Comparison and extension of methods for acoustic identification of burners

The prediction and the control of combustion instabilities require the identification of the combustion chamber response. This identification is usually performed by forcing the combustor (for example, modulating its inlet velocity) and measuring its response. Two methods may be found in the literature to analyze this response: identification of transfer matrices (ITM) and flame transfer functions (FTF). In ITM approaches, the burner is considered as a “black box” and a two-port formulation (based on acoustic pressure and velocity perturbations) is used to construct a transfer matrix linking acoustic fluctuations on both sides of the burner. A drawback of this method is that in experiments, the measurement of unsteady pressure and velocity in burnt gases can be difficult. In FTF approaches, pressure measurements are replaced by a global heat release measurement (usually based on optical methods). The heat release fluctuations are then related to the flow velocity modulations at a reference point (usually the combustor inlet) through a transfer function. This paper uses a compressible numerical simulation of a forced laminar Bunsen flame to analyze FTF and ITM methods. Results show that FTF approaches lead to an ill-defined problem as soon as the reference point is not close enough to the chamber. This “compactness” limit is quantified here in terms of distance between the reference point and the local chamber. The source of the problem is that FTF approaches correlate heat release fluctuations to velocity oscillations only: extended FTF models are then proposed using the local unsteady pressure as well as the velocity upstream of the flame to predict the heat release oscillations. These models are tested numerically and provide consistent values when the reference point location changes or when upstream and downstream conditions are varied. These results lead to simple recommendations for system identification.     

Effects of hydrogen addition on the forced response of H2/CH4 flames in a dual-nozzle swirl-stabilized combustor

The effects of hydrogen addition on the forced response of H₂/CH₄ flames are analyzed in a dual-nozzle swirl-stabilized combustor. The hydrogen volumetric content in the fuel is varied from 0% to 40%. Flame transfer function (FTF) is used to compare the forced response of the flames. The FTF gain featuring the local maximum and minimum values, which occurred commonly in the FTFs under all hydrogen contents, is determined by two different mechanisms: the change in the flame angle and the flame roll-up phenomenon. Among two mechanisms, the flame roll-up phenomenon has a more important role in determining the FTF characteristics. In addition, hydrogen addition attenuates the local maximum gains and decreases the FTF phase slope. The change in the flame roll-up behavior, which is induced by a short and compact flame distribution at high hydrogen contents, is the primary reason of these differences in the FTF.     

Measurements of triggering and transient growth in a model lean-premixed gas turbine combustor

Instability triggering and transient growth of thermoacoustic oscillations were experimentally investigated in combination with linear/nonlinear flame transfer function (FTF) methodology in a model lean-premixed gas turbine combustor operated with CH₄ and air at atmospheric pressure. A fully premixed flame with 10 kW thermal power and an equivalence ratio of 0.60 was chosen for detailed characterization of the nonlinear transient behaviors. Flame transfer functions were experimentally determined by simultaneous measurements of inlet velocity fluctuations and heat release rate oscillations using a constant temperature anemometer and OH¹/CH¹ chemiluminescence emissions, respectively. The phase-resolved variation of the local flame structure at a limit cycle was measured by planar laser-induced fluorescence of OH. Simultaneous measurements of inlet velocity, OH¹/CH¹ emission, and acoustic pressure were performed to investigate the temporal evolution of the system from a stable to a limit cycle operation. This measurement allows us to describe an unsteady instability triggering event in terms of several distinct stages: (i) initiation of a small perturbation, (ii) exponential amplification, (iii) saturation, (iv) nonlinear evolution of the perturbations towards a new unstable periodic state, (v) quasi-steady low-amplitude periodic oscillation, and (vi) fully-developed high-amplitude limit cycle oscillation. Phase-plane portraits of instantaneous inlet velocity and heat release rate clearly show the presence of two different attractors. Depending on its initial position in phase space at infinitesimally small amplitude, the system evolves towards either a high-amplitude oscillatory state or a low-amplitude oscillatory state. This transient phenomenon was analyzed using frequency- and amplitude-dependent damping mechanisms, and compared to subcritical and supercritical bifurcation theories. The results presented in this paper experimentally demonstrate the hypothesis proposed by Preetham et al. based on analytical and computational solutions of the nonlinear G-equation [J. Propul. Power 24 (2008) 1390–1402]. Good quantitative agreement was obtained between measurements and predictions in terms of the conditions for the onset of triggering and the amplitude of triggered combustion instabilities.     

Response of partially premixed flames to acoustic velocity and equivalence ratio perturbations

This article describes an experimental investigation of the forced response of a swirl-stabilized partially premixed flame when it is subjected to acoustic velocity and equivalence ratio fluctuations. The flame’s response is analyzed using phase-resolved CH^* chemiluminescence images and flame transfer function (FTF) measurements, and compared with the response of a perfectly premixed flame under acoustic perturbations. The nonlinear response of the partially premixed flame is manifested by a partial extinction of the reaction zone, leading to rapid reduction of flame surface area. This nonlinearity, however, is observed only when the phase difference between the acoustic velocity and the equivalence ratio at the combustor inlet is close to zero. The condition, Δφ_Φ^′-V^′≈0°, indicates that reactant mixtures with high equivalence ratio impinge on the flame front with high velocity, inducing large fluctuations of the rate of heat release. It is found that the phase difference between the acoustic velocity and equivalence ratio nonuniformities is a key parameter governing the linear/nonlinear response of a partially premixed flame, and it is a function of modulation frequency, inlet velocity, fuel injection location, and fuel injector impedance. The results presented in this article will provide insight into the response of a partially premixed flame, which has not been well explored to date.     

Spatially resolved heat release rate measurements in turbulent premixed flames

Heat release rate is a fundamental property of great importance for the theoretical and experimental elucidation of unsteady flame behaviors such as combustion noise, combustion instabilities, and pulsed combustion. Investigations of such thermoacoustic interactions require a reliable indicator of heat release rate capable of resolving spatial structures in turbulent flames. Traditionally, heat release rate has been estimated via OH or CH radical chemiluminescence; however, chemiluminescence suffers from being a line-of-sight technique with limited capability for resolving small-scale structures. In this paper, we report spatially resolved two-dimensional measurements of a quantity closely related to heat release rate. The diagnostic technique uses simultaneous OH and CH₂O planar laser-induced fluorescence (PLIF), and the pixel-by-pixel product of the OH and CH₂O PLIF signals has previously been shown to correlate well with local heat release rates. Results from this diagnostic technique, which we refer to as heat release rate imaging (HR imaging), are compared with traditional OH chemiluminescence measurements in several flames. Studies were performed in lean premixed ethylene flames stabilized between opposed jets and with a bluff body. Correlations between bulk strain rates and local heat release rates were obtained and the effects of curvature on heat release rate were investigated. The results show that the heat release rate tends to increase with increasing negative curvature for the flames investigated for which Lewis numbers are greater than unity. This correlation becomes more pronounced as the flame gets closer to global extinction.     

Investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations

Acoustically forced lean premixed turbulent bluff-body stabilized flames are investigated using turbulent combustion CFD. The calculations simulate aspects of the experimental investigation by Balachandran et al. [R. Balachandran, B. Ayoola, C. Kaminski, A. Dowling, E. Mastorakos, Combust. Flame 143 (2005) 37-55] and focus on the amplitude dependence of the flame response. For the frequencies of interest in this investigation an unsteady Reynolds-averaged Navier-Stokes (URANS) approach is appropriate. The combustion is represented using a modified laminar flamelet approach with an algebraic representation of the flame surface density. The predictions are compared with flame surface density (FSD) and OH^∗ chemiluminescence measurements. In the experiments the response of the flame has been quantified by means of a number of single-frequency, amplitude-dependent transfer functions. The predicted flame shape and position are in good agreement with the experiment. The dynamic response of the flame to inlet velocity forcing is also well captured by the calculations. At moderate frequencies nonlinear behavior of the transfer functions is observed as the forcing amplitude is increased. In the experiments this nonlinearity was attributed in part to the rollup of the reacting shear layer into vortices and in part to the collision of the inner and outer flame sheets. This transition to nonlinearity is also observed in the transfer functions obtained from the predictions. Furthermore, the vortex shedding and flame-sheet collapse may be seen in snapshots of the predicted flow field taken throughout the forcing cycle. The URANS methodology successfully predicts the behavior of the forced premixed turbulent flames and captures the effects of saturation in the transfer function of the response of the heat release to velocity fluctuations.     

Suppression limits of low strain rate non-premixed methane flames

The suppression of low strain rate non-premixed flames was investigated experimentally in a counterflow configuration for laminar flames with minimal conductive heat losses. This was accomplished by varying the velocity ratio of fuel to oxidizer to adjust the flame position such that conductive losses to the burner were reduced and was confirmed by temperature measurements using thermocouples near the reactant ducts. Thin filament pyrometry was used to measure the flame temperature field for a curved diluted methane-air flame near extinction at a global strain rate of 20 s⁻¹. The maximum flame temperature did not change as a function of position along the curved flame surface, suggesting that the local agent concentration required for suppression will not differ significantly along the flame sheet. The concentration of N₂, CO_2, and CF₃Br added to the fuel and the oxidizer streams required to obtain extinction was measured as a function of the global strain rate. In agreement with previous measurements performed under microgravity conditions, limiting non-premixed flame extinction behavior in which the agent concentration obtained a value that insures suppression for all global strain rates was observed. A series of extinction measurements varying the air:fuel velocity ratio showed that the critical N₂ concentration was invariant with this ratio, unless conductive losses were present. In terms of fire safety, the measurements demonstrate the existence of a fundamental limit for suppressant requirements in normal gravity flames, analogous to agent flammability limits in premixed flames. The critical agent volume fraction in the methane fuel stream assuring suppression for all global strain rates was measured to be 0.841 ± 0.01 for N₂, 0.773 ± 0.009 for CO₂, and 0.437 ± 0.005 for CF₃Br. The critical agent volume fraction in the oxidizer stream assuring suppression for all global strain rates was measured as 0.299 ± 0.004 for N₂, 0.187 ± 0.002 for CO₂, and 0.043 ± 0.001 for CF₃Br.     

Cinematographic OH-PLIF measurements of two interacting turbulent premixed flames with and without acoustic forcing

This paper describes an experimental investigation into the interactions that occur between two lean turbulent premixed flames stabilised on conical bluff-bodies when they are moved closer together. Cinematographic OH-PLIF measurements were acquired to investigate adjacent flame front interactions as a function of flame separation distance (S). Flame surface density (FSD) and curvature were determined to characterise the unforced flames. Acoustic forcing was then applied to explore the amplitude dependent thermo-acoustic response. Phase-averaged FSD and global heat release measurements in the form of OH¹ chemiluminescence were obtained for a range of forcing frequencies (f) and amplitudes (A) as a function of S. As the flames were brought closer together the adjacent annular jets were found to merge into a single jet structure. This caused adjacent flame fronts to merge above the wake region between the two flames at a location determined by the jet efflux (flame angle) and S. This region of flame–flame interaction we refer to as ‘interacting region’. In the unforced flames, a trend of increasingly negative curvature for decreasing S produced a small net increase in flame surface area via cusp formation. When subjected to acoustic forcing, S-dependent regimes were found in the global heat release response as a function A. The overall trend showed that the occurrence of jet/flame merging reduces the value of A at which non-linear response occurs. In support of previous findings for flames stabilised along shear layers, the phase-averaged FSD showed that the flame dynamics that drive the thermo-acoustic response result from the roll-up of vortices which generate large-scale vortex–flame interactions. Compared with axisymmetric flames, the occurrence of jet merging alters the vortex–flame interactions resulting in an asymmetric contribution to the heat release between the wall and interacting regions. The majority of the heat release was found to occur in the interacting region through the rapid production and destruction of flame surface area. The occurrence of jet merging and large-scale interactions between adjacent flames result in different physical mechanisms that drive the thermo-acoustic response compared with single axisymmetric flames.     

Studies of cellular flames in hydrogenoxygennitrogen mixtures

For downwardly propagating flames in pyrex tubes at atmospheric pressure and intial temperature of 295°K, measurements were made of the nitrogen dilution required for quenching as a function of the hydrogenoxygen ratio, as well as of flame temperatures, flame speeds, temperature gradients behind the flame, unburnt hydrogen, and cell sizes. Theory including relative diffusion of reactants was compared with measured cell sizes. Agreement of measured extinctions was obtained using theory based on importance of conductive heat loss rates in comparison with overall rates of chemical heat release.     

Skeletal reaction models based on principal component analysis: Application to ethylene–air ignition, propagation, and extinction phenomena

The development of a skeletal reaction model based on Principal Component Analysis of local Sensitivity (PCAS) coefficients is reported. The analysis presented is comprehensive in the sense that it includes sensitivity coefficients from three distinct canonical reacting configurations, namely ignition, flame propagation, and flame extinction phenomena. To minimize the computational effort involved in constructing sensitivity coefficients, and with the objective of accurately predicting global features or target functions such as ignition delay, burning velocity and extinction strain rates, optimal temporal and spatial locations to perform the local sensitivity are identified. Furthermore, it is shown that the sensitivity coefficients of temperature and heat release, and/or global flame properties (or eigenvalues) associated with burning velocity and extinction strain rate, are sufficient to extract an accurate skeletal model to predict stated target functions. Application of the PCAS approach to a C₁–C₄ hydrocarbon kinetic model consisting of 111 species and 784 reversible reactions, with ethylene as the fuel of interest, is presented. The results clearly indicate that the smallest skeletal model that can be developed is dictated by non-premixed extinction phenomenon that has been neglected in previous analyses using various reduction approaches.     

多孔介质稳焰器对旋流火焰振荡燃烧特性影响的试验研究

为研究多孔介质稳焰器孔密度变化对贫预混旋流火焰振荡燃烧特性的影响,通过光电倍增管测量全局火焰热释放率,采用双麦克风方法测量旋流器入口速度脉动,获得不同孔密度多孔介质稳焰器火焰传递函数;并通过高速相机测量不同孔密度多孔介质稳焰器振荡火焰结构的变化。试验结果表明：多孔介质能够改变燃烧室声模态,有效抑制燃烧振荡,但孔密度对受迫燃烧火焰热释放率和压力脉动影响具有非线性;高频入口扰动对火焰响应特性影响较弱,火焰受迫响应呈现低通滤波特性;火焰传递函数增益峰值对应入口激励频率存在差异,但相位分布斜率基本一致;多孔介质导致火焰向稳焰器中心轴线聚拢,相干结构更加明显;宽频扰动范围内的火焰张角分布趋势与火焰传递函数增益曲线的分布趋势相反。     

Monte Carlo modeling of radiative transfer in a turbulent sooty flame

The calculation of radiative transfer within a sooty turbulent ethylene-air diffusion jet flame has been carried out by using a Monte Carlo method and an accurate CK model for the gases. The influence of the turbulence-radiation interaction (TRI) has been studied. In the TRI modeling, the radiative properties of the assumed homogeneous turbulent structures are randomly obtained from a multidimensional probability density function (PDF) of the reaction progress variable, of the mixture ratio and of the soot volume fraction. This joint PDF is obtained from an Eulerian-Lagrangian turbulent combustion model and the sizes of the turbulent structures are directly derived from a k-? model. In the considered flame, the TRI effect is an increase of the radiative heat loss by about 30%. The radiative heat loss becomes almost equal to one-third of the chemical heat release. Soot particles play the most important role in the global radiative heat loss but the influence of gaseous species like CO₂ and H₂O can be important in the local energy balance.     

Condensation studies using cross-corrugated polymer film compact heat exchanger

Heat transfer has been examined in a polymer film compact heat exchanger between cross flowing liquid and gas. Condensation of water vapour through a non-condensable gas was used to supply heat through a corrugated poly-ether-ether-ketone (PEEK) film to a cooling liquid. Measurements of heat transfer rates in the system indicated overall heat transfer coefficients in the range of 50–300 W m⁻² K⁻¹ were achieved. Visual analysis and pressure drop measurements were used to provide insight into the fluid flow and the models used for heat transfer.     

Nonlinear combustion instability analysis based on the flame describing function applied to turbulent premixed swirling flames

Instability analysis of swirling flames is of importance in the design of advanced combustor concepts for aircraft propulsion and powerplant for electricity production. Thermoacoustic instabilities are analyzed here by making use of a nonlinear representation of flame dynamics based on a describing function. In this framework, the flame response is determined as a function of frequency and amplitude of perturbations impinging on the combustion region. This model is adapted to the case of confined swirling flames comprising an upstream manifold, an injection unit equipped with a swirler and a cylindrical flame tube. The flame describing function is experimentally determined and is combined with an acoustic transfer matrix representation of the system to provide growth rates and oscillation frequencies as a function of perturbation amplitude. These data can be used to determine regions of instability, frequency shifts with respect to the acoustic eigenfrequencies and they also yield amplitude levels when self-sustained oscillations of the system have reached a limit cycle. This equilibrium is obtained when the amplitude dependent growth rate equals the damping rate in the system. This requires an independent determination of this last quantity which is here based on measurements of the combustor resonance response curve, together with numerical estimates of the flame contribution to the system response. The geometrical parameters of the upstream manifold and flame tube are varied and the corresponding operating regimes are compared with those predicted with the FDF framework. The present demonstration of the FDF framework in a generic configuration indicates that this can be used in more general situations of technological interest.     

A numerical study of vortex interactions with flames developing from ignition kernels in lean methane/air mixtures

In this work, the outcomes of interactions of counter-rotating vortex pairs with developing ignition kernels are studied. The conditions are selected to represent those in a lean-burn natural-gas engine with hot-jet ignition. The evolution of flame surface area during kernel–vortex interaction is quantitatively and qualitatively examined. It is observed that flame development is accelerated and the net flame surface area growth rate, i.e. heat release rate, increased with increasing vortex velocity. In general, increasing the vortex length scale increases the surface growth rate, i.e. increases heat release rates, but for small length scales, i.e. when the ratio of vortex length scale to kernel diameter is small, high flame curvature induced during the interaction leads to flame weakening and slower growth rates. When the vortex velocity is high relative to the flame speed and the length scale is comparable to the kernel diameter, the vortex breaks through the ignition kernel carrying with it hot products of combustion. This accelerates growth of the flame surface area and heat release rates compared to a kernel with no vortex interaction. On decreasing the vortex velocity and increasing the length scale, the wrinkling of the kernel becomes important. This also results in increased surface growth rates and higher heat release rates.     

On the low-frequency limit of flame transfer functions

The response of a premixed flame to quasi-steady flow perturbations is considered. It is found that in this low-frequency limit, constraints on the flame transfer function can be established from global conservation laws for mass, energy, and momentum. For example, the transfer function between velocity fluctuations and heat release of a perfectly premixed flame without fluctuations of equivalence ratio should be unity in the limit of zero frequency, while for a combustion system with constant mass flow rate of fuel, the transfer function should tend toward zero. It is demonstrated that these considerations can be employed to reduce the number of unknowns in analytical flame models or identify invalid modeling assumptions.     

The combined dynamics of swirler and turbulent premixed swirling flames

The dynamics of premixed confined swirling flames is investigated by examining their response to incident velocity perturbations. A generalized transfer function designated as the flame describing function (FDF) is determined by sweeping a frequency range extending from 0 to 400 Hz and by changing the root mean square fluctuation level between 0% and 72% of the bulk velocity. The unsteady heat release rate is deduced from the emission intensity of OH^* radicals. This global information is complemented by phase conditioned Abel transformed emission images. This processing yields the distribution of light emission. By assuming that the light intensity is proportional to the heat release rate, it is possible to deduce the distribution of unsteady heat release rate in W m⁻³ and see how it evolves with time during the modulation cycle and for different forcing frequencies. These data can be useful for the determination of regimes of instability but also give clues on the mechanisms which control the swirling flame dynamics. It is found from experiments and demonstrated analytically that a swirler submitted to axial acoustic waves originating from the upstream manifold generates a vorticity wave on its downstream side. The flame is then submitted to a transmitted axial acoustic perturbation which propagates at the speed of sound and to an azimuthal velocity perturbation which is convected at the flow velocity. The net result is that the dynamical response and unsteady heat release rate are determined by the combined effects of these axial and induced azimuthal velocity perturbations. The former disturbance induces a shedding of vortices from the injector lip which roll-up the flame extremity while the latter effectively perturbs the swirl number which results in an angular oscillation of the flame root. This motion is equivalent to that which would be induced by perturbations of the burning velocity. The phase between incident perturbations is controlled by the convective time delay between the swirler and the injector. The constructive or destructive interference between the different perturbations is shown to yield the low and high gains observed for certain frequencies.     

Combustion dynamics of a low-swirl combustor

The methodology for the measurement of dynamic combustor behavior has never been clearly established, due to the complexities associated with unsteady premixed flames and the difficulties in their measurement. The global and local distribution of Rayleigh index and the flame response functions are the main parameters normally employed to quantify and describe combustion dynamics. The Rayleigh index quantifies the thermoacoustic coupling, while the flame response function is a measure of the response of the system to outside disturbances. The primary objective of this work is to investigate the combustion dynamics of a commonly used low-swirl burner and to develop tools and methods for examining the dynamics of a combustion system. To this end, the effect of acoustic forcing at various frequencies on flame heat release behavior has been investigated. The current work uses OH-PLIF imaging of the flame region to produce phase-resolved measurements of flame behavior at each frequency. The response of the flame to the imposed acoustic field over the range of 22-400 Hz is then calculated from the processed images. This provides a starting point for an extension/extrapolation to practical acoustic ranges (∼5000 Hz). It was found that the thermoacoustic coupling was mainly evident in the shear mixing zone, producing a toroidal Rayleigh index distribution pattern. The phase shift of the flame fluctuation from the imposed acoustic wave seems to be very closely coupled to the vortices generated at the flame boundary due to shear mixing (Kelvin-Helmholtz instability), thus inducing the alternating toroidal structures. The peak value of the flame response function coincides with the peak absolute value of the Rayleigh index.     

Pressure modeling of upward flame spread and burning rates over solids in partial gravity

Pressure-gravity modeling is proposed as a means to simulate upward flame spread and burning rates over vertical solid samples in partial gravity environments, such as on the Moon and on Mars. Based on experimental results in reduced gravity, the upward flame spread rate data over thin solids can be correlated by the expression p^1.8g (where p is the ambient pressure and g is the gravity level). This is close to the theoretical p²g factor in preserving the Grashof number and is also supported by detailed numerical simulations. Since the flame size, shape and standoff distance are preserved in this simulation, it is expected that combustion properties controlled chiefly by convective heat transfer are properly accounted for by the present technique. This includes upward flame spread rates, growth rates, and burning rates over thin and thick solids in both laminar and turbulent flames. In flames where the heat transfer is dominated by soot emission, more studies are needed to verify the validity of this correlation.