Daniel Durox

A unified model for the prediction of laminar flame transfer functions : comparisons between conical and V-flame dynamics

Transfer functions of premixed laminar flames submitted to incident flow perturbations are envisaged and a unified model is derived analytically. This model, based on a linearization of the G-equation for an inclined flame, includes convective effects of the flow modulations propagating upstream of the flame. It is shown that the flame dynamics is governed by two relevant parameters, a reduced frequency, ω∗, and the ratio of the flame burning velocity to the mean flow velocity, SL/ῡ, or equivalently the flame angle α with respect to the flow direction. In the limit of low driving frequencies, the flame motion is only controlled by ω∗ and the unified model reduces to previous kinematic formulations derived for rim stabilized conical flames and V-flames anchored on a central rod. Flame transfer functions for these flame geometries with the different velocity models proposed are derived and limiting cases are examined. In the conical flame case, the low-frequency model gives a good approximation of the gain, but only a fair approximation of the phase. Convective effects are shown to induce an increasing phase lag, while low-frequency models predict a saturation phenomenon. The convective model derived in this article improves results for the gain and the phase which agree with numerical simulations and experiments. It is shown in particular that 1) the correct transfer function phase trend is retrieved and depends on the flame angle α; 2) the reduced cut-off frequency corresponds to a situation where the convective wavelength along the flame front λ = (ῡ cos α)/f equals the flame length L; and 3) the flame response is weakly affected by the amplitude of these perturbations. In the V-flame case, the low-frequency model yields a good approximation of the phase but does not feature gain values in excess of one found in the simulations. This behavior is correctly predicted by the convective model and is shown to depend on the flame angle α. A V-flame behaves as an amplifier in a certain range of frequencies. It is shown that these types of flames are more susceptible to combustion instabilities than conical flames. The V-flame response is also shown to strongly depend on the amplitude of the fluctuations even for moderate perturbation levels.

Combustion Dynamics and Instabilities: Elementary Coupling and Driving Mechanisms

Elementary processes that can be involved in the development of combustion instabilities in gas turbine combustors are described. The premixed mode of combustion is considered more specie cally because it is used in most advanced gas turbine systems. The processes envisaged portray the combustion dynamics of real systems, but they are analyzed in simple laboratory cone gurations. Among the many possible interactions, the most relevant mechanisms are those that generate e uctuations in heat release or induce pressure perturbations. Some typical paths are highlighted to help in the understanding of the multiple links that can exist between elementary processes. Processes involving acoustic/e ame coupling, unsteady strain rates, e ame response to inhomogeneities, interactions of e ames with boundaries, and e ame/vortex interactions are specie cally examined. For each process, a driving or a coupling path is proposed relating heat release e uctuations to acoustic variables in certain cases or leading from acoustic variables to heat release e uctuations in other cases. Stress is also put on characteristic time lags, which are key parameters in the triggering and development of instabilities. Well-controlled experiments illustrate the many possibilities and can serve to guide the modeling effort and to validate computational tools for combustion dynamics.

Theoretical and experimental determinations of the transfer function of a laminar premixed flame

The dynamical behavior of laminar premixed flames is investigated in this article. The flame response to incident perturbations is characterized with a transfer function relating the flow velocity modulations and the heat release fluctuations. This function is obtained using the assumptions introduced in previous studies by Fleifil et al. , but the model is extended to account for any flame angle (i.e., any operating condition). The modeling shows that phenomena can be described using a single control parameter taking the form of a reduced frequency ω* . This quantity is derived as ωR/S L cos α 0 , where ω is the angular frequency, R is the burner radius S L is the laminar burning velocity, and α 0 is the half-cone angle of the steady flame. this parameter may be used to describe the response of the burner to acoustic modulation, knowing its geometry and the flame properties. Two characteristic times have been determined. The first one defines the cut-off frequency of the low-pass filter associated with the flame response. The second one enables the prediction of the time lag between the velocity modulation at the burner exit and the flame heat release the exact transfer function and an approximation in the form of a first-order model are compared with an extensive set of experimental data corresponding to a range of equivalence ratios and two burner diameters. Good agreement is obtained for low values of the reduced frequency. In an intermediate range of frequencies, the experimental phase exceeds the theoretical values by a significant amount, the difference between theory and experiment is due to the simplifying assumptions used in the model.

Modeling Tools for the Prediction of Premixed Flame Transfer Functions

The response of flames to incident perturbations is of central interest in combustion dynamics analysis. The problem can be described in the linear regime by a transfer function. It is shown in this article that the description of the perturbed velocity field incident on the flame front is of crucial importance when dealing with the flame transfer function. This is demonstrated in the special case of a premixed flame anchored on the rim of a burner submitted to flow perturbations. Previous studies of this problem have shown that in the low-frequency range the flame dynamics was governed by a single dimensionless frequency, and that a first-order model described the general behavior of the flame response when the disturbance wave length exceeds the flame height. Complementary experiments reported in this article indicate that this model fails when the modulation frequency is increased. On this experimental basis, a revised formulation of the velocity perturbation incident on the flame is proposed which accounts for the flame cusping phenomenon when more than one wavelength wrinkles the flame front. Combining this more realistic velocity field with a level set approach for the flame dynamics a full numerical integration of the G -equation is carried out. The transfer function is computed over the whole useful range of frequencies. Experimental data are then compared with analytical and numerical predictions. It is shown that the current first-order models underestimate the phase lag between velocity and heat release fluctuations. A constant phase shift is obtained in the high-frequency limit which does not correspond to observations. The new velocity model yields a better representation of the flame response in a wider range of frequencies. It is shown in particular that the modeled phase lag between combustion and flow perturbations increases with frequency, as is effectively observed.

Experimental and theoretical study of a premixed vibrating flame

Abstract An experimental study of vibrating flames above a cylindrical burner has been conducted in order to examine some of the fundamental characteristics of the flow perturbations-combustion interaction. Here the perturbation chosen is a space-time sinusoidal flow velocity. The vibrational nature of the flow has been studied with and without the flame, using a LDV setup and a tomography system. The prevalent kinematic phenomenon is an effect of flow pumping—indeed the velocity perturbation propagates along the vertical axis nearly at the mean flow velocity. A laminar flame in such a flow modulation (

Dynamics of and noise radiated by a perturbed impinging premixed jet flame

This paper presents an experimental study of an acoustically excited, premixed, laminar-jet flame impinging on a water-cooled plate. Without excitation, different types of flame shapes are identified. With excitation, a strong noise is produced. The mechanism of flame-induced noise generation is investigated in detail. The results show that the modulation of the flow upstream of the flame produces strong variations in the flames area and also intense noise emission. The amplitude of the sound exceeds by one or two orders of magnitude that associated with a flame under the same flow modulation, but without the plate. The source of sound is identified as the cyclic extinction of flame area as the jet interacts with the cool plate. The link between the far-field pressure, the chemiluminescence from the flame and the flame surface is successfully compared with classical results of combustion-noise theory.

Flame Dynamics and Combustion Noise: Progress and Challenges

This article proposes a review of the state of knowledge in the field of combustion noise. The survey comprises an initial discussion of indirect and direct noise sources and their general characteristics, a summary of expressions devised to estimate combustion noise from turbulent flames, a discussion of the fundamental equations describing sound emission from a reactive region and an evaluation of scaling methods for combustion noise. An account is provided of a set of experiments on noise radiation from perturbed laminar flames. Sources of intense radiation of sound are identified and theoretical expressions of the pressure field are compared with detailed measurements from well controlled experiments. These experiments indicate that flame dynamics determine to a great extent the radiation of sound from flames. This is further demonstrated with experiments dealing with effects of confinement. Links between combustion noise and combustion instabilities are drawn on this basis. These two aspects are usually treated separately but they are manifestations of similar processes. Much of the current effort in the field of combustion noise focuses on numerical estimation techniques using modern computational tools. The state of the art is less advanced than in computational aeroacoustics (CAA) but it is possible to foresee that computational combustion acoustics (CCA) will progressively evolve into a well established scientific field.

Influence of gravity and pressure on pool fire-type diffusion flames

Experiments are conducted to study the effects of gravity and pressure on the characteristics of diffusion flames of the pool fire type, that is, a diffusion flame stabilized on a burning horizontal fuel surface. In the experiments, the pool fire is simulated by injecting at very low velocity, a gaseous fuel (ethane) through a small-scale, porous, flat, horizontal surface burner and generating a diffusion flame over the burner by the reaction of the gaseous fuel with air. The resulting diffusion flame is characterized by a low Froude number. The diffusion flame characteristics (visual appearance, height, radiant output and temperature, and velocity distribution) are investigated at gravity levels ranging from microgravity (parabolic trajectory of an aircraft) to 12 times normal gravity (centrifuge facility—atmospheric pressure), and at ambient pressures ranging from 0.03 to 0.3 MPa (normal gravity). The results provide information about the effects of these variables on the flame characteristics and data for validation of numerical models of diffusion flames. Furthermore, they also help in understanding some of the limitations of Froude, or pressure, modeling of fires. The experiments indicate that the effect of gravity and pressure on the flame characteristics appears primarily through their effect on the buoyantly induced entrainment of air by the flame plume. Although at elevated pressures the effects are similar on the flame size and shape, important differences are observed on their effect on soot formation. It is found that for pressures above atmospheric, pressure has a major influence in soot formation and, consequently, on the radiant characteristics of the flames, increasing as pressure is increased. It is also found that at pressures below atmospheric pressure and gravity have opposite effects on flame size and soot formation and that consequently their effects on flame radiation also differ.

On the shape of flames under strong acoustic forcing : a mean flow controlled by an oscillating flow

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 3. This flame flattening is equivalent to the phenomenon of acoustic restabilization 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 a flame. The mean flow lines are strongly deflected when the hemispherical flame is present. We show that the presence of the flame creates an unusual situation where the oscillating flow controls the geometry of the mean flow.

Acoustically perturbed turbulent premixed swirling flames

The dynamics of a turbulent premixed confined swirling flame is investigated using large eddy simulation. The flame response is determined by introducing an external acoustic forcing at two modulation frequencies corresponding to characteristic values of the flame transfer function obtained experimentally. These values were found to give different responses in terms of gain in a previous series of experiments. The underlying physical mechanisms identified experimentally are investigated numerically. Simulations confirm that swirl number fluctuations and vortex roll-up govern the flame response. It is also confirmed that the first mechanism is associated with a mode conversion process taking place when acoustic waves impinge on the swirler unit. The axial acoustic velocity disturbance on the upstream side of the swirler generates an axial acoustic wave and an azimuthal convective disturbance in the downstream flow. These combined disturbances are retrieved in the simulation and their effect on the swirl number is extracted. Calculations also indicate that vortex shedding synchronized by the acoustic forcing takes place at the injector lip outlet. Vortices originating from this region are convected in the jet shear layer, impinge on the flame, and roll-up the flame tip. This process interferes with oscillations in the flame angle induced by swirl number fluctuations. The phasing of the flame angle with respect to the instant of vortex shedding from the injector lips determines the lifetime of the vortex before interaction with the flame and controls the strength of this interaction. When this lifetime is reduced, the vortex cannot fully develop and the flame response remains weak. For larger lifetimes, the vortex can fully develop and produce larger heat release rate perturbations. This process depends on the forcing frequency, which determines the phasing between swirl number fluctuations and vortices generation.