Heat Release Rate Fluctuations Research Articles

Modeling of the nonlinear flame response of a Bunsen-type flame via multi-layer perceptron

This paper demonstrates the ability of neural networks to reliably learn the nonlinear flame response of a laminar premixed flame, while carrying out only one unsteady CFD simulation. The system is excited with a broadband, low-pass filtered velocity signal that exhibits a uniform distribution of amplitudes within a predetermined range. The obtained time series of flow velocity upstream of the flame and heat release rate fluctuations are used to train the nonlinear model using a multi-layer perceptron. Several models with varying hyperparameters are trained and the dropout strategy is used as a regularizer to avoid overfitting. The best performing model is subsequently used to compute the flame describing function (FDF) using mono-frequent excitations. In addition to accurately predicting the FDF, the trained neural network model also captures the presence of higher harmonics in the flame response. As a result, when coupled with an acoustic solver, the obtained neural network model is better suited than a classical FDF model to predict limit cycle oscillations characterized by more than one frequency. The latter is demonstrated in the final part of the present study. We show that the RMS value of the predicted acoustic oscillations, together with the associated dominant frequencies are in excellent agreement with CFD reference data.

Effect of preheating of the reactants on the transition to thermoacoustic instability in a bluff-body stabilized dump combustor

In the present study, we investigate the effect of preheating of the reactants on the dynamics of a turbulent bluff-body-stabilized dump combustor during the onset of thermoacoustic instability. As we decrease the equivalence ratio towards a low fuel-lean value, we observe the dynamical transition of the combustor from the state of combustion noise to thermoacoustic instability via intermittency. Such an intermittency route to thermoacoustic instability is preserved for the range of preheat temperatures considered in this study. Further, we notice that an increase in the temperature of the reactants advances the point of the onset of thermoacoustic instability in the system. During the state of combustion noise, high temperature preheating of the reactants shifts the anchoring point of the flame from the shaft to the tip of the bluff-body and suppresses the oscillatory behavior of the global heat release rate in the system. We also observe a change in the multifractal characteristics of the heat release rate fluctuations such that the signal properties change from short-range to long-range correlations. On the other hand, preheating of the reactants to high temperatures during the state of thermoacoustic instability engenders a shift in the frequency of the acoustic field from the third unstable mode to the first unstable mode. Moreover, such preheating expanses the flame surface from one half of the combustor (lower) to both halves and, hence, increases the Pearson’s correlation between the local heat release rate fluctuations measured on both halves of the combustor. Thus, we report that the preheating of the reactants significantly alters the dynamical characteristics of a turbulent combustor during the transition to thermoacoustic instability from that observed in the absence of preheating.

Identification and early prediction of lean blowout in premixed flames

Lean premixed combustion is a state-of-the-art technology to meet the stringent emission norms, especially to reduce the NOx emission. In the present study, we focus on the transition to lean blowout of premixed flames. The main objective of the study is to explore some important measures for prediction of lean blowout as the existing methods are not always suitable in early detection of blowout in case of premixed flames. We further consider different cases through which lean condition can be attained. For such cases, we first discuss the flame dynamics prior to blowout. Among different statistical measures, mean, median, root mean square and coefficient of variance of heat release rate fluctuations are found to be useful in blowout prediction. On the other hand, skewness and excess of kurtosis do not show any predictive quality. We also observe that the flickering frequency defined in a specific manner also shows a significant variation near lean blowout. Further, the mean frequency evaluated using Hilbert transform is found to show indication of LBO well before its occurrence. Therefore, the frequency analysis along with statistical analysis of the heat release rate oscillations is found to be very relevant in the context of blowout prediction and can be applied in the practical combustors.

Large eddy simulation on combustion noise in a non-premixed turbulent free flame: Effect of oxygen enhancement

Present work examines the effect of a low-level oxygen concentration enhancement in the oxidizer stream, on the generation of direct combustion noise in a non-premixed turbulent free flame. A hybrid approach utilizing a large eddy simulation, partially stirred reactor combustion model, and Lighthill analogy was employed to predict the sound pressure level in the farfield of the flame. Contributions of different noise sources, including heat release rate and, mole consumption and production rate fluctuations are calculated to predict the sound pressure level in the farfield. Results show that, in comparison to the flame burning with air, the higher temperature in oxygen enhanced flame leads to an increase in the heat release rate and an increase in the rate of consumption and production of the species. The total sound pressure level found to increase by adding oxygen to the oxidizer stream, especially in low frequency ranges. Enhancement of molar oxygen by 10%, increases the noise contribution of the heat release rate fluctuations about 20 dB in low frequency range, and about 10 dB in high frequencies. Additionally, the noise contribution from the mole consumption and production rate decreases about 5 dB in low frequency range and 10 dB in high frequencies.

Experimental investigation of combustion instabilities of a mesoscale multinozzle array in a lean-premixed combustor

Self-excited combustion instabilities in a mesoscale multinozzle array, also referred to as a micromixer-type injector, have been experimentally investigated in a lean-premixed tunable combustor operating with preheated methane and air. The injector assembly consists of sixty identical swirl injectors of 6.5 mm inner diameter, which are evenly distributed across the combustor dump plane. Their flow paths are divided into two groups – inner and outer stages – to form radially stratified reactant stoichiometry for the control of self-excited instabilities. OH PLIF measurements of stable flames reveal that the presence of radial staging has a remarkable influence on stabilization mechanisms, reactant jet penetration/merging, and interactions between adjacent flame fronts. In an inner enrichment case, two outer (leaner) streams merge into a single jet structure, whereas the inner (richer) reactant jets penetrate far downstream without noticeable interactions between neighboring flames. The constructed stability map in the 〈ϕi, ϕo〉 domain indicates that strong self-excited instabilities occur under even split and outer enrichment conditions at relatively high global equivalence ratios. This is attributed to large-scale flame surface deformation in the streamwise direction, as manifested by vigorous detachment/attachment movements. The use of the inner fuel staging method was found, however, to limit the growth of large-amplitude heat release rate fluctuations, because the center flames are securely anchored during the whole period of oscillation, giving rise to a moderate lateral motion. We demonstrate that the collective motion of sixty flames – rather than the individual local flame dynamics – play a central role in the development of limit cycle oscillations. This suggests that the distribution pattern of the injector array, in combination with the radial fuel staging scheme, is the key to the control of the instabilities.

The role of differential diffusion during early flame kernel development under engine conditions – part II: Effect of flame structure and geometry

From experimental spark ignition (SI) engine studies, it is known that the slow-down of early flame kernel development caused by the (Le > 1)-property of common transportation-fuel/air mixtures tends to increase cycle-to-cycle variations (CCV). To improve the fundamental understanding of the complex phenomena inside the flame structure of developing flame kernels, an engine-relevant DNS database is investigated in this work. Conclusive analyses are enabled by considering equivalent flame kernels and turbulent planar flames computed with Le > 1 and Le=1. In Part I of the present study (Falkenstein et al., Combust. Flame, 2020), a reduced representation of the local mixture state was proposed for the purpose of this analysis. Fluctuations in heat release rate attributed to differential diffusion were found to be governed by the parameters local enthalpy, local equivalence ratio, and H-radical mass fraction. Here, a coupling relation for the diffusion-controlled mixture parameter local enthalpy with local flame geometry and structure is derived, characterized by the key parameters κ and |∇c|/|∇c|lam. The analysis shows that the large positive global mean curvature intrinsic to the flame kernel configuration may detrimentally affect the local mixture state inside the reaction zone, particularly during the initial flame kernel development phase. External energy supply by spark ignition may effectively bridge over this critical stage, which causes the impact of global mean flame kernel curvature to be small under the present conditions compared to the overall effect of Le ≠ 1 observed in a statistically planar flame. Once ignition effects have decayed, the mixture state inside the reaction zone locally exhibits an identical dependence on |∇c| as in a strained laminar flame. This implies that differential diffusion effects at Karlovitz numbers representative for part-load conditions are not weakened by small-scale turbulent mixing, which is undesirable for the engine application, but can be favorable in terms of modeling.

Influences of liquid fuel atomization and flow rate fluctuations on spray combustion instabilities in a backward-facing step combustor

Combustion instabilities occurring in spray combustion fields inside a backward facing step combustor have been investigated by performing large-eddy simulations (LES). In this study, the influence of fluctuations in the incoming oxidizer air velocity (caused by drastic pressure oscillations in the combustor during combustion instability) on the droplet diameter distribution (due to atomization) of the injected liquid fuel spray, as well as the influence of pressure oscillations on the fuel flow rate have been taken into consideration using appropriate models. For the temporal fluctuations in fuel droplet diameter distribution, a model for the Sauter Mean Diamter (SMD) of atomized droplets, obtained as a function of spray injection parameters and gas/liquid properties, is incorporated in the LES. Additionally, to consider the temporal fluctuations in fuel flow rate along with its phase difference with the pressure oscillations, a model derived from Bernoullis principle is proposed and employed in the LES. The objective is to examine in detail, the impacts of the fluctuations in fuel droplet diameter distribution and the fluctuations in fuel injection rate individually, as well as the impact of the mutual interaction of these two fluctuations, on the spray combustion instability characteristics. Results of the LES reveal that the temporal fluctuations in fuel droplet diameter distribution resulting from combustion instability, lead to a reduction in the intensity of pressure oscillations and hence the combustion instability’s strength. Additionally, the temporal fluctuations in liquid fuel flow rate strongly influence the intensity of spray combustion instability, and it is observed that the combustion instability intensity increases with the increase in phase difference between the fuel flow rate fluctuations and pressure oscillations. Furthermore, the effect of the temporal fluctuations in fuel droplet diameter distribution resulting in the reduction of combustion instability intensity, becomes more pronounced as the phase shift between the fuel flow rate fluctuations and pressure oscillations becomes larger. It is clarified that the above-mentioned behavior of spray combustion instability, results from the change in the correlation between heat release rate fluctuations and pressure oscillations near the combustor’s dump plane, which is caused by the change in the local residence time of fuel droplets and the local fuel droplet evaporation rate.

Exploring a critical diameter for thermo-acoustic instability of downward propagating flames in tubes

Thermo-acoustic oscillations are observed when a flame ignited at open end of a tube propagates towards the closed end due to interaction between unsteady heat release rate fluctuations from flame and acoustic fluctuations. In our past work, it was found that thermo-acoustic instability increases with decreasing diameter from 7.0 cm to 3.0 cm. A recent study in flame propagation in Hele–Shaw cells showed that thermo-acoustic instability is not observed for plate separation less than or equal to 0.4 cm. Thermoacoustic instabilities cannot be observed in very narrow tubes due to excessive damping from the wall. This opens up the possibility of a critical diameter where thermo-acoustic instability would be maximum. In this work we perform flame propagation experiments with diameter of combustion tube in the range 0.5 cm to 3 cm for a fixed length of 70.2 cm. It was found that thermo-acoustic parametric instability begins at lowest laminar burning velocity when the diameter is around 1.0 cm. This diameter is termed as critical diameter. Critical diameter is found to be independent of Lewis number of mixtures. Existence of a critical diameter is thus proved experimentally. Growth rates of primary instability increase with decreasing diameter and show a maximum around the critical diameter and decrease with further decrease in tube diameter. But, growth rates of secondary instability as well as maximum pressure fluctuation amplitude decreases continuously with decreasing diameter. Mechanisms responsible for these observations and existence of a critical diameter are clarified.

Response of lean premixed swirl tubular flame to acoustic perturbations

This study experimentally examined the response of a lean premixed methane/air swirl tubular flame to the longitudinal acoustic perturbations. Experiments were conducted by varying the acoustic frequency (f0), acoustic power (P0) and inlet air flow rate (QA) to systematically study the acoustic-excited flame dynamics, including the flame stability, flame structure, heat release rate and acoustic pressure fluctuations. The results demonstrated that the lean tubular flame was much sensitive to longitudinal perturbations below 210 Hz. Even at low power of P0, the flame was forced to oscillate intensively when the perturbation was operated in two discontinuous frequency ranges of f0 = 150–200 and f0 = 50–100 Hz, while a weakened oscillation regime was observed in the middle range of f0 = 100–150 Hz; a lower frequency (less than 50 Hz) would extinguish the flame. An increase in P0 intensified the flame oscillation under the perturbations of 50–100 Hz, and even resulted in flame lift-off and blow off with f0 between 150 and 200 Hz. In comparison to f0 and P0, the effects of air flow rate (QA) seemed to be weaker. The proper orthogonal decomposition (POD) analysis was performed to interpret the contributions from the mean mode and fluctuating axial and circumferential modes that led to combustion instability. It was found that as the energy fraction of the axial mode exceeded 5.0%, the flame lift-off appeared in the lean swirl tubular configuration.

Scaling and prediction of transfer functions in lean premixed H2/CH4-flames

Features of the flame transfer function (FTF) are characterized for turbulent, non-swirled, bluff body stabilized “M” flames for different hydrogen and methane blends including pure hydrogen flames. An increase in the cut-off frequency of the FTF is observed for increasing hydrogen concentration. Modulations in the form of peaks and troughs in the gain and the phase were also observed and are shown to be caused by the interaction of two different flow disturbances, acoustic and convective, originating upstream of the flame. The first mechanism is due to the acoustic velocity fluctuations imposed at the base of the flame. A Strouhal number scaling based on the flame height and bulk velocity is shown to collapse the phase slopes and the cut-off frequencies. The second mechanism is shown to be due to vortex shedding from the grub screws used to align the bluff body in the inlet pipe. The associated convective time-delay is used to define a second Strouhal number which collapses the modulations in the gain and phase.A model is developed that separately considers the impulse response of each mechanism and is interpreted as a distribution of time lags between velocity fluctuations and the unsteady heat release rate. The distributed time lag (DTL) model consists of two distributions that are shown to capture all the features of the FTFs. The distributions show that the acoustic and convective mechanisms behave as a low pass filter and band pass filter, respectively. This results in a band of frequencies where they interact through superposition driving fluctuations of heat release rate. Similar interactions are shown to exist in the forced cold flow revealing that they are of hydrodynamic origin. Further, the band of frequencies are shown to be centered around the natural shedding frequency of the grub screws appearing as peaks in the unforced energy spectra of the velocity at the dump plane.Finally, a generalized model which takes as an input the bulk velocity, flame height and a geometric parameter is derived assuming a linear dependency of the DTL parameters. The model is shown to predict the behavior of the FTFs relatively well and can potentially be used to analyse regions in the operating conditions map which have not been experimentally tested.

Fuel and Equivalence Ratio Effects on Transfer Functions of Premixed Swirl Flames

This paper reports on the effects of fuel and equivalence ratio on the response of lean premixed swirl flames to acoustic perturbations of the flow, at atmospheric pressure. The response is analyzed using flame transfer functions, which relate the relative heat release rate fluctuations from the flame to the relative velocity fluctuations of the incoming flow. Two fuels, propane and methane, and five equivalence ratios are considered. The 10 flames investigated are selected to exhibit the local maximum of the transfer function gain around the same frequency, 176 Hz. The results show that changing fuel and equivalence ratio influences both the gain and the phase of the transfer function. The changes observed at 176 Hz, where the dynamics of the flame is mainly controlled by the flame vortex roll-up mechanism, are discussed. Based on the analysis of the flowfields and the flame wrinkling, the laminar burning velocity and the flame temperature are identified as the main parameters controlling the gain. They have two competing effects: first, by enhancing the flame vortex roll-up and, second, by affecting the strength of the vortex generated by the acoustic forcing due to changes in the height of the flame stabilization location.

Experimental Investigation on the Route to Vortex-acoustic Lock-In Phenomenon in Bluff Body Stabilized Combustors

ABSTRACT We investigate the phenomenon of vortex-acoustic lock-in in a bluff body stabilized Rijke type combustor, which experiences self-excited thermoacoustic oscillations. The focus is to identify and understand the various regions (in airflow rate) occurring during the transition to lock-in. In this regard, an axisymmetric bluff body stabilized burner is used, which sheds Benard–Von Karman vortices. The dynamics of the combustor is monitored through the measurement of unsteady pressure and heat release rate fluctuations. At low airflow rates, peaks associated with both vortex shedding and acoustic modes are observed in the measured spectra. These peaks are far apart. As the airflow rate is increased, vortex shedding frequency increases. At a certain flow rate, it reaches the acoustic frequency. Beyond this flow rate, large amplitude oscillations occur and only one common peak is observed in the spectra. This common peak has the frequency close to the acoustic mode of the duct. Vortex shedding process locks in to this common frequency and the phenomenon is termed as vortex-acoustic lock-in. We observe a series of well-defined regions that appear as the system progresses toward lock-in. In this paper, we made an attempt to understand the characteristics of these regions in a systematic manner. The study will help in developing lower-order models, which capture the essential dynamics of lock-in observed in vortex shedding combustors.

Lagrangian Analysis of Flame Dynamics in the Flow Field of a Bluff Body-Stabilized Combustor

Abstract Experiments are performed in a partially premixed bluff body-stabilized turbulent combustor by varying the mean flow velocity. Simultaneous measurements obtained for unsteady pressure, velocity, and heat release rate are used to investigate the dynamic regimes of intermittency (10.1 m/s) and thermoacoustic instability (12.3 m/s). Using wavelet analysis, we show that during intermittency, modulation of heat release rate occurring at the acoustic frequency fa by the heat release rate occurring at the hydrodynamic frequency fh results in epochs of heat release rate fluctuations where the heat release rate is phase locked with the acoustic pressure. We also show that the flame position during intermittency and thermoacoustic instability are essentially dictated by saddle point dynamics in the dump plane and the leading edge of the bluff body.

Assessing fire-blocking effectiveness of barrier fabrics in the cone calorimeter

Cone calorimetry experiments of on flexible polyurethane foam and flexible polyurethane foam covered with a variety of fire-blocking barrier fabrics were used to characterize and rank the effectiveness of barrier fabrics with the ultimate goal being an ability to predict the effectiveness of barrier fabrics for reducing the flammability of residential upholstered furniture. The primary measure used to characterize the burning behavior was heat release rate. The effect of the underlying sample substrate was shown to have a large effect on the burning behavior of flexible polyurethane foam samples, and a thermally insulating substrate was used during composite experiments. At times, rapid heat release rate fluctuations were observed, and in such cases approximate corrections were applied to correct for finite cone calorimeter time response. Measurements using thermocouples placed within the flexible polyurethane foam provided insights on flexible polyurethane foam pyrolysis behavior, the collapse rate of flexible polyurethane foam, and the thermal protective properties of barrier materials. Heat release rate temporal profiles for flexible polyurethane foam showed two distinct burning stages with peak values which have been attributed to sequential burning of species (primarily) derived from the diamine ( PHRR1) and polyol components ( PHRR2) used to manufacture the flexible polyurethane foam. When a barrier fabric was added, many of the composites displayed a three-stage burning behavior which was attributed to an initial short, intense burning (termed flash burning) stage associated with the barrier fabric covering followed by the two flexible polyurethane foam stages. Seven out of 16 flexible polyurethane foam/barrier fabric composites exhibited flame extinction prior to fuel burn out. Five out of the seven composites reignited when the spark ignition source was reapplied. Reignition allowed barrier fabric effectiveness to be assessed even for cases with flame extinction. Barrier fabric performance was shown to be consistent with four properties that were previously identified as important barrier fabric properties: barrier fabric flammability, gas permeability, thermal protection, and physical integrity. In addition, the current experiments indicate the presence and effectiveness of gas-phase active flame retardants in the barrier fabric can also play an important role. A limited number of tests were conducted to de-couple the effects of flame-retardant chemicals and physical effects of barrier fabrics on flexible polyurethane foam burning behavior. These tests showed that while flame-retardant chemicals can be effective in quenching and extinguishing the flames, the presence of effective barrier fabric shells is also very important in lowering the heat release rate of burning flexible polyurethane foam. In general, the presence of a barrier fabric was shown to reduce the heat release rate peak values during both flexible polyurethane foam burning stages. The magnitude of the peak associated with second-stage flexible polyurethane foam burning was deemed the most appropriate for characterizing the thermal protection provided by a barrier fabric. Since the times for PHRR2also varied between composites, a measurement referred to as the peak fire growth rate (PFIGRA) parameter was calculated by dividing the heat release rate by time since time to ignition and PFIGRA2was also considered for characterizing the barrier fabrics. Three possible classification schemes, each consisting of three classes, were introduced based on composite flame extinction and reignition behavior, PHRR2values, and PFIGRA2values. Each scheme provided differentiation between barrier fabric effectiveness. While the schemes were able to assess whether the barrier fabrics were particularly effective or ineffective, there were variations among classes of barrier fabrics having intermediate levels of effectiveness. Further work will be required to assess which, if any, of the classification schemes are most appropriate for predicting barrier fabric performance in residential upholstered furniture.

Noise Sources of Lean Premixed Flames

The thermoacoustic sound generation mechanisms of lean premixed laminar and turbulent flames are investigated by a two-step approach. First, the conservation equations of a reacting compressible fluid are solved. This solution is used to determine the acoustic source terms of the acoustic perturbation equations (APE). Second, the contributions of the different source terms to the amplitude and phase of the acoustic pressure signal are analyzed by solving the APE in a computational aeroacoustics (CAA) simulation. The results show that it is not sufficient to only consider the unsteady heat release rate fluctuations which occur in the substantial pressure-density relation. The acceleration of density gradients occurring at the flame front is a significant contributor to the overall sound emission. For the investigated laminar and turbulent flames the amplitude and phase of the acoustic pressure signal can only be predicted accurately if both source terms are included in the acoustic analysis.

Attenuation behavior of thermoacoustic combustion instability analyzed by a complex-network- and synchronization-based approach.

We conduct an experimental study of the attenuation behavior of thermoacoustic combustion instability from the viewpoints of complex networks and synchronization. The spatiotemporally phase-synchronized state between the vertexes in weighted networks near an injector rim is notably degenerated as thermoacoustic combustion instability is suppressed by a steady air jet issued from the injector rim. The synchronization index clearly captures the attenuation of the mutual coupling between pressure and heat release rate fluctuations. The decrease in the periodicity of noisy-periodic oscillations in a flow velocity field significantly affects the mutual coupling, resulting in the suppression of thermoacoustic combustion instability.

Impact of the Acoustic Forcing Level on the Transfer Matrix of a Turbulent Swirling Combustor with and Without Flame

Thermoacoustic instabilities are a major issue for industrial and domestic burners. One possible framework to study these instabilities is to represent the system by a network of Dimensionless Acoustic Transfer Matrices (DATM) that link pressure and velocity fluctuations upstream and downstream each element of the network. In this article, the DATM coefficients of a turbulent swirling combustor are determined for a thermoacoustically stable configuration using harmonic acoustic forcing. Since the dynamics of the whole system is controlled by nonlinearities, the impact of the forcing level needs to be considered. The four DATM coefficients are thus measured for reactive operating conditions (premixed flame) and cold flow conditions for increasing acoustic excitation levels. The velocity level is controlled by a hot wire located inside the injector, in a region with a laminar top-hat velocity profile. The upstream and downstream specific acoustic impedances are also measured. Results for the acoustic response under cold flow conditions are first presented. In this case, the DATM coefficients are found to be independent of the forcing level except for the modulus of the coefficients linking the downstream velocity fluctuations to the upstream pressure and velocity fluctuations. This behavior is linked to the nonlinear response of the injector but is not entirely captured by the acoustic network model developed in this work. For reactive operating conditions, measurements indicate that all DATM coefficients depend on the forcing level to a certain extent. The Flame Describing Function, linking heat release rate fluctuations to velocity fluctuations, is used to reconstruct the transfer matrix through an acoustic network model. This network model accurately predicts the trend of the measured coefficients but the impact of the forcing level is not reproduced. Saturation for reactive operating conditions is shown to be not only related to the nonlinear flame response but also to the nonlinear injector dynamics. Finally, a data-driven reconstruction of the FDF using the acoustic network model along with the hot wire and microphone measurements is performed. This data-driven acoustic reconstruction is subsequently compared with the FDF determined with an optical technique.

Model for Acoustic Induced Aluminum Combustion Fluctuations in Solid Rocket Motors

Combustion of aluminum droplets released by the solid propellant is widely used to increase the thrust in solid rocket motors. The combustion dynamics of the released droplet cloud in the unsteady flow is however susceptible to trigger thermoacoustic instabilities. A theoretical analysis is conducted to determine the heat release rate fluctuations produced by the burning droplet cloud for small acoustic disturbances. Two contributions to heat release fluctuations are identified. The first originates from fluctuations of the evaporation rate due to the oscillating flow around the droplets. This leads to local fluctuations of the volumetric rate of heat release within the droplet cloud. The second one originates from the motion of the boundary of the burning droplet cloud at the end of the combustion process. This motion is due to droplet lifetime oscillations leading to an additional source of heat release disturbances. Both contributions to heat release disturbances take place within the acoustic boundary layer along the solid propellant surface. Quasi-steady models for the response of the droplet diameter fluctuations and droplet velocity fluctuations are derived. Combined with a model for the gas velocity fluctuations within the acoustic boundary layer they lead to expressions for the resulting heat release rate disturbances within the droplet cloud and at its boundary. Results are compared to a previous low order model and to numerical flow simulations. It is shown that the new model leads to close agreement with simulations over the entire flow. The derived expressions yield a better understanding on heat release disturbances and can be used to predict the linear stability of a solid rocket motor at reduced computational costs.

Annihilation events topology and their generated sound in turbulent premixed flames

This paper studies the contribution of flame annihilation events to the sound radiated by turbulent, premixed flames. Previously published direct numerical simulation (DNS) datasets of stoichiometric and lean (ϕ=0.7) flames (Haghiri et al. 2018) are first examined using an efficient formulation of the method of Griffiths et al. (2015) to identify the annihilation events. Four classes of annihilation event are observed. Three of these - pocket burn-out, tunnel closure and tunnel formation - were defined by Griffiths et al. A ‘multi-feature’ event is also defined in this paper as any combination of the other three annihilation events occurring close enough such that their radiated sound can be considered as originating from a single event.Further post-processing of these stoichiometric and lean datasets shows that the fluctuations in heat release rate associated with these 4 observed types of annihilation events are responsible for the broadband sound radiated by both flames. This, in turn, suggests that flame annihilation is the physical mechanism by which air-fuel ratio affects the radiated sound amplitude at high frequencies. This result is supported by previous works which have shown that the sound radiated from individual annihilation events scales with the laminar flame speed and the temperature ratio.

Discussion of laser interferometric vibrometry for the determination of heat release fluctuations in an unconfined swirl-stabilized flame

Fluctuations in heat release, hot and cold spots convected by the flow and sound waves are all related to density fluctuations, a number easily detected by interferometry. Same as chemiluminescence, interferometry is a line-of-sight method and therefore needs optical access and tomographic reconstruction of density fields. In this work we discuss the use of Laser Interferometric Vibrometry (LIV) as an alternative or extension to chemiluminescence when detecting heat release fluctuations in the flame, convection of hot and cold spots in the non-reacting flow field and sound waves emitted from a 3.4 kW turbulent, unconfined swirl-stabilized methane/air flame under perfectly premixed conditions. For this discussion local temperatures, local ratios of heat release and local Gladstone-Dale constants are determined and their influence on the result discussed. Global and local fluctuations in heat release rate recorded by LIV and chemiluminescence are compared, resulting in the same global values if local temperature fields and local equivalence ratios are used for LIV data evaluation. In contrast, local fluctuations in OH* chemiluminescence emission are influenced by turbulence and strain in this type of flame.