optimal valve timing

7/27/2019 Optimal Valve Timing

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Energy 27 (2002) 757775 www.elsevier.com/locate/energy

Optimization of variable valve timing for maximizingperformance of an unthrottled SI enginea theoretical study

E. Sher , T. Bar-Kohany

The Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion

University of the Negev, Beer-Sheva 84105, Israel

Received 25 May 2001; received in revised form 16 April 2002

Abstract

Previous investigations have demonstrated that improvements in gasoline engine performance can beaccomplished if the valve timing is variable. In this work valve timing strategies for maximizing enginetorque and minimizing bsfc in terms of the exhaust opening (EO), intake opening (IO) and intake closing(IC) timings of a commercial SI engine are studied. The MICE (Modeling Internal Combustion Engines)computer program, which simulates an actual SI cycle, has been used. Overall performance characteristics

such as the cycle efficiency, engine power, and exhaust gas composition are calculated. The model hasbeen calibrated with data obtained from a measured indicator diagram, and validated against the overallperformances of the engine. It is concluded that when both valves and spark timings are optimized, theoptimal timing of each valve, depends apparently linearly on the engine load, linearly (in a goodapproximation) on the engine speed, while the slope depends in a weak manner on the engine load. WhenVVT is employed, the maximum engine power has been increased by 6%, and the engine bsfc has beendecreased by 13%. The maximum torque has been shifted towards a lower engine speed. The presentresults are summarized as working maps for the engine designer. These show the influence of the intakeand exhaust valve timing on the engine performance at the entire range of operation conditions (engineload and speed). 2002 Elsevier Science Ltd. All rights reserved.

1. Introduction

Variable valve timing relates to both the opening time and opening duration. In customaryinternal combustion engines the intake and exhaust valve timing is fixed. The timing is selectedsuch as an optimal performance is achieved at a single well-defined design point (corresponds toa specific engine speed and load).

Corresponding author. Fax: +972-8-627-1474.

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

0360-5442/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.PII: S 0 3 6 0 - 5 4 4 2 ( 0 2 ) 0 0 0 2 2 - 1


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758 E. Sher, T. Bar-Kohany / Energy 23 (2002) 757775

Nomenclature

A instantaneous port area, availabilitycp specific heat at constant pressurecv specific heat at constant volume

D bore

E internal energyf residual mass fractiong gravitation constanth enthalpyK thermal conductivityk specific heat ratio

m massN engine speedp pressureQ heat

R universal gas constantSL laminar burning velocity

T temperature

t time

up piston linear velocityV volumeW work

X mass fraction of the burned mixture inside the cylindery pressure ratio

Greek letters

b Constant, mass fraction of fresh charge in the exhaust gases fuel-air equivalence ratiohch charging efficiency delivery ratio

l dimensionless air-fuel equivalence ration kinematic viscosityq crank-angleqig start of combustion (in crank-angle)qspark spark time (in crank-angle)qb combustion duration (in crank-angle)r densitys Stefan-Boltzmann constantt dimensionless crank-angle


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759E. Sher, T. Bar-Kohany / Energy 23 (2002) 757775

Subscripts and superscripts

a fresh chargeb burnt gas, constantc combustion, constante exit,equilibriumH upstreami intakeL downstreamref reference valuestd standard

w wall

Abbreviations

BC Bottom center

bsfc brake specific fuel consumptionEC exhaust valve closesEO exhaust valve opens

fmep friction mean effective pressureIC intake valve closes

IO intake valve opensTC top centerVVT variable valve timing

Traditionally, valve timing has been designed to optimize operation at high engine speed, andwide-open throttle operating conditions [1]. Controlling valves events can improve the torquecurve, the brake power curve, or the indicator power curve of a given engine design. Variablevalve timing can also be used to reduce fuel consumption and to a small extent the engine emis-sions [2]. This is achieved by controlling the in-cylinder maximum temperature, and the amount

of residuals remaining at the commencement of the compression stroke (EGR control). In a pre-vious paper [3] we have presented a strategy for varying valve timing (VVT) in a throttled SIengine with the aim of maximizing its torque. It is expected however, that a more significantbenefit of using VVT will be achieved in an unthrottled engine. It appears that in gasoline engines,load control can be obtained without throttling by using variable intake closing time [4], i.e.,severe throttling losses normally experienced at low loads, can be substantially reduced by reduc-ing the intake valve duration with decreasing load, thus, regulating the amount of induced mixture.Several methods were suggested to regulate the load with VVT. Lenz et al. [5], claim that withoutthrottling, control of the charge in SI engines can be realized by means of an early closure ofthe intake valve. Under low engine speeds, closing the intake valve at a proper time will increase


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the volumetric efficiency of the gas exchange process. An early intake valve closing time (beforeBC), will cause the fresh mixture to expand till BC and therefore its temperature at the commence-ment of the compression stroke will be lower. As a result, lower amount of NOx, but higheramount of HC are expected to be emitted. A way of controlling the load while improving thefuel economy was suggested by Ma [6]. Ma has concluded that a late intake valve closing isshown to be a practical concept applicable to engines with two intake valves per cylinder wherethe intake valves can be phased relative to each other to extend the total intake-opening period.In diesel engines, the most promising application is the control of the valve overlap in highlyturbocharged engines [4]. Better starting performance in controlled valve-overlap diesel engineshas also been argued.

Because of the difficulties associated with providing a variable valve timing mechanism withacceptable cost, durability and reliability, only few automotive engines in normal production haveever been equipped with variable timing valves (see review and classification of variable valve

timing mechanisms in Dresner and Barkan [1], and Gray [7]). However, owing to recent tech-nology developments associated with electromagnetic and hydraulic valve control (see forexample [8] and [9]), and owing to recent progress in microprocessors utilization, application ofVVT in the near future is quite feasible [10]. Moreover, since the advent of the more recentfederal gas mileage and emission requirements, with their emphasis on lower engine speed andlow pollution emissions, alternate valve timing strategies have to be considered. Continuouslyvariable valve timing permits optimization of valve events for each operating condition withoutany compromise. Strategies for optimizing intake and exhaust valve timings and recent develop-ments in the application of VVT to gasoline engines can be found in some recent publications;Duckworth and Barker [11], have examined the effect of the valve overlap on an engine perform-ance with an emphasize on the internal EGR, Leone et al. [12] have examined different variablecamshaft timing strategies for reducing NOx, CO and HC emissions from a part-load operatingengine, Shiga et al. [13] have looked at the effect of early-closing of intake-valve on the cylinderpressure and engine performance, and Badami et al. [14], and Ueda et al. [15] have examinedthe influence of late intake valve closing on the idle and part load performance of the engine.Moro et al. [16], examined theoretically a possible strategy to control engine load by means ofboth intake and exhaust variable valve timing. They showed that when the IVC and EVC correlatelinearly with the engine load, such as the intake pressure and EGR amount are controlled, thecycle efficiency is improved from 31 to 37% at partial loads. Bozza et al. [17] have developeda 1-D mathematical model to simulate the operation of a SI engine equipped with VVT. Theyexamined the effect of the two valves timing on the engine performance, and demonstrated the

potential of employing variable inlet and exhaust valve timing. They did not propose any strategyof optimizing the valve timing to maximize the engine performance. Nakayasu et al. [18]developed a variable intake and exhaust control valve system for in-line four-cylinder motorcycleengine for realization of the concept potential. Two modes were provided to the intake control,and three for the exhaust. They showed that the engine output power has been increased by 10%as compared to the original engine design. No further study has been performed to optimize thevalve timing.

It is the purpose of the present paper to analyze the performance of an unthrottled SI engineinstalled with VVT. This is in order to postulate optimal valve timing strategies for minimizingfuel consumption or maximizing engine torque in terms of the intake valve duration, and theopening and closing timings of the exhaust valve.


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2. Theoretical considerations

In order to analyze the complete cycle with the objective of predicting the engine performancevs. the valves timings, the following approach has been employed.

2.1. Cylinder content

The cylinder content is divided into two zones; fresh charge and burned gases (the latter includeresidual gases from the previous cycle). The pressure inside the cylinder is calculated by usinga global energy balance:

Q W dE

dt

e

mehei

mihi (1)

where W is the rate of work done by the open system (which is equal to pdVdt

), Q Qc Qw,

Qc is the rate of heat releases during combustion, Qw is the rate of heat transferred from the

cylinder wall to the cylinder contents,dE

dtis the rate of energy increase inside the open system

(which is equal to d(mcvT) / dt) and he and hi are the enthalpies of the leaving and entering mol-ecules through the ports, respectively. The rate of the pressure change inside the cylinder isobtained by introducing the ideal gas law in the form of:

pdV

dt V

dp

dt mR

dT

dt RT

dm

dt(2)

into Eq. (1). Then after rearranging:

dp

dt

(k1)(Qe

mecpTe i

micpTi)kpdV

dt

V(3)

where k is the instantaneous specific heat ratio.The instantaneous mass flowrate, m, through any port in any direction (including backflows

through the intake and exhaust ports) is determined by:

m A2kpHrHg

k1 1/2

y1/k

1yk1

k1/2

(4)

where,

y pL

pHfor

pL

pH

2

k 1

k

k1(5)

and

y 2

k 1

k

k1(6)


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for critical flow. A is the instantaneous effective port area, which was taken as 80% for its actualvalue, and H and L denote upstream and downstream conditions, respectively.

2.2. Valve overlap period

A semi-empirical model, the S shape model [19], is employed to simulate the gas exchangeprocess inside the cylinder during the valve overlap period. The model is based on the assumptionthat the time variation of the mass fraction of fresh charge content in the gas passing through theexhaust port, b, exhibits a sigmoid type curve. The instantaneous charging efficiency, may there-fore be estimated by:

hch

t

0

bd

dt

b (1b)Tb/Ta(7)

where Tb and Ta are the temperatures of the burned gas and the fresh charge, respectively, isthe delivery ratio, t is the dimensionless crank-angle which is defined by:

tqqIOqECqIO

(8)

and b, by definition is calculated by:

b 1exp

1.7

qqIOqECqIO

2.0

(9)

Here q is the crank-angle, and qIO and qEC are the angles at which the intake valve opens andexhaust valve closes, respectively. The period between qIO and qEC is the valve overlap period.In this equation, the form and shape factors were set to b 2.0 and c 1.7 [19].

2.3. Combustion process

The combustion process is assumed to occur through a one step global reaction scheme. Themass fraction of the burned mixture at any time is calculated by using the Wiebe function asfollows [20]:

X 1exp c qqig

qb

b (10)where qig is the crank-angle at which the combustion starts, qb is the crank-angle interval fromstart to completion (90%) of combustion, c is an efficiency parameter and b is the form factor.The values of b and c were determined by matching the computed pressure-crank angle diagramwith experimental measurements.

The crank-angle interval from the spark onset to the start of combustion (qsparkqig), as wellas the interval from the start to completion of combustion, qb, were estimated by using theproposed correlations of Hires et al. [21]:


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qsparkqig(qsparkqig)ref

N

Nref1

3 SL,refSL2

3(11)

where N is the engine speed and SL is the laminar burning velocity,

qbqb,ref

N

Nref1

3 SL,refSL

2

3(12)

The laminar burning velocity of the fuel-air mixture, SL, is calculated by using the correlation ofMetghalchi and Keck [22], as follows:

SL T

Tstd

a ppstd

d

(12.1f) (13)

where f is the mass fraction of the residuals, std stands for standard,

a 2.180.8(1) (14)

d 0.16 0.22(1) (15)

is the fuel-air equivalence ratio, and,

0.27580.7834(1.11)2 (16)

2.4. Composition of the cylinder content

For the present case, a stoichiometric (or lean) mixture is used (l1), and therefore the cylinder

content is assumed to be composed of fuel (CaHb), CO2, H2O, O2 and N2. Consequently, thefollowing global reaction has been considered:

CaHb lJO2 3.76lJN2aCO2 b

2H2O J(l1)O2 3.76lJN2 (17)

where

J ab

4(18)

In the present work, the gasoline is represented best by a 8.26 and b 15.5. The exact amount

of each species is determined by the instantaneous mass fraction of the burned mixture, X [Eq.(10)], and the residuals mass fraction, f.

2.5. Heat transfer

The instantaneous heat interaction between the cylinder content and its confined walls is calcu-lated by using the empirical expression of Annand [23] for four-stroke SI engine as follows:

Qw

A 0.26

K

D

upD

n0.75

(TTw) 0.69s(T4T4w) (19)


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where K is the thermal conductivity of the gas, n is its kinematic viscosity, up the instantaneouspiston linear velocity, D, cylinder bore, s the Stefan-Bolzmann constant, and Tw the temperatureof the inner side of the cylinder wall. For the present calculations, the wall temperature was takenas 780 K to fit best the indicator-diagram expansion process.

2.6. Friction power

The friction power is estimated by using fundamentally based scaling laws for reciprocatingspark-ignition engines, as recommended by Patton et al. [24]. Friction between the piston and thecylinder liner, piston rings and cylinder liner (which include the effect of the increasing cylinderpressure), the connecting rod bearings, and valve system, were taken into consideration. Theseare represented by the first nine terms of the comprehensive expression [24] for the total enginefriction mean effective pressure (fmep).

2.7. Nitric oxide formation

In the present study, the kinetic model for NO is based on the theory developed by Lavoie etal [25]. In this model, only the process occurring in the burned gas behind the reaction zone areconsidered, and it is assumed that the rates of the energy-producing reactions in a flame aresufficiently fast so that the burned gases are close to thermodynamic equilibrium. For the calcu-lation of the NO concentration, we may therefore assume equilibrium concentrations for all thespecies involved except for the NO. Lavoie et al. [25] have shown that on the time scale of interest,only the following three kinetic reactions are important (the extended Zeldovich mechanism):

N NON2 O k1 21011

(20)N O2NO O k2 210

11exp(7.1/RT) (21)

N OHNO H k3 71011 (22)

where ki is in units of cubic centimeters per second. An explicit equation for nitric oxide formationis then obtained to yield:

1

V

d([NO]V)

dt 2(1a2)

R1

1 aR1/ (R2 R3)(23)

where Ri is the one-way equilibrium rate of the ith reaction (for example R1 k1[N]e[NO]e with

the subscipt e denoting equilibrium concentration), and a [NO]/[NO]e. An equilibrium model(Weinberg [26]), was used to determine the species concentrations required for the NO formationrate equation. In this model, 14 elementary reactions were considered.

2.8. Carbon monoxide formation

In this model the CO concentration followed the same trend as the peak equilibrium value.However, during expansion, the CO concentration was found to lag between the current equilib-rium value and the peak equilibrium value obtained in the cycle. Benson and Baruah [27],sug-gested that the following simple model may best fit experimental observations:


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Table 1

Engine specifications

Engine model VW PassatEngine type Four-cylinder, 4-stroke, spark-ignited, water-cooled engine

Cylinder stroke/bore 73.4/75 mm

Displacement volume 1297 cm3

Rated power 44 kW at 4800 rpm

[CO] [CO]e f([CO]peak [CO]e) (24)

where the factor f is a calibration constant, which lies between 0 and 1. Following a previouswork (Hacohen and Sher [28]), a value of 0.2 was adopted.

3. Model validation and calibration

In order to calibrate the relevant constants used in the theoretical model, a set of well-controlledexperimental tests has been performed. A 1297 cm3 VW Passat four-cylinder (Table 1) has beenmounted on a test bench which included a controlled load (a calibrated electric generator), tem-perature and pressure gauges, a Kistler pressure transducer type UP4 to record the cylinder press-ure trace, and a BEI encoder having a resolution of 0.6 crank angle degree. The transducer signalwas amplified by a Hewlett-Packard amplifier model 2460 A MI, and then was stored in a PC.The indicator diagram was then analyzed with the aid of an EXCEL software.

The following parameters have been calibrated to best fit the computed to the measured indi-

cated diagram at the engine rated conditions (full engine load at 4800 rpm):For the ignition and combustion processes [Eq. (11) and (12)]: (qsparkqig)ref 7, qb,ref

49, Nref 3000 rpm, SL,ref 1.283 m/s. For Eq. (10): b 2, c 5, and relative air-fuel ratio,l 1.00. The average cylinder wall temperature [Eq. (19)]: Tw 780 K.

Fig. 1(a) shows a typical calculated indicated diagram. Under these operation conditions the

Fig. 1. Calculated indicated diagram on linear pressure-volume co-ordinates (a) and logarithmic pressure-volume co-

ordinates (b), at the rated engine conditions (full load at 3800 rpm).


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Fig. 2. Predicted and measured engine brake power, at partial engine load. Exhaust and intake valve timings are fixed.

pressure in the cylinder reaches a maximum value of 5600 kPa while the corresponding cylindervolume is slightly higher than the clearance volume, this corresponds to a crank angle of 18after TC. Though our model considers the temperature dependence of the heat capacity of eachof the relevant species and thus the weighted heat capacity of the cylinder charge at any timestep, it is interesting to note that the polytropic coefficients of each, the compression and expansionprocesses in the entire range of operation conditions, may be considered quite closely as constants[Fig. 1(b)]. The first stage of the compression stroke which spans between IC (intake valve close)and about 20 before the spark onset seems to fit well a polytropic process with a constantpolytropic coef

ficient of 1.31. The second stage of the expansion stroke, which spans between a

short time after the end of combustion and EO (exhaust valve open) seems to fit a polytropicprocess with a constant polytropic coefficient of 1.26.

Fig. 2 and 3 show a comparison between the predicted and measured engine performancecharacteristics. These include the engine brake power and maximum cylinder pressure vs. engine

Fig. 3. Predicted and measured maximum cylinder pressure at full engine load. Exhaust and intake valve timings are

fixed.


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Fig. 4. The effect of exhaust port opening time on the engine torque (a), its specific fuel consumption (b), CO (c),and NOx (d), emissions under full engine load at different engine speeds. Intake opening time and intake closing time

are optimized. Exhaust closes at top center.

speed all at full engine load. Exhaust and intake valve timings were set to those selected by the

engine manufacturer. The model seems to predict quite well the experimental observation within

an error of5%. The predicted value of the engine speed at which a maximum brake power isobtained seems to occur at 4800 rpm which is in total agreement with the observed value. Since

the curvature of the indicated power curve is strongly affected by the flow phenomena at theexhaust and intake valves, the good fitting indicates that these phenomena were predicted quiteclose to reality. The friction losses are the main contributors to the deviation of the brake power

curve from the indicated curve. Here again, the predictions seem to fit well the experimentalresults. Another parameter to be compared is the maximum cylinder pressure. Fig. 3 shows how

close are the model predictions to the experimental observations.


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Fig. 5. The effect of exhaust port opening time on the engine torque (a), its specific fuel consumption (b), CO (c),

and NOx (d), emissions under 35% engine load at different engine speeds. Intake opening time and intake closing time

are optimized. Exhaust closes at top center.

4. Results

4.1. The effect of the exhaust port opening time (EO)

Fig. 4 and 5 show the effect of the exhaust port opening time on the engine torque, its specificfuel consumption, CO and NOx emissions under 35% and 100% engine full load at differentengine speeds. Intake opening time and intake closing time are optimized, while the exhaust closesat top center. It is expected that for a given engine speed, an early opening will shorten theexpansion stroke, thus reducing the work done on the piston and therefore the engine torque.Owing to the flow dynamic through the exhaust port, a late exhaust opening, will not allowenough time for the in-cylinder pressure to reach the ambient pressure, and a high work will berequired to displace the exhaust gas during the exhaust stroke. For an engine speed of 2000 rpmat full engine load, an advance or retard of 10 will deteriorate the engine torque by about 2%.


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Fig. 6. The effect of intake port closing time on the engine torque, its specific fuel consumption, CO and NOxemissions under engine full load at different engine speeds. Exhaust opening time and intake opening time are optimized.

Exhaust closes at top center.

A similar trend appears at partial engine load (35%). At higher engine speeds, the optimal EOshould clearly be advanced. It seems that an increasing of the engine speed from 1000 to 4000rpm at full load, requires an EO advance of 32, from 158 to 128. At partial load a smalleradvance of 30 is neededfrom 174 to 144. It seems that the optimal EO for minimizing bsfc

occurs when the engine torque maximizes in the entire range of operation conditions. It alsoappears that the CO and NOx emissions are practically insensitive to the EO time.

4.2. The effect of the intake port opening time (IO)

The effect of the intake port opening time on the engine torque, its specific fuel consumption,CO and NOx emissions under 35% and 100% engine full load at different engine speeds, hasbeen examined in a similar manner as demonstrated above for the exhaust opening time. For anyof the above criteria (max. torque, min. bsfc, and min CO and NOx emissions), the optimal time(IO) was found to be practically insensitive to the engine speed, and to a very limited degree of


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Fig. 8. Calculated optimization strategy of intake valve opening time (IO), and intake valve closing time (IC), forminimum bsfc, vs engine load at an engine speed of 4000 rpm.

effect of the intake port closing time on the engine torque, its specific fuel consumption, CO andNOx emissions. Here, exhaust opening time and intake opening time are optimized, while theexhaust closes at top center. At high engine speeds, the optimal IC should clearly be retarded. Itseems that an increase of the engine speed from 1000 to 5000 rpm at full load, requires an ICretard of 22, from 541 to 563. It appears that the optimal IC for minimizing bsfc occurs in agood approximation when the engine torque maximizes. It also transpires that the CO and NOxemissions are practically insensitive to the IC time. For partial load, the load control can be

obtained without throttling by using variable intake closing time. Throttling losses normallyexperienced at low engine loads, can be substantially reduced by advancing the intake valveclosing time with decreasing load, thus regulating the amount of induced mixture.

4.4. Optimal timing strategy and optimal performances

Because the IC timing affects the amount of the cylinder charge, it thus affects the maximumtemperature and pressure in the cycle and therefore the progress of the combustion process. Asa result, the optimal timing of the exhaust valve is also affected by the IC timing and should beset accordingly. Also, since the efficiency of the gas exchange process may be influenced, by the

timing of the exhaust valve, variation in EO timing may affect the optimized closing timing ofthe intake valve. It is therefore expected that when the timing of both valves are considered tobe controllable, both the EO and IC timings should be optimized simultaneously. Fig. 7 showsthe calculated optimization strategy for the exhaust valve open and intake valve open and closetimings, respectively. Spark timing has been optimized (MBT) for each set of operating conditions.It appears that the optimal timing of each valve depends linearly (in a good approximation), onthe engine speed, while the slope depends apparently in a weak manner on the engine load. Foran example, at full load conditions when the engine speed increases from 2000 to 5000 rpm, inorder to operate the engine under optimal operation conditions for minimum bsfc, the exhaustvalve opening timing should be advanced from 152 to 123, the intake valve opening time should


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Fig. 9. Calculated engine torque, bsfc, and major pollutants vs engine speed at full load conditions, with optimal

VVT, and without VVT, for minimum bsfc.

be kept at a fixed crank-angle of 330, and the intake closing timing should be retarded from536 to 550.

Fig. 8 shows the calculated optimization strategy of the intake valve opening time (IO), andthe intake valve closing time (IC), for minimum bsfc, vs engine load at an engine speed of 4000

rpm. As expected, when a higher power is required, the IC time has to be retarded and the IObe advanced. This results also in a significant increase in the intake port opening duration. Anincrease in the engine load from 35% to full load, requires an IO advance from 370 to 300,and IC retard from 440 to 560 [Fig. 7(b)]. This results in an increase in the opening durationfrom 50 to 200.

A comparison between the full-load performances envelop of an original engine (having fixedvalves timing), and a modified engine operating with VVT (when the valve timing is optimized),is shown in Fig. 9. It appears that while the CO and NOx emissions are not improved nor notice-ably deteriorated, both the engine torque and the engine bsfc are improved (though to a smallextent) specifically at low engine speed. An improvement of 6% in the torque, and 2% in the


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Fig. 10. Calculated engine torque, bsfc, and major pollutants vs engine speed at partial conditions, with optimal VVT,

and without VVT, for minimum bsfc.

bsfc is observed. For a partial engine load of 35% (Fig. 10), a torque increase of 4% and bsfcdecrease of 6% is observed at low engine speed of 2000 rpm, and a torque increase of 3% andbsfc decrease of 14% at high engine speed of 5000 rpm. As expected, it also appears that whilethe CO is lower when VVT is in operation, in the entire range of engine speed, the NOx isslightly higher. It is important to note that when VVT is applied, the maximum torque at any

engine load, is shifted towards a lower engine speed. The advantage of using VVT in particularat low engine load is clearly demonstrated.

5. Conclusions

In the present work the performance of a commercial unthrottled SI engine installed with VVTwere analyzed. This is in order to postulate optimal valve timing strategies for maximizing enginetorque in terms of the exhaust opening, intake opening and intake closing timings. The followingconclusions have been drawn:


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1. The optimal EO and IC for minimizing bsfc occurs in a good approximation when the enginetorque maximizes in the entire range of operation conditions.

2. It appears that the CO and NOx emissions are practically insensitive to the EO and IC time.3. The optimal IO is practically insensitive to the engine speed, and to a very limited degree of

sensitivity to the engine load.4. The optimal timing of each valve depends apparently linearly on the engine load, linearly (in

a good approximation) on the engine speed, while the slope depends in a weak manner on theengine load.

5. When VVT is employed, the CO and NOx emissions are not improved nor noticeably deterio-rated. The engine torque and the engine bsfc are however improved, in particular at partialload and low engine speed.

6. When VVT is applied, the maximum torque at any engine load, is shifted towards a lowerengine speed.

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optimal valve timing

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