Swaminathan N., Bray K.N.C. (eds.) Turbulent Premixed Flames

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3.3 Simulation of Thermoacoustic Instability 223

(

)(

)

Angle (rad)

Figure 3.45. (a) Angular variation of

Prms

Pmean

on a ring passing through probes located in the

lower part of the chamber casing and (b) pressure signal phase for probes located in front of

all swirlers (Fig. 3.44). Note that sector 1 is used as reference: - model, ◦ LES.

outlet to the high-pressure stator nozzle by a 9 009 065-node and 42 287 640-cell

mesh.

The LES captures the self-excited instability and results (unsteady pressure

rms and phase ﬁelds) show that it is characterised by two superimposed rotating

modes with different amplitudes,

showninFig.3.45. The turning modes.

are found

to modulate the ﬂow rate through the 15 burners, and the ﬂames oscillate back and

forth in front of each burner shown in Fig. 3.46, leading to local heat release ﬂuctua-

tions. Because of the rotating motion of the modes, all individual transfer functions of

all the burners are the same, i.e., no mechanism of ﬂame interactions between burn-

ers within the chamber is identiﬁed. Note that, although such computations are very

CPU demanding and not realistically possible in an industrial context, they allow

validation of the hypotheses introduced in the use of a hierarchy of computational

modelling based on single-sector LES (b) and Helmholtz s olvers (c).

The ﬂow-rate ﬂuctuations in this computation are such that they have an im-

pact on the ﬂame response and the heat release perturbations, Fig. 3.47.Swirler

ﬂow-rate and pressure ﬂuctuations are out of phase. The phase between global

heat release and swirler ﬂow-rate ﬂuctuations satisﬁes a Rayleigh criterion for the

15 sectors.

It is possible to evaluate the response to the ﬂow-rate oscillations by comput-

ing the transfer function between inlet velocity ﬂuctuations and mean single-sector

unsteady heat release [182, 183]. Figure 3.48 shows the modulus n and the phase τ

of the classical n − τ model for each of the 15 burners. Amplitudes and delays are

fairly constant, suggesting a common response for all burners. This has important

implications for steps (b) and (c) of the proposed computational hierarchy.

Resolution effects on LES of real conﬁgurations have been addressed in [272, 277].

Paschereit et al. [203, 278] propose a nonlinear theoretical approach showing that standing-wave

modes can be found at low oscillation amplitudes but that only one rotating mode is found for

large-amplitude limit cycles.

A simple model can be used to recover the amplitude and phase of the pressure signals found in the

LES for the different burners by considering two counter-rotating acoustic modes P

and P

−

such

that

= A

i·k·θ−iωt

, P

−

= A

−

−i·k·θ−iωt

. (3.106)

When A

−

= 0.33A

, the amplitude and phase of the resulting acoustic pressure P

+ P

−

compare

very well with the LES data (Fig. 3.45).

224 Combustion Instabilities

Figure 3.46. Detailed view of half of the burners. top, temperature ﬁeld with temperature

isocontour; bottom, pressure ﬂuctuations with p



= 0 isoline.

SINGLE-SECTOR LES: FTF EVALUATION. Based on the previous observations, single-

sector forced LES should be sufﬁcient to retrieve the FTF necessary for the 3D

Helmholtz solver computations. For the case of interest, a single-sector forced LES

is obtained for an inlet acoustic modulation at 600 Hz. The local response ampli-

tude coefﬁcient, n(x) at 600 Hz, is plotted in three different planes in Fig. 3.49.One

remarks that the ﬂame response is spread in the primary zone; it is neither homoge-

nous nor symmetric. In the following discussion, the response amplitude coefﬁcient

n(x) is kept in its local formulation in order to take into account the ﬂame-response

inhomogeneities. This ﬂame response is assumed to be independent of the frequency

Time (s) Time (s)

(a) (b)

Figure 3.47. (a) –, Maximum ﬂame position (along the burner axis), ▲ average heat release;

(b) •, Heat release; – pressure ﬂuctuation average. All results are obtained for sector 1.

3.3 Simulation of Thermoacoustic Instability 225

( )

Figure 3.48. Sector-by-sector ﬂame response to the self-exited mode: ◦, response amplitude;

•, response delay (ms).

Figure 3.49. Inhomogeneities of the amplitude response coefﬁcient n(x).

226 Combustion Instabilities

of the acoustic forcing. This assumption is false if the forcing frequency varies in

a broad band, but because in this particular case the known frequency of the ﬁrst

azimuthal mode varies between 550 and 610 Hz, the ﬂame response can be considered

constant. To obtain the ﬂame r esponse over a broader frequency range, a white-

noise inlet forcing, together with a Whiener–Hopf inversion, should be used [251].

At the oscillation frequency of 600 Hz, the delay and the phase obtained between

peak ﬂow-rate oscillation and peak global heat release is 0.6761 ms or 2.548 rad,

respectively, and they compare quite well with the data obtained on the full chamber;

see Fig. 3.48.

THERMOACOUSTIC STABILITY PREDICTION – 3D HELMHOLTZ SOLVER. In this subsec-

tion, a detailed thermoacoustic study of the annular helicopter combustor is provided

by use of a 3D Helmholtz solver. First, the inﬂuence of the geometry of the chamber

in a non-reactive ﬂow is investigated. It is shown that the casing, the swirler, and

the primary holes have a strong inﬂuence on the acoustics of the azimuthal mode. A

methodology to compute azimuthal instabilities in the context of Helmholtz solvers

is then presented. The main advantages of this approach is its low CPU time cost.

The coupling between acoustics and combustion is accounted for by a classical n − τ

model. These n and τ parameters are computed by post-processing of the previous

single-sector LES, and the corresponding ﬁelds are extended to a multi-injection

annular combustion chamber under the independence sector assumption in annular

combustor [250] (ISAAC). This assumption is validated thanks to the LES of the

full annular helicopter combustion chamber previously discussed. Then the stability

of the ﬁrst azimuthal mode is investigated.

Because Helmholtz equations are essentially elliptic in their nature, the solution

of the model equation strongly depends on the geometry and boundary conditions.

This raises a simple but critical question in the context of industrial systems: What

computational domain, technological devices, asperities, and boundary conditions

are needed to properly capture the right physics as observed in LES or on the engine?

To illustrate the impact of this critical step, several 3D Helmholtz simulations are

provided in Table 3.3. For these results, combustion effects (FTFs) are not taken into

account and geometrical complexity is increased while the boundary conditions are

kept identical. The vector P gives the pressure distribution in the domain, the real

part of ω gives the eigenfrequency of the mode, and the imaginary part of ω gives

the growth rate or the damping of the eigenmode that is due to acoustic ﬂux at the

boundaries ∂

. In the calculation presented in Table 3.3 there is no acoustic ﬂux

at the boundaries because Z =∞is imposed everywhere. The combustion chamber

(CC) and the casing (C) are ﬁrst computed separately. Then they are connected

with the swirler (CC+C+S) and ﬁnally primary holes are taken into account in the

calculation (CC+C+S+PH).

In this particular case, the frequency of the ﬁrst azimuthal mode remains within

a narrow band between 500 and 700 Hz, which is typically the range of frequency

involved in combustion instabilities. A ﬁrst approximation of the frequency can be

easily obtained with the formula f

approx

mean

/(2πR

mean

), where

mean

stands for

the mean sound speed in the domain and R

mean

is the mean radius of the annular

conﬁguration. With

mean

= 750 m/s, f

approx

= 680 Hz. This approximation is in the

3.3 Simulation of Thermoacoustic Instability 227

Table 3.3. Inﬂuence of the geometry on the ﬁrst azimuthal eigenmode calculated by Helmholtz

solver (light grey denotes a pressure antinode and blackish grey a pressure node)

range of the results of the full calculation given in Table 3.3, as well as the frequency

observed in the full annular LES. It is clear that the frequency of the ﬁrst azimuthal

mode is greater for CC+C+S than for CC and it is lower than for C. Note also that

the computed modes are not purely azimuthal and that the azimuthal modes also

have a longitudinal component. Adding the primary holes in the calculation changes

this longitudinal component as well as the mode frequency. Those results emphasize

the necessity of treating carefully all the geometrical details to model correctly the

acoustics involved in combustion instabilities.

The coupling between acoustics and combustion is accounted for by a classical

n − τ model. In its global formulation, it relates the ﬂuctuations of the total heat

release to the ﬂuctuating velocity at a reference point, denoted as x

ref

. As underlined

previously, this reference point must be chosen in the injection zone where acoustic

ﬂuctuations inﬂuence the ﬂow rate or the equivalence ratio and it must be as close as

possible to the combustion zone [240].



ˆu

ref

) ·n is the longitudinal velocity leaving

the swirler. The time delay τ controls the stability of the conﬁguration according to

the Rayleigh criterion [29]. The local n − τ approach allows us to account for the

inhomogeneities of the ﬂame response. Obviously, in this full annular chamber, the

coupling between the ﬂuctuating heat release and the acoustic ﬂuctuation cannot be

described by a FTF involving only one point of reference. The local formulation is

228 Combustion Instabilities

Im(f )

(1/s)

Re(f )

(Hz)

(ms)

(a) (b)

(ms)

Figure 3.50. Inﬂuence of the parameter τ on the frequency and the stability of the ﬁrst

azimuthal mode: (a) eigenfrequency, • with and - - without combustion; (b) growth rate, 

with and - - without combustion.

thus extended as follows:





(x)



tot

⎧

⎪

⎨

⎪

⎩

n(x,ω)e

iωτ(x)



ˆu



ref

) . n

bulk

for x ∈ Sector 1

n(x,ω)e

iωτ(x)



ˆu



ref

) . n

bulk

for x ∈ Sector 2

...

n(x,ω)e

iωτ(x)



ˆu



ref

) . n

bulk

for x ∈ Sector 15.

(3.107)

In this approach, the annular combustion chamber is split into 15 sectors and the

Independence Sector Asumption in Annular Combustor (ISAAC) is assumed. The

heat release ﬂuctuations in a given sector are driven only by the ﬂuctuating mass ﬂow

rates that are due to the velocity perturbations through its own swirler. The ISAAC

assumption is implicitly used in most studies of annular combustors [119, 170, 203].

It is true only if ﬂames issuing from neighbouring burners do not interact, a property

that is known to be false in certain cases [279] but seems to be accceptable in this

case, as presented previously in the massively parallel LES of the full helicopter

combustion chamber, Fig. 3.48. Based on ISAAC, the FTF can be retrieved from the

single-sector LES previously presented and used in the context of the full annular

Helmholtz solver, as previously described.

Note that, in the following section, τ will be used in its global form and a

sensitivity analysis of the combustor stability to this parameter is performed. The

reaction index coefﬁcient is used in its local form, n

(x), to take into account the

space inhomogeneities of the ﬂame response to a given excitation.

Under the ISAAC assumption, the local amplitude single-sector response coef-

ﬁcient n

(x) is duplicated in all sectors and test values for τ are chosen between 0 and

2 ms. Because of the geomtry, which is azimuthally periodic, the stability behaviour

in this direction is also periodic in τ. Results are plotted in Fig. 3.50. When τ varies,

the frequency of t he azimuthal eigenmode varies between 555 and 610 Hz. When τ is

in [0, T/2], with T the period, the azimuthal mode is damped. The delay measured in

the full LES and in the single-sector LES is ≈ 0.65 ms so that the burner is obviously

operating very close to its stability limits. The same stability ranges are predicted

analytically in a simple annular conﬁguration with an inﬁnitely thin ﬂame [280].

References 229

3.3.6 Conclusions

The prediction of thermoacoustic instabilities in aeronautical gas turbine engines

and more generally premixed and partially premixed burners is not an easy task.

Currently, industrials are faced with such instabilities at the end of the design pro-

cess. Recent developments in numercial applications allow us to partially apprehend

such problems. In this book, a strategy based on the use of the fully unsteady LES ap-

proach and Helmoholtz solvers is proposed. Applications to a single sector and a full

annular gas turbine helicopter combustion chamber proves the methodology to be

applicable. Technological details such as the swirler geometry and primary and sec-

ondary holes are proven to be of importance in the determination of the eigenmodes

and eigenfrequencies of the acoustics ﬁeld obtained with the Helmholtz solver. With

the help of the ISAAC hypothesis, the prediction of the azimuthal instabilities is also

accessible and in very good agreement with full annular LES for the same conﬁg-

uration. Note, however, that current limitations, applicable to LES and Helnholtz

solvers, rely on the proper determination of the acoustic impedances at the inlet and

the outlet of the computational domains. Simple approximations are possible, but

their extension to more complex systems is not so clear and further investigations

seem needed. Finally, the estimation of the FTF, needed for the Helmholtz solver

to determine the stability of the eigenmodes, remains a critical point. Although it

can be retrieved from single-sector LES for a given forcing frequency, determina-

tion of the FTF for the entire frequency range of interest implies large computer

costs.

REFERENCES

[1] A. Smithells and H. Ingle, The structure and chemistry of ﬂames, J. Chem. Soc.

61, 204–216 (1892).

[2] M. Hertzberg, Selective diffusional demixing: Occurrence and size of cellular

ﬂames, Prog. Energy Combust. Sci. 15, 203–239 (1989).

[3] J. Buckmaster, P. Clavin, A. Lin

an, M. Matalon, N. Peters, G. Sivashinsky, and

F. A. Wiiliams, Combustion theory and modelling, Proc. Combust. Inst. 30,

1–19 (2005).

[4] M. Matalon, Flame dynamics, Proc. Combust. Inst. 32, 37–82 (2009).

[5] D. Bradley, P. H. Gaskell, and X. J. Gu, Burning velocities, Markstein lengths,

and ﬂame quenching for spherical methane–air ﬂames: A computational study,

Combust. Flame 104, 176–198 (1996).

[6] D. Bradley, M. Lawes, K. Liu, S. Verhelst, and R. Woolley, Laminar burning

velocities of lean hydrogen–air mixtures at pressures up to 1.0 MPa, Combust.

Flame 149, 162–172 (2007).

[7] D. Bradley, P. H. Gaskell, and X. J. Gu, The mathematical modeling of liftoff

and blowoff of turbulent non-premixed methane jet ﬂames at high strain rates,

Proc. Comb. Inst. 27, 1199–1206 (1998).

[8] X. J. Gu, M. Z. Haq, M. Lawes, and R. Woolley, Laminar burning velocity

and Markstein lengths of methane–air mixtures, Combust. Flame 121, 41–58

(2000).

[9] G. Darrieus, Propagation d’un front de ﬂamme: Assai de th

eorie des vitesses

anomales de d

eﬂagration par developpement spontan

e de la turbulence, pre-

sented at the Sixth International Congress on Applied Mechanics, Paris,

1946.

230 Combustion Instabilities

[10] L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1987).

[11] J. K. Bechtold and M. Matalon, Hydrodynamic and diffusion effects on the

stability of spherically expanding ﬂames, Combust. Flame 67, 77–90 (1987).

[12] D. Bradley, Instabilities and ﬂame speeds in large-scale premixed gaseous ex-

plosions, Philos. Trans. R. Soc. London A 357, 3567–3581 (1999).

[13] P. Clavin, Dynamic behaviour of premixed ﬂame fronts in laminar and turbulent

ﬂows, Prog. Energy Combust. Sci. 11, 1–59 (1985).

[14] D. Bradley and C. M. Harper, The development of instabilities in laminar

explosion ﬂames, Combust. Flame 99, 562–572 (1994).

[15] D. Bradley, Flame propagation in a tube: The legacy of Henri Gu

enoche,

Combust. Sci. Technol. 158, 15–33 (2000).

[16] G. Jomaas, C. K. Law, and J. K. Bechtold, On transition to cellularity in ex-

panding spherical ﬂames, J. Fluid Mech. 583, 1–26 (2007).

[17] D. Bradley, R. A. Hicks, M. Lawes, C. G. W. Sheppard, and R. Woolley, The

measurement of laminar burning velocities and Markstein numbers for iso-

octane air and iso-octane-n heptane mixtures at elevated temperatures and

pressures in an explosion bomb, Combust. Flame 115, 126–144 (1998).

[18] D. Bradley, M. Lawes, and M. S. Mansour, Explosion bomb measurements of

ethanol-air laminar gaseous ﬂame characteristics at pressures up to 1.4 MPa,

Combust. Flame 156, 1462–1470 (2009).

[19] D. Bradley, C. G. W. Sheppard, R. Woolley, D. A. Greenhalgh, and R. D.

Lockett, The development and structure of ﬂame instabilities and cellularity at

low Markstein numbers in explosions, Combust. Flame 122, 195–209 (2000).

[20] L. Filyand, G. I. Sivashinsky, and M. L. Frankel, On self-acceleration of outward

propagating wrinkled ﬂames, Physica D 72, 110–118 (1994).

[21] Yu. A. Gostintsev, A. G. Istratov, and Yu. V. Shulenin, Self-similar propagation

of a free turbulent ﬂame in mixed gas mixures, Combust. Explos. Shock Waves

24, 563–569 (1988).

[22] D. Bradley, T. M. Cresswell, and J. S. Puttock, Flame acceleration due to ﬂame-

induced instabilities in large-scale explosions, Combust Flame 124, 551–559

(2001).

[23] V. Karlin and G. Sivashinsky, Asymptotic modelling of self-acceleration of

spherical ﬂames, Proc. Combust. Inst. 31, 1023–1030 (2007).

[24] I. R. Hurle, R. B. Price, T. M. Sugden, and A. Thomas, Sound emission from

open turbulent premixed ﬂames, Proc. R. Soc. London A 303, 409–427 (1968).

[25] G. A. Batley, A. C. McIntosh, and J. Brindley, Baroclinic distortion of laminar

ﬂames, Proc. R. Soc. London A 452, 199–221 (1996).

[26] G. H. Markstein, in Non-Steady Flame Propagation, AGARDograph 75

(Pergamon, Oxford, 1964).

[27] D. P. J. McCann, G. O. Thomas, and D. H. Edwards, Gas dynamics of vented

explosions. Part 1: Experimental studies, Combust. Flame 59, 233–250 (1985).

[28] H. Gu

enoche, in G. H. Markstein, (ed.), Non-Steady Flame Propagation,

AGARDograph 75 (Pergamon, Oxford, 1964), Chap. E, pp. 107–181.

[29] Lord Rayleigh (John William Strutt), The explanation of certain acoustic phe-

nomena, Nature (London) 18, 319–321 (1878).

[30] Lord Rayleigh (John William Strutt), The Theory of Sound (Dover, New York,

1945), Vol. II.

[31] A. P. Dowling and S. Hubbard, Instability in lean premixed combustors, Proc.

Inst. Mech. Eng. A 214, 317–332 (2000).

[32] A. S. Al-Shahrany, D. Bradley, M. Lawes, K. Liu, and R. Woolley, Darrieus–

Landau and thermoacoustic instabilities in closed vessel explosions, Combust.

Sci Technol. 178, 1771–1802 (2006).

[33] A. S. Al-Shahrany, D. Bradley, M. Lawes, and R. Woolley, Measurement of

unstable burning velocities of iso-octane-air mixtures at high pressure and

the derivation of laminar burning velocities, Proc. Combust. Inst. 30, 225–232

(2005).

References 231

[34] W. E. Kaskan, An investigation of vibrating ﬂames, Proc. Combust. Inst. 4,

575–591 (1953).

[35] G. Searby, Acoustic instability in premixed ﬂames, Combust. Sci. Technol. 81,

221–231 (1992).

[36] Luc Bauwens, C. Regis Bauwens, and I. Wierzba, Oscillating ﬂames: multiple

scale analysis, Proc. R. Soc. London A 465, 2089–2110 (2009).

[37] S. Kerampran, D. Desbordes, B. Veyssi

ere, Study of the mechanisms of ﬂame

acceleration in a tube of constant cross section, Combust. Sci. and Technol. 158,

71–91 (2000).

[38] V. Bychkov, Analytical scalings for ﬂame interaction with sound waves, Phys.

Fluids 11, 3168–3173 (1999).

[39] R. C. Aldredge, Saffman–Taylor inﬂuence on ﬂame propagation in thermo-

acoustically excited ﬂow, Combust. Sci. Technol. 177, 53–73 (2005).

[40] D. Durox, T. Schuller, N. Noiray, A. L. Birbaud, and S. Candel, The Rayleigh

criterion and acoustic energy balance in unconﬁned self-sustained oscillating

ﬂames, Combust. Flame 156, 106–119 (2009).

[41] P. Cambray and G. Joulin, Length scales of wrinkling of weakly-forced, unstable

premixed ﬂames, Combust. Sci. Technol. 97, 405–428 (1994).

[42] V. Bychkov, Importance of Darrieus–Landau instability for strongly corrugated

turbulent ﬂames, Phys. Rev. E 68, 0066304-1066304-12 (2003).

[43] R. N. Paul and K. N. C. Bray, Study of premixed turbulent combustion including

Landau–Darrieus instability effects, Proc. Combust. Inst. 26, 259–266 (1996).

[44] D. Bradley, P. H. Gaskell, X. J. Gu, and A. Sedaghat, Premixed ﬂamelet mod-

elling: Factors inﬂuencing the turbulent heat release rate source term and the

turbulent burning velocity, Combust. Flame 143, 227–245 (2005).

[45] I. G. Shepherd and R. K. Cheng, The burning rate of premixed ﬂames in

moderate and intense turbulence, Combust. Flame 127, 2066–2075 (2001).

[46] J. F. Driscoll, Turbulent premixed combustion: Flamelet structure and its effect

on turbulent burning velocities, Prog. Energy Combust. Sci. 34, 91–134 (2008).

[47] D. Bradley, M. Lawes, and M. S. Mansour, correlation of turbulent burning ve-

locities of ethanol–air, measured in a fan-stirred bomb, up to 1.2 MPa, Combust.

Flame 158, 123–138 (2011).

[48] D. Bradley, A. K. C. Lau, and M. Lawes, Flame stretch rate as a determinant

of turbulent burning velocity, Philos. Trans. R. Soc. London A 338, 357–387

(1992).

[49] D. Bradley, M. Lawes, K. Liu, and R. Woolley, The quenching of premixed

turbulent ﬂames of iso-octane, methane and hydrogen at high pressures, Proc.

Combust. Inst. 31, 1393–1400 (2007).

[50] C. K. Law, D. L. Zhu, and G. Yu, Propagation and extinction of stretched

premixed ﬂames, Proc. Combust. Inst. 21, 1419–1426 (1986).

[51] Y. Dong, A. T. Holley, M. G. Andac, F. N. Egolfopoulos, S. G. Davis, P. Middha,

and H. Wang, Extinction of premixed H

/air ﬂames: Chemical kinetics and

molecular diffusion effects, Combust. Flame 142, 374–387 (2005).

[52] J. M. Donbar, J. F. Driscoll, and C. D. Carter, Strain rates measured along the

wrinkled ﬂame contour within turbulent non-premixed jet ﬂames, Combust.

Flame 125, 1239–1257 (2001).

[53] S. R. N. De Zilwa, I. Emiris, J. H. Uhm, and J. H. Whitelaw, Combustion of

premixed methane and air in ducts, Proc. R. Soc. London A 457, 1915–1949

(2002).

[54] D. Bradley, P. H. Gaskell, X. J. Gu, M. Lawes, and M. J. Scott, Premixed turbu-

lent ﬂame instability and NO formation in a lean-burn swirl burner, Combust.

Flame 115, 515–538 (1998).

[55] D. Bradley, M. Lawes, and K. Liu, Turbulent ﬂame speeds in ducts and the

deﬂagration/detonation transition, Combust. Flame 154, 96–108 (2008).

[56] D. Bradley, Hot spots’ and gasoline engine knock, J. Chem. Soc. Faraday Trans.

92, 2959–2964 (1996).

232 Combustion Instabilities

[57] N. Kawahara, E. Tomita, and Y. Sakata, Auto-ignited kernels during knocking

combustion in a spark-ignition engine, Proc. Combust. Inst. 31, 2999–3006

(2007).

[58] D. Bradley and G. T. Kalghatgi, Inﬂuence of autoignition delay time character-

istics of different fuels on pressure waves and knock in reciprocating engines,

Combust. Flame 156, 2307–2318 (2009).

[59] D. Bradley and R. A. Head, Engine autoignition: The relationship between

octane numbers and autoignition delay times, Combust. Flame 147, 171–184

(2006).

[60] K. Fieweger, R. Blumenthal, and G. Adomeit, Self-ignition of S.I. engine model

fuels: A shock tube investigation at high pressure, Combust. Flame 109, 599–619

(1997).

[61] A. E. Lutz, R. J. Kee, J. A. Miller, H. A. Dwyer, and A. K. Oppenheim, Dynamic

effects of autoignition centers for hydrogen and C1,2-hydrocarbon fuels, Proc.

Comb. Inst. 22, 1683–1693 (1988).

[62] D. Bradley, C. Morley, X. J. Gu, and D. R. Emerson, Ampliﬁed pressure

waves during autoignition: Relevance to CAI engines, SAE paper 2002-01-

2868 (2002).

[63] X. J. Gu, D. R. Emerson, and D. Bradley, Modes of reaction front propagation

from hot spots, Combust. Flame 133, 63–74 (2003).

[64] D. Bradley, X. J. Gu, and D. R. Emerson, Modes of reaction front propagation

from hot spots in ﬂammable gaseous mixtures, in D. Bradley, D. Drysdale, and

V. Molkov (eds.), Proceedings of The Fourth International Seminar on Fire and

Explosion Hazards, FireSERT (University of Ulster, 2004), pp. 201–208.

[65] J. Pan and C. G. W. Sheppard, A theoretical and experimental study of the

modes of end gas autoignition leading to knock in SI engines, SAE paper

942060 (1994).

[66] G. T. Kalghatgi, D. Bradley, J. Andrae, and A. J. Harrison, A possible mech-

anism for superknock events, in Internal Combustion Engines: Performance,

Fuel Economy and Emissions (Institution of Mechanical Engineers, London,

2009).

[67] J. Stokes, T. H. Lake, and R. J. Osborne, A gasoline engine concept for improved

fuel economy – the lean boost system, SAE paper 2000-01-2902 (2000).

[68] P. Van Blarigan, Development of a hydrogen fueled internal combustion engine

designed for single speed/power operation, SAE paper 961690 (1996).

[69] C. G. Bauer and T. W. Forest, Effect of hydrogen addition on the performance

of methane-fueled vehicles. Part 1: Effect on SI engine performance, Int. J.

Hydrogen Energy 26, 55–70 (2001).

[70] S. M. Aceves and J. R. Smith, Hybrid and conventional hydrogen engine vehi-

cles that meet EZEV emissions, SAE paper 970290 (1997).

[71] J. Nygren, J. Hult, M. Richter, M. Ald

en, M. Christensen, A. Hultqvist, and

B. Johansson, Three dimensional laser induced ﬂuorescence of fuel distribu-

tions in an HCCI enguine, Proc. Combust. Inst. 29, 679–685 (2002).

[72] J. E. Dec, W. Hwang, and M. Sj

oberg, An investigation of thermal stratiﬁcation

in HCCI engines using chemiluminescent imaging, SAE paper 2006-01-1518

(2006).

[73] J. H. Chen, E. R. Hawkes, R. Sankaran, S. D. Mason, and H. G. Im, Direct

numerical simulation of ignition front propagation in a constant volume with

temperature inhomogeneities. Fundamental analysis and diagnostics, Combust.

Flame 145, 128–144 (2006).

[74] F. Culick, Combustion instabilities in liquid-fueled propulsion systems: An

overview, presented at the AGARD Conference on Combustion Instabilities in

Liquid-Fueled Propeller Systems, Seuille-Sur-Seine, France, 1998.

[75] A. Putnam, Combustion Driven Oscillations in Industry (Elsevier, New York,

1971).