Response Of Laminar Premixed Flames Research Articles

Nonlinear response of laminar premixed flames to dual-input harmonic disturbances

In gas turbines, aero-engines and rocket engines, flames are always disturbed by perturbations of dual or multiple harmonic frequencies, resulting in corresponding combustion instability. This paper analyses the nonlinear response of laminar premixed flames to dual-input harmonic disturbances to further understand those associated combustion instability. Nonlinear results of flame dynamics were derived from analytical and numerical solutions of the G-equation. The spatial front-tracking of premixed flames was obtained, where types of nonlinear behaviors were classified and related mechanisms of that were elucidated. A dual-input flame description function (DIFDF) was proposed to separately determine global nonlinearities of flame responses of fundamental and higher harmonics frequencies under dual-input disturbances. The fundamental frequency response consists of linear and nonlinear components, and the higher harmonic frequency one is purely nonlinear. The DIFDF properties of conical and "V" flames were compared, with particular emphasis on their differences in nonlinear behavior. The spatial and global effects of the second input frequency on the flame kinematics perturbed by the first frequency were also clarified. Furthermore, the roles of perturbation amplitude and flame height in spatial flame dynamics and DIFDF were quantified.

Analysis of Lewis number effects on dynamic response of laminar premixed flames

The dynamic response of premixed flames with different fuel Lewis numbers is crucial to understand for the design of safe combustion chambers with wide operating range. Due to preferential diffusion effects associated with fuel Lewis number for lean mixtures, a premixed flame responds differently to flame stretch. These responses could manifest in the flame’s response to small perturbations. In order to investigate this effect, in this study, lean premixed hydrogen, methane and propane flames at the same adiabatic unstretched flame speed are studied using numerical simulations. Steady unperturbed flames show significant differences in flame stand-off distances, flame height, flame stabilization limits, burner temperature and recirculation zone length. Flames are perturbed using a step function excitation and noticeable changes in the gain and phase of the flame transfer function are found even when the flame burning velocity and the inlet flow speed are kept the same. Maximum gain of the response is found to increase with the mixture Lewis number and is shown to be directly dependent on the flame tip burning strong or weak. Phase difference at low frequencies is found to depend on the average of the time scales of the recirculation vortex which in turn depends on the flame burning stronger or weaker under the influence of positive stretch at the flame base, axial convective wave and perturbation travelling along the flame front. Time for the flame to settle to a new position after the step excitation is found to correlate well with the sum of time scales of vortex, flame tangential speed and flame tip speed. Overall, it is found that hydrogen flame responds the fastest to the perturbations and exhibits smaller increase in gain compared to methane and propane.

A novel reduced-order model method for characterization of acoustic response of laminar premixed flames

This study presents a general, predictive and cost-efficient reduced-order modeling (ROM) technique for characterization of laminar premixed flame response under acoustic modulation. The model is built upon the kinematic flame model–G-equation to describe the flame topology and dynamics, and the novelties of the ROM lie in i) a procedure to create the compatible base flow that can reproduce the correct flame geometry and ii) the use of a physically-consistent acoustic modulation field for the characterization of flame response. This ROM addresses the significant limitations of the classical kinematic model, which is only applicable to simple flame configurations and relies on ad-hoc models for the modulation field. The ROM is validated by considering the acoustically-excited laminar premixed methane/air flames in conical and M-shape configurations, experimentally study by Durox et al. Proc. Combust. Inst., 32 (2009). To test the model availability to practical burners, a confined flame configuration Cuquel et al., Proc. Combust. Inst., 34 (2013) is also employed for model evaluation. The model accuracy is evaluated concerning flame geometrical features and flame describing function, and assessed by comparing the ROM results with both the experimental measurements and the direct-numerical-simulation results. It is found that the flame describing/transfer functions predicted by the ROM compare well with reference data, and are more accurate than those obtained from the conventional kinematic model built upon heuristically-presumed modulation fields.

Consequences of flame geometry for the acoustic response of premixed flames

This study investigates the consequences of flame geometry for the linear response of laminar premixed flames to acoustic perturbations, as expressed by the flame transfer function (FTF). Analytical G-equation-based response models are derived for Slit, Bunsen and Wedge type flames; their respective characteristics are analyzed and validated against data obtained from high fidelity numerical simulations. Motivated by the poor agreement between numerical and analytical flame response predictions, particularly for Slit flames, an extension to the well-established incompressible-convective velocity model is proposed, which employs a Gaussian kernel function. Such a kernel disperses the flame response in time and leads to very good agreement with high fidelity numerical simulations. The validity of the model is further confirmed by comparing model predictions with experimental data taken from the literature. Analyzing the analytical flame response modeling concepts in detail, we find that the surface integration, which is required to compute the change of the global heat-release rate from the instantaneous flame front deflections, constitutes the most significant geometry-related property affecting the FTF. The linearized global heat-release rate of stiffly anchored Slit flames reacts only to movements of the flame tip and, hence, these flames respond time delayed to imposed flame front perturbations. Bunsen flames continuously transform convected flame front deflections to changes in the heat-release rate and, therefore, show a more pronounced low-pass behavior than Slit flames. The heat-release rate of Wedge flames reacts to both movements of the flame tip and the integral of instantaneous flame front deflections. Hence, perturbations of the flame front initially have a rather weak effect until they reach the flame tip, where a sudden and strong response is provoked. This leads to the occurrence of high peak gain values in the corresponding FTF.

Transient response of a laminar premixed flame to a radially diverging/converging flow

Laminar flamelets are often used to model premixed turbulent combustion. The libraries of rates of conversion from chemical to thermal enthalpies used for flamelets are typically based on counter-flow, stained laminar planar flames under steady conditions. The current research seeks further understanding of the effect of stretch on premixed flames by considering laminar flame dynamics in a cylindrically-symmetric outward radial flow geometry (i.e., inwardly propagating flame). This numerical model was designed to study the flame response when the flow and scalar fields align (i.e., no tangential strain on the flame) while the flame either expands (positive stretch) or contracts (negative stretch, which is a case that has been seldom explored) radially. The transient response of a laminar premixed flame has been investigated by applying a sinusoidal variation of mass flow rate at the inlet boundary with different frequencies to compare key characteristics of a steady unstretched flame to the dynamics of an unsteady stretched flame. An energy index (EI), which is the integration of the source term in the energy equation over all control volumes in the computational domain, was selected for the comparison. The transient response of laminar premixed flames, when subjected to positive and negative stretch, results in amplitude decrease and phase shift increase with increasing frequency. Other characteristics, such as the deviation of the EI at the mean mass flow rate between when the flame is expanding and contracting, are non-monotonic with frequency. Also, the response of fuel lean flames is more sensitive to the frequency of the periodic stretching compared to a stoichiometric flame. An analysis to seek universality of transient flame responses across lean methane–air flames of different equivalence ratios (i.e., 1.0–0.7) using Damköhler Numbers (i.e., the ratio of a flow to chemical time scales) had limited success.

An analytical model for the impulse response of laminar premixed flames to equivalence ratio perturbations

The dynamic response of conical laminar premixed flames to fluctuations of equivalence ratio is analyzed in the time domain, making use of a level set method (“G-Equation”). Perturbations of equivalence ratio imposed at the flame base are convected towards the flame front, where they cause modulations of flame speed, heat of reaction and flame shape. The resulting fluctuations of heat release rate are represented in closed form in terms of respective impulse response functions. The time scales corresponding to these mechanisms are identified, their contributions to the overall flame impulse response are discussed. If the impulse response functions are Laplace transformed to the frequency domain, agreement with previous results for the flame frequency response is observed. An extension of the model that accounts for dispersion of equivalence ratio fluctuations due to molecular diffusion is proposed. The dispersive model reveals the sensitivity of the premixed flame dynamics to the distance between the flame and the fuel injector. The model results are compared against numerical simulation of a laminar premixed flame.

Experimental investigation of the response of laminar premixed flames to equivalence ratio oscillations

A detailed experimental analysis of laminar premixed methane/air flames subject to equivalence ratio oscillations is presented. The equivalence ratio of methane/air flames was periodically modulated by the addition of methane into the stationary fuel/air flow of a lean premixed flame. The reaction of the flame as a function of amplitude and frequency of the modulation was investigated in a parametric study. The flames were operated at reduced pressure (70 mbar) in order to increase the spatial resolution across and within the flame front and to approximate the time and length scales of the flame and the induced equivalence ratio oscillations in an order of magnitude of 10 Hz. The detection and evaluation of OH*-chemiluminescence revealed the shape and position of the flame front. One-dimensional laser Raman scattering was applied in order to simultaneously and quantitatively determine the concentration profiles of the major species and the temperature along the symmetry axis of the flame. The results show that several interacting effects occur, which have different dependencies on the oscillation frequency: first, a “macroscopic” reaction of the flame arises from the variation of the laminar flame speed and the flow velocity and, hence, its location. Second, the structure of the flame front is affected by the diffusional transport processes and the influence of the oscillation on the species concentrations. At low frequencies, the flame can follow the oscillations reaching temporarily quasi-steady states at the minimum and maximum fuel fraction levels. At sufficiently high frequencies, the flame tip location remains virtually unchanged. However, the species profiles across the flame front show a significant phase shift relatively to each other and cannot be described by steady states throughout the oscillation period.

Time-domain analysis of thermo-acoustic instabilities in a ducted flame

The present study focuses on a time-domain approach for investigating the response of laminar premixed flames to acoustic flow perturbations in a straight duct of a uniform cross-section. This alternative perspective has recently been found to facilitate the analysis and interpretation of thermo-acoustic instabilities by providing a more intuitive description of the interaction of the acoustics with the heat-release rate. A framework is first introduced to generate accurate time-series that provide a complete description of the thermo-acoustic system. Advantages include the flexibility to account for different models (delayed, local, and non-local terms), as well as the separation of numerical and modeling errors. Advanced dynamical system techniques are then employed to analyze the low-amplitude (linear) regime. Detailed representation of the acoustic signal inside the duct allows for accurate characterization of the transition from the linear to the non-linear regime, and gives access to the coupled dynamics of complex limit-cycles. In particular, the effect of the heat release on the linear and non-linear response of the duct is analyzed in detail. The presented capabilities are found to yield physical insight with relative ease, and are expected to produce interesting results by revisiting existing experimental and numerical strategies for the study of thermo-acoustic instabilities.

Novel perspectives on the dynamics of premixed flames

The present study develops an alternative perspective on the response of premixed flames to flow perturbations. In particular, the linear response of laminar premixed flames to velocity perturbations is examined in the time domain, and the corresponding impulse response functions are determined analytically. Different flame types and shapes as well as different velocity perturbation models are considered. Two contributions to the flame response are identified: a convective displacement of the flame due to velocity perturbations, and a restoration mechanism, which is a consequence of the combined effects of flame propagation and flame anchoring. The impulse responses are used to identify the relevant time scales and to form non-dimensional frequencies. The link of the present results to previous studies formulated in the frequency domain is established. The time domain approach is found to facilitate analysis and interpretation of well-known properties of premixed flames such as excess gain, periodic cutoff and self-similar aspects of flame response. Characteristic time scales of response appear naturally and can be interpreted in a straightforward manner.

Transient electric field response of laminar premixed flames

In this study the effects of weak electric fields on laminar premixed Bunsen flames were studied using planar laser-induced fluorescence (PLIF) of the formaldehyde molecules and the OH-radicals for flame structure characterization. Simultaneously particle image velocimetry (PIV) is applied to determine the changed flow field of the flame when a positively charged electrode is placed over a laminar Bunsen type flame while the burner is grounded. By application of static fields the flame front is pushed towards the burner and is constrained, which can be attributed to the momentum transfer by the ionic wind. For rich flames the ionic wind effect is intensified due to the increase of the charge carriers and larger momentum transfer of positively charged ions to the neutral species. Consequently, a stronger flow deceleration results in the order of 0.8–1.6m/s in the post-oxidation zone at supply voltages of 6kV. The ionic wind was maximized for increased flow velocity which is attributed to the increased flame surface and number of charged species. An excitation of the flame with voltage step functions was conducted to study its transient behavior. First flame response was detected at the flame root point with a response time of 2–4ms, which is an order of magnitude faster than values provided in the literature for the integral flame. This first flame response occurred after the space charge zones were built-up and the main flame response was detected 6ms after the voltage rising edge in the whole flame.