Heat Release Perturbations Research Articles

Nonlinear dynamical features of vortex-acoustic lock-on in a backward-facing step combustor

Unstable shear layers characteristic of step combustors display strong vortex shedding and play a dominant role in combustion instability. Past non-premixed flame experiments with Reynolds number (Re) as the bifurcation parameter showed that during instability, the frequency of acoustic oscillations locks-on to the natural vortex shedding mode for a range of Re. In the present work, we study the dynamical features of this type of lock-on. We employ a vortex model to bring out the nonlinearity in the flame response to vortical perturbations. This is coupled with a Galerkin model for the acoustic field. Regimes of aperiodic oscillations, low-amplitude lock-on and high-amplitude lock-on are predicted in agreement with experimental trends. Phase portraits show a transition to instability during lock-on via a supercritical Hopf bifurcation with an increase in limit cycle amplitudes. Synchronisation between the acoustic pressure and vortex-driven heat release perturbation is studied using recurrence analysis. The system transitions from asynchronous to phase synchronisation in the low-amplitude lock-on regime, characterised by an increasing degree of phase correlation. In the high-amplitude lock-on regime, a state of generalised synchronisation exists, where in addition to the phase, the amplitudes also show strong correlation.

Velocity and mass diffusivity effects on the linear and nonlinear phenomena of the Burke-Schumann flame with acoustic excitation

The dynamics of the Burke-Schumann flame in terms of the Peclet number variation were investigated. The effect of the Peclet number on the flame shape and heat release perturbation in the theoretical study was experimentally confirmed. This number changed through alterations in the average velocity and fuel composition. In addition, the nonlinear effects were reported. These effects were made by different magnitude of velocity oscillation of harmonic frequencies. The effect on the 2nd harmonic frequency is larger when the 1st harmonic flame transfer function showed the lower value. Therefore, the nonlinear characteristics are shown within the range of this study. Also, the specific forcing frequency that makes a non-oscillated flame phenomenon is shown. This frequency makes the very low heat release perturbations and 2nd harmonic oscillations.

Stability switching behavior of thermoacoustic oscillation in Rijke tube

Large-amplitude self-excited thermoacoustic oscillations arising due to the interaction between unsteady heat release and acoustic pressure fluctuations have been encountered in many thermal devices. These oscillations may lead to unwanted structural vibrations and efficiency reduction while emitting loud noises, and thus the predicting of such oscillations is very important. Physically, oscillation is a kind of instability, so stability analysis can be applied to understanding such a phenomenon. The present work focuses on the role of time delay between unsteady heat release and flow perturbation in the stability of thermoacoustic system. To this end, one-dimensional Rijke tube model with both open ends is numerically investigated. In the Rijke tube model, an electric heater is located at the first quarter of the Rijke tube and its unsteady heat release rate is modeled by an empirical model proposed by Heckl. Non-dimensional momentum equation and energy equation of the acoustic perturbation are derived and solved in time domain by using the Galerkin technique. The time evolution of the thermoacoustic oscillations with continuous increase in the time delay is calculated in two different acoustic damping cases, namely the heavily damped case and the weakly damped case, while other parameters are fixed. It is found that in both the heavily damped case and the weakly damped case, the system stability switches between stability and instability as the time delay increases, which is called stability switching and is a typical nonlinear phenomenon in a delay-dependent system. However, compared with in the heavily damped case, in the weakly damped case, the stability region is enlarged and the amplitude of the limit cycle oscillation is increased. Besides, in the weakly damped system, the dominating mode of system shifts in the first three modes instead of keeping in the first mode during increasing the time delay, which suggests that for the weakly damped system, the higher modes cannot be neglected and the system cannot be analyzed with a single-mode model either. Further, the bifurcation plots for the variation of the time delay for these two cases show that the system stability changes with time delay for a period of two, which is equal to the period of the first acoustic mode. As a conclusion, the results of present work indicate that the time delay between unsteady heat release and flow perturbations plays a critical role in generating thermoacoustic oscillations, and the findings of stability switching can help to understand the nonlinear phenomena in thermoacoustic systems.

Acoustic transfer function of a combustion system with premixing chamber

In this study we develop an analytic thermoacoustic model of a combustor for gas turbines. The combustor under consideration is composed of a premixing chamber, a nozzle, and a combustion chamber. Our thermoacoustic model is given as an acoustic transfer function from a heat release perturbation to a velocity perturbation at a flame location. It is shown that the resonance frequencies are functions of three turnaround periods of acoustic waves at each stage, and the area ratios between stages. The resonance modes can be well captured by calculating the poles of the acoustic transfer function, our analytic results show a good agreement with existing measurement data in the literature.

Acoustic damping optimization of the injector based on dynamic mode decomposition in a subscale combustor

The acoustic tuning of a swirl coaxial jet injector mounted upstream a combustion chamber is investigated in the aspect of stabilization of unstable combustion. The injector, which has a primary function to mix the oxidizer injected through the central passage and the fuel injected through the peripheral holes, is designed to be used as a half-wave resonator. The least damped modes are extracted by applying Dynamic mode decomposition (DMD) and the injector length is tuned to damp the second longitudinal mode. Then, the sensitivity of the heat release perturbation to the velocity perturbation at the frequency of the second longitudinal mode is evaluated by flame transfer function calculated by DMD. The relation between these two quantities is achieved by combining two equations, that is, the Crocco’s model and the inhomogeneous wave equation, and enables us to compute Flame transfer function (FTF) at a specific mode. The gain field of FTF shows that the sensitivity of the heat release fluctuation to the inlet velocity fluctuation is minimal with the optimal injector length. The proposed approach for application of dynamic mode decomposition would be a valuable tool in tuning a resonator acoustically, computing efficiently flame transfer function, and quantifying the relative stability of a combustion chamber.

LES Study of Transverse Acoustic Instabilities in a Swirled Kerosene/Air Combustion Chamber

LES is used to study self-excited transverse modes in an atmospheric, square combustor (p = 1 bar). Simulations over a range of different mass flow rates show that transverse modes are present for all cases and exhibit varying RMS pressure amplitudes up to 0.4 bar. Analysis of LES results shows that transverse modes are due to a lock-in mechanism between an hydrodynamic unstable mode typical of swirling flows (the PVC mode or Processing Vortex Core) and the cavity modes. A control method using damping compliant walls (named DCWs) is applied to control the acoustic mode in the LES and to characterize the PVC in the absence of acoustic forcing. This method shows that the highest pressure oscillations appear when the PVC frequency is close to the frequency of the first transverse acoustic mode. A 3D Helmholtz solver is then used to predict the stability limits obtained by 3D LES. To capture transverse modes, a new flame transfer function (FTF) formulation is derived where local heat release perturbations are controlled by the orthoradial acoustic velocity fluctuations. The FTF is measured in the LES and when it is included in the Helmholtz solver, it allows to recover the stability zones observed in the LES.

Rankine vortex evolution in a gas with heat release source

The influence of a heat release source with temperature-dependent power on the stability of a Rankine vortex has been studied. A condition for the formation of a radially convergent swirling flow with increasing vorticity is found for a medium with a positive feedback between nonequilibrium heat release perturbations and the pressure at the vortex core.

Experimental analysis of nonlinear flame transfer functions for different flame geometries

Nonlinear features of flame dynamics are characterized by measuring the flame transfer functions for different input levels. This provides a family of gain and phase curves, which constitute the Flame Describing Functions (FDF) and can be used to analyze self-sustained combustion oscillations. Experiments correspond to four different flame geometries established for the same injection conditions: a single conical flame (CF), a “V”-flame, an “M”-flame and a collection of small conical flames (CSCF) stabilized on a perforated plate. It is shown that the gain and phase evolve with the level of modulation and that the response notably depends on the steady-state configuration. In the conical flame case, the gain weakly depends on the level of modulation while the phase changes linearly with frequency at low amplitudes. At higher amplitudes the phase first evolves linearly and then saturates. In the “V” and “M”-flame cases the gain exceeds unity in an intermediate range of frequencies. In that range the gain decreases monotonically as the amplitude increases. The phase evolves in a quasi-linear fashion with frequency and is essentially independent of the amplitude. In the CSCF case the gain also exceeds unity in a narrow range of frequencies and drops first slowly and then more rapidly with the amplitude of input perturbations. The phase is also quasi-linear with frequency but its slope rises as the amplitude increases indicating that the time lag associated to heat release perturbations measured with respect to the incoming disturbances is augmented when the amplitude level becomes large. All these features strongly influence the nonlinear response of the flame, its dynamics under sustained oscillations and the steady-state level reached at the limit cycle.

Regions of Self-Excitation of a Singing Flame

Based on the analysis of experimental self-excitation regions of a diffusion singing flame of methane its transfer functions considering correlation of heat release perturbations with oscillations of air velocity and gas injection have been determined. Self-excitation region boundaries for the range of parameters have been calculated using the obtained data.

Dynamics of confined premixed flames submitted to upstream acoustic modulations

Dynamics of inverted conical flames anchored on a central bluff-body is investigated in confined and unconfined conditions. The flames are modulated by a driver unit placed upstream. Flame dynamics is strongly coupled to the evolution of large scale structures induced by the modulation and shed from the injector nozzle lip. To study the influence of confinement on the flame motion, the response is measured for different diameters of the duct bounding the flame. This induces changes in the confinement parameter defined as the ratio of the injection duct diameter to the combustor diameter. Natural emission imaging, transfer function measurements and PIV data serve to determine the effect of confinement on the flame response for a set of modulation amplitudes. It is found that when the confinement ratio is low, the time delay between the velocity signal at the burner outlet and heat release perturbations remains essentially constant indicating that the flame is weakly affected by the presence of the wall. As the confinement ratio is increased, the time delay and the gain of the flame transfer function are modified. It is found that interaction with the wall strongly influences the dynamics of the flame tip, the flame wrinkling geometry in the vicinity of the boundary, and to a great extent the amplitude of response. A numerical simulation provides additional information on the fresh stream dynamics inside the tube, and on the dynamical interactions between the flow and the flame.

Background Noise Effects on Combustor Stability

This paper considers the effects of background turbulent fluctuations upon a combustor's stability boundaries. Inherent turbulent fluctuations act as both additive and parametric excitation sources to acoustic waves in combustors. Although additive noise sources exert primarily quantitative effects upon combustor oscillations, parametric noise sources can exert qualitative impacts upon its dynamics; particularly of interest here is their ability to destabilize a system that is stable in the absence of these noise sources. The significance of these parametric noise sources increases with increased background noise levels and, thus, can play more of a role in realistic, high-Reynolds-number systems than experiments on simplified, lab-scale combustors might suggest. The objective of this paper is to determine whether and/or when these effects might be significant. The analysis considers the effects of fluctuations in damping rate, frequency, and combustion response. It is found that the effects of noisy damping and frequency upon the combustor's stability limits is relatively small, at least for the fluctuation intensities estimated here. The effects of a noisy combustion response, particularly of a fluctuating time delay between flow and heat-release perturbations, can be quite significant, however, in some cases for turbulence intensities as low as u' r m s /u ∼ 5-10%. These results suggest that deterministic stability models calibrated on low turbulence intensity, lab-scale combustors might not adequately describe the stability limits of realistic, highly turbulent combustors.

Response of a laminar premixed flame to flow oscillations: A kinematic model and thermoacoustic instability results

Combustion instability is a resonance phenomenon that arises due to the coupling between the system acoustics and the unsteady heat release. The constructive feedback between the two processes, which is known to occur as a certain phase relationship between the pressure and the unsteady heat release rate is satisfied, depends on many parameters among which is the acoustic mode, the flame holder characteristics, and the dominant burning pattern. In this paper, we construct an analytical model to describe the dynamic response of a laminar premixed flame stabilized on the rim of a tube to velocity oscillation. We consider uniform and nonuniform velocity perturbations superimposed on a pipe flow velocity profile. The model results show that the magnitude of heat release perturbation and its phase with respect to the dynamic perturbation depend primarily on the flame Strouhal number, representing the ratio of the dominant frequency times the tube radius to the laminar burning velocity. In terms of this number, high-frequency perturbations pass through the flame while low frequencies lead to a strong response. The phase with respect to the velocity perturbation behaves in the opposite way. Results of this model are shown to agree with experimental observations and to be useful in determining how the combustion excited mode is selected among all the acoustic unstable modes. The model is then used to obtain a time-domain differential equation describing the relationship between the velocity perturbation and the heat release response over the entire frequency range.

Theory of Laminar Flame Stability. I. Analytic Stability Condition

The stability of propagation of a laminar flame or combustion wave is studied for a general type of flame propagating medium. This is done by investigating the stability of the steady-state solution of the flame equations for such a system. The method is to solve the linearized system of partial differential equations resulting from an instantaneous heat release perturbation of the steady-state solution. An approximate solution in analytic form to this linearized partial system is obtained. This permits the statement of an analytic stability condition, and shows the existence of stability limits. The existence of stability limits is suggested as an explanation of inflammability limits.