The effect of ambient temperature on the propagation of nonadiabatic combustion waves

Gubernov, Vladimir; Sidhu, Harvinder; Mercer, G. N.

doi:10.1007/s10910-004-1447-7

Cited by 8 publications

(8 citation statements)

References 26 publications

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“…As seen in figure 2a, the increase of u a shifts both the boundary of the existence of travelling solutions and the Hopf loci towards higher values of the dimensionless activation energy. In other words, the ambient temperature rise has a stabilizing effect on the propagation of the combustion waves, which correlates with the results in Gubernov et al (2005). This issue is further clarified in figure 2b where the loci for extinction (solid line) and Hopf bifurcation (dashed line) are plotted in b versus u a plane for L A = 10 and L B = 1.…”

Section: Properties Of the Travelling Wave Solutionsupporting

confidence: 81%

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

et al. 2010

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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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Section: Properties Of the Travelling Wave Solutionsupporting

confidence: 81%

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

et al. 2010

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“…This method is relatively new for combustion science. Previously the Evans function approach was employed to study the onset of pulsating instabilities in premixed flames with Lewis number L > 1 for both the adiabatic [15] and nonadiabatic flames [16,17]. In our earlier studies [12], we also extended the applicability of the method to investigate the instabilities of a different nature, namely, transversal or cellular instabilities in diffusion flames, which are dominant for the case of L < 1.…”

Section: Methodsmentioning

confidence: 99%

“…Employing this approach, the spectral problem in equations (7) and (8) can be reduced to the search of zeroes of the Evans function D(S), which has an important property (see [15][16][17] and references therein): D(S) = 0 for some given value of S if and only if for this value of S equation (7) has at least one solution bounded for both ξ → ±∞ and satisfying the boundary conditions in equation (8). Consequently, we can look for zeroes of the Evans function, instead of solving the linear stability problem in equations (7) and (8) directly.…”

Section: Methodsmentioning

confidence: 99%

“…This is another point for considering the planar instabilities. Following the convention of the authors' previous papers [12,[15][16][17], the zeroes of the Evans function will be referred as the eigenvalues (or points) of the corresponding discrete spectrum. The mean-field solution becomes linearly unstable if there exists at least one zero S of the Evans function D(S) such that Re S is positive (Re S is sometimes called the growth rate coefficient).…”

Section: Instability Characteristics With K =mentioning

confidence: 99%

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On the fast-time oscillatory instabilities of Liñán's diffusion-flame regime

Gubernov

Kim

2006

Combustion Theory and Modelling

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Fast-time instability for diffusion flames, with Lewis numbers set equal for fuel and oxidizer but greater than unity, is numerically analysed by the activation energy asymptotics and Evans function method. The time and length scales being chosen to be those of the inner reactive-diffusive layer, the problem corresponds to the instability problem for the Liñán's diffusion-flame regime. The instability is primarily oscillatory and emerges prior to reaching the turning point of the characteristic C-curve, usually known as the Liñán's extinction condition. A critical Lewis number, L c , is also found, across which the instability changes its qualitative character. Below L c , the instability possesses primarily a pulsating nature in that the two real branches of the dispersion relation existing for small wave numbers merge at a finite wave number, from which a pair of complex conjugate branches bifurcate. The maximum growth rate is found at the zero wave number. For Lewis numbers greater than L c , the eigensolution branch for small reactant leakages is found to be purely complex with the maximum growth rate found at a finite wave number, thereby exhibiting a travelling nature. As the reactant-leakage parameter is further increased, the instability characteristics turns into a pulsating type, similar to that for 1 < L < L c . The switching between different instability characters is found to correspond to the Bogdanov-Takens bifurcation.

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“…This is called the cold boundary difficulty: traveling waves only exist when the ambient temperature is absolute zero. Nevertheless, approximate traveling waves have been studied numerically [12].…”

Section: Literature On the Gasless Combustion Modelmentioning

confidence: 99%

Gasless Combustion Fronts with Heat Loss

Ghazaryan¹,

Schecter²,

Šimon³

2013

SIAM J. Appl. Math.

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Abstract. For a model of gasless combustion with heat loss, we use geometric singular perturbation theory to show existence of traveling combustion fronts. We show that the fronts are nonlinearly stable in an appropriate sense if an Evans function criterion, which can be verified numerically, is satisfied. For a solid reactant and exothermicity parameter that is not too large, we verify numerically that the criterion is satisfied.

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The effect of ambient temperature on the propagation of nonadiabatic combustion waves

Cited by 8 publications

References 26 publications

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

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

On the fast-time oscillatory instabilities of Liñán's diffusion-flame regime

Gasless Combustion Fronts with Heat Loss

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