Measurements of self-excited instabilities and nitrogen oxides emissions in a multi-element lean-premixed hydrogen/methane/air flame ensemble

Understanding the distinguishing physical properties of multi-element lean-premixed high hydrogen content flames is expected to be integral to the development of carbon-neutral, and ultimately carbon-free, gas turbine combustion systems. Despite their fundamental importance, the thermoacoustic and emission-related characteristics of such small-scale flame ensembles are not thoroughly understood, particularly for the full range of 0 to 100% hydrogen content blended with methane fuel. Here we investigate the structure and collective behavior of a multi-element lean-premixed hydrogen/methane/air flame ensemble using measurements of nitrogen oxides emissions and self-excited instability, combined with OH* and OH PLIF flame visualizations. Our results indicate that the system's responses can be classified into several distinctive stages according to their static and dynamic stability, including flame blowoff and thermoacoustically stable regions under relatively low hydrogen concentration conditions, low-frequency self-excited instabilities in intermediate hydrogen concentration, and triggering of intense pressure perturbations at about 1.7 kHz under high- or pure hydrogen combustion conditions. While the low-frequency combustion dynamics are dominated by axisymmetric translational movements of parallel flame fronts, the higher frequency response originates from significant lateral modulations accompanied by small-scale vortical rollup and flame surface annihilation due to front merging and pinch-off. Longitudinal-to-transverse dynamic transition is observed to play a mechanistic role in kinematically accommodating higher-frequency heat release rate fluctuations, and this newly identified mechanism suggests the possibility of high-frequency transverse modes, if such lateral motions are strong enough to induce inter-element flame interactions. In contrast to the substantial differences in thermoacoustic properties for different fuel compositions, the total nitrogen oxides emissions are found to depend primarily on adiabatic flame temperature; the influence of fuel composition is limited to approximately 20% under the inlet conditions considered.     

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 〈?_i, ?_o〉 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.     

Nonlinear hydrodynamic and thermoacoustic oscillations of a bluff-body stabilised turbulent premixed flame

Turbulent premixed flames often experience thermoacoustic instabilities when the combustion heat release rate is in phase with acoustic pressure fluctuations. Linear methods often assume a priori that oscillations are periodic and occur at a dominant frequency with a fixed amplitude. Such assumptions are not made when using nonlinear analysis. When an oscillation is fully saturated, nonlinear analysis can serve as a useful avenue to reveal flame behaviour far more elaborate than period-one limit cycles, including quasi-periodicity and chaos in hydrodynamically or thermoacoustically self-excited system. In this paper, the behaviour of a bluff-body stabilised turbulent premixed propane/air flame in a model jet-engine afterburner configuration is investigated using computational fluid dynamics. For the frequencies of interest in this investigation, an unsteady Reynolds-averaged Navier–Stokes approach is found to be appropriate. Combustion is represented using a modified laminar flamelet approach with an algebraic closure for the flame surface density. The results are validated by comparison with existing experimental data and with large eddy simulation, and the observed self-excited oscillations in pressure and heat release are studied using methods derived from dynamical systems theory. A systematic analysis is carried out by increasing the equivalence ratio of the reactant stream supplied to the premixed flame. A strong variation in the global flame structure is observed. The flame exhibits a self-excited hydrodynamic oscillation at low equivalence ratios, becomes steady as the equivalence ratio is increased to intermediate values, and again exhibits a self-excited thermoacoustic oscillation at higher equivalence ratios. Rich nonlinear behaviour is observed and the investigation demonstrates that turbulent premixed flames can exhibit complex dynamical behaviour including quasiperiodicity, limit cycles and period-two limit cycles due to the interactions of various physical mechanisms. This has implications in selecting the operating conditions for such flames and for devising proper control strategies for the avoidance of thermoacoustic instability.     

Characteristics of self-excited spinning azimuthal modes in an annular combustor with turbulent premixed bluff-body flames

In this paper we investigate self-excited azimuthal modes in an annular combustor with turbulent premixed bluff-body stabilised flames. Previous studies have shown that both swirl and equivalence ratio influence modal dynamics, i.e. the time-varying nature of the modes. However, self-excited azimuthal modes have not yet been investigated in turbulent flames without bulk swirl, which do not generate any preferential flow in either azimuthal direction, and may therefore lead to different behaviour. Joint probability density functions of the instability amplitudes at various flowrates and equivalence ratios showed a strong bi-modal response favouring both ACW and CW spinning states not previously observed. Operating conditions leading to a bi-modal response provide a unique opportunity to investigate whether the structure of the global fluctuating heat release rate of self-excited spinning modes in both directions exhibit similar dynamics and structure. This was investigated using high-speed OH* chemiluminescence images of the annular combustor and a new rotational averaging method was applied which decomposes the spinning components of the global fluctuating heat release rate. The new rotational averaging, which differs from standard phase-averaging, produces spatial averages in a frame of reference moving with the spinning wave. The results show that the structure of the fluctuating heat release rate for spinning modes is highly asymmetric as characterised by large, crescent shaped regions of high OH* intensity, located on the far side of each flame, relative to the direction of the azimuthally propagating pressure wave. In comparison with interacting swirling flames, these results indicate that the previously observed radial asymmetry of OH* fluctuations may be introduced through advection by local swirl.     

Evaluation of heat release indicators in lean premixed H2/Air cellular tubular flames

Heat release rate in combustion systems must be understood in order to control thermoacoustic instabilities, flame extinction, and heat losses. Traditionally OH chemiluminescence (OH*) is used to trace heat release rate (HRR) in H₂/air flames, but its accuracy as a tracer has not been assessed. Lean premixed H₂/air cellular tubular flames are a good test case to evaluate HRR tracers due to the presence of highly reactive flame cells surrounded by regions of near extinction. Comparing the calculated heat release rate to OH* concentration, one finds that [OH*] profiles correlate with the regions of high reactivity (flame cells) but the correlation fails in the low reactivity regions where the HRR is much higher than the [OH*] value indicates. Alternate HRR tracers including [H] and pixel-by-pixel products of [O₂]x[H], [OH]x[H₂], and [O]x[H₂] are analyzed with detailed numerical simulations. The chosen products derive from the main chain reaction steps that contribute to overall HRR in lean, premixed H₂/air flames. Findings suggest that [H] is an accurate yet simple way of tracking HRR. Planar measurements of HRR are possible if LIF measurements of [H] are improved.     

Mechanism of combustion dynamics in a backward-facing step stabilized premixed flame

Combustion dynamics leading to thermoacoustic instability in a rearward-facing step stabilized premixed flame is experimentally examined with the objective of investigating the fluid dynamic mechanism that drives heat release rate fluctuations, and how it couples with the acoustic field. The field is probed visually, using linear photodiode arrays that capture the spatiotemporal distribution of CH* and OH*; an equivalence ratio monitor; and a number of pressure sensors. Results show resonance between the acoustic quarter wave mode of the combustion tunnel and a fluid dynamic mode of the wake. Under unstable conditions, the flame is convoluted around a large vortex that extends several step heights downstream. During a typical cycle, while the velocity is decreasing, the vortex grows, and the flame extends downstream around its outer edge. As the velocity reaches its minimum, becoming mostly negative, the vortex reaches its maximum size, and the flame collides with the upper wall; its leading edge folds, trapping reactants pockets, and its trailing edge propagates far upstream of the step. In the next phase, while the velocity is increasing, the heat release grows rapidly as trapped reactant’ pockets are consumed by flames converging towards their centers, and the upstream flame is dislodged back downstream. The heat release rate reaches its maximum halfway into the velocity rise period, leading the maximum velocity by about 90°. In this quarter-wave mode, the pressure leads the velocity by 90° as well, that is, it is in phase with the heat release rate. Numerical modeling results support this mechanism. Equivalence ratio contribution to the instability mechanism is shown to be minor, i.e., heat release dynamics are governed by the cyclical formation of the wake vortex and its interaction with the flame.     

Simultaneous stereo‐PIV and OH×CH2O PLIF measurements in turbulent ultra lean CH4/H2 swirling wall‐impinging flames

We present experimental results from turbulent low-swirl lean H₂/CH₄ flames impinging on an inclined, cooled iso-thermal wall, based on simultaneous stereo-PIV and OH×CH₂O PLIF measurements. By increasing the H₂ fraction in the fuel while keeping Karlovitz number (Ka) fixed in a first series of flames, a fuel dependent near-wall flame structure is identified. Although Ka is constant, flames with high H₂ fraction exhibit significantly more broken reaction zones. In addition, these high H₂ fraction flames interact significantly more with the wall, stabilizing through the inner shear layer and well inside the near-wall swirling flow due to a higher resistance to mean strain rate. This flame-wall interaction is argued to increase the effective local Ka due to heat loss to the wall, as similar flames with a (near adiabatic) ceramic wall instead of a cooled wall exhibit significantly less flame brokenness. A second series of leaner flames were investigated near blow-off limit and showed complete quenching in the inner shear layer, where the mean strain rate matches the extinction strain rate extracted from 1D flames. For pure CH₄ flames (Ka ≈ 30), the reaction zone remains thin up to the quenching point, while conversely for the 70% H₂ flames (Ka ≈ 1100), the reaction zone is highly fragmented. Remarkably, in all near blow-off cases with CH₄ in the fuel, a large cloud of CH₂O persists downstream the quenching point, suggesting incomplete combustion. Finally, ultra lean pure hydrogen flames were also studied for equivalence ratios as low as 0.22, and through OH imaging, exhibit a clear transition from a cellular flame structure to a highly fragmented flame structure near blow-off.     

氢、碳氢燃料对向扩散火焰

对氢、正烷烃碳氢燃料与氧的对向扩散火焰,其中正烷烃包含了在工业用燃料中广泛应用的C_nH_2n+2正烷烃CH₄～C1₆H₃₄,对这些燃料的火焰结构进行了分析和比较,系统地分析了压力和拉伸率对火焰行为和热释放率等的影响,其中包含了2115个组分8157个可逆反应．研究结果表明,所有燃料的火焰厚度和热释放率与压力和拉伸率的乘积的平方根成线性关系．在相同工况下,氢的火焰厚度总是大于所有的碳氢燃料,而CH₄～C1₆H₃₄所有的碳氢燃料在相同工况下总是具有几乎相同的燃烧温度分布、燃烧产物分布、火焰厚度和热释放率,该结果表明由这些碳氢燃料组成的混合燃料具有同样的火焰特性.     

Lean or ultra-lean stretched planar methane/air flames

Lean premixed combustion has potential advantages of reducing pollutants and improving fuel economy. In some lean engine concepts, the fuel is directly injected into the combustion chamber resulting in a distribution of lean fuel/air mixtures. In this case, very lean mixtures can burn when supported by hot products from more strongly burning flames. This study examines the downstream interaction of opposed jets of a lean-limit CH₄/air mixture vs. a lean H₂/air flame. The CH₄ mixtures are near or below the lean flammability limit. The flame composition is measured by laser-induced Raman scattering and is compared to numerical simulations with detailed chemistry and molecular transport including the Soret effect. Several sub-limit lean CH₄/air flames supported by the products from the lean H₂/air flame are studied, and a small amount of CO₂ product (around 1% mole fraction) is formed in a “negative flame speed” flame where the weak CH₄/air mixture diffuses across the stagnation plane into the hot products from the H₂/air flame. Raman scattering measurements of temperature and species concentration are compared to detailed simulations using GRI-3.0, C₁, and C₂ chemical kinetic mechanisms, with good agreement obtained in the lean-limit or sub-limit flames. Stronger self-propagating CH₄/air mixtures result in a much higher concentration of product (around 6% CO₂ mole fraction), and the simulation results are sensitive to the specific chemical mechanism. These model-data comparisons for stronger CH₄/air flames improve when using either the C₂ or the Williams mechanisms.     

Control of oscillating combustion and noise based on local flame structure

To control combustion oscillations, the characteristics of an oscillating swirl injection premixed flame have been investigated, and control of oscillating combustion and noise based on local flame structure has been conducted. The r.m.s. value of pressure fluctuations and noise level show significantly large values between = 0.8 and 1.1. The beating of pressure fluctuations is observed for the large oscillating flame conditions in this combustor. Relationship between beating of pressure fluctuations and local flame structure was observed by the simultaneous measurement of CH/OH planar laser induced fluorescence and pressure fluctuations. The local flame structure and beating of pressure fluctuations are related and the most complicated flame is formed in the middle pressure fluctuating region of beating. The beating of pressure fluctuations, which plays important roles in noise generation and nitric oxide emission in this combustor, could be controlled by injecting secondary fuel into the recirculating region of oscillating flames. Injecting secondary fuel prevented lean blowout, and low NO_x combustion was also achieved even for the case of pure methane injection as a secondary fuel. By injecting secondary fuel into the recirculating region near the swirl injector, the flame lifted from the swirl injector and its reaction region became uniform and widespread, hence resulting in low nitric oxide emission. Secondary mixture injection, fuel diluted with air, is not effective for control of combustion oscillations suppression and lean blowout prevention.     

Modeled quenching limits of spherical hydrogen diffusion flames

Hydrogen–air diffusion flames were modeled with an emphasis on kinetic extinction. The flames were one-dimensional spherical laminar diffusion flames supported by adiabatic porous burners of various diameters. Behavior of normal (H₂ flowing into quiescent air) and inverse (air flowing into quiescent H₂) configurations were considered using detailed H₂/O₂ chemistry and transport properties with updated light component diffusivities. For the same heat release rate, inverse flames were found to be smaller and 290 K hotter than normal flames. The weakest normal flame that could be achieved before quenching has an overall heat release rate of 0.25 W, compared to 1.4 W for the weakest inverse flame. There is extensive leakage of the ambient reactant for both normal and inverse flames near extinction, which results in a premixed flame regime for diffusion flames except for the smallest burners with radii on the order of 1 μm. At high flow rates H + OH(+M) → H₂O(+M) contributes nearly 50% of the net heat release. However at flow rates approaching quenching limits, H + O₂(+M) → HO₂(+M) is the elementary reaction with the largest heat release rate.     

Structure of partially premixed n-heptane–air counterflow flames

To avoid the complexities associated with the droplet/vapor transport and nonuniform evaporation processes, a fundamental investigation of liquid fuel combustion in idealized configurations is very useful. An experimental–computational investigation of prevaporized n-heptane nonpremixed and partially premixed flames established in a counterflow burner is described. There is a general agreement between various facets of our nonpremixed flame measurements and the literature data. The partially premixed flames are characterized by a double flame structure. This becomes more distinct as the strain rate decreases and partial premixing increases, which also increases the separation distance between the two reaction zones. The peak partially premixed flame temperature increases with increasing premixing of the fuel stream. The peak CO₂ and H₂O concentrations are relatively insensitive to partial premixing. The CO and H₂ peak concentrations on the premixed side increase as the fuel-side equivalence ratio decreases. These species are transported to the nonpremixed reaction zone where they oxidize. The C₂ species have peaks in the premixed reaction zone. The concentrations of olefins are ten times larger than those of the corresponding paraffins. The oxidizer is present in partially premixed flames throughout the combustion system and there are no regions characterized by simultaneous high temperature and high fuel concentration. As a result, pyrolysis reactions leading to soot formation are greatly diminished.     

Combustion characteristics of Mg vapor jet flames in CO2 atmospheres

An experimental study was performed on the combustion characteristics of a jet diffusion flame of Mg vapor injected through a small nozzle into CO₂ atmospheres at low pressures from 8 to 48 kPa with a view to using Mg as fuel for a CO₂-breathing turbojet engine in the Mars atmosphere. The Mg vapor jet produced three types of the flame. At lower pressures and higher injection velocities, a red-heated jet flame formed, in which the injected Mg vapor was heated by spontaneous reactions, turning red. At medium pressures and injection velocities, a stable luminous lifted-like flame developed above the rim of the chimney, a tube-like combustion product for the Mg vapor passage that grew on the nozzle during combustion. The flame had similar flame length properties to laminar jet diffusion flames of gaseous fuels. At higher pressures and lower injection velocities, a stable luminous attached flame developed at the rim of the chimney. The same reactions, producing MgO(g), CO and MgO(c), proceeded preferentially for all flames and chimneys. Carbon was only subordinately generated. Burning behavior of Mg vapor jets in a CO₂ atmosphere has been represented, including the homogeneous reaction of Mg vapor with CO₂, the diffusion of CO₂, and the condensation and deposit of MgO. The injection velocity of Mg vapor at the rim of the chimney and the exothermic reactions with diffused CO₂ that occur there play a crucial role in the attachment and development of the flames. The flame structure may be explained in terms of the relatively low gas-phase reaction rate of Mg with CO₂.     

Suppression of self-excited thermoacoustic instabilities by convective-acoustic interference

In this paper we demonstrate direct suppression of self-excited thermoacoustic instabilities over a range of operating conditions using targeted convective-acoustic interference. Premixed hydrogen enriched methane-air flames were confined in a cylindrical pipe resulting in self-excited instabilities that corresponded to the quarter wave mode of the pipe. To suppress the instability, the phenomenon of lock-in (synchronisation) between the acoustic mode and vortex shedding from a set of cylinders placed upstream was used to produce destructive interference and suppress the self-excited modes. This was done by varying the location of the cylinders to control the convective time-delay between the convective and acoustic modes so that their combined effect on the flame response was tuned to suppress the global fluctuation of the heat release rate. This leads to a reduction in the limit-cycle amplitude and stable operation without a significant change to the flame structure. Measurements were taken over a wide range of equivalence ratios to demonstrate that the method is capable of stabilising the system for all conditions. Using a methodology which relies on time-delays related to hydrodynamic instability, rather than flame-related parameters, enables its application to fuel-flexible systems, often designed to operate within a wide range of power outputs.     

An experimental study of partially premixed flame sound

The occurrence of oscillating combustion and combustion instability has led to resurgence of interest in the causes, mechanisms, suppression, and control of combustion noise. Noise generated by enclosed flames is of greater practical interest but is more complicated than that by open flames, which itself is not clearly understood. Studies have shown that different modes of combustion, premixed and non-premixed, differ in their sound generation characteristics. However, there is lack of understanding of the region bridging these two combustion modes. This study investigates sound generation by partially premixed flames. Starting from a non-premixed flame, air was gradually added to achieve partial premixing while maintaining the fuel flow rate constant. Methane, ethylene, and ethane partially premixed flames were studied with hydrogen added for flame stabilization. The sound pressure generated by methane partially premixed flames scales with M⁵ compared to M³ for turbulent non-premixed methane flames. Also, the sound pressure generated by partially premixed flames of ethane and ethylene scales as M^4.5. With progressive partial premixing, spectra level increases at all frequencies with a greater increase in the high-frequency region compared to the low-frequency region; flames develop a peak and later a constant level plateau in the low frequency region. The partially premixed flames of methane, ethylene, and ethane generate a similar SPL as a function of equivalence ratio when the fuel volume flow rate is matched. However, when fuel mass flow rate is matched, the ethane and ethylene flames produce a similar SPL, which is lower than that produced by the methane flame.     

An experimental and numerical study on the adequacy of CH as a flame marker in premixed methane flames

The CH radical is frequently used as a flame marker because it is relatively short-lived and is present over a narrow region in flames. Discontinuities in the CH field are thus often interpreted as localized extinction of the flame. Recently, however, the adequacy of CH laser-induced fluorescence (LIF) as a flame marker was questioned by an experimental study of flame–vortex interactions in highly N₂-diluted premixed methane flames. We demonstrate both experimentally and numerically that anomalies in the transient response of CH in this earlier study were due to reactant composition variations in the vortex. In addition, we evaluate the adequacy of CH LIF as a flame marker over a much broader range of conditions. Previous numerical studies showed that heat release rate correlates reasonably well with peak [HCO] and the concentration product [OH][CH₂O], but poorly with [CH], in highly N₂-diluted premixed methane flames. Here, the correlation between heat release rate and CH is investigated both experimentally, by performing simultaneous measurements of CH, OH, and CH₂O LIF, and numerically. We consider undiluted and N₂-diluted premixed methane flames over a range of strain rates and stoichiometries. Results are reported for flames subjected to unsteady stretch and reactant composition variations. For all N₂-dilution levels considered, the peak CH LIF signal correlates poorly with heat release rate when the stoichiometry of the reactant mixture changes from rich to lean. However, when flames are subjected to stretch, the correlation between CH and heat release rate improves as the N₂-dilution level decreases. The correlation is reasonably good for undiluted flames with equivalence ratios of 0.8 < Φ < 1.2. This result is particularly encouraging, given the relevance of undiluted flames to practical applications, and it motivates further investigation of the parameter space for which difficulties may exist in using CH as a flame marker.     

Ignition and volatile combustion behaviors of a single lignite particle in a fluidized bed under O2/H2O condition

O₂/H₂O combustion, as a new evolution of oxy-fuel combustion, has gradually gained more attention recently for carbon capture in a coal-fired power plant. The physical and chemical properties of steam e.g. reactivity, thermal capacity, diffusivity, can affect the coal combustion process. In this work, the ignition and volatile combustion characteristics of a single lignite particle were first investigated in a fluidized bed combustor under O₂/H₂O atmosphere. The flame and particle temperatures were measured by a calibrated two-color pyrometry and pre-buried thermocouple, respectively. Results indicated that the volatile flame became smaller and brighter as the oxygen concentration increased. The ignition delay time of particle in dense phase was shorter than that in dilute phase due to its higher heat transfer coefficient. Also, the volatile flame was completely separated from particles (defined as off-flame) in dense phase while the flame lay on the particle surface (defined as on-flame) in dilute phase. The self-heating of fuel particles by on-flame in dilute phase was more obvious than that in dense phase, leading to earlier char combustion. At low oxygen concentration, the flame in the H₂O atmosphere was darker than that in the N₂ atmosphere because the heat capacity of H₂O is higher than that of N₂. With the increase of oxygen concentration, the flame temperature in the O₂/H₂O atmosphere was dramatically enhanced rather than that in the O₂/N₂ atmosphere, where the diffusion rate of oxygen in O₂/N₂ atmosphere became the dominant factor.     

Ethanol turbulent spray flame response to gas velocity modulation

A numerical investigation of the interaction between a spray flame and an acoustic forcing of the velocity field is presented in this paper. In combustion systems, a thermoacoustic instability is the result of a process of coupling between oscillations in heat released and acoustic waves. When liquid fuels are used, the atomisation and the evaporation process also undergo the effects of such instabilities, and the computational fluid dynamics of these complex phenomena becomes a challenging task. In this paper, an acoustic perturbation is applied to the mass flow of the gas phase at the inlet and its effect on the evaporating fuel spray and on the flame front is investigated with unsteady Reynolds averaged Navier-Stokes numerical simulations. Two flames are simulated: a partially premixed ethanol/air spray flame and a premixed pre-vaporised ethanol/air flame, with and without acoustic forcing. The frequencies used to perturb the flames are 200 and 2500 Hz, which are representative for two different regimes. Those regimes are classified based on the Strouhal number St = (D/U)f_f: at 200 Hz, St = 0.07, and at 2500 Hz, St = 0.8. The exposure of the flame to a 200 Hz signal results in a stretching of the flame which causes gas field fluctuations, a delay of the evaporation and an increase of the reaction rate. The coupling between the flame and the flow excitation is such that the flame breaks up periodically. At 2500 Hz, the evaporation rate increases but the response of the gas field is weak and the flame is more stable. The presence of droplets does not play a crucial role at 2500 Hz, as shown by a comparison of the discrete flame function in the case of spray and pre-vaporised flame. At low Strouhal number, the forced response of the pre-vaporised flame is much higher compared to that of the spray flame.