Field equation for interface propagation in an unsteady homogeneous flow field

Kerstein, Alan R.; Ashurst, Wm. T.; Williams, Forman A.

doi:10.1103/physreva.37.2728

Cited by 359 publications

(174 citation statements)

References 9 publications

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“…Results obtained in the present DNS will be compared with recent DNS data [24] computed by solving the level-set equation [29] …”

Section: Governing Equationsmentioning

confidence: 99%

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence

Lipatnikov

2017

Phys. Rev. E

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A three-dimensional (3D) direct numerical simulation (DNS) study of the propagation of a reaction wave in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is performed by solving Navier-Stokes and reaction-diffusion equations at various (from 0.5 to 10) ratios of the rms turbulent velocity U to the laminar wave speed, various (from 2.1 to 12.5) ratios of an integral length scale of the turbulence to the laminar wave thickness, and two Zeldovich numbers Ze = 6.0 and 17.1. Accordingly, the Damköhler and Karlovitz numbers are varied from 0.2 to 25.1 and from 0.4 to 36.2, respectively. Contrary to an earlier DNS study of self-propagation of an infinitely thin front in statistically the same turbulence, the bending of dependencies of the mean wave speed on U is simulated in the case of a nonzero thickness of the local reaction wave. The bending effect is argued to be controlled by inefficiency of the smallest scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles are rapidly smoothed out by molecular transport within the local reaction wave.

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“…Results obtained in the present DNS will be compared with recent DNS data [24] computed by solving the level-set equation [29] …”

Section: Governing Equationsmentioning

confidence: 99%

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence

Lipatnikov

2017

Phys. Rev. E

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“…We have neglected the y-dependence, replacing it with a constant β which takes into account the average effect of the vertical component of the velocity field along the path followed by (x M , y M ). By solving (17) in the interval x M ∈ (0, 2π) one obtains the time, T , needed for x M to reach the end of the cell. The front speed, as the speed of the edge particle, is then given by v f = 2π/T .…”

Section: Front Speed In the Geometrical Optics Regimementioning

confidence: 99%

Front speed enhancement in cellular flows

Abel

Cencini

Vergni

et al. 2002

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The problem of front propagation in a stirred medium is addressed in the case of cellular flows in three different regimes: slow reaction, fast reaction and geometrical optics limit. It is well known that a consequence of stirring is the enhancement of front speed with respect to the non-stirred case. By means of numerical simulations and theoretical arguments we describe the behavior of front speed as a function of the stirring intensity, $U$. For slow reaction, the front propagates with a speed proportional to $U^{1/4}$, conversely for fast reaction the front speed is proportional to $U^{3/4}$. In the geometrical optics limit, the front speed asymptotically behaves as $U/\ln U$.Comment: 10 RevTeX pages, 10 included eps figure

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“…In this limit the problem can be formulated in terms of the evolution of a scalar field, G(r, t), where the iso-line (in 2D) G(r, t) = 0 represents the front: G > 0 is the inert material and G < 0 is the fresh one. G evolves according to the so-called G-equation [8,15,[25][26][27][28] …”

Section: The Geometrical Optics Limitmentioning

confidence: 99%

“…Formally, this corresponds to the limit τ → 0 and D 0 → 0 maintaining the ratio D 0 /τ constant [15]: from (2) this means that v 0 is finite and ξ → 0. In this regime the front is identified as a surface (a line in 2d), and the effect of the velocity field is to wrinkle the front increasing its area (length in 2d) and thereby its speed [8].…”

Section: Introductionmentioning

confidence: 99%

Thin front propagation in steady and unsteady cellular flows

et al. 2003

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Front propagation in two dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case, by means of a simplified model, we provide an analytical approximation for the front speed, v f , as a function of the stirring intensity, U , in good agreement with the numerical results and, for large U , the behavior v f ∼ U/ log(U ) is predicted. The large scale of the velocity field mainly rules the front speed behavior even in the presence of smaller scales. In the unsteady (time-periodic) case, the front speed displays a phase-locking on the flow frequency and, albeit the Lagrangian dynamics is chaotic, chaos in front dynamics only survives for a transient. Asymptotically the front evolves periodically and chaos manifests only in the spatially wrinkled structure of the front.

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Field equation for interface propagation in an unsteady homogeneous flow field

Cited by 359 publications

References 9 publications

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence

Front speed enhancement in cellular flows

Thin front propagation in steady and unsteady cellular flows

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