Experimental-stochastic investigation of the combustion cyclic variability in HSDI diesel engine using ethanol–diesel fuel blends

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Fuel 87 (2008) 1478–1491

Experimental-stochastic investigation of the combustion cyclicvariability in HSDI diesel engine using ethanol–diesel fuel blends

D.C. Rakopoulos a, C.D. Rakopoulos a,*, E.G. Giakoumis a,R.G. Papagiannakis b, D.C. Kyritsis c

a Internal Combustion Engines Laboratory, Thermal Engineering Department, School of Mechanical Engineering, National Technical University of Athens,

9 Heroon Polytechniou St., Zografou Campus, 15780 Athens, Greeceb Thermodynamic and Propulsion Systems Section, Aeronautical Sciences Department, Hellenic Air Force Academy, Dekelia Air Force Base,

1010 Dekelia, Attiki, Greecec University of Illinois at Urbana Champaign, Department of Mechanical Science and Engineering, 1206 West Green Street, Urbana, IL 61801, USA

Received 30 June 2007; received in revised form 19 August 2007; accepted 21 August 2007Available online 14 September 2007

Abstract

An experimental investigation is conducted to evaluate the combustion characteristics of a fully instrumented, high-speed, direct injec-tion (HSDI), standard ‘Hydra’ diesel engine, at various loads when using ethanol–diesel fuel blends up to 15% by vol. ethanol. In eachtest, combustion chamber and fuel injection pressure diagrams of many consecutive cycles were obtained using a specially developed,high-speed, data acquisition and processing system. Following a performance and exhaust emissions investigation and a heat releaseanalysis of the measured cylinder pressure diagrams reported by the authors, the present work focuses on the cycle-by-cycle combustionvariation (cyclic variability) as reflected in the pressure indicator diagrams, by analyzing for the maximum pressure, maximum pressurerate, (gross) indicated mean effective pressure, and dynamic injection timing and ignition delay. These parameters were analyzed usingstochastic analysis techniques for averages, standard deviations, coefficients of variation, probability density functions, auto-correlations,power spectra and cross-correlation coefficients. Thus, any cause and effect relationship between cyclic pressure variations and the injec-tion system or the kind of fuel used can be revealed, given the concern for the low cetane number of ethanol blends promoting cyclicvariability that can lead to degraded performance and emissions characteristics.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Diesel engine; Ethanol–diesel blends; Combustion; Cyclic variability; Stochastic analysis

1. Introduction

Engine manufacturers worldwide have achieved todevelop diesel engines with high thermal efficiency and spe-cific power output, always trying to keep inside the limits ofimposed emissions regulations. Significant achievementsfor the development of cleaner diesel engines have beenmade by following various engine-related techniques [1,2].Moreover, especially for the reduction of pollutant emis-sions, researchers have focused their interest on the domainof fuel-related techniques [3–7].

0016-2361/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.fuel.2007.08.012

* Corresponding author. Tel.: +30 210 7723529; fax: +30 210 7723531.E-mail address: [email protected] (C.D. Rakopoulos).

Another aspect of the problem concerns the use not onlyof diesel fuel (and gasoline), but also of alternative renew-able fuels. Favorable fuels of the last class are bio-fuelsmade from agricultural products [8,9]. Furthermore, con-cerning the environmental aspect, rational and efficientend-use technologies are identified as key options for theachievement of the Kyoto targets for the reduction ofgreenhouse gas (e.g., CO2) emissions. Replacement of fossilfuels with renewable bio-fuels has been set as a targetworldwide to reduce greenhouse effect and energy depen-dence as well as to improve agricultural economy. TheEuropean Union has set as target in its state membersthe use of bio-fuels of at least 2% by the end of 2005 and5.75% by the end of 2010 in the transportation sector

mailto:[email protected]

Nomenclature

AVER mean valueb beforeb.m.e.p. brake mean effective pressure (bar)COV coefficient of variation (percentage)DPG maximum cylinder pressure rate (bar/deg.)DI direct injectionDIGN ignition delay (deg.)DINJ dynamic injection timing (�CA bTDC)E15-D 15% (by vol) ethanol blend in diesel fuelHSDI high-speed, direct injection

IDI indirect injectionIMEP (gross) indicated mean effective pressure (bar)LOAD b.m.e.p. (bar)PAR parameterPG maximum cylinder pressure (bar)rpm revolutions per minuteSDEV standard deviationTDC top dead center�CA degrees of crank angle

D.C. Rakopoulos et al. / Fuel 87 (2008) 1478–1491 1479

[10–13]. Greece is now attempting to conform to the Euro-pean Commission directives and produce bio-diesel or bio-ethanol using feedstock available from the current agricul-tural activities, as well as from cultivations of new plantswith improved production and land utilization [13].

Among the bio-fuels (oxygenated by nature), bio-etha-nol, vegetable oil derived bio-diesels, and to a lesser extentraw vegetable oils are recently considered as most promis-ing [14–21]. A recent work by the authors [22] studied andcompared an extended variety of vegetable oils and bio-die-sels of various origins tested as supplements to the normaldiesel fuel in blend ratios of 10/90 and 20/80 (by vol.) in theRicardo/Cussons ‘Hydra’ diesel engine of the presentstudy, while in [23] the investigation was extended up tothe neat cottonseed and its methyl ester cases. A morerecent work [24] studied the performance and exhaust emis-sion levels of sunflower and cottonseed methyl esters inblend ratios of 10/90 and 20/80 with diesel fuel, in afully-instrumented, six-cylinder, turbocharged and after-cooled, heavy duty, direct injection, Mercedes-Benz dieselengine; these engines are used to power the mini-bus sub-fleet of the Athens Urban Transport Organization(AUTO).

Because of its high octane number, ethanol is a goodspark-ignition engine fuel [2], while vegetable oils andbio-diesels are good diesel engine fuels owing to their rea-sonably high cetane number. It is true that alcohols, mainlyethanol and to a much lesser extent methanol, have beenconsidered as alternative fuels for diesel engines too [14–17]. Methanol can be produced from coal or petrol basedfuels with low cost production, but it has a restrictive sol-ubility in the diesel fuel. On the other hand, ethanol is abiomass based renewable fuel (bio-ethanol), which can beproduced by alcoholic fermentation of sugar from vegeta-ble materials, such as corn, sugar cane, sugar beets, barley,sweet sorghum and the like, and agricultural residues, suchas straw, feedstock and waste woods, showing better misci-bility with diesel fuel.

While anhydrous ethanol is soluble in gasoline, additivesmust be used to ensure solubility of anhydrous ethanol(that is highly hygroscopic) in diesel fuel, especially atlower temperatures where miscibility is limited. Moreover,

adding ethanol to diesel fuel can reduce lubricity and createpotential wear problems in sensitive fuel pumps. Ethanolpossesses also lower viscosity and calorific value, with thelater imposing minor changes on the fuel delivery systemfor achieving maximum power [25,26]. By all estimates,ethanol has a very low cetane number that reduces thecetane level of the diesel–ethanol blend, requiring normallyuse of cetane enhancing additives that improve ignitiondelay [27,28].

Various techniques have been developed to make dieselengine technology compatible with the properties of etha-nol-based fuels. They can be divided into the followingthree classes: (a) ethanol fumigation to the intake aircharge [14,29–31], (b) dual injection system, which, how-ever, requires an extra high-pressure injection system [14],and (c) blends (emulsions) of ethanol and diesel fuel byusing an emulsifier to mix the two fuels for separation pre-vention, requiring no technical modifications on the engineside [14,32–35].

Stable emulsions usually refer to both solutions andmicro-emulsions of anhydrous ethanol in diesel fuel. Anhy-drous ethanol (200 proof) does not require an emulsifyingagent (surfactant) to form a transparent solution in dieselfuel, but this can tolerate only up to 0.5% water. Then, inthe practical cases of using lower proof ethanol (say 190proof or lower), an emulsifying agent is required to formthe opaque macro-emulsion [14]. Blends with up to 15%ethanol in diesel fuel are considered relatively safe fromthe engine durability point of view.

A work has been reported by the present group [36] con-cerning the performance and emission characteristics forthe same engine as of the present study, when operatingwith ethanol-diesel fuel blends of 5/95, 10/90 and 15/85(by vol.) blending ratios. The experiments were performedwithout any modification on the engine and with no igni-tion-improving additives. Moreover, in Ref. [37] a compre-hensive experimental heat release analysis was conductedfor the same engine, fuels and conditions. The experimentalcylinder pressure (indicator) diagrams were directly pro-cessed in connection with the pertinent application of theenergy and state equations [38–41] to provide the heatrelease rates and other related parameters in the combus-

1480 D.C. Rakopoulos et al. / Fuel 87 (2008) 1478–1491

tion chamber, revealing some very interesting features ofthe combustion mechanism and associated emissions withthe use of ethanol–diesel fuel blends in diesel engines.

Theoretical aspects of diesel engine combustion, takinginto account the widely differing physical and chemicalproperties of these ethanol blends against the normal dieselfuel, were used in the above two works to aid the correctinterpretation of the observed engine behavior. It is men-tioned that, unlike the advanced models existing for thestudy of diesel engines using the conventional diesel fuel[42–44], there seems to be scarcity of theoretical modelsscrutinizing the formation mechanisms of combustion gen-erated emissions when using bio-fuels [45–47].

On the other hand, it is known that in a running recip-rocating internal combustion engine wide variations in thecylinder pressure from one cycle to another are displayed,even under nominally constant operating conditions [48].Any deviation in the pressure time development reducesthe efficiency and reliability of the engine, increases itsnoise and exhaust-gas emissions, and is one of the causesof the power fluctuations [49]. It is the cycles with pressuretraces deviating from the averaged (desired ‘optimum’) thatsuffer degradation in their performance and emissioncharacteristics.

Although measurements and analysis of cycle-by-cyclevariations in Otto (spark-ignition) engines have been madeby many investigators [50–56], it seems that correspondinganalyses for diesel engines have not kept pace at all, thoughrandomness in the cylinder pressure was known to exist,probably because of the lower strength cycle-by-cycle pres-sure variations encountered in diesel engines.

Sagdeo [57], Strahle [58], and Wolschendorf et al. [59]linked combustion randomness of two- and four-strokeDI diesel engines with the noise radiated by these engines,while Selim [60] investigated the influence of the gaseousfuel type of a dual fuel engine. Important studies of thecycle-by-cycle variations of pressure in diesel engines havebeen reported by Koizumi et al. [61], Sczomak and Henein[62], and Wing [63].

Wing [63] was the first to deal, in depth, with this aspectof diesel engine operation, and his experimental study con-cerns a multi-cylinder, four-stroke, DI diesel engine fittedwith a rotary fuel injection pump, which was suspect asthe source of cyclic pressure variation. Koizumi et al. [61]dealt with a two-stroke IDI diesel engine trying to connectthe irregularity of injected fuel mass with the cycle-by-cyclevariation of the indicated mean effective pressure. Sczomakand Henein [62], in an extensive experimental investigationon a CFR pre-chamber diesel engine running with variouslow-ignition quality fuels, tried to correlate cyclic pressurevariations with ignition delay and dynamic injection timingand pointed out that low cetane number fuels may causecyclic irregularity in the diesel engine. Their results seemto contradict, in some respects, those of Wing [63] concern-ing correlations. Kouremenos et al. [64] have made anextensive investigation of this phenomenon in a single-cyl-inder engine operating on diesel fuel, at various loads and

injection timings, using stochastic techniques, and foundno correlation between cyclic pressure variations and theinjection system.

Therefore, following the performance and exhaust emis-sions investigation and the heat release analysis of the mea-sured cylinder pressure diagrams reported by the authors in[36,37], as referred to above, the present work focuses onthe study of the cycle-by-cycle combustion variations (cyc-lic variability) in the same, high-speed, direct injection(HSDI), automotive type (light duty), standard Ricardo/Cussons ‘Hydra’ diesel engine, running with the same eth-anol–diesel fuel blends and the same operating conditionsin the authors’ laboratory. The need for such a study ema-nates from the concern of the low cetane number of ethanolblends promoting cyclic variability (and thus degraded per-formance and emission characteristics), since the longerignition delay periods can allow more time for the airmovement variations to influence combustion.

The combustion variation (cyclic variability) is tackledhere in the way it is reflected in the pressure indicator dia-grams, by analyzing for the maximum pressure, maximumpressure rate, (gross) indicated mean effective pressure, anddynamic injection timing and ignition delay. These param-eters are analyzed using stochastic analysis techniques, overa record of 480 consecutive (combustion cycles) pressurediagrams obtained, for averages, standard deviations, coef-ficients of variation, probability density functions, auto-correlations, power spectra and cross-correlation coeffi-cients. Thus, any cause and effect relationship between cyc-lic pressure variations and injection system or the kind offuel used can be revealed.

2. Description of the engine experimental facilities

Facilities to monitor and control engine variables areinstalled on a fully automated test bed, single-cylinder,four-stroke, water cooled, Ricardo-Cussons ‘Hydra’, highspeed, experimental standard engine coupled to a ‘McC-lure’ DC dynamometer that is located in the first author’slaboratory. This engine has the ability to operate on theOtto (spark-ignition) or DI diesel or IDI diesel, four-strokeprinciple, by changing various parts of the crank gearmechanism, cylinder and head.

For the present study it is used as a naturally aspirated,DI diesel engine, which can operate in a rotational speedrange of 1000–4500 rpm. The engine cylinder bore is0.08026 m, the piston stroke 0.08890 m and the compres-sion ratio 19.8:1. It has a re-entrant bowl-in-piston com-bustion chamber, with an injector nozzle having fourholes, 0.25 mm diameter each, drilled symmetricallyaround its tip, forming a spray cone angle of 160�. The die-sel fuel injection pump is fitted with an 11 mm diameterplunger. A ‘Bosch’ injector body is used, which opens ata pressure of 250 bar. A range of 0 up to 40 oCA advance(static) is provided.

For fuel consumption measurements, a glass burette ofknown volume was used with the time measured for its

Exhaust

TDC pick up

Pressure &

Pres

sure

Pres

sure

Schenck U1 -40 Mercedes - Benz OM 366 LA

T/CA/C

Cyl

Data Acquisition Card

(engine speed)

temperature

Boost

Fuel Measure -ment

NOx HC CC

PC

Smok

e

inj

Amplifier

Filter

Fig. 1. Schematic arrangement of the engine test bed, instrumentation and data logging system.


complete evacuation of the fuel sample feeding the engine.A system of pipes and valves was constructed for achievinga quick drain of a fuel sample, including the return-fuelfrom the pump and injector, and the refill of metering sys-tem with the new fuel sample. The exhaust gas analysis sys-tem consisted of a group of analyzers for measuring soot(smoke), nitrogen oxides (NOx), carbon monoxide (CO)and total unburned hydrocarbons (HC) in the engineexhaust [36,37].

Fig. 1 shows a full schematic arrangement of the enginetest bed, instrumentation and data logging system.

3. Transducers measuring set-up and data acquisition system

For measuring the pressure in the cylinder, a ‘Kistler’miniature piezoelectric transducer is used, flush mountedto the cylinder head, and connected to a ‘Kistler’ chargeamplifier. Also, a ‘Kistler’ piezoelectric transducer is con-nected on the injector side of the pipe linking the injectionpump and injector, in order to provide the fuel pressure sig-nal. The signal from a ‘Tektronix’ TDC magnetic pick-upmarker is used for time reference and speed measurement.

The output signals from the above three transducers,while they are continuously monitored on a dual beam‘Tektronix’ storage oscilloscope, are connected to the inputof a ‘Keithley’ DAS-1801ST A/D board installed on anIBM compatible Pentium III PC. This board can acquireinput data at a total throughput rate of 312,500 samplesper second from up to eight differential analogue inputs;it utilizes dual-channel Direct Memory Access (DMA)operation. It is thus appropriate for the recording of high

frequency engine signals, with the added advantage of highsignal resolution (much less than 1 degree CA, dependingalso on the number of simultaneous recorded signals).

Control of this high-speed data acquisition system isachieved by developing a computer code based on the‘TestPoint’ control software. The resulted program, spe-cially designed for steady or transient internal combustionengine applications, is an object-oriented functional codeallowing for direct on-screen selection of the desired valuesof all acquisition parameters.

4. Properties of fuels and blending

The conventional diesel fuel was supplied by the Aspro-pyrgos Refineries of the ‘Hellenic Petroleum SA’ and repre-sents the typical, Greek automotive, low sulfur (0.035 wt%)diesel fuel (gas oil); it forms the baseline fuel of the presentstudy. The properties of the diesel fuel and the ethanol aresummarized in Table 1.

The ethanol (CH3CH2OH) is blended with the normaldiesel fuel at blend ratios of 5/95, 10/90 and 15/85 (byvol). For the present experiments, no cetane improvingadditives (ignition improvers) were used. An emulsifyingagent by ‘Betz GE’, a division of General Electric, Inc.,was used in proportions of 1.5 vol%, to satisfy mixturehomogeneity and prevent phase separation.

The emulsifier replaced a corresponding part of the die-sel fuel. Thus, the 15/85 blend ratio corresponds to 83.5%diesel fuel, 1.5% emulsifier and 15% ethanol (by vol.),and similarly for the other two blends. The mixing protocol

Table 1Properties of diesel fuel and ethanol

Fuel properties Diesel fuel Ethanol

Density at 20�C, kg/m3 837 788Cetane number 50 5–8Kinematic viscosity at 40�C, mm2/s 2.6 1.2Surface tension at 20�C, N/m 0.023 0.015Lower calorific value, MJ/kg 43 26.8Specific heat capacity, J/kg K 1850 2100Boiling point 180–360 78Oxygen, % weight 0 34.8Latent heat of evaporation, kJ/kg 250 840Bulk modulus of elasticity, bar 16,000 13,200Stoichiometric air–fuel ratio 15.0 9.0Molecular weight 170 46


consisted of first blending the emulsifier into the ethanoland then blending this mixture into the diesel fuel.

5. Parameters tested and experimental procedure

The experiments were performed without any modifica-tion on the engine. The series of tests are conducted usingeach of the above fuel blends, with the engine working at aspeed of 2000 rpm, at a static (pump spill) injection timingof 29 �CA before TDC, and four loads corresponding tob.m.e.p. (brake mean effective pressure) of 0.00, 1.40,2.57 and 5.37 bar, denoted as no-load, low load, mediumload and high load, respectively. Owing to the differencesamong the lower calorific values and oxygen contents ofthe fuels tested, the comparison must be effected at thesame b.m.e.p. (load) and not the same injected fuel massor air–fuel ratio. The differences in the measured perfor-mance and exhaust emission parameters from the baselineoperation of the engine, i.e. when working with neat dieselfuel, were determined and compared. In each test, volumet-ric fuel consumption rate, exhaust gas temperature,exhaust smokiness and exhaust regulated gas emissionssuch as nitrogen oxides, carbon monoxide and totalunburned hydrocarbons were measured [36,37].

At the same time, during each test, combustion chamber(indicator) and fuel injection pressure diagrams wereobtained using the specially developed data acquisition sys-tem described above. The pressures are measured withaccuracy better than within ±1% of full-scale output(fso), and the accuracy of the analogue input readings ofthe data acquisition system is within ±0.01%. The electriccharacteristics of the charge amplifiers, such as drift, donot contribute to the total error because the drift and lineartrend are remedied via software routines during the pro-cessing of signals.

The experimental work started with a preliminary inves-tigation of the engine running on neat diesel fuel, in orderto determine the engine’s operating characteristics andexhaust emission levels, constituting the ‘baseline’ that iscompared with the corresponding cases when using the eth-anol–diesel fuel blends. The same procedure is repeated for

each fuel blend by keeping the same operating conditions.For every fuel change, the fuel lines were cleaned and theengine was left to run for about 30 min to stabilize at itsnew operating condition.

6. Preliminary treatment of the experimental pressure

diagrams and determination of various parameters

A recording is made of the cylinder (indicator) and fuelmeasured pressure data for 480 cycles in a contiguous file,with a sampling rate corresponding to 0.5 oCA. Initially,the indicator diagrams are corrected for any drifting ofthe signals obtained from the charge amplifiers, by takingthe mean value of the pressures in the gas exchange periodand ‘setting’ this equal to the atmospheric pressure value.

A signal from a magnetic pick-up, which is simulta-neously recorded, indicates the position of the TDC in eachcycle. This signal (due to its nature) presents a very sharpchange from its maximum positive to a corresponding neg-ative value; by taking the bisection on these two values, theposition of TDC is accurately determined in every cycle.Further, by considering the TDC position of any two con-secutive cycles and knowing the sampling rate of the mea-surements (e.g., in the present case, at 0.5 oCA with anominal speed of 2000 rpm), it allows easily the calculationof the accurate engine speed in each cycle from the first tothe last one.

For the heat release analysis, the ‘mean’ of the cylinder(indicator) and the fuel pressure diagrams are obtainedfrom 10 consecutive cycles, while a ‘light smoothing’ forthe pressure signals is applied that is based on performinga four-data points weighted smoothing. This seems to offera reasonable compromise between no loss of valuable sig-nal information and of relatively smooth values for the firstderivative of the cylinder pressure with respect to crankangle, since sudden changes in the indicator diagram wouldgrossly be transferred to the ‘sensitive’ heat release rate dia-gram. Details can be found in Ref. [37].

In contrast, concerning the stochastic analysis this workis dealt with, all the 480 pressure diagrams (cycles) are usedseparately (the ‘mean’ is meaningless here), again with‘light smoothing’, since by definition the parameters drawnfrom them will form the data record values to be statisti-cally processed. A cubic spline interpolation curve was usedto fit the discrete pressure diagram of each cycle, so that themaximum pressures and maximum pressure rates and theirangles could be determined accurately. For assessing theerrors involved with respect to the number of cycles chosen[64], the variations of the mean value and of the standarddeviation of the maximum pressures and pressure rateswere plotted against the number of cycles, revealing thata number of cycles greater than 400 form a conservativelimit for a statistical analysis.

As no apparatus for measuring the injector needle liftwas available, by processing the fuel pressure diagram thedynamic injection timing was assumed to coincide withthe crank angle where the fuel pressure reaches the value

200

400

600

UE

L P

RE

SS

UR

E (

bar)

Diesel, b.m.e.p.=5.37 barE15-D, b.m.e.p.=5.37 barDiesel, b.m.e.p.=2.57 barE15-D, b.m.e.p.=2.57 bar

a


of the injector nozzle opening pressure, following the per-iod of the, almost constant, residual (in the connecting fuelpipe) pressure value. The difference between dynamic injec-tion timing and pump spill (static) timing forms the injec-tion delay.

By processing the cylinder pressure diagram, the ignitiontiming was located at the crank angle where the first deriv-ative of this pressure with respect to crank angle suddenlychanges slope, immediately following the event of thedynamic injection timing, going from a negative to a posi-tive value and so presenting a local minimum. The ignitiontiming was then determined either by using this condition,or by locating the corresponding ‘zeroing’ crank angle ofthe second derivative of pressure with respect to crankangle, assuming that this signal is ‘smooth’ enough. Notethat with every differentiation of the original pressuresignal the noise-to-signal ratio increases, while if over-smoothing is applied this ‘zero’ point might disappear asbeing ‘ill conditioned’. The difference between ignition tim-ing and dynamic injection timing forms the ignition delay.

From the first and second derivatives of the cylinderpressure diagram with respect to crank angle, which arefound numerically, the crank angles of the maximum val-ues of the first derivative of pressure and of the pressureitself can be determined, bearing also in mind that theyimmediately follow the ignition timing and in that order.

CRANK ANGLE (deg.)

0

F

-40 -20 0 20

CRANK ANGLE (deg.)

0

100

200

300

400

FU

EL

PR

ES

SU

RE

(ba

r)

Diesel, b.m.e.p.=1.40 barE15-D, b.m.e.p.=1.40 barDiesel, b.m.e.p.=0. barE15-D, b.m.e.p.=0. bar

-40 -20 0 20

b

Fig. 2. Fuel (injection) pressure against crank angle diagrams for the neatdiesel fuel and the 15% ethanol blend cases, at the high and medium loads(a), and at the low and no loads (b).

7. Experimental data stochastic analysis: background

The following statistical definitions are used for theanalysis of the N raw data values ui (i = 1,2, ... ,N) con-tained in a record:

Average valueð1st momentÞ : �u ¼PN

i¼1ui

Nð1Þ

Variance (2nd moment) var, standard deviation r, andcoefficient of variation cv:

var ¼PN

i¼1ðui � �uÞ2

N � 1; r ¼ ðvarÞ1=2 and cv ¼ r=�u ð2Þ

The probability density function of the N data values canbe estimated by

pðuÞ ¼ Nu=ðNW Þ ð3Þ

where W is a narrow interval centered at u, and Nu is thenumber of data values that fall within the range u ± W/2.In order to effect a comparison, the value of a Gaussian(or normal) probability density function pn with the samemean value �u and standard deviation r as that of the datarecord is also calculated, i.e.

pnðuÞ ¼1

rffiffiffiffiffiffi2pp exp � 1

2

u� �ur

� �2" #

ð4Þ

For the computation of the auto- and cross-correlations ofthe parameters involved, the mean value �u has been sub-

tracted from each value u, i.e. we consider the new time his-tory record:

xðtÞ ¼ xðt0 þ nhÞ ¼ ui � �u ði ¼ 1; 2; . . . ;NÞ ð5Þ

where h is the sampling time interval and n = 1,2, . . . ,N.

The auto-correlation function (note that superscript ^denotes estimate in the following) is estimated by directcomputation [65] after any linear trend removal. For N

data values xi (i = 1, 2,... ,N), from a transformed recordx(t), the estimated auto-correlation function at the timedisplacement rh is defined by the formula [65,66]

-20 0 20 40 60 80CRANK ANGLE (deg.)

-10

0

10

20

30

40

50

GR

OS

S H

EA

T R

ELE

AS

E R

AT

E (

J/de

g.)

Diesel, b.m.e.p.=5.37 barE15-D, b.m.e.p.=5.37 barDiesel, b.m.e.p.=2.57 barE15-D, b.m.e.p.=2.57 bar

Fig. 4. Gross heat release rate against crank angle diagrams, at the twohigher loads, for the neat diesel fuel and the 15% ethanol blend cases.


Rr ¼1

N � r

XN�r

i¼1

xixiþr r ¼ 0; 1; 2; :::;m ð6Þ

where r is the lag number, m is the maximum lag number,and Rr is the estimate of the true value Rr at lag r, corre-sponding to the displacement rh. A normalized value forthe auto-correlation function [66] is obtained by dividingRr by R0, where

R0 ¼ Rxð0Þ ¼1

N

XN�r

i¼1

x2i ¼ x2 ð7Þ

The power spectra estimates are calculated via the correla-tion estimates [65], i.e. they are also normalized. For sam-pled data, from a transformed time record x(t), asmoothed estimate Gk at harmonic k = 0,1,2, ... ,m of atrue power spectral density function Gxðf Þ is defined by

Gk ¼ Gkkfc

m

� �¼ 2h R0 þ 2

Xm�1

r¼1

DrRr cosprkm

� �" #ð8Þ

where Rr is the estimate of the auto-correlation function atlag r, m is the maximum lag number, fc (=1/2h) is the cut-off (Nyquist) frequency, and Dr is the Hanning lag weight-ing function [67] defined by

Dr ¼ DðrhÞ ¼ 1

21þ cos

prm

� �ð9Þ

for r = 0,1,2,... ,m and Dr = 0 for r > m.The cross-correlation between two transformed time

records x(t) and y(t) at lag numbers r = 0,1,2, ... ,m isgiven by the relation

Rxy ¼1

N � r

XN�r

i¼1

xiyiþr and Ryx ¼1

N � r

XN�r

i¼1

yixiþr ð10Þ

-20 0 20 40CRANK ANGLE (deg.)

0

20

40

60

80

100

CY

LIN

DE

R P

RE

SS

UR

E (

bar)

Diesel, b.m.e.p.=5.37 barE15-D, b.m.e.p.=5.37 barDiesel, b.m.e.p.=2.57 barE15-D, b.m.e.p.=2.57 barDiesel, b.m.e.p.=1.40 barE15-D, b.m.e.p.=1.40 barDiesel, b.m.e.p.=0. barE15-D, b.m.e.p.=0. bar

Fig. 3. Cylinder pressure against crank angle diagrams, at the four loads,for the neat diesel fuel and the 15% ethanol blend cases.

The maximum value of r in the auto- and cross-correlationestimates should normally be less than 10% of the numberof data values N [66]. The normalization of the cross-corre-lation function defines the sample cross-correlation coeffi-cient [65]

qxyðrhÞ ¼ RxyffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiRxð0ÞRyð0Þ

q ¼ Rxyffiffiffiffiffiffiffiffix2y2

q ð11Þ

A similar formula applies for qyx.

0 2 4 6b.m.e.p. (bar)

65

70

75

80

85

90

Max

. pre

ssur

e (b

ar)

DieselE15-D

Fig. 5. Cyclic variation of the maximum cylinder pressure, as a functionof load, for the neat diesel fuel and the 15% ethanol in the blend cases.


A computer program was written in Fortran V languageand executed on a Pentium-IV Personal Computer, toimplement the analysis above.

0 2 4 6b.m.e.p. (bar)

2

3

4

5

Max

. pr

essu

re r

ate

(bar

/deg

.)

Diesel E15-D

Fig. 6. Cyclic variation of the maximum cylinder rate of pressure rise, as afunction of load, for the neat diesel fuel and the 15% ethanol in the blendcases.

0 2 4 6b.m.e.p. (bar)

8

9

10

11

Dyn

amic

inje

ctio

n tim

ing

(deg

. bT

DC

)

DieselE15-D

4

4.4

4.8

5.2

Igni

tion

dela

y (d

eg.)

Fig. 7. Cyclic variation of the dynamic injection timing (lower sub-diagram) and of the ignition delay (upper sub-diagram), as a function ofload, for the neat diesel fuel and the 15% ethanol in the blend cases.

8. Fuel pressure, cylinder pressure and heat release rate

diagrams

It is pointed out that only the results for the neat dieselfuel and the blend of 15% (by vol) ethanol in diesel fuel,denoted hereafter as E15-D, will be shown. This is dictated,on the one hand, by the conservation of space of this paperand, on the other, by the differences in the respective dia-grams of values (of neat diesel fuel against those for theE15-D blend) that are relatively well discernible in thiscase.

Table 2Mean values, standard deviations and coefficients of variation of thevarious parameters, at the four engine loads considered, for the neat dieselfuel case and the 15% ethanol in the blend case

Para Fuel Load Aver Sdev Cov

PG Diesel 0.0 68.774 0.471 0.685DPG Diesel 0.0 2.645 0.136 5.135DINJ Diesel 0.0 9.531 0.157 1.645DIGN Diesel 0.0 4.800 0.105 2.182IMEP Diesel 0.0 1.715 0.083 4.857




PG E15-D 0.0 68.836 0.579 0.842DPG E15-D 0.0 2.958 0.150 5.059DINJ E15-D 0.0 8.728 0.171 1.960DIGN E15-D 0.0 5.106 0.098 1.926IMEP E15-D 0.0 1.763 0.071 4.031




a For the explanation of abbreviations and their units consult theNomenclature.


Fig. 2a at the high and medium loads and Fig. 2b at thelow and no loads show the fuel (injection) pressure againstcrank angle diagrams, for the neat diesel fuel and the E15-D blend. First it can be seen, as expected, that the injectionduration increases with engine load for both fuels; the sameholds true for the injection pressures. It can be observedthat for each load considered, the fuel pressure diagramfor the E15-D blend against the corresponding one forthe neat diesel fuel case does not show any appreciable dif-ferences in shape and thus in the injection duration or max-imum pressure. The E15-D blend diagram shows, however,a small displacement-delay that is also translated into a

3.6 4 4.4 4.8 5.2 5.6

Max. pressure rate (bar/deg.)

0

1

2

3

Pro

babi

lity

dens

ity f

unct

ion DIESEL FUEL

Exper. - High loadGauss. - High loadExper. - Medium loadGauss. - Medium load

3.6 4 4.4 4.8 5.2 5.6


0

1

2

3

4

Pro

babi

lity

dens

ity f

unct

ion

ETHANOL 15%Exper. - High loadGauss. - High loadExper. - Medium loadGauss. - Medium load

a

c

Fig. 8. Probability density function of the maximum rate of pressure rise, togeththe neat diesel fuel (a), at the low and no loads for the neat diesel fuel (b), at theand no loads for the 15% ethanol in the blend (d).

corresponding delay of the dynamic injection timing whilethe static injection timing (at pump spill) was kept con-stant, a fact attributed to the different densities and bulkmoduli of elasticity, as is evidenced from Table 1, and thusa different value for the speed of sound as. Details for thisbehavior and explanation can be found in [45].

Fig. 3 shows, at the four loads considered, the cylinderpressure against crank angle diagrams, for the neat dieselfuel and the E-15D blend, focusing on their part aroundTDC. First it can be seen, as expected, that the pressuresincrease with load (with the compression line remainingthe same), while the delay decreases with the engine load

2 2.4 2.8 3.2 3.6 4 4.4


0

1

2

3

4

5

Pro

babi

lity

dens

ity f

unct

ion

DIESEL FUELExper. - Low loadGauss. - Low loadExper. - No loadGauss. - No load

2.4 2.8 3.2 3.6 4 4.4 4.8


0

1

2

3

4

Pro

babi

lity

dens

ity f

unct

ion

ETHANOL 15%Exper. - Low loadGauss. - Low loadExper. - No loadGauss. - No load

b

d

er with the corresponding Gaussian one, at the high and medium loads forhigh and medium loads for the 15% ethanol in the blend (c), and at the low

8 8.5 9 9.5 10 10.5Dynamic injection timing (deg. bTDC)

0

1

2

3

4

Pro

babi

lity

dens

ity f

unct

ion

HIGH LOADExper. - Diesel Gauss. - Diesel Exper. - E15-DGauss. - E15-D

Fig. 9. Probability density function of the dynamic injection timing,together with the corresponding Gaussian one, at the high engine load(b.m.e.p. = 5.37 bar), for the neat diesel fuel and the 15% ethanol in theblend cases.

3.8 4 4.2 4.4 4.6

Ignition delay (deg.)

0

2

4

6

8

Pro

babi

lity

dens

ity f

unct

ion

HIGH LOADExper. - DieselGauss. - Diesel Exper. - E15-DGauss. - E15-D

Fig. 10. Probability density function of the ignition delay, together withthe corresponding Gaussian one, at the high engine load (b.m.e.p. = 5.37bar), for the neat diesel fuel and the 15% ethanol in the blend cases.


for both fuels. The latter is mainly due to the increasinggas temperatures with load. One can observe that for eachload considered, the ignition delay for the E15-D blend ishigher (the pressure rise due to combustion starts later)than the one for the corresponding neat diesel fuel case,while there is no appreciable difference in the maximumpressure.

It is worth explaining this behavior also with referenceto Fig. 4, which shows, at the two higher loads considered(the other two lower loads are not shown for the sake of theclarity of this figure), the corresponding gross heat releaserate against crank angle diagrams, for the neat diesel fueland the E15-D blend. First it can be seen, as expected, thatthe ignition delay decreases with engine load for both fuels,while the heat release rate values become higher. For thehigher load, both parts of combustion, i.e. the premixedcombustion (the part under the first ‘abrupt peak’) andthe diffusion combustion (the last part under the second‘rounded peak’), are apparent, with the diffusion combus-tion diminishing for the lower load. One can also observethat for each load considered, the ignition delay for theE15-D blend is higher than the corresponding one for theneat diesel fuel case, while its premixed combustion peakis much higher and sharper. It is the lower cetane numberof ethanol (cf. these values in Table 1) that causes theincrease of ignition delay and so the increased amount of‘prepared’ fuel (to this end may also assist the easier evap-oration of ethanol) for combustion after the start of igni-tion. However, as noticed in Fig. 3, this is not translatedinto higher pressures, probably because of the counteract-ing effect of later combustion in a lower temperature envi-ronment. Details for this behavior can be found in [37].

9. Presentation and discussion of the analysis results for the

variations, probabilities, correlations and power spectra of

combustion parameters

In the figures to follow, results are presented at all fourloads considered, and for the neat diesel fuel and the blendof 15% (by vol) ethanol in diesel fuel. From the largeamount of data collected at each operating condition, onlyrepresentative sample plots are presented in this work dueto the imposed conservation of space.

Preliminary tests, to determine the extent of cyclic vari-ation in combustion over the load range examined, usedboth the maximum cylinder pressure and the maximumcylinder pressure rate as measures of the cyclic variation(the ‘effect’). Here, the use of the maximum pressure rateis chosen, since its variations are more distinct and obvi-ously it has a closer reference to the combustion processitself. In any case, a rather strong degree of correlationexists between those, as will be shown in the last figure.The dynamic injection timing was chosen [63] as potential‘cause’ of any influence of the injection process on the cyc-lic variation, while the ignition delay was chosen as corre-sponding potential ‘cause’ of any influence of the fuel viaits cetane number [62].

Figs. 5 and 6 present the cyclic variation of the maxi-mum cylinder pressure and the maximum cylinder rateof pressure rise, respectively, expressed as average valuesand standard deviations (note that one standard deviation


is denoted on either side of the mean value as a small ‘ver-tical line segment’), as a function of the engine b.m.e.p.(load) for the cases of the neat diesel fuel and the 15%addition of ethanol in the blend. The observed variationwith either the load or the addition of ethanol in the blendhas already been discussed with reference to Figs. 3 and 4.By observing the standard deviation values, one can saythat the addition of ethanol in the blend, at least for upto 15% ethanol in the blend, does not practically affectthe cyclic variability with respect to the neat diesel fuelcase, which in any case is already small for a diesel engine[64].

0 10 20 30 40 50Cycle difference

-0.4

0

0.4

0.8

1.2

Aut

o-co

rrel

atio

n fu

nctio

n (n

orm

.)

MAX. PRESSURE RATEHigh load

Diesel fuelEthanol 15%

0 10 20 30 40 50Cycle difference

-0.4

0

0.4

0.8

1.2

Aut

o-co

rrel

atio

n fu

nctio

n (n

orm

.)

IGNITION DELAYHigh load

Diesel fuelEthanol 15%

a

c

Fig. 11. Normalized auto-correlation functions of the maximum rate of pressuand power spectral density function of the maximum rate of pressure rise (d), a15% ethanol in the blend cases.

Fig. 7 presents the corresponding cyclic variation of thedynamic injection timing (lower sub-diagram). Theobserved variation with the load pertains to the particularfunctioning of the pump system, while the variation withthe addition of ethanol in the blend has already beendiscussed with reference to Fig. 2. Fig. 7 also shows the cor-responding cyclic variation of the ignition delay (uppersub-diagram). The observed variation with either the loador the addition of ethanol in the blend has already beendiscussed with reference to Figs. 3 and 4. From both sub-diagrams, one can again conclude, by observing the stan-dard deviation values, that the addition of ethanol in the

0 10 20 30 40 5 0Cycle difference

-0.4

0

0.4

0.8

1.2

Aut

o-co

rrel

atio

n fu

nctio

n (n

orm

.)DYNAMIC INJECTION TIMING

High loadDiesel fuelEthanol 15%

0 2 4 6 8 10Frequency (Hz)

0

0.2

0.4

0.6

0.8

1

Pow

er s

pect

ral d

ensi

ty f

unct

ion

MAX. PRESSURE RATEHigh load

Diesel fuel Ethanol 15%

b

d

re rise (a), of the dynamic injection timing (b), and of the ignition delay (c),t the high engine load (b.m.e.p. = 5.37 bar), for the neat diesel fuel and the

0 2 4b.m.e.p. (bar)

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cor

rela

tion

coef

ficie

nts

Diesel, pr. - pr. rateE15-D, pr. - pr. rateDiesel, dyn. inj. - pr. rateE15-D, dyn. inj. - pr. rateDiesel, dyn. inj. - ign. del.E15-D, dyn. inj. - ign. del.Diesel, ign. del. - pr. rateE15-D, ign. del. - pr. rate

6

Fig. 12. Correlation coefficients between dynamic injection timing andmaximum rate of pressure rise, dynamic injection timing and ignitiondelay, ignition delay and peak rate of pressure rise, and maximum cylinderpressure and maximum rate of pressure rise, as a function of load, for theneat diesel fuel and the 15% ethanol in the blend cases.


blend, at least for up to 15% ethanol in the blend, does notpractically affect the cyclic variability with respect to theneat diesel fuel case.

Table 2 summarizes the values of mean (AVER), stan-dard deviation (SDEV) and (percentage) coefficient of var-iation (COV) for the maximum cylinder pressure (PG),maximum cylinder pressure rate (DPG), dynamic injectiontiming (DINJ), ignition delay (DIGN) and (gross) indi-cated mean effective pressure (IMEP) (i.e. that due onlyto the ‘closed’ cycle), for the net diesel fuel and the E15-D blend cases, at the four engine loads considered. It canbe observed that the coefficients of variation of the (gross)indicated mean effective pressures take their usual values[1,2], reducing (smoothening) from about 4.5% at the noload condition to about 1.5% at the high load one.

Fig. 8a at the high and medium loads and Fig. 8b at thelow and no loads display, for the neat diesel fuel case, theprobability density function of the maximum rate of pres-sure rise, together with the corresponding Gaussian onehaving the same mean value and standard deviation. Also,Fig. 8c at the high and medium loads and Fig. 8d at the lowand no loads display the corresponding functions, for the15% addition of ethanol in the blend case. It can be seenthat the experimental probability density functions followthe Gaussian curve quite closely, showing a slightly differ-ent skewness and kurtosis. Hence, the error of the analysiswill be insignificant, if a normal distribution is assumed forthe purpose of determining the statistical nature of themaximum rate of pressure rise; this has already been tacitlyassumed in previous Figs. 5–7. This then implies that thecause of the maximum rate of pressure rise fluctuation israther random (stochastic) and does not depend on itsvalue of any other cycle, i.e. on any residual effects of theprevious combustions taken place in the cylinder [63,64].The computation of the auto-correlation function for theabove parameters, which follows later, confirms also theabove conclusion.

Fig. 9 displays, for the cases of the neat diesel fuel andthe 15% addition of ethanol in the blend, at the high engineload (b.m.e.p. = 5.37 bar), the probability density functionof the dynamic injection timing, together with the corre-sponding Gaussian one. Also, Fig. 10 displays the corre-sponding functions for the ignition delay. As can easilybe seen, the conclusions are the same concerning the sto-chastic nature of these parameters.

Sample normalized auto-correlation functions of themaximum rate of pressure rise, the dynamic injection tim-ing and the ignition delay, for the cases of the neat dieselfuel and the 15% addition of ethanol in the blend, at thehigh engine load (b.m.e.p. = 5.37 bar), are shown inFig. 11a–c, respectively. The autocorrelation function forthe other engine loads and the other parameters were sim-ilar, not exceeding the critical value (�0.20) at the 1% sig-nificance level. From observation of the auto-correlationvalues, it is concluded that there is no correlation betweenthe fluctuations of different cycles. Therefore, the sameconclusion can be drawn as that from the examination of

the sample probability density function plots. Also,Fig. 11d displays the (normalized) power spectral densityfunction of the maximum rate of pressure rise correspond-ing to the auto-correlation plot case presented in Fig. 11a.From this figure, it can be seen that the power spectrum israther flat, since it is spread out, and every peak containsless than 20% of the total power content, so that the sameconclusion is reached for the absence of correlationbetween the fluctuations of different cycles.

In order to examine the influence of the injection process(potential ‘cause’) and of the kind of fuel used via its cetanenumber (another potential ‘cause’) on the cyclic pressurevariation, a cross-correlation analysis was carried out thatcomputed the degree of correlation between the dynamicinjection timing and the maximum rate of pressure rise,between the dynamic injection timing and the ignitiondelay, and between the ignition delay and the peak rateof pressure rise. Also, for comparison purposes, the degreeof correlation between the maximum cylinder pressure andthe maximum rate of pressure rise was computed. The rea-son is that the values of the maximum rate of pressure risewere selected as the measure of cyclic variation (the ‘effect’)in the combustion chamber. Thus, Fig. 12 presents all thesecorrelation coefficients, for the cases of the neat diesel fueland the 15% addition of ethanol in the blend, as a functionof load. It can be observed that there is a minimal to slightcorrelation of these parameters, with the exception, asexpected, of the rather strong (positive) correlationbetween the maximum cylinder pressure and the maximumcylinder rate of pressure rise that seems to be decreasingwith load.


The result of the analysis is that neither the injectionprocess (through the dynamic injection timing), in contrastto the findings of Wing [63] for a special rotary type fuelpump used, nor the kind of fuels used (through their cetanenumbers) have any practical effect on the above cyclic vari-ations, with the latter one being in accordance with thefindings of Sczomak and Henein [62] for the low contentsof ethanol in the blends.

10. Conclusions

An extended experimental study is conducted to evalu-ate and compare the use of ethanol as supplement to theconventional diesel fuel at blend ratios (by vol) of 5/95,10/90 and 15/85 in a high-speed, direct injection dieselengine located at the authors’ laboratory. The series of testsare conducted using each of the above fuel blends, with theengine working at a speed of 2000 rpm and at four engineloads.

The work concerned the statistical analysis of the cycle-by-cycle variation of measured engine combustion param-eters. The analysis was carried out on a specially developedmeasuring assembly consisting of piezoelectric transducers,charge amplifiers and a very fast data acquisition boardinstalled on an IBM compatible microcomputer.

Heat release analysis results for the relevant combustionmechanism, combined with the widely differing physicaland chemical properties of the ethanol against the onesfor the diesel fuel, were used to aid the correct interpreta-tion of the observed engine behavior. It is revealed thatwith the use of ethanol blends instead of neat diesel fuel,the ignition delay is increased, fuel injection pressure dia-grams are slightly displaced (delayed), maximum pressurerates increase and maximum cylinder pressures are hardlyaffected.

The acquired data of 480 successive cylinder pressurecycles, for each engine operating condition and fueltested, were statistically analyzed and shown in this paperfor the maximum rate of pressure rise, the dynamic injec-tion timing and the ignition delay, where the measuredpressure signal before the injector was used for computingthe injection process parameters. The cycle-by-cycle varia-tion is expressed as the mean and standard deviation ofthese parameters. The analysis of probability density,auto-correlation and power spectral density functions ofthe various parameters, reveal the randomness (stochasticnature) of the fluctuation phenomena observed in the die-sel engine.

The important conclusion is drawn from the analysis ofthe pressure in the fuel pipeline in relation to the ignitiondelay that the fuel pump system has no influence on thecyclic pressure variations. The same holds true for theinfluence of the kind of fuels used (with different cetanenumbers), at least for the low contents (up to 15%) of eth-anol in its blends with the diesel fuel, thus ensuring that thiswill not be a cause of any degraded performance or emis-sion characteristics.

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Experimental-stochastic investigation of the combustion cyclic variability in HSDI diesel engine using ethanol–diesel fuel blends