85 research outputs found
Premixed flame shapes and polynomials
The nonlinear nonlocal Michelson-Sivashinsky equation for isolated crests of
unstable flames is studied, using pole-decompositions as starting point.
Polynomials encoding the numerically computed 2N flame-slope poles, and
auxiliary ones, are found to closely follow a Meixner Pollaczek recurrence;
accurate steady crest shapes ensue for N>=3. Squeezed crests ruled by a
discretized Burgers equation involve the same polynomials. Such explicit
approximate shape still lack for finite-N pole-decomposed periodic flames,
despite another empirical recurrence.Comment: Accepted for publication in Physica D :Nonlinear Phenomen
Stationary solutions and Neumann boundary conditions in the Sivashinsky equation
New stationary solutions of the (Michelson) Sivashinsky equation of premixed
flames are obtained numerically in this paper. Some of these solutions, of the
bicoalescent type recently described by Guidi and Marchetti, are stable with
Neumann boundary conditions. With these boundary conditions, the time evolution
of the Sivashinsky equation in the presence of a moderate white noise is
controlled by jumps between stationary solutions
Flame Wrinkles From The Zhdanov-Trubnikov Equation
International audienceThe Zhdanov-Trubnikov equation describing wrinkled premixed flames is studied, using pole decomposi tions as starting points. Its one-parameter (â1 0 (over-stabilisation) such analytical solutions can yield accurate flame shapes for 0 < c < 0.6. Open problems are invoked
Wrinkled flames and geometrical stretch
Localized wrinkles of thin premixed flames subject to hydrodynamic
instability and geometrical stretch of uniform intensity (S) are studied. A
stretch-affected nonlinear and nonlocal equation, derived from an inhomogeneous
Michelson-Sivashinsky equation, is used as a starting point, and pole
decompositions are used as a tool. Analytical and numerical descriptions of
isolated (centered or multicrested) wrinkles with steady shapes (in a frame)
and various amplitudes are provided; their number increases rapidly with 1/S >
0. A large constantS > 0 weakens or suppresses all localized wrinkles (the
larger the wrinkles, the easier the suppression), whereasS < 0 strengthens
them; oscillations of S further restrict their existence domain. Self-similar
evolutions of unstable many-crested patterns are obtained. A link between
stretch, nonlinearity, and instability with the cutoff size of the wrinkles in
turbulent flames is suggested. Open problems are evoked
Shapes and speeds of forced premixed flames
Steady premixed flames subjected to space-periodic steady forcing are studied
via inhomogeneous Michelson-Sivashinsky (MS) and then Burgers equations. For
both, the flame slope is posited to comprise contributions from complex poles
to locate, and from a base-slope profile chosen in three classes (pairs of
cotangents, single-sine functions or sums thereof). Base-slope-dependent
equations for the pole locations, along with formal expressions for the
wrinkling-induced flame-speed increment and the forcing function, are obtained
on excluding movable singularities from the latter. Besides exact few-pole
cases, integral equations that rule the pole-density for large wrinkles are
solved analytically. Closed-form flame-slope and forcing-function profiles
ensue, along with flame-speed increment vs forcing-intensity curves; numerical
checks are provided. The Darrieus-Landau instability mechanism allows MS flame
speeds to initially grow with forcing intensity much faster than those of
identically forced Burgers fronts; only the fractional difference in speed
increments slowly decays at intense forcing, which numerical (spectral)
timewise integrations also confirm. Generalizations and open problems are
evoked.Comment: Revised version submitted to Phys. Rev.
Supernovae: an example of complexity in the physics of compressible fluids
The supernovae are typical complex phenomena in fluid mechanics with very
different time scales. We describe them in the light of catastrophe theory,
assuming that successive equilibria between pressure and gravity present a
saddle-node bifurcation. In the early stage we show that the loss of
equilibrium may be described by a generic equation of the Painlev\'e I form. In
the final stage of the collapse, just before the divergence of the central
density, we show that the existence of a self-similar collapsing solution
compatible with the numerical observations imposes that the gravity forces are
stronger than the pressure ones. This situation differs drastically in its
principle from the one generally admitted where pressure and gravity forces are
assumed to be of the same order. Our new self-similar solution (based on the
hypothesis of dominant gravity forces) which matches the smooth solution of the
outer core solution, agrees globally well with our numerical results. Whereas
some differences with the earlier self-similar solutions are minor, others are
very important. For example, we find that the velocity field becomes singular
at the collapse time, diverging at the center, and decreasing slowly outside
the core, whereas previous works described a finite velocity field in the core
which tends to a supersonic constant value at large distances. This discrepancy
should be important for explaining the emission of remnants in the
post-collapse regime. Finally we describe the post-collapse dynamics, when mass
begins to accumulate in the center, also within the hypothesis that gravity
forces are dominant.Comment: Workshop in Honor of Paul Manneville, Paris (2013
Rich Spray-Flame Propagating through a 2D-Lattice of Alkane Droplets in Air
International audienceIn a recent numerical paper (Nicoli et al. Combust. Sci. Technol. vol. 186, pp. 103-119; 2014) [1], a model of isobaric flame propagation in lean sprays has been proposed. The initial state of the monodisperse mists was schematized by a system of individual alkane droplets initially located at the nodes of a face-centered 2D-lattice, surrounded by a saturated mixture of alkane and air. In the present study, the previous model is complemented with an original chemical scheme that allows us to study the combustion of rich alkane/air mixtures
Spray-Flame Dynamics in a Rich Droplet Array
International audienceIn a recent numerical paper (Nicoli et al. Combust. Sci. Technol. vol. 186, pp. 103-119; 2014) [1], a model of isobaric flame propagation in lean sprays has been proposed. The initial state of the monodisperse mists was schematized by a system of individual alkane droplets initially located at the nodes of a face-centered 2D-lattice, surrounded by a saturated mixture of alkane and air. In the present study, the previous model is complemented with an original chemical scheme that allows us to study the combustion of rich alkane/air mixtures
Premixed flames propagating freely in tubes
International audienceThis paper reports an experimental investigation of premixed propane and methane-air flames propagating freely in tubes 1.5 m long and with diameters 54 and 94 mm. Two regimes of propagation are distinguished by correlating the flame speed and the radius of curvature at the flame tip. The characteristic lengths are then related to the cut-off wavelengths estimated from linear theories and compared to previous results of Michelson-Sivashinsky simulations
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