired. The COV of the in-cylinder pressure iscalculated on each crank angle using the formula:

COV 1001

n1

Pni1Pi P

2 1=2

P1

with n 200 cycles, Pi for the given crank angle, the in-cylinder pressure of each cycle, andP the average in-cylinder pressure at this crank angle for all the 200 cycles.

3. Results and discussion

3.1. COV versus crank angle curve

Fig. 1 presents a typical example of the COV versus crank angle curve and the corresponding

average in-cylinder pressure curve, with a zoom in the 310420 ca area. As shown in this figure,the COV curve presents initially a plateau of about 710% up to 230 ca. The COV values arequite high due to noise, which is quite important comparative to the low in-cylinder pressure value

at this area. After the intake valve closing, the COV decreases to reach its first minimum value.For this part of the curve, the COV values depend only on the average in-cylinder pressure. This

part can be fitted by the equation:

COV a=P 2

with, P the average in-cylinder pressure, and a constant. The value of a is the same for all theexperimental points used, for fired and motored cycles, and the fitting equation has a r2 greater

Fig. 1. COV of the in-cylinder pressure and average in-cylinder pressure versus crank angle. Entire curve and zoom in

the 310420 ca area. SA 20 ca, VE 0.5, U 0:75.

E. Zervas / Applied Thermal Engineering 24 (2004) 20732081 2075


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than 0.98 for all these curves. The value of a is a characteristic number of each experimentalsystem used and, as it is proved from the COV definition, it reflects the noise level.

At the end of this descent, the COV curve presents its first minimum point, then it increases,

forming a local maximum point, and then it decreases again, forming a second local minimumpoint. These points can be explained by the combustion process in the cylinder. The COV is quite

constant during the first quarter of the cycle (0180 ca) during the intake period, because in-cylinder pressure is quite constant. After the intake valve closing, the COV decreases because thein-cylinder pressure increases. The COV value reaches the minimum point just at the combustion

beginning, because after it, the in-cylinder pressure differs from one cycle to the other due to cycle-to-cycle variations. This hypothesis is confirmed by the comparison between the COV versus

crank angle values of fired and motored cycles. Fig. 2 presents this comparison for a motoredcycle and two fired ones at different fuel/air equivalence ratios and a zoom in the 310 to 470 ca

area. The three curves are identical up to the combustion beginning and differ just after it. Thepeak corresponding to the combustion area does not exist in the case of the motored cycle. Asecond confirmation of this hypothesis is the comparison between the combustion limits as

determined from different methods and the two local minima angles of the COV versus crankangle curve. Different methods are used for the determination of the average cycle combustionlimits [2,3,9]:

the dP method, using the first derivative of the in-cylinder pressure. Combustion beginning isconsidered as the moment when the fired in-cylinder curve sharply deviates from the motored

curve (only for the ignition delay), the d lnP method, where the combustion limits correspond to the two minimum points of the

d lnP versus crank angle curve (for both ignition delay and combustion duration),

the k method, using the polytropic exponent curve: k dP=P=dV=V, (combustion limitscorrespond to the points where this curve becomes constant),

Fig. 2. Comparison between the COV versus crank angle curves of a motored and two fired cycles. Entire cycle and

zoom in the 310470 ca area. VE 0.5. For the fired curves: SA 20 ca and U 0:6 and 0.75.



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the dQ method, where the combustion limits correspond to the two minimum points of the dQ

curve (net heat released from the combustion, for both ignition delay and combustion dura-tion).

Fig. 3 presents the angle of the combustion beginning of the average cycle, determined by thesefour methods, and the angle of the first local minimum point of the COV curve. A good agreementis observed between these values.

After the combustion beginning, the COV increases following the cyclic dispersions and reachesa local maximum value, which corresponds to the burned fraction rate x of 50%, which is, in thecase of the engine used, very near (12 ca) to the maximum of the net heat release dQ curve(Fig. 4). Following the local maximum point, as combustion becomes progressively less importantcomparing to piston motion, the COV versus crank angle curve decreases to reach the second

minimum point, which corresponds to the combustion end. Combustion end is quite difficult todetermine due to late burning phenomenon [10], but a quite good agreement is obtained between

the combustion end determined by different methods and the second minimum point of the COVcurve (Fig. 3).

At this moment of the cycle, the piston is found at the expansion period, the in-cylinder

pressure decreases, and the COV curve increases again to reach a local plateau. It increases an-other time after the 540 ca, during the exhaust period. Between the second local minimum pointand the 540 ca, the COV is again related with the in-cylinder pressure, but not as well as before

the combustion beginning. Fluctuations are more important in this area and the Eq. (2) does notfit very well the curves of all experimental points. The reason is that, at this time of the cycle, thein-cylinder pressure depends on the in-cylinder pressure during the combustion process and

cannot return to the in-cylinder pressure of the motored cycle. Pressure curves cannot converge

after combustion; thus the COV values after 397 ca are more important than before 348 ca

0 10 20 30 40

Experimental point

340

360

380

400

420

Com

bus

tion

beg

inn

ingan

den

d(ca

)

dP

k

dQ

dlnP

COV b

COV e

Fig. 3. Comparison between the angle of the two minimum points (COV) and the combustion beginning and end of the

average cycle, determined by dP, k, dlnP and dQ methods. All experimental points used. COV b: combustion beginning

determined by the COV method, COV e: combustion end determined by the COV method.



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(Fig. 1). In the area from 540 to 720 ca, during the exhaust period, COV is not related with the in-cylinder pressure.

3.2. Influence of the engine operating conditions

The COV curve shape is the same for all the experimental points used, but the two local

minimum point angles and the local maximum point angle are influenced by the engine operatingconditions (SA, VE and U). Fig. 5 (bottom curves) presents the ignition delay (calculated as angleof the first minimum pointangle of ignition), the first and second half combustion duration

(calculated respectively as angle of the maximum pointangle of ignition and angle of the secondminimum pointangle of the maximum point) and the combustion duration (calculated as angle of

the second minimum pointangle of the first minimum point) as a function of these three engineoperating parameters. The behaviour of these combustion parameters agrees with those reportedin literature [11,12], confirming the hypothesis that the two local minimum points correspond to

the combustion beginning and combustion end, and the local maximum point at the half com-bustion duration point.

3.3. First and second period of combustion

The combustion phenomenon can be divided in two periods: the first, where the mass burned

fraction x is between 0 and 0.5, and the second where x is between 0.5 and 1. The influence of thethree engine parameters on these two combustion periods is presented in the bottom curves of

Fig. 5, which show that:

the first period is almost constant (it has a very slight decrease) with the spark advance increase.The increase of the combustion duration in this case is due to the increase of the second period,

320 360 400

Crank angle (ca)

0

4

8

12

16

COV

(%)

-10

0

10

20

30

40

dQ

(J/ca

)

0.0

0.2

0.4

0.6

0.8

1.0

x

COV

dQ

x

Fig. 4. COV, net heat release dQ and mass burned fraction x curves versus crank angle. SA 20 ca, VE 0.5,U 0:65.



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the duration corresponding to both periods decreases the same way with the increase of volu-metric efficiency,

both durations decrease with U, but the second one more sharply than the first.

The durations (expressed in crank angles) corresponding to these two periods and their per-

centages are presented in Fig. 6 as a function of the total combustion duration. This figure showsthat the first combustion period is always shorter than the second one. Both periods increase withcombustion duration (white symbols), but the specific weight of the first period decreases, while

this of the second one increases (black symbols). In fact, the second period of combustion ismainly responsible for the increase of the total combustion duration.

3.4. Total cyclic dispersion criterion

A criterion for the total process qualification is the integral of the local peak corresponding tothe combustion process in Fig. 1. This integral takes into account the total fluctuations of the in-

cylinder pressure during the combustion process and, therefore, it can be used to quantify thecyclic dispersion phenomenon. This integral is more accurate for the description of the cyclicdispersion phenomenon than the one usually employed, because it takes into account the total

dispersion during the combustion phenomenon, which can be determined by using the twominimum values of the COV curve. The other criteria (IMEP excepted) use average values or

10 20 30

SA (ca)

0

40

80

Cran

kang

le(ca

)

0.4 0.5 0.6

VE

0.6 0.7 0.8 0.9

Ingition Delay

Combustion Duration

First half duration

Second half duration

0

200

400

600

ICOV(%

.ca

)

x(0-0.5)

x(0.5-1)

Total

Fig. 5. Influence of the engine operating parameters (SA, VE and U) on: 1. the ignition delay and combustion duration

of the average cycle, determined by the two local minimum points of the COV versus crank angle curve (bottom curves),

2. duration (in crank angles) corresponding to the first and second combustion period and the combustion duration, 3.

the integral of the COV local peak versus crank angle curve and the integrals of the areas corresponding to x 00:5and x 0:51.



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standard deviation of a parameter just at one point of the cycle (i.e. maximum pressure, angle ofmaximum pressure etc., [2,3] and do not take into account the total dispersion during the com-bustion phenomenon.

The integral of the COV curve and the integrals corresponding to the two parts of combustion

(x 00:5 and x 0:51) are presented in Fig. 5 (upper curves). This figure shows that:

the integral of the first period COV is always smaller than the second one, which indicatesthat the latter stages of combustion are less repetitive,

the total integral is almost constant with SA, while the integral corresponding to the first period

presents a slight decrease, and this to the second an increase, the total integral decreases with VE, while the two partial integrals decrease,

the total and the partial integrals decreases with U. It is already known that cycle-to-cycle vari-ations are more important at lean conditions [2]. The integral corresponding to the second per-iod decreases more sharply than this corresponding to the first one, indicating that the decrease

of COV total integral is mainly due to the improvement of the combustion second period.

Both Figs. 5 and 6 present that a control of the total combustion duration or of the cyclic

dispersion phenomenon must be more oriented towards the second half of the combustion pro-cess, as this last one is more sensitive to the combustion duration increase and less repetitive.

4. Conclusions

The relative standard deviation of the in-cylinder pressure curve at each crank angle has been

studied in the case of a natural gas feed spark ignition engine operating under lean conditions.This curve can be used to find the beginning and the end of the average cycle combustion and the

30 40 50 60 70 80

Combustion duration (ca)

10

20

30

40

50

60

Com

bus

tionperio

d(ca

)

0

20

40

60

80

Spec

ificwe

ight(%

)

x(0,0.5)

x(0.5,1)

Fig. 6. First and second combustion period duration (full black symbols) and percentage of these periods as a function

of the total combustion duration. All experimental points used.



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point where the mass burned fraction is 50%. The peak integral of the COV curve can be used as a

criterion for the cyclic dispersion. This integral takes into account the cyclic dispersion of the totalcombustion process and not only a single point of the cycle. The second period of combustion is

more responsible for the total cyclic variation than the first one.

References

[1] M. Berckuller, N.P. Tail, D.A. Greenhalgh, The influence of local fuel concentration on cyclic variability of a lean

burn stratified-charge engine, SAE Technical Paper 970826, 1997.

[2] J.B. Heywood, Internal Combustion Engine Fundamentals, McGraw Hill, 1988.

[3] R. Stone, Introduction to Internal Combustion Engines, Society of Automotive Engineers, 1992.

[4] G.C. De Soete, Propagation behaviour of spark ignited flames in the early stages, International Conference on

Combustion in Engineering, vol. 1, Mech. E. Conf. Proc. MEP, London, 1983.

[5] D. Lyon, Knock and cyclic dispersion in a spark ignition engine, petroleum based fuels and automotiveapplications, I. Mech. E. Conf. Proc. MEP, London, 1986.

[6] L. Zhang, T. Ueda, T. Takatsuki, K. Yokota, Cycle-to-cycle variation ofcylinder flow in a motored engine,

JSME Int. J. B 38 (3) (1995) 426431.

[7] J.B. Roberts, J.C. Peyton Jones, K.J. Landsborough, Cylinder pressure variations as a stochastic process, SAE

Technical Paper Series 970059, 1997.

[8] J.C. Peyton Jones, K.J. Landsborough, J.B. Roberts, Identification of stochastic models for cyclic variations from

measured pressure data, SAE Technical Paper Series 970060, 1997.

[9] R. Varaprasada, K. Nehru, V. Ganesan, Evaluation of S.I. engine combustion parameters: a new approach,

Combust. Sci. Technol. 89 (1993) 4755.

[10] K. Ishii, T. Sasaki, Y. Urata, K. Yoshida, T. Ohno, Investigation of cyclic variation of IMEP under lean burn

operation in spark-ignition engine, SAE Technical Paper 972830, 1997.

[11] V. Ganesan, Internal Combustion Engines, McGraw Hill, 1996.

[12] F.A. Matekunas, Modes and measures of cyclic combustion variability, SAE Technical Paper Series 830337, 1983.


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