Period doubling and chaotic transient in a model of chain-branching combustion wave propagation

The propagation of planar combustion waves in an adiabatic model with two-step chain-branching reaction mechanism is investigated. The travelling combustion wave becomes unstable with respect to pulsating perturbations as the critical parameter values for the Hopf bifurcation are crossed in the parameter space. The Hopf bifurcation is demonstrated to be of a supercritical nature and it gives rise to periodic pulsating combustion waves as the neutral stability boundary is crossed. The increase of the ambient temperature is found to have a stabilizing effect on the propagation of the combustion waves. However, it does not qualitatively change the behaviour of the travelling combustion waves. Further increase of the bifurcation parameter leads to the period-doubling bifurcation cascade and a chaotic regime of combustion wave propagation. The chaotic regime has a transient nature and the combustion wave extinguishes when the bifurcation parameter becomes sufficiently large. For Lewis numbers of fuel close to unity, the parameter regions where pulsating solutions exist become very close to each other and this makes it difficult to experimentally observe the period-doubling. It is shown that the average velocity of pulsating waves is less than the speed of the travelling wave for the same parameter values.

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PULSATING INSTABILITIES OF COMBUSTION WAVES IN A CHAIN-BRANCHING REACTION MODEL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409023354 ◽

2009 ◽

Vol 19 (03) ◽

pp. 873-887 ◽

Cited By ~ 8

Author(s):

V. V. GUBERNOV ◽

A. V. KOLOBOV ◽

A. A. POLEZHAEV ◽

H. S. SIDHU ◽

G. N. MERCER

Keyword(s):

Activation Energy ◽

Hopf Bifurcation ◽

Combustion Wave ◽

Traveling Wave ◽

Lewis Number ◽

Flame Speed ◽

Traveling Wave Solution ◽

Solution Branch ◽

Combustion Waves ◽

Parameter Values

In this paper we investigate the properties and linear stability of traveling premixed combustion waves and the formation of pulsating combustion waves in a model with two-step chain-branching reaction mechanism. These calculations are undertaken in the adiabatic limit, in one spatial dimension and for the case of arbitrary Lewis numbers for fuel and radicals. It is shown that the Lewis number for fuel has a significant effect on the properties and stability of premixed flames, whereas varying the Lewis number for the radicals has only qualitative (but not qualitative) effect on the combustion waves. We demonstrate that when the Lewis number for fuel is less than unity, the flame speed is unique and is a monotonically decreasing function of the dimensionless activation energy. Moreover, in this case, the combustion wave is stable and exhibits extinction for finite values of activation energy as the flame speed decreases to zero. However, for the fuel Lewis number greater than unity, the flame speed is a C-shaped and double valued function. The linear stability of the traveling wave solution was determined using the Evans function method. The slow solution branch is shown to be unstable whereas the fast solution branch is stable or exhibits the onset of pulsating instabilities via a Hopf bifurcation. The critical parameter values for the Hopf bifurcation and extinction are found and the detailed map for the onset of pulsating instabilities is determined. We show that a Bogdanov—Takens bifurcation is responsible for both the change in the behavior of the traveling wave solution near the point of extinction from unique to double valued type as well as for the onset of pulsating instabilities. We investigate the properties of the Hopf bifurcation and the emerging pulsating combustion wave solutions. It is demonstrated that the Hopf bifurcation observed in our present study is of supercritical type. We show that the pulsating combustion wave propagates with the average speed smaller than the speed of the traveling combustion wave and at certain parameter values the pulsating wave exhibits a period doubling bifurcation.

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PROPAGATION OF THE BURNING WAVE IN A PULSED DETONATION COMBUSTOR OPERATING ON MIXTURES OF HEPTANE AND JET A-1 WITH AIR AND OXYGEN AT [O2/AIR] < 1

PROGRESS IN DETONATION RESEARCH ◽

10.30826/icpcd12a21 ◽

2020 ◽

Author(s):

M. S. ASSAD ◽

◽

O. G. PENYAZKOV ◽

I. I. CHERNUHO ◽

K. ALHUSSAN ◽

...

Keyword(s):

Wave Propagation ◽

Combustion Wave ◽

Equivalence Ratio ◽

Pressure Sensors ◽

Jet Fuel ◽

Propagation Time ◽

Burning Wave ◽

Pulsed Detonation ◽

Combustion Wave Propagation ◽

Fuel Jet

This work is devoted to the study of the dynamics of combustion wave propagation in oxygen-enriched mixtures of n-heptane with air and jet fuel "Jet A-1" in a small-size pulsed detonation combustor (PDC) with a diameter of 20 mm and a length less than 1 m. Experiments are carried out after the PDC reaches a stationary thermal regime when changing the equivalence ratio (ϕ = 0.73-1.89) and the oxygen-to-air ratio ([O2/air] = 0.15-0.60). The velocity of the combustion wave is determined by measuring the propagation time of the flame front between adjacent pressure sensors that form measurement segements along the PDC.

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DEFECT-LINE DYNAMICS IN OSCILLATORY SPIRAL WAVES

Fluctuation and Noise Letters ◽

10.1142/s0219477506003537 ◽

2006 ◽

Vol 06 (04) ◽

pp. L379-L386

Author(s):

STEVEN WU

Keyword(s):

Critical Point ◽

Period Doubling ◽

Spiral Wave ◽

Chaotic Regime ◽

Spiral Waves ◽

Bifurcation Parameter ◽

Local Dynamics ◽

Total Length ◽

Defect Line ◽

Large Fluctuations

We study defect-line dynamics in a 2-D spiral-wave pair in the Rössler model for its underlying local dynamics in period-N and chaotic regimes with a single bifurcation parameter κ. We find that a spiral wave pair is always stable across the period-doubling cascade and in the chaotic regime. When N ≥ 2 defect lines appear spontaneously and a loop exchange occurs across the defect line. There exists a "critical point" κ c below and above which the time-averaged total length of defect lines L converges to almost constant but different values L1 and L2. When κ > κ c defect lines show large fluctuations due to creation and annihilation processes.

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