Time-averaged Flame Research Articles

Performance study of a central reentrant step pilot-flameholder in a dual-mode combustor

The augmented/ramjet combustion chambers are characterized by wide operating ranges, large flow state variations, and harsh operating conditions. The reliable ignition of these chambers urgently needs to be achieved. To improve the pilot ignition and blowout performance based on the centerbody in augmented/ramjet combustion chambers, a reentrant step flameholder is proposed on the basis of a conventional backward step. In this paper, the flow characteristics, ignition and blowout boundary under the non-premixed inflow, dynamic ignition process and flame stabilization mechanism of the reentrant step flame holder are investigated by using an experimental method with numerical simulation. The results show that the reentrant step flame holder exhibits better ignition and blowout performance than the conventional step flame holder without increasing the flow resistance. The ignition and blowout equivalence ratios of the reentrant step flame holder decrease by 22.86 % and 24.34 %, respectively, compared with those of the conventional step flame holder. The radial reentrant expansion is more effective than the axial reentrant expansion. Analyzing different reentrant structures shows that radial expansion can shorten the ignition delay time and improve the time-averaged integral flame intensity; axial expansion can improve the time-averaged integral flame intensity and reduce the flame pulsation rate; and the structure Da30Dr30 (the conventional step structure expands axially and radially by 30 mm simultaneously within the centerbody.) whose pilot flames are all stabilized in front of the reentrant step flame holder under different incoming flow conditions, exhibits the best ignition and blowout performances.

Effect of excitation Strouhal number on a backward-inclined jet flame in crossflow

Combustion is often accompanied by environmental pollution due to incomplete reaction. A non-excited flame usually exhibits poor combustion performance with features of diffusion flame such as dual-peak temperature distributions and large combustion product concentrations. Efficient fuel-air mixing has been identified as a key factor in mitigating this issue. The present study investigated the effects of the acoustic excitation Strouhal number on the combustion performance of a backward-inclined jet flame in crossflow. A loudspeaker was used to induce jet pulsations with excitation Strouhal numbers ranging from 0.47 to 1.54 at a pulsation intensity of 0.90. Time-averaged and instantaneous flame images were captured using digital cameras. A customized R-type thermocouple and a commercial gas analyzer were employed to analyze the thermochemical structures. A critical excitation Strouhal number of approximately 0.9, distinguishing two characteristic flame modes: strongly affected flame (SA flame) and weakly affected flame (WA flame), was found. At excitation Strouhal numbers lower than the critical value, the SA flame featured single-peak temperature profiles and low unburned hydrocarbon, carbon monoxide, and nitric oxide emissions. The combustion performance was significantly improved due to the strong mixing effect induced by the acoustic excitation. The WA flame appeared at excitation Strouhal numbers higher than the critical value. It exhibited dual-peak temperature distributions and slightly improved combustion performance. The dynamic behavior and emissions of acoustically excited jet flames offered a fascinating insight into the influence of excitation Strouhal numbers on combustion characteristics. More excitation conditions were expected for future research.

Flame stabilization characteristics in the supersonic combustor based on a circular cross-section strut

Flame stabilization characteristics in the supersonic combustor with a circular cross-section strut were experimentally investigated. The Mach number, stagnation pressure, and stagnation temperature of the inflow were 2.52, 1.60 MPa, and 1486 K, respectively. Compared to the wedge-shaped recirculation flow at the base of the rectangular cross-section strut, the conical recirculation flow at the base of the circular cross-section strut possessed a more favorable geometry characterized by a longer length, a larger volume, and a small surface. When fueled by hydrogen, the combustor equipped both with a circular cross-section strut and a rectangular cross-section strut could achieve self-sustaining combustion. In the tests with equivalence ratios of 0.08 and 0.12, the time-averaged flame chemiluminescence intensity in the combustor with a circular cross-section strut was higher than its counterpart in the combustor with a rectangular cross-section strut by 80% and 53%, respectively. Nevertheless, the standard deviations of the flame chemiluminescence intensities showed an opposite trend. Therefore, the reaction zone downstream of the circular cross-section strut was more vigorous and stable. When both kerosene and hydrogen were supplied to the combustor, these two struts failed to stabilize the flame. Although an unsteady hydrogen–kerosene flame was witnessed in the combustor, it extinguished within 2 ms because the recirculation flow at the base of the strut was too small. Shock wave generators were employed to enhance the flame stabilization ability of the strut with a circular cross section. The experimental results suggested that shock wave generators significantly enlarged the recirculation flow and created a region with high temperature and high pressure. The self-sustaining hydrogen–kerosene flame was achieved in the combustor equipped with shock wave generators.

The effect of main stage flow velocity on thermoacoustic instability of stratified swirl burner

In this paper, two group experiments were conducted to study the effect of the main stage flow velocity on thermoacoustic instability and flame macrostructure. The experiments were carried out under atmosphere condition, and namely the pilot stage flame mode and the stratified swirl flame mode. The experimental results show that in the pilot stage flame mode, the thermoacoustic oscillation amplitude remains constant (around 1000 Pa) with the decrease of the main stage flow velocity. But when the velocity is zero (without main stage air), the thermoacoustic instability disappeared. In the stratified swirl flame mode, the amplitude of thermoacoustic instability is the largest (around 300 Pa) when the main stage flow velocity is 6.2 m/s, and the amplitude is slightly smaller in other working conditions. The time-averaged flame shape under the two flame modes is recorded and discussed. This paper highlights the effect of interactions between the pilot stage flame and main stage air or flame on thermoacoustic instability.

Models of the time-averaged heat release rate of the two-dimensional laminar premixed slit flame subjected to the transverse disturbance

A two-dimensional laminar premixed slit flame subjected to the transverse oncoming flow disturbance has been modelled in this work. The time-averaged flame heat release rate is theoretically studied. The time-averaged flame fronts can be assumed to be constant as the oncoming flow disturbance is weak. This assumption is not appropriate as the nonlinear flame dynamics are accounted for in the present work. The G-equation method is applied to capture the flame front dynamic evolutions. The perturbation method is used to conduct the nonlinear dynamics analysis. Analytical solutions of responses of time-averaged heat release rates of the slit flame to transverse perturbations are derived using different velocity perturbation models. Results show that the time-averaged flame fronts can be perturbed by the second order nonlinear term at different forcing frequencies in the perturbation analysis. The time-averaged flame fronts therefore include the unperturbed flame fronts and the perturbed zero order flame fronts. The flame aspect ratio has a significant effect on the transfer function of the time-averaged slit flame front surface area (TFSF). The velocity perturbation model has a significant effect on the TFSF and the TFSF using the uniform model has two states: the expanded state and the contracted state. The transverse bulk mean flow velocity has an important effect on the response of the time-averaged slit flame heat release rate to the transverse disturbance.

Flame characteristics of backward-inclined pulsating combusting jet in crossflow

The flame appearances, thermal characteristics, and combustion product concentrations of a backward-inclined pulsating combusting jet in crossflow were experimentally studied. The time-averaged and streak instantaneous flame images were acquired using a still camera and a high-speed camera, respectively. The flame extinguishment processes were captured and analysed on the basis of streak instantaneous images. The flame temperatures and combustion product concentrations were measured using a homemade fine-wire thermocouple and a gas analyser, respectively. Three characteristic flame modes (crossflow dominated, transitional, and jet-dominated) were found when the backward-inclined jet flame in crossflow was subject to acoustic excitation. These characteristic flame modes were observed in different regimes of pulsation intensity and jet backward inclination angle. Discrete flame puffs with a frequency equal to the acoustic excitation frequency appeared in the jet-dominated flame. Periodic flame puffing became unstable when the pulsation intensity was increased to values near the instability limit. When the pulsation intensity was beyond the instability limit, a strong stretching effect caused the recirculation flame, which played the role of a flame ignitor, to almost vanish (misfire). The flame extinguishment then occurred from the area around the lee side of the burner tube tip. The temperature and gas concentration measurement results showed the significant improvement of combustion performance in low inclination angle even at small pulsation intensity in the regime of the crossflow dominated flame. To enhance combustion performance at a large jet backward inclination angle, the pulsation intensity must be large enough to push the flame in the regime of the jet-dominated flame.

Effects of mechanically-induced oscillations on soot formation and flame temperature in laminar diffusion flames of ethylene

An experimental study was performed to measure the effects of flame oscillations on soot concentration and flame temperature in co-flow laminar diffusion flames of ethylene. One novel aspect of this study is that flame oscillations were mechanically induced by moving the burner assembly in a reciprocating motion with an industrial computer-controlled linear stage. Motor speed was used to control the oscillation frequency. The peak-to-peak oscillation amplitude was defined as stroke, which was then used to calculate the Strouhal number. Oscillation frequencies of 5‒20 Hz and peak-to-peak amplitudes of 0.5‒3 mm were studied. At 1 mm peak-to-peak oscillation amplitude, flame oscillations switched from tip flickering type to tip-clipping type oscillations above 10 Hz. Time-averaged soot concentration increased from its value in the steady-state flame when the flame was perturbed by small oscillation frequencies and amplitudes but then decreased as the oscillation intensity was increased. The peak time-averaged soot volume fraction was 9.5 ppm in the steady-state flame and 4.5 ppm at a peak-to-peak oscillation amplitude and an oscillation frequency of 1 mm and 20 Hz, respectively. Similarly, the peak soot volume fraction was 5.8 ppm at a peak-to-peak oscillation amplitude and an oscillation frequency of 3 mm and 10 Hz, respectively. The time-averaged flame temperatures were in the range of 1500‒2000 K. The low-temperature zone was observed at the flame core in the steady-state flame and for low-intensity oscillations, and at the flame tip for high-intensity oscillations. The literature has discrepancies on how flame oscillations affect the total soot loading in ethylene flames. Our results show that the total soot loading increased by about 10% from steady-state to low-intensity oscillations, then slightly decreased as either oscillation frequency or amplitude was increased. The effects of increasing the oscillation frequency or amplitude were similar and well captured by the revised Strouhal number.

Dual-fuel, dual-swirl burner for the mitigation of thermoacoustic instabilities in turbulent ammonia-hydrogen flames

In this paper, a novel dual-fuel, dual-swirl burner is presented and its potential to mitigate thermoacoustic coupling for ammonia-hydrogen-air flames is explored. The key feature of this burner is that the extent of mixing between ammonia and hydrogen before injection into the combustion chamber can be tuned by recessing an inner dividing tube. Non-reacting, 1-D Raman measurements confirm that recessing the dividing tube changes the radial profile of fuel composition at the injector's outlet. Time-averaged flame imaging shows that this modifies, in turn, the flame morphology. Specifically, the more stratified is the fuel, the least compact is the flame. In the most stratified case, a “blue” flame, predominantly burning hydrogen, pilots another “orange” flame, predominantly burning ammonia, further downstream. Acoustic measurements show that the least stratified (most compact) flame exhibits intrinsic thermoacoustic modes (ITA), while these modes are not featured for the most stratified (least compact) flame. Consequently, this study demonstrates that the thermoacoustic behavior of this carbon-free burner can be altered by tailoring the injection of ammonia and hydrogen while keeping the thermal power (7.4 kW), global equivalence ratio (0.64), and fuel flow rates strictly constant. This lays the foundation for the development of future practical burners in which the extent of mixing between ammonia and hydrogen upstream of the flame would be actively controlled to mitigate thermoacoustic coupling.

Heat release and transfer of premixed propane/air flames in high g-load centrifugal force fields

Rapid combustion and propagation are crucial for energy conversion and utilization equipment, such as power plants and thrust engines. High g-load in centrifugal flow fields has been demonstrated to be able to elevate turbulent flame speed. However, more details of flame behaviors in strong centrifugal force fields still need to be investigated. This paper focuses on flame bubble behaviors and related aspects by conducting Large Eddy Simulations (LES) of high g-load centrifugal flames stabilized by a backward step in an annual combustor. A centrifugal force was produced by setting different circumference inlet velocities (0 ms/, 4 m/s, 8 m/s, 12 m/s and 16 m/s) while axial velocity was constant (12 m/s). Wall-adapting Local Eddy-viscosity (WALE) model was used as the subgrid-scale model. Flamelet Generated Manifold (FGM) model and a 31-species and 107-step propane/air reaction mechanism were used for combustion modeling. The centrifugal body force exerted on flame bubbles and cold gas parcels is found to be able to make them move oppositely in the radial direction, and thus makes the flame surface more wrinkled. This effect leads to reinforced heat exchange between hot burned gas and cold fresh mixture. The consequent results are not only that the flame propagation speed is increased and the flame zone is broadened, but also that the local heat loss is enhanced, which leads to a weaker local heat release rate and might even lead to flame extinction. Additionally, the time-averaged flame front consists of a preheating zone and a reaction zone, along with a centrifugal-force-induced heat transfer from the post-flame zone to the cold fresh mixture.

Investigation of flame characteristics and cooling effectiveness of jet-cooled wall flameholders in vitiated flow

Experimental and numerical studies were performed to understand the flame characteristics and cooling effect of jet-cooled wall flameholders in a simplified augmented combustor. The time-averaged flame structure and wall temperature were investigated employing an instantaneous flame capturing system with image processing technology and a wall temperature measurement system, respectively. Flow and fuel distribution simulations were carried out to analyze the flame structure and cooling effect of the jet-cooled flameholders in high-temperature and high-velocity vitiated flows. It was found that the jet cooling type and the cooling jet angle on the oblique plate α and on the rear plate β greatly affect the flame features and cooling effect of the flameholder. The external-inhaled air cooling schemes can increase the flame luminosity and temperature and create a flame hollowed-out zone in the near-wall region to reduce flame radiation and heat convection, thereby achieving an excellent cooling effect. The pressure-driven gas jet cooling schemes yielded a weaker flame luminosity and its flame structure in the cavity more sensitive to the cooling jet angle than external-inhaled air cooling schemes. Moreover, the external-inhaled air cooling schemes have significantly better cooling effects than the pressure-driven gas jet cooling schemes under different mainstream conditions and fuel flow rates. Notably, the cooling schemes with α=30∘ and β=30∘ have more uniform wall temperature than that of α=90∘ and β=150∘ on the above two plates. Furthermore, the external-inhaled air cooling scheme with α=90∘ and β=150∘ has the best cooling performance under different mainstream and cooling air conditions and presents great cooling effectiveness in the case of enhancing cooling air temperature.

Investigation on flame characteristics approaching thermal chocking in a cavity-based supersonic combustor

This study experimentally investigated the combustion process in a cavity-based supersonic combustor at the inflow condition of Mach 2.92 with stagnation pressure 2.6 MPa and stagnation temperature 1530 K. Time-averaged flame distribution and oscillation characteristics were revealed by post-processing CH* chemiluminescence images. Wall pressures along the combustor bottom wall were also measured to provide quantitative information. Representative cascaded injection set-ups upstreaming the cavity were selected to compare ethylene flame characteristics. It is found that the combustion process is approaching thermal chocking when increasing the equivalence ratio to 0.8 according to the one-dimensional analysis of the Mach number distribution. At the same equivalence ratio, increasing the number of the cascaded injectors by lowering the injection pressure is not beneficial for the combustion enhancement, indicating that the injection pressure is also a key factor affecting the combustion heat release. However, increasing the injection pressure can cause obvious flame oscillations above the cavity as well as increasing the axis distance of the injectors. As a result, the injection scheme with two cascaded injectors which have the injection distance of 0.1 and 0.4 time the length of the cavity floor, respectively, upstreaming the cavity is suggested as a favorable scheme for scramjet applications.

Experimental study of the effect of air split ratio on thermoacoustic instability in a centrally-staged swirl burner

This study focuses on one of the critical design parameters of lean premixed (LPM) combustors—the air split ratio (ASR) between the pilot and main stages. The effect of the air split ratio on thermoacoustic instability is experimentally studied based on a centrally staged model combustor. It is found that the thermoacoustic instability is suppressed with the ASR higher than 20%. The acoustic modes of ASR lower than 20% are dominated by the main stage mode, while the others are controlled by the pilot stage mode. The time-averaged flame shapes and the flame dynamics are processed and discussed. With the increase in ASR, the pilot flame becomes longer, whereas the main flame becomes shorter. Meanwhile, the pilot and main flames become less separated. Moreover, the flame in the outer shear layer (OSL) is extinguished, which is the key to suppressing the thermoacoustic instability. The flame with lower ASR exhibits large-scale periodic axial motion of flame dynamics. The flow fields of ASR = 15% (unstable) and ASR = 30% (stable) are analyzed and discussed to help reveal the differences in thermoacoustic instability between the two cases. It is found that the primary recirculation zone is smaller with ASR = 30%. Higher vorticity and strain rate distributions found in the OSL are believed to quench the flame there. The present study illustrates that a higher air split ratio improves the thermoacoustic stability, which is helpful in designing LPM combustors.

Models of the time-averaged heat release rate of laminar premixed conical and V-shape flames subjected to flow disturbances

The time-averaged heat release rates of two-dimensional laminar premixed flames subjected to axial oncoming flow perturbations are theoretically studied in this paper. The proposed models of both the two-dimensional conical flame and V-shape flame are derived from the G-equation method. The weakly nonlinear perturbation analysis has been applied in the present work. The origins of time-averaged flame fronts consist of two parts: the unperturbed flame fronts caused by the balance between the laminar flame burning velocity and the incident normal velocity; the perturbed zero order time-averaged flame fronts caused by the second order nonlinear items in the perturbation analysis. For the conical and V-shape flame models, the analytical solution of the time-averaged flame heat release rate is derived based upon the perturbation method (analytical perturbation model) using different velocity perturbation models, in order to reveal the time-averaged flame heat release rate response mechanism to the axial disturbances. Results show that the velocity perturbation models and the flame aspect ratio have significant effects on the time-averaged flame heat release rates.

Evolutionary background-oriented schlieren tomography with self-adaptive parameter heuristics.

For volumetric reconstruction of the refractive index field in a flow, background-oriented schlieren (BOS) imaging which measures the deflection of light rays due to refractive index variations is combined with an evolutionary tomographic algorithm for the first time, called evolutionary BOS tomography (EBOST). In this work application to reactive flows is presented. Direct non-linear ray-tracing of the reconstruction domain is used to evaluate the fitness of solution candidates during the evolutionary strategy that was implemented to run on a multi-GPU system. The use of a diversity measure and its consideration in a migration policy was tested against a simple scheme that distributes the best chromosome (solution candidate) in an island-based genetic algorithm. The extensive set of control parameters of the presented algorithm was harnessed by a self-adaptive strategy taking into account the fitness function and operator rates. Quantitative characterisation of the EBOST via numerical phantom studies, using flame simulations as ground truth data is presented. A direct comparison to a state-of-the-art BOST algorithm demonstrates similar accuracy for a turbulent swirl flame phantom reconstruction. A series of experimental applications of the EBOST on several unsteady and turbulent flames is also presented. In all cases, the instantaneous and time-averaged flame structure is revealed, proving the benefit of EBOST for volumetric flow diagnostics.

Experimental Study on Dynamic Combustion Characteristics in Swirl-Stabilized Combustors

An experimental study was performed to investigate the combustion instability characteristics of swirl-stabilized combustors. A premixed gas composed of ethylene and air was burned under various flow and geometric conditions. Experiments were conducted by changing the inlet mean velocity, equivalence ratio, swirler vane angle, and combustor length. Two dynamic pressure sensors, a hot-wire anemometer, and a photomultiplier tube were installed to detect the pressure oscillations, velocity perturbations, and heat release fluctuations in the inlet and combustion chambers, respectively. An ICCD camera was used to capture the time-averaged flame structure. The objective was to understand the relationship between combustion instability and the Rayleigh criterion/the flame structure. When combustion instability occurred, the pressure oscillations were in-phase with the heat release oscillations. Even if the Rayleigh criterion between the pressure and heat release oscillations was satisfied, stable combustion with low pressure fluctuations was possible. This was explained by analyzing the dynamic flow and combustion data. The root-mean-square value of the heat release fluctuations was observed to predict the combustion instability region better than that of the inlet velocity fluctuations. The bifurcation of the flame structure was a necessary condition for combustion instability in this combustor. The results shed new insight into combustion instability in swirl-stabilized combustors.

Flame Structure Characterization in a Dual-Mode Scramjet Using Hydroxyl Planar Laser-Induced Fluorescence

The flame front of a premixed ethylene–air turbulent flame in a high-speed flowfield was imaged using hydroxyl radical (OH) planar laser-induced fluorescence (PLIF). An electrically heated continuous flow facility produced inflow conditions with a total temperature of 1200 K, corresponding to a flight Mach number of about five. A statistically stationary turbulent flame stabilized over a scaled-down cavity was used to generate experimental data for future comparisons with direct numerical simulations. A laser sheet with a wavelength of 283.55 nm was used to excite the (8) transition of OH. The sheet waist had a full width at half-maximum of . Two-dimensional OH-PLIF images were collected at high in-plane spatial resolution (approximately ) with a field of view of . The images spanned a region of along the spanwise centerplane. The local OH gradient was used to isolate the flame front in all images through an automated process. Each image was processed to obtain the appropriate statistics, time-averaged flame surface density, and flame front curvature values. The distribution of local flame front curvature values was approximately constant across the domain.

Monitoring combustion instabilities of stratified swirl flames by feature extractions of time-averaged flame images using deep learning method

The present article investigates the application of deep learning methods to monitor combustion instabilities based on time-averaged flame images. Experiments on BASIS (Beihang Axial Swirler Independently-Stratified) burner are carried out in a wide range of operating conditions to cover various flame shapes. We design a CNN (Convolutional Neural Networks) named BIM (BASIS Image Monitor) to extract features from flame shapes and determine the thermoacoustic states of the flames ahead of time. Experiments of 112 operating conditions are conducted, and their images are fed into BIM for training and testing purposes. BIM achieves around 99% prediction accuracy after a short training process lasting less than 20 minutes. Features extracted by BIM and visualized by Class Activation Maps (CAM) method reflect the underlying statistical links between flame images and their stabilities. Several phenomena (lift-off flame, flame-wall interaction, outer shear layer (OSL) flame and fuel mixing process) and their contributions to stabilities can be captured and quantified by CAM. After that, we test BIM with eight unknown operating conditions, and BIM can still perform well, identifying their stabilities and unstable features accurately. This paper explores the monitoring accuracy and feature extraction abilities of CNN in combustion. The BIM model shows potential to be a precursor in monitoring and active control systems of combustion instabilities.

Numerical Simulation of a GH2/LOx Single Injector Combustor and the Effect of the Turbulent Schmidt Number

A large-eddy simulation (LES) of a gaseous hydrogen/liquid oxygen (GH2/LOX) single-injector rocket combustor is performed in this study. The Redlich–Kwong–Peng–Robinson (RK–PR) equation of state is used to simulate the real-gas effect under high-pressure conditions, and the steady laminar flamelet model (SLFM) is implemented to simulate fast chemistry, such as a H2/O2 reaction. From the numerical simulation, the characteristics of time-averaged flow and flame fields are obtained, and their relationship with the real-gas effect is investigated. It is possible to investigate unsteady flame features and the mixing mechanism of propellants in detail by examining multiple snapshots of the field contour. Another purpose of the study is to investigate the differences in flow and flame structures according to the variation in the turbulent Schmidt number. By comparing the simulation result with the natural OH* emission image and temperature profiles from experimental data, the appropriate range of the turbulent Schmidt number for the simulation is obtained. Furthermore, this paper suggests the usefulness and validity of the current research by quantitatively comparing (i.e., temperature profiles) numerical results with those of existing literature.

Effects of Jet Flow Pulsation on Diffusion Flame Performance

he objective of the current research is the experimental investigation of the pulsating flow effects on the combustion performance in terms of the flame temperature distribution, the heat transfer rate, the combustion efficiency and the exhaust gas analysis. The flow pulsation provided through a rotary ball valve in accordance with a variable speed motor arrangement increased the flame temperature fluctuation and the magnitude of heat release. The flow pulsation provides a highly turbulent flame wherein the vortices are enlarged. Increasing Strouhal number [St] of the LPG fuel and air flow increases the time-averaged flame temperature of the pulsating flame up to a saturation level that is dictated by the heat transfer rate enhancement. The maximum average flame temperature is 1263oC at St= 0.041, r= 0 mm and 100 mm from the burner inlet. In addition, increasing the pulsating flow amplitude increases the convection and radiation heat fluxes from the pulsating flame. While increasing the pulsation decreases the exhaust UHC due to increasing the turbulent kinetic energy across the pulsating flame, the exhaust NOx slightly increases due to increasing the heat release rate and the flame temperatures. Pulsation thus enhances the combustion efficiency inside the industrial combustors.

Nonlinear response of swirling premixed flames to helical flow disturbances

This paper considers the relationship between nonlinearly interacting helical flow disturbances and flame area response in a swirling premixed flame. The present study was performed to determine whether there are nonlinear mechanisms through which helical modes ( ) can lead to non-zero unsteady heat release rate oscillations. The results show that for single frequency content (at ), helical modes excite unsteady heat release rate response of and that two-frequency excitation (e.g. at and ), leads to a response of at . There are two mechanisms through which this can occur: First, helical flow disturbances can distort the time-averaged flame shape to have an azimuthal component that matches that of the incident disturbance, . Second, multiple helical modes can nonlinearly interact to cause axisymmetric unsteady flame wrinkling. The paper derives the various modal contributions in the incident velocity disturbance that satisfy these criteria. These results suggest that it is only the mode which controls the linear dynamics (e.g. instability inception conditions) of these flames (where ), but that their nonlinear dynamics is also controlled by the helical modes.