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Experimental studies of instabilities of laminar premixed flames
On the GlugGlug of ideal bottles
Dynamics of long bubbles in vertical tubes
Markstein numbers in counterflow, methane- and propane-air flames: a computational study
Determination of Markstein numbers in counterflow premixed flames
A numerical investigation of stretch effects in counterflow laminar premixed flames
First experimental study of the Darrieus-Landau instability.
Sound emission by non-isomolar combustion at low Mach numbers
Parametric response of a conical flame to acoustic waves.
On the shape of flames under strong acoustic forcing: a mean flow controlled by an oscillating flow.
On the 'Tulip Flame' Phenomenon.
A
numerical study of lean CH4/H2/air premixed flames at high pressure.
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G. Searby
We first briefly recall the basic mechanisms controlling the hydrodynamic and thermo-diffusive stability of planar laminar premixed flames, and give the state of the theoretical analysis. We then describe some novel experiments to observe and measure the growth rate of cellular structures on initially planar flames. The first experiment concerns the observation of the temporal growth of wrinkling on a freely propagating planar flame. A second experiment concerns the spatio-temporal growth of structures of controlled wavelength on an anchored flame. The experimental observations are compared to theoretical dispersion relation. Finally, we compare observations of the non-linear evolution to saturation with the predictions of an extended Michelson-Sivashinsky equation.
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C. Clanet and G. Searby
We present an experimental study of the emptying of an ideal vertical bottle under gravity g. The idealisation reduces the bottle to a cylinder of diameter D0, length L, closed at the top and open at the bottom through a circular thin-walled hole of diameter d, on the axis of the cylinder. The study is performed in the low viscosity limit. The oscillatory emptying of the "bottle" is referred to as the GlugGlug, and is characterised by its period T, whereas the whole emptying process is characterised by a time Te. Concerning the long time scale, Te, we show that:
where Te0 = 3.0 L / √(g D0). On the short time scale T, we show that the physical origin of the oscillations lies in the compressibility of the surrounding gas. The period can be written as:
Finally, this analysis of time scales involved in the emptying of a vertical cylinder is applied to other liquid-gas oscillators.
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C. Clanet, P. Héraud and G. Searby
We study the rising velocity Ub of long bubbles in vertical tubes of different cross sections, under the acceleration of gravity g. The vessel being initially filled with a liquid of kinematic viscosity nu, it is known that for cylindrical tubes of radius R, high Reynolds number bubbles (Re = Ub R / nu » 1) are characterized by Newton's law Ub proportional to √( gR ) and low Reynolds number bubbles by Stokes' law, Ub proportional to gR2/nu. We show experimentally that for vessels of "arbitrary" cross sections (rectangles, regular polygons, toroidal tubes). The high Reynolds number domain is shown to be characterized by Ub ≈ 0.2 √(g P), and the low-Reynolds number range by Ub ≈ 0.012g S / nu, where P and S respectively stand for the wetted perimeter and the area of the normal cross section of the tube. We derive an analytical justification of these results, using the rectangular geometry. Finally, the problem of long bubble propagation in an unsteady acceleration field is analysed. The theory is compared to existing data.
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S. G. Davis and G. Searby
We briefly review the concept of Markstein lengths with respect to unburned and burned gases and also the problem of defining the correct reference plane to measure flame speed and stretch. We then present numerical simulations of hydrogen/air flames in the counterflow configuration, using full chemistry and multi-component transport. The values of flame speed derived by extrapolating the stretched burning velocities to zero stretch and those calculated using planar flame modeling are within 2% of each other over most of the equivalence ratios studied. The Markstein lengths of these flames were computed, as a function of equivalence ratio, with respect to both the unburned and burned gases and can be used to model the response of stretched hydrogen/air flames. We show that the values measured with respect to the burned and unburned gases are different, yet in accordance with asymptotic theory. The values from our numerical simulations are then compared to the values published in the literature for the same mixtures. The numerical and experimental values in the literature, obtained from the expansion rates of spherical flames, are in very good agreement with our evaluations of the values of the Markstein lengths with respect to the burned gases in the counterflow configuration. These results also confirm the idea that, for small stretch rates, flames have the same response to stretch arising from either strain or curvature.
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S. G. Davis, J. Quinard, and G. Searby
The concept of Markstein numbers with respect to unburned and burned gases is first reviewed. We next present numerical simulations of methane–air and propane–air flames in the counterflow configuration using a detailed chemical kinetic model consisting of 469 reactions and 71 species. Markstein numbers of these flames, as a function of equivalence ratio, are computed with respect to both the unburned and burned gases. It is shown that the values of Markstein number relative to the unburned and burned gases are not equal and may even have opposite signs, as supported by asymptotic theory. The values from these numerical simulations are then compared to the values published in the literature for the same mixtures. We show that experimental values in the literature, obtained from the expansion rates of spherical flames, are very close to our numerical values of the Markstein numbers with respect to the burned gases, simply re-normalized by the gas density ratio. These results support the idea that flames respond similarly for equal values of a small characteristic stretch. We also find close agreement with an experimental measurement made in the unburned gases on a counterflow propane flame. However, some of our values evaluated in the unburned gases are significantly different from those in the literature, obtained indirectly using measurements of the growth rate of unstable structures on planar flames. We present evidence to suggest that the results of asymptotic flame theory, used to obtain the indirect measurements of Markstein numbers, are not quantitatively applicable when the effective Lewis number of the mixture is not close to unity.
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S. G. Davis, J. Quinard, and G. Searby
This paper attempts to settle a long-standing issue concerning the differences in Markstein numbers measured by different experimental protocols. Numerical simulations of a counterflow flame with full transport coefficients, but using a fictive reactive mixture having properties close to those assumed in asymptotic laminar flame analysis, are used to show how to correctly identify the burning velocity and stretch of a stretched flame with a finite width chemical zone. We show how to measure the Markstein number of the flame with respect to both the unburned and burned gases. The numerical values of these numbers differ by a quantity that depends on the internal flame structure. The physical origin of this difference is made evident. Our numerical results are in close agreement with the predictions of asymptotic theory. We show that laboratory experiments on counterflow flames give Markstein numbers related to the unburned gas, whereas laboratory experiments on spherical expanding flames give Markstein numbers related to the burned gases.
The range of validity of asymptotic theory, for Lewis numbers departing from unity, is also examined. We conjecture that the so-called consumption velocity of a flame (normal integral of the species consumption rate) may allow a measure of the Lewis number dependent part of the Markstein number, even for realistic flames with complex chemistry and an effective Lewis number not close to unity.
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S. G. Davis, J. Quinard, and G. Searby
We use direct numerical simulation of propane/air flames with full chemistry in the stagnation flow geometry to investigate the effect of different definitions of local flame stretch in the presence of space-varying velocity gradients. Specifically, we compare simulations with potential- and plug-flow inlet conditions, and show that the widely used definition of upstream stretch leads to unphysical results for flames having the "same" stretch. We then show that a reasonable re-definition of local stretch allows us to produce the "same" flame in the presence of the "same" stretch.
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G. Searby, J-M. Truffaut and G. Joulin*
* LCD ENSMA / Université de Poitiers, 86960 FUTUROSCOPE, France.
Abstract. We extend the Michelson-Sivashinsky equation, for arbitrary gas density ratio, to model the dynamics of an inclined anchored flame front. A flow velocity component tangential to the flame front transforms temporally developing structures into spatially developing ones. Closer investigation shows that a transition from absolute to convective instability should occur for a finite flow velocity Using pole-decomposition, we give a particular solution to this equation in the limit of high flow velocity compared to laminar flame speed. The analytical results are compared to measurements on a 2-D laminar flame. The growth rate, shape and amplitude of the saturated structures, as well as the width of the cross-over region are all well described. However we experimentally observe the presence of a large scale transverse gas circulation not predicted by the analysis We attribute this effect to the streamwise variation of the pressure jump across the flame brush.
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Combustion, Science & Technology, Vol 149, pp. 35-52, 1999.
J.M. Truffaut and G.Searby.
Abstract. We present an experimental study of the growth rate of the Darrieus-Landau instability on propane-air and on oxygen enriched propane-air flames using a two-dimensional inverted 'V' flame on a slot burner. We use a novel system of electrostatic deflection to produce an initial perturbation of controlled wavelength and amplitude. The growth rate of this spatially growing perturbation is measured as a function of wavenumber, of equivalence ratio and of oxygen enrichment using high speed flame imaging. The results are analyzed using the Clavin-Garcia laminar flame stability theory (including temperature dependent diffusivities). The dependence of the growth rate on wavenumber and flame speed is reasonably well represented by this theory. As a by-product of this analysis, we obtain values of the Markstein number, which, for rich flames, are found to decrease with equivalence ratio and to increase with oxygen concentration.
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C. Clanet and G. Searby
Abstract. This paper presents the first direct experimental measurements of the growth rate of the Darrieus-Landau instability on a planar laminar premixed flame front. Prior to measurements, the intrinsically unstable flame is maintained stable by a novel technique based on the response of the flame to an acoustic parametric forcing. The growth rates of the instability, measured when the forcing is removed, are in agreement with the theoretically predicted values.
Keywords: Experimental, Laminar flame, Markstein number.
PACS Numbers : 47.20.k, 82.40.Py
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Journal of Fluid Mechanics , Vol. 385, pp.157-197,
1999
C. Clanet, G.Searby and P.Clavin
Abstract. This paper is concerned with the coupling mechanisms leading to the spontaneous generation of sound during flame propagation in a tube open at one end. We consider the cases of premixed gaseous combustion and of premixed spray combustion of decane droplets in air. The flame front propagates from the open to the closed end of a tube and, for a particular position, starts to amplify a longitudinal acoustic mode of the tube. We call this mode the primary acoustic instability and focus our study on the physical mechanisms responsible for sound amplification. Measured amplification rates are compared to calculated values In the gaseous case, it is shown that the instability results from a coupling between the acoustic acceleration field and the geometry of the flame front separating the burnt gases from the denser unburnt mixture The situation is quite different in the spray case. The primary acoustic instability is much stronger and results from a modification of the inner structure of the flame. This modification arises from the velocity lag of the droplets in the acoustic velocity field, leading to a modulation of the fuel flux at the flame.
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Jean-Marie Truffaut, Geoff Searby and Louis Boyer
Abstract. This communication shows that the change in the number of moles of species during combustion can make a strong contribution to the acoustic power radiated by turbulent flames and cannot be systematically neglected. Starting from standard conservation equations, we derive an expression for the acoustic pressure radiated in the far field of a compact region of fluid where low Mach number non-isomolar combustion takes place In this formulation, the contributions from 'molar' and thermal expansion appear explicitly. We also give a formulation in which the sound emission arising from purely non-stationary and from purely convective effects appear independently. As an application of the theory, we derive the acoustic power emitted by a premixed flame in the flamelet regime. Numerical evaluations show that the contribution of molar expansion to the acoustic power is between 2 and 5.6 dB (260 % increase) for some common hydrocarbon-oxygen flames.
Pacs 43.28, 43.50, 47.70
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F. Baillot*, D. Durox**, S. Ducruix**, G. Searby***, L. Boyer***.
*LMFN / CORIA UMR-6614, CNRS / INSA / Université, 76821 Mont-St-Aignan
Cédex, France.
**Laboratoire EM2C, CNRS / ECP, 92295 Châtenay-Malabry, France.
***IRPHE, UMR-6594 du CNRS, service 252, Université St-Jêrôme,
13397 Marseille Cédex 20, France.
Abstract . This paper reports experiments on initially quasi-conical premixed flames subjected to acoustic forcing of the cold gases with high amplitude and high frequency (= 1000 Hz). The resulting hemispherical-shaped flame, induced by a restabilization effect described previously by Durox et al., shows a parametric instability when stronger acoustic forcing is applied (the oscillating acceleration is typically about 1000g). In this case, the front exhibits unsteady cusp-shaped cells. These patterns oscillate with a period which is twice the acoustic period. This state is identified as the parametric response of a harmonic oscillator.
Key Words: Acoustic forcing, parametric instability, premixed conical flames.
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D. Durox**, F. Baillot*, G. Searby*** and L. Boyer***.
*LMFN / CORIA UMR-6614, CNRS / INSA / Université, 76821 Mont-St-Aignan
Cédex, France.
**Laboratoire EM2C, CNRS / ECP, 92295 Châtenay-Malabry, France.
***IRPHE, UMR-6594 du CNRS, service 252, Université St-Jêrôme,
13397 Marseille Cédex 20, France.
Abstract. A conical flame, in the presence of high frequency
(= 1000 Hz) and high amplitude acoustic modulation of the cold gases, deforms
to a shape which is approximately hemispherical. It is shown that the acoustic
level required to produce a hemispherical flame is such that the ratio
of acoustic velocity to laminar combustion velocity is about three. This
flame flattening is equivalent to the phenomenon of acoustic restabilisation
observed for cellular flames propagating in tubes The transition between
the conical flame and a hemispherical flame is described. The surface area
of the reaction zone of the flame is found to be unmodified when the flame
flattens. The velocity field at the burner outlet is examined with and
without flame The mean flowlines are strongly deflected when the hemispherical
flame is present.
We show that the presence of the flame creates an unusual situation
in which the oscillating flow controls the geometry of the mean flow.
Keywords: Acoustic interaction, Experimental, Laminar flame.
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C. Clanet and G.Searby
Abstract. We present an experimental study of the 'tulip flame' phenomenon using high-speed photography. Contrary to most previous studies, the work is in a simplified quasi constant pressure configuration in a half-open tube. It is shown that the salient features of the different stages of the flame propagation and shape can be explained by a simple geometrical model of the interaction between the flame front and the gas dynamics. In particular, the tulip flame results from an inversion of the flame front curvature caused by the deceleration related to loss of flame surface area. Finally, the experimental results obtained by other authors in closed vessels are in reasonable agreement with the analysis presented.
Keywords: Premixed laminar flames, Fluid dynamic aspects of combustion, Unsteady combustion
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J.L. Gauducheau , B. Denet and G. Searby.
Combustion Science & Technology, Vol. 137, pp.81-99, 1998.
Abstract: We perform a numerical study of the effect of including a small amount of hydrogen in lean methane-air premixed flames at high pressure and high temperature conditions. It has been shown recently (Bell and Gupta (1997)) that hydrogen addition extends the lean operating limit of natural gas engines, leading to a potential decrease in pollutant formation. We suggest here that the origin of this effect is that, at constant global equivalence ratio, the stretch resistance of these flames is considerably increased by hydrogen blending, while other flame properties, such as ignition time and burnt gas temperature, are comparatively little modified.
Keywords: Lean methane-hydrogen-air flames, Stretched flames, Extinction, Pollutant formation, Spark ignition engines.
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