A Method to Determine Ignition Delay Times for Diesel Surrogate Fuels From

1

2

3

4 Q1

5

67

9101112131415

16

1 8

1920212223

24252627282930

3 1

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Q2

Fuel xxx (2012) xxx–xxx

JFUE 6301 No. of Pages 10, Model 5G

1 August 2012

Contents lists available at SciVerse ScienceDirect

Fuel

journal homepage: www.elsevier .com/locate / fuel

A method to determine ignition delay times for Diesel surrogate fuels fromcombustion in a constant volume bomb: Inverse Livengood–Wu method

M. Reyes ⇑, F.V. Tinaut, C. Andrés, A. PérezDepartment of Energy and Fluid Mechanics Engineering, University of Valladolid, Paseo del Cauce s/n, E-47011 Valladolid, Spain

h i g h l i g h t s

" We present a methodology to obtain ignition delay times." A combustion bomb with homogeneous mixtures has been used." The methodology presented increases the usability of the combustion bombs." Here are provided set of data valuable for the validation of kinetic mechanism.

323334353637383940414243

a r t i c l e i n f o

Article history:Received 16 March 2011Received in revised form 13 July 2012Accepted 16 July 2012Available online xxxx

Keywords:Auto-ignition timeIgnition delayDiesel surrogateChemiluminescenceLivengood–Wu method

0016-2361/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.fuel.2012.07.041

⇑ Corresponding author. Tel.: +34 983184411.E-mail address: [email protected] (M. Reyes

Please cite this article in press as: Reyes M et avolume bomb: Inverse Livengood–Wu method.

a b s t r a c t

In this work a method to determine the ignition delay of Diesel surrogate fuels using data from a constantvolume combustion bomb is presented. The studied fuels are n-heptane (a common PRF) and a mixture of50% of n-heptane and 50% of toluene (in mass) because both fuels have been proposed as Diesel fuel sur-rogates under HCCI. There are different concepts of spontaneous ignition times in engines or otherdevices. Auto-ignition times are experimentally obtained in a constant volume combustion bomb or incompression ignition engines, for variable conditions of pressure and temperature. In this work theyare obtained in a combustion bomb using four different criteria (pressure, mechanical vibrations, OH�

and CH� chemiluminescence emissions). The paper describes an original approach based on an inverseLivengood–Wu method to obtain the ignition delays (as a function of pressure and temperature) fromthe auto-ignition times. The obtained expressions for the fuels and their mixtures are compared withthose of other authors with a reasonable agreement.

� 2012 Elsevier Ltd. All rights reserved.

44

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

1. Introduction

In order to reduce the dependence on fossil fuels, improve en-gine performance, and reduce the exhaust emissions in Diesel en-gines, there are several research lines. One of them is the study ofnew combustion concepts, such as the homogeneous charge com-pression ignition of mixtures (HCCI) [1]. However, one of the prob-lems of the HCCI combustion is to control the onset of the auto-ignition and the further combustion development [2]. Therefore,it is important to determine the dependence of the ignition delayon pressure and temperature for new fuels in order to be able topredict the start of combustion.

The ignition delay s(T,p) of a fuel/air mixture at a given pressureand temperature is the time interval at the end of which the mixturespontaneously auto-ignites. Not all fuels and fuel/air mixturesexperiment such behaviour since it is characteristic for radical-

77

78

79

80

ll rights reserved.

).

l. A method to determine ignitFuel (2012), http://dx.doi.org/1

chain explosions, and in addition pressure and temperature mustbe high enough. Due to the thermodynamic conditions, some chem-ical reactions in the fuel/air mixture generate chemical intermedi-ate compounds. Once the intermediate chemical compoundsreach a critical concentration, the fuel/air mixture auto-ignites [3,4].

In the context of this paper, we reserve the term ignition delay tothe cases in which pressure and temperature are constant. In manydevices, such as compression-ignition engines, pressure and tem-perature vary prior to ignition, and in that situation we call ofauto-ignition time. A more detailed discussion on these terms isshown later.

Ignition delay can be determined in a rapid compression ma-chine (RCM) [5], in a shock tube (ST) or in a combustion bomb(with injector) in which fuel is introduced in a hot, high pressureoxidizer. In all these devices pressure and temperature are con-stant during the ignition delay which ends with the ignition andfurther combustion of the fuel/air mixture.

There are several criteria to determine the fuel auto-ignition.One criterion is based on the detection of the chemiluminescenceproduced inside the combustion chamber. During the ignition de-

ion delay times for Diesel surrogate fuels from combustion in a constant0.1016/j.fuel.2012.07.041

http://dx.doi.org/10.1016/j.fuel.2012.07.041

mailto:[email protected]


http://www.sciencedirect.com/science/journal/00162361

http://www.elsevier.com/locate/fuel


81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

Nomenclature

A parameter of the ignition delay correlationCVCB constant volume combustion bombEa activation energy (J/mol)Fr fuel/air equivalence ratioFWHM full width at half maximumHCCI homogeneous charge compression ignitionIC intermediate compoundsn pressure exponent in the ignition delay correlationNTC negative temperature coefficientp pressure (MPa)PMT photomultiplierPRF primary reference fuelR gas constant (8.314 J/mol K)RCM rapid compression machineST shock tubeT temperature (K)TDC top dead centretb auto-ignition time (in a CVCB)td auto-ignition delay (in Diesel engines)V volume

GreekF chemiluminescence emissions (nlm)aSa determined excited states standard deviationt ignition delay (in RCMs)

Subscriptsa airad adiabaticaut auto-ignitionb burnedf fuelmax maximumub unburned

Superscripts� excited radical

2 M. Reyes et al. / Fuel xxx (2012) xxx–xxx


1 August 2012

lay, the detected chemiluminescence is zero, because inside thecombustion chamber the occurring reactions taking place do notsignificantly emit radiation, while the auto-ignition event providesa high rate of heat and radiation. Several authors have usedthe chemiluminescence emissions to determine the beginning ofthe auto-ignition process. For example, Sirjean et al. [6] used thechemiluminescence of the OH� radical to determine the beginningof the ignition process for different fuels (cyclopentane and cyclo-hexane) in a shock tube. He et al. [7] studied the iso-octane auto-ignition process in a RCM through the detection of the OH� stimu-lated emission, previously excited with an external laser. Theirmain objective was to determine the beginning of the combustionby auto-ignition. The ignition delay was calculated by two differentcriteria: The first, when the OH� radicals reach their maximum va-lue; and the second, when the pressure curve reaches its maximumslope. They compared both criteria and obtained a good agreement.

Other authors have determined ignition delays in shock tubesalso by means of chemiluminescence emissions. Noguchi et al.[8] showed how the maximum of the CH� chemiluminescencewas a good indicator of the onset of the auto-ignition process. Inthe work developed by Fieweger et al. [9] they used the maximumchemiluminescence of the OH� radical to determine the beginningof the auto-ignition process. Zhukow et al. [10] used the maximumOH� chemiluminescence to calculate the timing of the auto-igni-tion process, in this case using n-pentane.

Augusta et al. [1], in a study made in an engine running in HCCI-mode fuelled with iso-octane, showed that the chemiluminescenceemissions start to be detected at the auto-ignition onset. In thework developed by Corcione [11] in a direct injection Diesel enginethey demonstrate how the OH� radical was one of the main prod-ucts in the first thermal decomposition reactions of moleculeswhich precede the auto-ignition process. Kosaka et al. [12] studiedthe formaldehyde chemiluminescence in a Diesel engine, and con-cluded that this radical is mainly produced by the slow tempera-ture reactions that precede the high temperature reactions whichgive rise to the auto-ignition event.

Fuels such as those used in this work show a complex auto-ignition chemistry. Hydrocarbons with a short chain (as methane,benzene, etc.) are autoignited in only one step, however, longchain hydrocarbons (as paraffins, for example n-heptane, etc.)

Please cite this article in press as: Reyes M et al. A method to determine ignivolume bomb: Inverse Livengood–Wu method. Fuel (2012), http://dx.doi.org/1

are autoignited in two steps. This two-step mechanism originatesa characteristic dependence of ignition delay with temperature,with a cool flame region in which there is negative temperaturecoefficient (NTC) behaviour, resulting in an ignition curve withthe shape of an inverted S [13,14].

In a compression ignition engine (i.e. Diesel engine), the fuel isinjected during the compression stroke, and pressure and temper-ature are varying (increasing) during the time interval precedingauto-ignition. Then we call auto-ignition delay the time betweenthe fuel injection and the auto-ignition onset, td (in the literaturethis delay is commonly referred to as ignition delay [15], but it isbetter to distinguish it from the delay relevant when pressureand temperature are constant). In an HCCI-type engine the relevanttime leading to combustion start is again the auto-ignition delay,because the homogeneous mixture is obtained either with a veryearly injection or by injection in the intake manifold.

In a constant volume combustion bomb (CVCB), homogeneouscombustions can be easily achieved by filling the bomb with a mix-ture of oxidizers and a gaseous fuel. Initial conditions (i.e. pressure,temperature, and equivalence ratio) can be selected in order tocharacterize flame development and combustion speeds [16]. Inparallel with the normal combustion due to the flame front ad-vance, auto-ignition of the unburned fuel/air mixture may arise,since the heat released by combustion increases pressure and theunburned mixture compresses almost adiabatically. In certain con-ditions, if the normal combustion duration is longer than the auto-ignition delay, the unburned mixture ignites before is reached bythe flame. In these cases, the auto-ignition time, tb, can be definedas the time between the start of the premixed combustion, at cer-tain initial conditions, and the auto-ignition onset of the mixture.During the auto-ignition time the pressure and temperaturechange, due to the compression by the flame front propagation in-side the CVCB, as it would happen during the compression strokein a Diesel engine.

Livengood and Wu [17] developed a method to calculate theauto-ignition delay for varying pressures and temperatures (suchas in compression ignition engines and CVCB), once the ignition de-lay (s(T,p)) is known as a function of constant pressure and tem-perature, usually determined in RCMs. This method is based onthe consideration of the auto-ignition process in a simplified way,

tion delay times for Diesel surrogate fuels from combustion in a constant0.1016/j.fuel.2012.07.041


161

163163

164

165

166

167

168

169

170

171

172

173174

176176

177

178179

181181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

M. Reyes et al. / Fuel xxx (2012) xxx–xxx 3


1 August 2012

Reagentsðfuel and airÞ ! Intermediate Compounds

! Final Products ð1Þ

When the intermediate compounds, IC, reach a critical concen-tration the auto-ignition takes place. The Livengood–Wu methodconsiders that, when the pressure and temperature vary, the criti-cal concentration is reached by summing up the intermediate com-pounds formed at each particular condition of pressure andtemperature. Mathematically this requires the use of an integralextended to the thermodynamic conditions of the mixtures. Thisis expressed by Eq. (2), where the auto-ignition delay td is theupper limit of the integral of the inverse of the ignition delays(T,p) when the value of this integral is the unity.

Z td

0

dtsðT;pÞ ¼

Z td

0

dtAp�n exp Ea

RT

� � ¼ 1 ð2Þ

In Eq. (2), the ignition delay has been expressed as usually [15] interms of pressure and temperature:

sðT;pÞ ¼ Ap�n expEa

RT

� �ð3Þ

where Ea is the activation energy, R is the universal gas constant(8.314 J/mol K), A and n are parameters that are adjusted for eachfuel and equivalence ratio, and for the range of pressure and tem-perature conditions of the tests.

The Livengood–Wu method is thus based on the utilization ofonly one reaction rate for a global reaction, but the chemical reac-tions occurring are very numerous and complicated. For that rea-son this method does not consider the slow pre-reactions whichproduce the cool flames, nor the two-step ignition and the negativetemperature coefficient of some fuels. The main advantage of thismethod is its speed and that it works successfully for a determinedfuel at a given range of pressure and temperature, in which A, n andEa parameters are obtained with the ignition delay expression.

In this work a method to determine ignition delays of Diesel sur-rogate fuels is presented. The method makes use of experimentalresults of auto-ignition times obtained by inducing auto-ignitionin an unburned mixture in a spherical constant volume combus-tion bomb. This method can be considered as an inverse Liven-good–Wu method since it allows obtaining analytical expressionsof ignition delay (values of A, n and Ea in Eq. (3), for independentp and T) from auto-ignition times (varying p and T), such as de-picted in Fig. 1. The expressions of ignition delay can then be usedfor predicting auto-ignition delays in compression-ignition engineswith the direct Livengood–Wu method.

The structure of the work is as follows: First, the auto-ignitiontimes (tb) for several fuel/air mixtures are experimentally obtainedin a constant volume combustion bomb (CVCB) by using four dif-ferent criteria: OH� and CH� chemiluminescence signals, vibrations

τIgnition

(constant

tbAuto-ignition time

in the CVCB (varying p and T)

Inverse Livengood-Wu

Method

Method developed in this work

Fig. 1. General procedure used in this work to obtai

Please cite this article in press as: Reyes M et al. A method to determine ignitvolume bomb: Inverse Livengood–Wu method. Fuel (2012), http://dx.doi.org/1

inside the CVCB and pressure curve. These criteria will be ex-plained in more detail in the following sections. Next, the inverseLivengood–Wu method is explained. Finally this method is appliedto the auto-ignition time data to calculate analytical expressions ofignition delays. The studied fuels are n-heptane (a common PRF)and a mixture of n-heptane and toluene in 50% (in mass). Bothfuels have been proposed as Diesel fuel surrogates under HCCI con-ditions [18,19].

2. Experimental setup

2.1. Constant volume combustion bomb

The experimental setup used in this work consists of a test facil-ity designed for the study and characterization of the combustionprocess of gaseous and liquid fuels. The main components are aconstant volume combustion bomb (CVCB), a measurement systemand a rig for the introduction of fuels. In [16] a full description anda schematic of the complete equipment can be seen. The CVCB isa stainless steel spherical cavity of 0.2 m of diameter, with twooptical accesses to detect the chemiluminescence emitted by theexcited chemical radicals during the combustion process. One opti-cal access is radial pointing at the centre of the CVCB. The second ishorizontal and points to the outer region of the combustion cham-ber near the wall. A simplified sketch is shown in Fig. 2. The CVCBhas been designed to resist pressures of up to 40 MPa and temper-atures of up to 1073 K during the development of the combustion.There are two electrodes inside the CVCB to ignite the mixture andstart combustion at the geometric centre of the sphere.

Before the start of the combustion, the initial conditions of pres-sure, temperature and fuel/air ratio of the unburned mixture arefixed experimentally. Once combustion is started, a spherical flamefront is established. The increase of pressure due to heat releaseoriginates a temperature increase in the unburned mixture bycompression. The analysis of pressure by means of a two-zonecombustion model [20–22] allows obtaining the evolution ofburned and unburned temperatures and volumes, and so the flamefront position. In particular auto-ignition times can be calculatedfor the unburned mixture.

During normal combustion and especially when auto-ignitionhappens there are emissions of radiation associated to chemicalradicals (chemiluminescence). The cheluminescence of hydroxylradical results from the emission of light from electronically ex-cited hydroxyl radicals (OH�) with a wavelength near 307 nm[23–27]. Chemiluminescence of CH� is from excited state CH�

(CH(A2D)) produced primarily through the reaction of C2H withmolecular oxygen [24,28], with a wave length near 430 nm. Theexcited OH� and CH� lose their energy either through spontaneousfluorescence (chemiluminescence) or through physical quenching(collisions).

delay p and T)

tdAuto-ignition delay in a Diesel engine (varying p and T)

Engine-condition prediction

Livengood-Wu Method

n ignition delays from data obtained in a CVCB.



257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

Fig. 2. Sketch of the constant volume combustion bomb (CVCB).



1 August 2012

2.2. Measurement methodology

In the combustion facility, pressure, vibration and OH� and CH�

chemilumescence are directly measured during the combustionprocess. Two Hammamatsu 9536 photomultipliers (PMTs) areused for the detection of the chemiluminescence emitted by OH�

and CH� radicals at 306 nm and 430 nm, respectively. Radiationis collected through the optical access fused silica windows ofthe CVCB, a beam splitter and a group of pass-band optical filterscentred at the required wavelengths.

The time-resolved signals from the PMTs are recorded by a dataacquisition system which consists of a digital oscilloscope and acomputer for data collection. Much care is taken to shield all cablesand reduce the noise of the signals. In all results shown in this pa-per, OH� and CH� chemiluminescence signals were detectedthrough the horizontal optical access, placed at 85 mm above theCVCB centre.

Chemiluminescence is measured in lumens (lm or better nlm-10�9 lm), and the conversion factor is obtained with the correlationcurve of the PMTs as a function of the input voltage.

A piezoelectric pressure transducer (Kistler type 7063) locatedat the wall of the CVCB registers the pressure in the chamber dur-ing combustion.

The vibrations of the wall of the CVCB are acquired with a pie-zoelectric accelerometer type PZ 23 (Brüel & Kjaer model 4382)placed on the top surface of the CVCB. The temperature, burningvelocity, burned mass fraction and other parameters during thecombustion are obtained by using the two zone analysis model ex-plained above. More details of the experimental installation andmeasurement methodology can be seen in [16].

316

317Q3

318

319

2.3. Experimental procedure to fix test conditions

Once the spark plug starts the combustion, a conventional pre-mixed combustion takes place inside the CVCB. The flame front

320

321

322

323

324

325

326

327

328

329

330

331

332

333

200

400

600

800

1000

0 2 4 6 8 10 12 14

p (MPa)

T (K

) CVCB

DieselCVCB ∩ Diesel

Fig. 3. Conditions of pressure and temperature of the unburned mixture reachedinside the CVCB, compared with those in a Diesel engine at the end of thecompression stroke.


propagates spherically across the combustion chamber increasingpressure and temperature in the chamber, and consequently alsoin the unburned fuel/air mixture. In a given experiment, the depen-dence of temperature with pressure is approximately adiabatic(curved lines in Fig. 3). As the pressure and temperature increaseenough as a consequence of combustion development, this maycause auto-ignition of the still unburned mixture ahead of theflame front, in the outer regions of the combustion bomb. Withthe combustion-induced compression it is possible to reach thepressure and temperature conditions in the unburned mixturesimilar to those of in a Diesel engine at the end of the piston com-pression, as shown in Fig. 3, where the some adiabatic tempera-ture–pressure lines (evolution) are plotted for different initialconditions. Then if the final unburned mixture temperature andpressure are high enough to auto-ignite the mixture, this methodis a good way to reproduce and study the combustion of fuels un-der HCCI-type conditions.

Examples of the temporal evolution of the pressure, vibrations,OH� and CH� chemiluminescence curves obtained in combustionswith auto-ignition can be seen in Fig. 4, for n-heptane with 1.1fuel/air equivalence ratio, 0.8 MPa initial pressure and 413 K initialtemperature. The four recorded signals can be used to determinethe auto-ignition onset, as described in the following paragraph.

3. Auto-ignition time

3.1. Procedure for the determination of the auto-ignition time

In the CVCB, the auto-ignition time, tb, has been defined as thetime between the start of the premixed combustion and the auto-ignition onset and can be determined using four different criteria.

3.1.1. PressureThe first criterion is based on the observation of the pressure

curve because the auto-ignition causes a sudden increment onthe pressure curve slope due to the heat released. Then, with thiscriterion the auto-ignition event occurs when the pressure curvereaches its maximum slope, see Fig. 4i.

3.1.2. Mechanical vibrationsThe second criterion is based on the detection of the mechanical

vibrations produced in the CVCB structure due to auto-ignition.Mechanical vibrations increase several orders of magnitude whenthe auto-ignition takes place (Fig. 4ii). According to this criterionthe auto-ignition occurs when the maximum increment of themechanical vibrations is reached.

3.1.3. OH� chemiluminescenceThe third criterion is based on the chemiluminescence emitted

by the OH� radical (at 307 nm) when the auto-ignition takes place.With this criterion, the auto-ignition begins when the OH� chemi-



334

335

336

337

338

339

340

341

342

343

344

(ii) Mechanical vibrations(i) Pressure

(iii) OH* chemiluminescence (iv) CH* chemiluminescence

Autoignition

Autoignition Autoignition

Autoignition

t

t

tt

b

b

b

b

Fig. 4. Examples of auto-ignition curves obtained in a CVCB induced by the combustion of n-heptane with pi = 0.8 MPa, Ti = 413 K and fuel/air equivalence ratio = 1.1.



1 August 2012

luminescence emissions reach their maximum value, see Fig. 4iii.Notice that the chemiluminescence signal plot can be divided intotwo different parts: combustion (during tb) and postcombustion, inwhich CO is oxidized to CO2. For more details see [16].

345

346

347

348

349

350

3.1.4. CH� chemiluminescenceThe fourth criterion used is based on the chemiluminescence of

the CH� radical at 430 nm. The auto-ignition time is defined by the

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

0

1

2

3

4

5

0 0.02 0.04 0.06 0.08 0.1t (s)

p(M

Pa),

Acel

. (a.

u.)

0

0.5

1

1.5

2

2.5

3

3.5

FC

H* a

nd 1

0FO

H*(n

lm)tpres = 36.40 ms

tOH* = 36.19 ms

tCH* = 36.39 ms

tacel = 36.43 ms

pressure mechanical vibrations

OH* radicals CH* radicals

Fig. 5. Values of the auto-ignition time obtained with the four criteria for astoichiometric combustion of n-heptane with an initial pressure of 0.6 MPa and aninitial temperature of 473 K.


maximum value of the CH� chemiluminescence curve in the com-bustion zone, where the auto-ignition takes place (Fig. 4iv).

The auto-ignition times determined with pressure and mechan-ical vibrations are quite similar, since the mechanical vibrationsdetected by the accelerometer are the result of the propagationthrough the walls of the CVCB of the pressure waves generatedby the auto-ignition, see Fig. 5.

The auto-ignition times determined with the OH� and CH�

chemiluminescent emissions show the same trends as the valuesobtained with pressure and mechanical vibrations. However, it ispossible to observe a difference between them: the auto-ignitiontime obtained with the OH� radical is slightly less than the auto-ignition time determined with the CH� radical, i.e. the maximumof both emissions during the combustion process are not producedat the same time.

Due to the similarity between the auto-ignition times deter-mined by the three first criteria, the three of them would be ade-quate to calculate the ignition delays with the inverse method ofLivengood–Wu. In the present work auto-ignition times deter-mined with the pressure criterion have been used.

3.2. Method for the calculation of the ignition delay from the auto-ignition time data: the inverse Livengood–Wu method

Here, we propose a method to determine expressions for theignition delay of Diesel fuel surrogates from data obtained of theauto-ignition time experimentally obtained in a CVCB. In generalthe method can be used if auto-ignition times can be determined



367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385 Q4

386

387

389389

390

391

392

393

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

447447

448



1 August 2012

in other devices in which pressure and temperature of the fuel/airmixture vary during the leading to auto-ignition. In particular eventhe data acquired in running Diesel engines can be processed to ob-tain an expression of the ignition delay.

The Livengood–Wu method is used to calculate auto-ignitiondelays (with varying pressure and temperature) once an expres-sion of the ignition delay as a function of pressure and temperatureis known (Eq. (3)).

This method can be applied in an inverse way to process theauto-ignition data obtained for the CVCB or a Diesel engine, whereauto-ignition times for the variable conditions of pressure andtemperature are registered, in order to derive an analytical expres-sion for the ignition delay. The parameters to be determined are A,n and Ea from the Arrhenius expression of the ignition delay, seeEq. (3).

The integral of the inverse of the ignition delay (Eq. (2)) can bediscretized as the summation for all time intervals during whichthe pressure is registered, taking into consideration the tempera-tures of the unburned zone calculated with the two-zone diagnosismodel,

1 �Xtb

0

Dts¼Xtb

0

Dt

A0p�n0 exp E0aRT

� � ð4Þ

To apply the inverse Livengood–Wu method, for a given auto-ignition experiment tb is known. An initial set of guess values forA0, n0 and E0a must be introduced in Eq. (4) to start calculation. Aniterative Newton method is used to obtain (by applying minimalsquare techniques) the values of parameters A, n and Ea which min-imize the error when Eq. (4) is applied for all the auto-ignitionexperiments considered. Since there are three unknown parame-ters, at least three experimental data series (pressure, temperatureand auto-ignition time for a fuel at a given fuel/air equivalence ra-tio) are necessary to solve the system, but to reduce the error of theestimation in the iterative process at least ten experiments it isnecessary to introduce.

449

450

451

452

453

454

455

456

457

458

459

460

461

462

4. Results and discussion

4.1. Design of experiments

A D-optimal design of experiments of third order has been uti-lized to combine the n-heptane initial combustion conditions (ini-tial pressure and temperature), under auto-ignition conditions, fortwo different equivalence ratios of 1 and 0.9. This design proposesto carry out eighteen experiments for the auto-ignition of stoichi-ometric n-heptane and 17 for an equivalence ratio of 0.9. The de-tailed initial conditions of pressure and temperature of theexperiments carried out can be found in [16]. The range of pressureand temperature during auto-ignition time is detailed in the fol-lowing paragraphs.

Table 1Values of parameters A, n and Ea of Eq. (2) for the ignition delay of stoichiometric n-heptane, as a function of the number of experiments considered in the iterativemethod.

Number of experiments considered A (10�6) n Ea/R

12 33.58 0.270 �85513 32.85 0.271 �75114 32.94 0.270 �76715 30.46 0.276 �38516 33.46 0.283 �80217 34.30 0.253 �111618 3.27 0.242 10202


4.2. Ignition delay of n-heptane with fuel/air equivalence ratios 0.9and 1

4.2.1. n-Heptane in stoichiometric mixtureTable 1 shows the values of parameters A, n and Ea obtained by

the iterative method as a function of the number of experimentsconsidered, in all cases combustion processes of n-heptane stoichi-ometric mixtures with slightly different initial conditions of pres-sure and temperature, as defined by the design of experiments.In all the sets of values an exponential dependence with the in-verse of absolute temperature is observed, in most cases with anegative activation energy while a positive one is observed in thelast experimental condition. In addition, a negative value of param-eter n means a direct dependence with pressure (see Eq. (3)). Theerror of estimation is reduced as the number of experiments con-sidered is increased. Much care was paid to test the robustnessof the method, by changing the values of the initial set of valuesof A, n and Ea needed to initiate the iterative method and also bychanging the order in which the experimental values are consid-ered when the number is less than the maximum (18). When eigh-teen experiments are considered the error of estimation is 2.17%.

The values of the ignition delay obtained by considering a dif-ferent number of experiments are plotted in Fig. 6 against the in-verse of mixture temperature and for different pressures.

For all the pressures considered there are two tendencies, onewhen the number of experiments is less than 18 and other when18 experiments are considered. The expression obtained for 18experiments reproduces the tendency of the activation energy.For that reason the resulting expression obtained for 18 experi-ments, which groups all the information obtained in the experi-ments, is proposed for the ignition delay of stoichiometric n-heptane,

sn-heptaneðFr ¼ 1Þ ¼ 3:27 � 10�6 � p�0:242 exp10202

RT

� �ð5Þ

where the ignition delay time results in seconds, pressure p is in MPa,temperature T is in K and the apparent activation energy Ea is in J/mol,for the range of temperature and pressure determined by the exper-imental design (323 K < T < 850 K and 0.6 MPa < p < 12.0 MPa).

To see in more detail the influence of temperature and pressurein Eq. (5), the ignition delay is plotted in Fig. 7 versus the inverse oftemperature for different pressures in the range of interest.

463

464

466466

467

468

469

470

471

472

473

474

4.2.1.1. n-Heptane with a 0.9 equivalence ratio. The values of param-eters A, n and Ea for the auto-ignition of n-heptane with a fuel/airequivalence ratio of 0.9 are shown in Table 2, when 17 experimentsare considered in the iterative procedure. For other number ofexperiments the model does not converge. In this table it is possi-ble to observe a negative dependence with pressure and an expo-nential dependence with the inverse of temperature. The value ofthe activation energy is coherent with results show by otherauthors [15]. The error of estimation is 5.12%.

sn-heptaneðFr ¼ 0:9Þ ¼ 10:26 � 10�6 � p�0:439 � exp7474

RT

� �ð6Þ

where the pressure is in MPa, the temperature in K and the activa-tion energy in J/mol.

The range of validity for this correlation is determined by theexperimental design, i.e. 323 K < T < 850 K and 0.8 MPa < p< 12.0 MPa.

The evolution of the ignition delay given by Eq. (6) is repre-sented In Fig. 8 as a function of the temperature for differentpressures.



475

476

477

478

479

480

481

482

483

484

485

486

487

488

489

490

491

492

493

494

495

496

497

498

499

500

501

502

503

504

505

506

507

508

509

510

511

512

513

514

515

516Q5

aPM5.0=p)ii(aPM1.0=p)i(

aPM0.5=p)vi(aPM0.2=p)iii(

Fig. 6. Values of stoichiometric n-heptane ignition delay calculated by considering different number of experiments, as described in Table 1.

Fig. 7. Dependence of the ignition delay of stoichiometric n-heptane (Eq. (5)) withtemperature for different pressures.

Table 2Values of parameters A, n and Ea of Eq. (2) for the ignition delay of n-heptane with a0.9 fuel/air equivalence ratio, when 17 experiments are considered in the iterativemethod.

Number of experiments considered A (10�6) n Ea/R

17 10.26 0.439 7474

0

0.1

0.2

0.3

0.4

0.5

0.6

0.5 1 1.5 2 2.5 3 3.5

1000/T(K)

t(s)

0.1 MPa0.2 MPa0.5 MPa1.0 MPa1.5 MPa2.0 MPa5.0 MPa

Fig. 8. Dependence of the ignition delay of n-heptane for a 0.9 fuel/air equivalenceratio with temperature for different pressures.

1 For interpretation of colour in Figs. 5–12, the reader is referred to the web versionof this article.



1 August 2012

4.2.1.2. Comparison with results obtained by other authors. In thissection a comparison with expressions determined by other authorsis presented, once expressions for the ignition delay of n-heptane


have been calculated. Only it is possible to make the comparisonwith results for stoichiometric fuel/air equivalence ratio, becausein the literature there are no results for other equivalence ratios [29].

The maximum temperature reached in the CVCB is around850 K, in the unburned zone, for this reason, the obtained correla-tion is only valid until that temperature. This zone is the low andintermediate temperature zone. To study other intervals of tem-perature higher than 850 K it is necessary to use other experimen-tal installations (as can be the RCM until 1000 K and shock tubes,to reach more than 1000 K) or theoretical programs. Experimentaldata found in the literature are obtained, mainly, in shock tubes, sothat, the direct comparison with present results is complicated.However, with kinetics models it is possible to simulate the inter-val of temperatures reached with the CVCB.

In Fig. 9 the correlation obtained for the ignition delay of stoi-chiometric n-heptane (Eq. (7)) and the correlations obtained byother authors at low pressures (0.1, 0.7 and 0.9 MPa) are repre-sented. In Fig. 9i it is represented the present correlation withthe obtained by Peters et al. [30], Law [31] and Guerrassi [32]. Pe-ters et al. obtained this correlation with a kinetics model whichconsiders a mechanism of 56 reactions for the auto-ignition of n-heptane, and they obtained the negative temperature coefficient(denoted as NTC in the figure) between 700 and 850 K of temper-ature. Law also used a kinetics mechanism of 56 reactions for thestoichiometric n-heptane and they obtained a curve with the sameshape and the NTC behaviour. However, with the difference that inthis case the NTC starts at 650 K of temperature.

The correlation obtained in this work is a straight line (when isplotted against the inverse of temperature) because it is the resultof the simplification of the auto-ignition process in only one step,considering that the ignition delay is only an Arrhenius functionof the temperature, and for this reason this correlation does notreproduce the NTC behaviour of the n-heptane fuel. However, thepresent correlation reproduces the tendency in the interval of tem-peratures before the NTC. Guerrassi determined a correlation forthe Diesel fuel, similar to the present correlation, and it is easy toobserve the similitude between both curves in Fig. 9i.

In Fig. 9ii it is compared the present correlation with the ob-tained by Griffiths et al. [33] in a RCM (green1 curve), with a kinet-



517

518

519

520

521

522

523

524

525

526

527

528

529

530

531

532

533

534

535

536

537

538

539

540

(i) n-heptane, Fr = 1, p = 0.1 MPa

(ii) n-heptane, Fr = 1, p = 0.7 MPa

(iii) n-heptane, Fr = 1, p = 0.9 MPa

1000/T (K)

1000/T (K)

1000/T (K)

Fig. 9. Correlations for the ignition delays of stoichiometric n-heptane at highpressures and comparison with results obtained by Peters et al. [30], Law [31],Guerrassi cited in [32] and Griffiths et al. [33].

(i) n-heptane, Fr = 1, p = 1.35 MPa

(ii) n-heptane, Fr = 1, p = 4.2 MPa

1000/T (K)

1000/T (K)

Fig. 10. Correlations of the ignition delay for stoichiometric n-heptane at highpressures and comparison with results obtained by Peters et al. [30], Ciezki andAdomeit [34], Guerrassi [32], Zheng [35] and Curran et al. [38].

(i) p = 4.2 MPa

(ii) p = 1.35 MPa.

(K)

(K)

(ms)

(ms)

Fig. 11. Comparison between ignition delay correlations of n-heptane, a mixture of50% of n-heptane and 50% of toluene and a mixture of 65% n-heptane and 35% oftoluene (Herzler et al. [36]), at stoichiometric equivalence ratio and differentpressures.



1 August 2012

ics model and by Guerrassi at 0.7 MPa of pressure. In this figure it ispossible to appreciate that the present correlation is inside therange, but without being able to reproduce the NTC behaviour.The same happens in Fig. 9iii, where the same correlations for apressure of 0.9 MPa are plotted.

Then, at low pressures the correlation obtained in the presentwork reproduces the tendency of the ignition delay when it is com-pared with the ignition delays obtained by other authors. Whenthe present correlation is compared with the Guerrassi correlation,that has a similar form and it is based on the same approximations,it is obtained a good agreement for all the pressures considered.

In Fig. 10 are compared the ignition delays obtained in the pres-ent work with the obtained by Peters et al. [30], by Ciezki and Ado-meit [34], by Zheng [35], by Curran et al. [38] and by Guerrassicited in [32] at high pressures. In the first subfigure, Fig. 10i theignition delays at 1.35 MPa are represented. Zheng obtain this datain a shock tube, Peters and Curran with a kinetics model and Ciezkiet al. in a RCM. In this case the present correlation reproduces therange experimentally obtained by the other authors, and it is quitesimilar to the Guerrassi correlation, as it happened with lowerpressures. In Fig. 10ii it is represented a comparison with the cor-relation of Peters, Curran and Guerrassi at very high pressures of4.2 MPa, and the trends are similar to the obtained at 1.35 MPa.


4.2.1.3. Comparison with other fuels. In this section a comparison



541

542

543

544

545

546

547

548549

551551

552

553

554

555

556

557

558

559

560

561

562

563

564

565

566

567

568

569

570

571

572

573

574

575

576

577

578

579

580

581

582

583

584

585

586

587

588

589

590

591

592

593

594

595

596

597

598

599

600

601

602

603

604

605

606

607

608

609610611612613614615616617618619620621622623624625

Fig. 12. Comparison of the ignition delays of different mixtures of n-heptane andtoluene fuels.



1 August 2012

between the ignition delay correlation obtained with data from theCVCB with a fuel composed by a mixture of 50% of n-heptane and50% of toluene, see [18] and Eq. (11) (where the pressure is in MPa,the temperature is in K and the activation energy in J/mol), withthe correlation obtained by Herzler et al. [36] for a mixture of65% of n-heptane and 35% of toluene, see Fig. 11, where two figuresare plotted, the first for a pressure of 4.2 MPa and the second for apressure of 1.35 MPa.

sð50% n-heptane=50% tolueneÞ

¼ 18:90 � 10�3 � p0:309 � exp2644

RT

� �ð7Þ

In the corresponding figure, Fig. 11, the ignition delay of n-hep-tane 100% is the minimum, although ignition delays of the twomixtures considered are quite similar. With the increment of thepressure the tendencies are the same, and as the percentage of tol-uene increases in the mixture also increases the ignition delay.

Finally, in Fig. 12 are introduced a correlation for the ignitiondelay of a mixture of 50% of n-heptane and 50% of toluene calcu-lated by Hernández et al. [37]. The ignition delay predicted by Her-nández et al. for intermediate temperatures is lower than thepredicted by the present work for the same fuel mixture. Their va-lue is quite similar to the obtained in this work for 100% n-heptane.

626627628629630631632633634635636637638639640641642643644645646647648649650651652653654655656657658659660

5. Conclusions

In this work a method to determine ignition delays from exper-imental data obtained in a combustion bomb has been developed.

A distinction has been established between the ignition delay inthe cases in which pressure and temperature are constant duringthe induction period, and the auto-ignition time, characteristic ofsituations in which pressure and temperature vary prior to ignitiononset (such as Diesel engines).

Auto-ignition times for mixtures of air and n-heptane stoichi-ometric and 0.9 equivalence ratio are obtained in a constant vol-ume combustion bomb. Four different criteria for auto-ignitiononset have been used: pressure rise, mechanical vibrations, andOH� and CH� chemiluminescence emissions. The four criteria showsimilar results for the auto-ignition time.

A so-called inverse Livengood–Wu method has been developed inorder to obtain analytical expressions of ignition delays from theauto-ignition time experimental results. This method is a powerfultool to transform experimental auto-ignition results obtained fromnon-constant pressure and temperature conditions into more use-ful ignition delay expressions as explicit functions of constant pres-sure and temperature.

As an example of the results, three analytical expression of theignition delay have been obtained: stoichiometric n-heptane, 0.9equivalence ratio n-heptane and a stoichiometric mixture of 50%


of n-heptane and 50% of toluene (in mass). As expected, the addi-tion of toluene to n-heptane decreases the auto-ignition tendency.

The expressions obtained for the ignition delays reproduce thetrends of the correlations obtained by other authors in the pressure(0.6–12.0 MPa) (323–850 K) and temperature ranges of validity ofthe author’s expressions.

The methodology presented has shown its potential to provideignition delay data at so-called low temperature conditions forauto-ignition phenomena. However, due to the occurrence of theNTC region (intermediate temperatures), the ignition delay corre-lation for the studied fuels cannot be extended to that region justas the single Arrhenius expression used in the paper. A more com-plex methodology (involving more complex ignition delay correla-tions) should be developed for the study of the intermediatetemperatures region.

Acknowledgements

The authors of this paper would like to thank the Spanish Min-istry of Science and Innovation for the financial support of this re-search through the Project TRA2007-67961-C03/AUT and theRegional Government of Castilla y León through the funding forthe GR 203 Excellence Research Group.

References

[1] Augusta R, Foster DE, Ghandhi JB, Eng J, Najt PM. Chemiluminescencemeasurements of homogeneous charge compression ignition (HCCI)combustion. SAE Technical Paper; 2006 [2006-01-1520].

[2] Hultqvist A, Christensen M, Johansson B, Franke A, Richter M, Aldén M. A studyof the homogeneous charge compression ignition combustion process bychemiluminescence imaging. SAE technical paper; 1999 [1999-01-3680].

[3] Williams FA. Combustion theory. The Benjamin/Cummings PublishingCompany; 1985.

[4] Kuo KK. Principles of combustion. John Wiley & Sons; 2001.[5] Tanaka K, Endo H, Imamichi A, Oda Y, Takeda Y, Shimada T. Study of

homogeneous charge compression ignition using a rapid compressionmachine. SAE technical paper; 2001 [2001-01-1033].

[6] Sirjean B, Buda F, Hakka H, Glaude PA, Fournet R, Warth V, et al. Theautoignition of cyclopentane and cyclohexane in a shock tube. Proc CombustIns 2007;31:277–84.

[7] He X, Zigler BT, Walton SM, Wooldridge MS, Atreya A. A rapid compressionfacility study of OH time histories during iso-octane ignition. Combust Flame2006;145:552–70.

[8] Noguchi M, Tanaka Y, Tanaka T, Takeuchi Y. A study on gasoline engine-combustion by observation of intermediate products during combustion. SAEtechnical paper; 1979 [790840].

[9] Fieweger K, Blumenthal R, Adomeit G. Self-ignition of S.I. engine model fuels: ashock tube investigation at high pressure. Combust Flame 1997;109:599–619.

[10] Zhukov VP, Sechenov VA, Starikovskii A. Self-ignition of a lean mixture of n-pentane and air over a wide range of pressures. Combust Flame2004;140:196–203.

[11] Corcione FE, Costa M, Vaglieco BM, De Maio A. The role of radical species indiesel engine auto-ignition detection. SAE technical paper; 2001 [2001-01-1003].

[12] Kosaka H, Drewes VH, Catalfamo L, Aradi AA, Lida N, Kamimoto T. Two-dimensional imaging of formaldehyde formed during the ignition process of adiesel fuel spray. SAE technical paper; 2000 [2000-01-0236].

[13] Griffiths JF, Barnard JA. Flame and combustion. Blackie Academic &Professional; 1995 [an imprint of Chapman & Hall].

[14] Lewis B, von Elbe G. Combustions, flames and explosions of gases. AcademicPress, Inc., London Ltd.; 1961.

[15] Heywood JB. Internal combustion engine fundamentals. McGraw Hill; 1988.[16] Tinaut FV, Reyes M, Giménez B, Pastor JV. Measurements of OH� and CH�

chemiluminescence in premixed flames in a constant volume combustionbomb under autoignition conditions. Energy Fuels 2011;1(25):119–29.

[17] Livengood JC, Wu PC. Correlation of autoignition phenomena in internalcombustion engines and rapid compression machines. In: Proceedings of thefifth international, symposium on combustion; 1955. p. 347–56.

[18] Hernandez JJ, Sanz-Argent J, Benajes J, Molina S. Selection of a diesel fuelsurrogate for the prediction of auto-ignition under HCCI engine conditions.Fuel 2008;87(6):655–65.

[19] Tinaut FV, Reyes M, Iglesias D, Lafuente A. Characterization of HCCI-typecombustion in a constant volume combustion bomb. In: 1st Meeting of theSpanish section of the combustion institute, León, Spain; 2007.

[20] Horrillo A. Utilization of multi-zone models for the prediction of the pollutantemissions in the exhaust process in spark ignition engines. PhD thesis,University of Valladolid; 1998 [in Spanish].



661662663664665666667668669670671672673674675676677678679680681682683684685

686687688689690691692693694695696697698699700701702703704705706707708709

710



1 August 2012

[21] Reyes M. Characterization of the combustion and auto-ignition processes ofliquid fuels in homogeneous mixtures for using in internal combustionengines running in HCCI mode. PhD thesis, University of Valladolid; 2008 [inSpanish].

[22] Tinaut FV, Melgar A, Horrillo AF. Utilization of a quasi-dimensional model forpredicting pollutant emissions in SI engines. SAE technical paper; 1999 [1999-01-0223].

[23] Gaydon AG. The spectroscopy of flames. London: Chapman and Hall; 1974.[24] Najm HN, Paul PH, Mueller CJ, Wyckoff PS. On the adequacy of certain

experimental observables as measurements of flame burning rate. CombustFlame 1998;113:312–32.

[25] Krishnamachari SLNG, Broida HP. Effect of molecular oxygen on the emissionspectra of atomic oxygen–acetylene flames. J Chem Phys 1961;34(5):1709–11.

[26] Becker KH, Kley D. The formation of CH radicals in hydrocarbon atom flames.Chem Phys Lett 1969;4(2):62–4.

[27] Lee SW, Tananka D, Daisho Y. Two-dimensional laser induced fluorescencemeasurement of spray and OH radicals of LPG in constant volume chamber.JSAE 2002;23:195–203.

[28] Devriendt K, Van Look H, Ceursters H, Peeters J. Kinetics of formation ofchemiluminescent CH(A2D) by the elementary reactions of C2H(X2S+) withO(3P) and O2ðX3S�g Þ: a pulse laser photolysis study. Chem Phys Lett1996;261(4–5):450–6.

[29] Tinaut FV, Reyes M, Melgar A. Characterization of n-heptane autoignition in acombustion bomb. In: 2nd Meeting of the Spanish section of the combustioninstitute, Valencia-Spain; 2008.


[30] Peters N, Paczko G, Seiser R, Seshadri K. Temperature cross-over and non-thermal runaway at two-stage ignition of n-heptane. Combust Flame2002;128:38–59.

[31] Law CK. Combustion physics. Cambridge University Press; 2006.[32] Guerrassi N. Etude experimentale et modelisation des phenomenes internes

en moteur diesel a injection directe. PhD thesis, L’Ecole Centrale de Lyon; 1993[in French].

[33] Griffiths JF, Halford-Maw PA, Mohamed C. Spontaneous ignition delays as adiagnostics of the propensity of alkanes to cause engine knock. Combust Flame1997;111:327–37.

[34] Ciezki HK, Adomeit G. Shock-tube investigation of self-ignition of n-hepatne–air mixtures under engine relevant conditions. Combust Flame1993;93:421–33.

[35] Zheng J. A study of homogeneous ignition and combustion processes in CI, SI,and HCCI engine systems. PhD thesis, Drexel University; 2005.

[36] Herzler J, Fikri M, Hitzbleck K, Starke R, Schulz C, Roth P, Kalghatgi GT. Shock-tube study of the autoignition of n-heptane/toluene/air mixtures atintermediate temperatures and high pressures. Combust Flame2007;149:25–31.

[37] Hernández JJ, Sanz-Argent J, Carot JM, Jabaloyes JM. Ignition delay timecorrelations for a diesel fuel with application to engine combustion modelling.Int J Eng Res 2010;11(3):199–206.

[38] Curran HJ, Gaffuri P, Pitz WJ, Westbrook CK. A comprehensive modelling studyof n-heptane oxidation. Combust Flame 1998;114:149–77.



Documents

A Method to Determine Ignition Delay Times for Diesel Surrogate Fuels From