Acoustic Pressure Fluctuations Research Articles

Mean-field model of synchronization for open-loop, swirl controlled thermoacoustic system.

Open-loop control is known to be an effective strategy for controlling self-excited periodic oscillations, known as thermoacoustic instability, in turbulent combustors. Here, we present experimental observations and a synchronization model for the suppression of thermoacoustic instability achieved by rotating the otherwise static swirler in a lab-scale turbulent combustor. Starting with the state of thermoacoustic instability in the combustor, we find that a progressive increase in the swirler rotation rate leads to a transition from the state of limit cycle oscillations to the low-amplitude aperiodic oscillations through a state of intermittency. To model such a transition while also quantifying the underlying synchronization characteristics, we extend the model of Dutta et al. [Phys. Rev. E 99, 032215 (2019)] by introducing a feedback between the ensemble of phase oscillators and the acoustic. The coupling strength in the model is determined by considering the effect of the acoustic and swirl frequencies. The link between the model and experimental results is quantitatively established by implementing an optimization algorithm for model parameter estimation. We show that the model is capable of replicating the bifurcation characteristics, nonlinear features of time series, probability density function, and amplitude spectrum of acoustic pressure and heat release rate fluctuations at various dynamical states observed during the transition to the state of suppression. Most importantly, we discuss the flame dynamics and demonstrate that the model without any spatial inputs qualitatively captures the characteristics of the spatiotemporal synchronization between the local heat release rate fluctuations and the acoustic pressure that underpins a transition to the state of suppression. As a result, the model emerges as a powerful tool for explaining and controlling instabilities in thermoacoustic and other extended fluid dynamical systems, where spatiotemporal interactions lead to rich dynamical phenomena.

CFD-Based Prediction of Combustion Dynamics and Nonlinear Flame Transfer Functions for a Swirl-Stabilized High-Pressure Combustor

Thermoacoustic instabilities in gasturbine combustor systems can be predicted in the design phase with a thermoacoustic network model. In this model, the coupling between acoustic pressure fluctuations and the combustion rate is described by the Flame Transfer Function. The present paper introduces a new, efficient, and robust method for deriving the FTF from CFD predictions by means of a discrete multi-frequency sinusoidal fuel flow excitation method. The CFD-based FTF result compares well with experimental data for the time delay, but for the gain, only up to 400 Hz. Above 400 Hz, the CFD result reveals a smooth low-amplitude gain, which is not found in the measured data. A novel, accurate continuous correlation function for the FTF gain is computed based on the results for discrete frequencies. When this is implemented into a 1D acoustic network model, the stability map shows, below 600 Hz, two eigenfrequencies, by both the experiment and CFD-based FTF, that are identical. The CFD-based FTF correctly predicts marginal activity at the highest eigenfrequency, while the experimentally based FTF suggests an unstable operation. The unstable operation is not observed in the experiments. This suggests that the CFD-based FTF is also correct for high frequencies.

Research on wake and potential flow effects of rotor–stator interaction in a centrifugal pump with guided vanes

In this paper, the wake and potential flow effects of the rotor–stator interaction in a centrifugal pump with guide vanes are investigated from the view of the separation of turbulent and acoustic pressure fluctuations. The highest vibration levels in pumps are, in general, originated in the potential flow and wake effects. However, it is challenging to distinguish their effects on flow evolution. The pellicular mode decomposition method is applied to innovatively separate potential flow and wake disturbances in a centrifugal pump. By pellicular, we mean an infinitely thin layer of air located on the monitoring surface. The pellicular modes are a set of acoustic modes, with which a set of normalized orthogonal basis can be constructed. The impacts of potential flow and wake disturbances are visualized and evaluated quantitatively. The results show that only a very limited region is where the potential flow disturbance works. The higher the harmonics, the smaller the disturbance range. The wake disturbance is responsible for the modal pressure field. Modal pressure fields with low diametrical nodes decay more slowly than those with low harmonics. In addition, special attention is paid to the impact of the geometric asymmetry of the volute on the impeller force. The circular volute with a two-stage pressure drop improves the radial force of the impeller. More deep understandings on the mechanism of the rotor–stator interaction are reached by decoupling the potential flow and wake disturbances. This work serves as a guide for further research in fault diagnosis and vibration control of centrifugal pumps.

Inhibiting the onset of thermoacoustic instability through targeted control of critical regions

This experimental study investigates the dynamical transition from stable operation to thermoacoustic instability in a turbulent bluff-body stabilised dump combustor. We conduct experiments to acquire acoustic pressure and local heat release rate fluctuations and use them to characterise this transition as we decrease the equivalence ratio towards a fuel-lean setting. More importantly, we observe a significant increase in local heat release rate fluctuations at critical locations well before thermoacoustic instability occurs. One of these critical locations is the stagnation zone in front of the bluff-body. By strategically positioning slots (perforations) on the bluff-body, we ensure the reduction of the growth of local heat release rate fluctuations at the stagnation zone near the bluff-body well before the onset of thermoacoustic instability. We show that this reduction in local heat release rate fluctuations inhibits the transition to thermoacoustic instability. We find that modified configurations of the bluff-body that do not quench the local heat release rate fluctuations at the stagnation zone result in the transition to thermoacoustic instability. We also reveal that an effective suppression strategy based on the growth of local heat release rate fluctuations requires an optimisation of the slots' area-ratio for a given bluff-body position. Further, the suppression strategy also depends on the spatial distribution of perforations on the bluff-body. Notably, an inappropriate distribution of the slots, which does not quench the local heat release rate fluctuations at the stagnation zone but creates new critical regions, may even result in a dramatic increase in the amplitudes of pressure oscillations.

An ultra-thin low-frequency broadband metasurface with near-zero suppression of aerodynamic acoustic pressure

A near-zero suppression mechanism of aerodynamic acoustic pressure is revealed by adopting the ultra-thin low-frequency broadband lotus-pods-neck Helmholtz resonator (LPNHR) metasurface presented in this paper. The LPNHR is designed by changing the single neck of a Helmholtz resonator (HR) to a lotus-pods multi-layer-hole neck and keeping the number and equivalent diameter of the holes in the upper layer greater than that in the lower layer, and the bandwidth of LPNHR could be much widened than that of HR since the reduced acoustic mass. During the incident fluid flow, compared with HR, greater pressure difference formed at the interface of each hole of LPNHR generates stronger multi-vortexes inside its neck. Larger multi-vortex areas with greater absorption area ratio significantly increase the average flow velocity at the neck interface of LPNHR, resulting in decreased impedance. Moreover, the stronger multi-vortexes weaken the influence of the main-flow on the fluid flow inside the neck, that is, the flow from the external flow field into the LPNHR neck is enhanced under the action of the strong vortexes. The impedance decreases further and the effective length of the neck and acoustic mass increase, the shift of the flow-influenced sound attenuation to higher frequencies is suppressed and turned to lower frequencies. When the impedance approaches zero, the incident and scattered acoustic pressure match in phase and the acoustic pressure fluctuation at the wall will be fundamentally suppressed. Which is the physical mechanism of LPNHR to achieve near-zero suppression of low-frequency aerodynamic acoustic pressure. Furthermore, by adjusting the multiple parameters of LPNHR, the near-zero suppression of lower-frequency and larger-bandwidth aerodynamic acoustic pressure at higher speed could be achieved. Finally, an average reduction of sound pressure level by 3.71 dB (A) in the range of 550 Hz–4150 Hz on the 1/4-scale Ahmed body surface at a speed of 50 m/s is experimentally verified through 26 mm thick LPNHR metasurface with a basic unit composed of six parallel cells. The near-zero aerodynamic acoustic pressure suppression mechanism with metasurface presented provides new approaches for low frequency aerodynamic noise control, showing great potential in engineering applications.

Rotorcraft thickness noise control by tip ventilation

The paper explains further developments of a new concept called TNC (Thickness Noise Control) of the application of surface ventilation to the reduction of helicopter rotor low-frequency in-plane harmonic (LF-IPH) noise. The TNC method is based on introduction of four cavities covered by perforated plates (connected to low and high pressure reservoirs) and positioned symmetrically at the front and rear extremities of the blade tip. Two operational modes are analyzed: constant (steady) and periodically varying (unsteady) transpiration mass-fluxes. For exemplary two-bladed model helicopter rotor of Boxwell et al. (Bell UH-1H Iroquois helicopter) in hover conditions, the results of numerical simulations, based on the CFD code SPARC (Spalart-Allmaras turbulence and Bohning-Doerffer transpiration models), suggest that the acoustic pressure fluctuations are significantly reduced in the near-field of the blade tip. Moreover, the unsteady approach (designed for forward located observers) is almost equally efficient to the basic (steady) operation mode, while substantially lowering penalties in terms of the aerodynamic performance and required transpiration flow intensity. Finally, it is proven that when TNC is activated, the twisted blade (operating in low-thrust conditions) exhibits lower deterioration of the aerodynamic performance compared to its straight (untwisted) counterpart.

Hydrodynamic and acoustic pressure fluctuations in water pipes due to an orifice: Comparison of measurements with Large Eddy Simulations

The present article investigates the turbulent wall pressure fluctuations due to flow through single-hole sharp-square-edged orifices (opening area ratios of 11%, 20% and 31%) in a water-filled pipe by means of measurements and incompressible Large Eddy Simulations (LES) for opening area ratios of 20% and 31%. The orifice plate thickness was half the orifice diameter. The static pressure measurements and simulations show that the vena-contracta factors of the orifices are dependent on Reynolds numbers, which is due to the finite thickness of the orifices. These LES simulations provide a good prediction of the near-field hydrodynamic wall pressure fluctuations, which dominate up to the first three pipe diameters downstream of the orifice. Upstream and far downstream wall pressure fluctuations are dominated by acoustic pressure fluctuations. The source of the radiated sound field was estimated from the surface integral of the fluctuations across the orifice in the LES. The sound field was calculated by implementing the sound source in a one dimensional acoustic model of the test section. The power spectrum density (PSD) of the wall pressure fluctuations for pipe Reynolds numbers varying from 4000 to 10000 collapsed when presented in dimensionless form, which uses the dynamic pressure in the orifice as reference pressure and the ratio of cross-sectional averaged orifice velocity and orifice diameter as characteristic frequency. In the inertial range of the turbulence a global decay of the pressure PSD and of the sound source show a power of the Strouhal number between −113 and −2.8. For higher frequencies the pressure fluctuations were dominated by acoustic resonances. For wider orifices the magnitude of these acoustic pressure fluctuations is predicted within a factor two by the acoustic model. For the narrowest orifice (opening ratio of 11%) the measured PSD of pressure fluctuations displays sharp peaks due to self-sustained oscillations (whistling). A simple power law of the sound source is not accurate due to the unstable hydrodynamic modes related to orifice thickness. However, using the simple model for the sound source the acoustic model predicts the acoustic pressure fluctuations reasonably well for all orifices. At low frequency one observes a peak in the PSD hydrodynamic wall-pressure fluctuations at one pipe diameter downstream of the orifice. It is probably due to an acoustically silent “edge-tone-like” sinusoidal self-sustained motion of the jet.

波数・周波数スペクトル測定用マイクアレイのマイク配置の最適化

In order to develop microphone array for the wavenumber-frequency spectrum analysis that separates the hydrodynamic pressure fluctuations (HPF) and acoustic pressure fluctuations (APF), it is necessary to consider the spatial resolution to capture both eddy scale of the turbulent flow and wavelength of the sound which has relatively large scale compared to the flow eddy. In this study, the effects of the number of microphones and their arrangement on the accuracy of the analysis were investigated, and the optimized microphone array arrangement was explored. The results of comparison of the wavenumber-frequency spectrum indicated that the microphone array with a well-balanced combination of sparse and dense microphone arrays (such as the logarithmic spiral array and localized random array) of 96 channels or more is required to separate APF and HPF in the frequency band of 500~5 kHz which is required for the analysis of automobile aeroacoustics noises.

Neural ODE to model and prognose thermoacoustic instability.

Thermoacoustic instability in a reacting flow field is characterized by high amplitude pressure fluctuations driven by a positive coupling between the unsteady heat release rate and the acoustic field of the combustor. In a turbulent flow, the transition of a thermoacoustic system from a state of chaos to periodic oscillations occurs via a state of intermittency. During the transition to periodic oscillations, the unsteady heat release rate synchronizes with the acoustic pressure fluctuations. Thermoacoustic systems are traditionally modeled by coupling the model for the heat source and the acoustic subsystem, each estimated independently. The response of the unsteady heat source, i.e., the flame, to acoustic fluctuations is characterized by introducing unsteady external forcing. The forced response of the flame need not be the same in the presence of an acoustic field due to their nonlinear coupling. Instead of characterizing individual subsystems, we introduce a neural ordinary differential equation (neural ODE) framework to model the thermoacoustic system as a whole. The neural ODE model for the thermoacoustic system uses time series of the heat release rate and the pressure fluctuations, measured simultaneously without introducing any external perturbations, to model their coupled interaction. Furthermore, we use the parameters of neural ODE to define an anomaly measure that represents the proximity of system dynamics to limit cycle oscillations and thus provide an early warning signal for the onset of thermoacoustic instability.

Experimental investigation of aerofoil tonal noise at low Mach number

This paper presents an experimental investigation of aerofoil tones emitted by a controlled-diffusion aerofoil at low Mach number ( $0.05$ ), moderate Reynolds number based on the chord length ( $1.4 \times 10^{5}$ ) and moderate incidence ( $5^{\circ }$ angle of attack). Wall-pressure measurements have been performed along the suction side of the aerofoil to reveal the acoustic source mechanisms. In particular, a feedback loop is found to extend from the aerofoil trailing edge to the regions near the leading edge where the flow encounters a mean favourable pressure gradient, and consists of acoustic disturbances travelling upstream. Simultaneous wall-pressure, velocity and far-field acoustic measurements have been performed to identify the boundary-layer instability responsible for tonal noise generation. Causality correlation between far-field acoustic pressure and wall-normal velocity fluctuations has been performed, which reveals the presence of a Kelvin–Helmholtz-type modal shape within the velocity disturbance field. Tomographic particle image velocimetry measurements have been performed to understand the three-dimensional aspects of this flow instability. These measurements confirm the presence of large two-dimensional rollers that undergo three-dimensional breakdown just upstream of the trailing edge. Finally, modal decomposition of the flow has been carried out using proper orthogonal decomposition, which demonstrates that the normal modes are responsible for aerofoil tonal noise. The higher normal modes are found to undergo regular modulations in the spanwise direction. Based on the observed modal shape, an explanation of aerofoil tonal noise amplitude reduction is given, which has been previously reported in modular or serrated trailing-edge aerofoils.

Dynamical Characterization of Thermoacoustic Oscillations in a Hydrogen-Enriched Partially Premixed Swirl-Stabilized Methane/Air Combustor

Abstract In this study, we systematically analyze the effects of hydrogen enrichment in the well-known PRECCINSTA burner, a partially premixed swirl-stabilized methane/air combustor. Keeping the equivalence ratio and thermal power constant, we vary the hydrogen percentage in the fuel. Successive increments in hydrogen fuel fraction increase the adiabatic flame temperature and also shift the dominant frequencies of acoustic pressure fluctuations to higher values. Under hydrogen enrichment, we observe the emergence of periodicity in the combustor resulting from the interaction between acoustic modes. As a result of the interaction between these modes, the combustor exhibits a variety of dynamical states, including period-1 limit cycle oscillations (LCO), period-2 LCO, chaotic oscillations, and intermittency. The flame and flow behavior is found to be significantly different for each dynamical state. Analyzing the coupled behavior of the acoustic pressure and the heat release rate oscillations during the states of thermoacoustic instability, we report the occurrence of 2:1 frequency-locking during period-2 LCO, where two cycles of acoustic pressure lock with one cycle of the heat release rate. During period-1 LCO, we notice 1:1 frequency-locking, where both acoustic pressure and heat release rate repeat their behavior in every cycle.

Broadband suppression of aerodynamic pressure on the high-speed bluff body surface with periodic square-cavity acoustic metasurface

In this paper, a Multiphysics coupling simulation model of flow and acoustics is proposed using COMSOL software, and its results are verified by comparing with experimental results of others. Then, the aerodynamic pressure above the bluff body surface at a speed of 350 km/h is simulated. Moreover, a near-zero-impedance acoustic metasurface composed of periodic square cavities is theoretically studied with respect to the lowest acoustic pressure, which is consistent with simulation results. The wake vortices are greatly reduced due to the suction effect formed in the cavities when the fluid flow passes through the square-cavity metasurface. The vertical velocity above the square-cavity boundary is significantly increased, essentially leading to the decrease in acoustic impedance. The presence of high-speed fluid flow weakens the attenuation effect of the square-cavity acoustic metasurface on the acoustic field. The reduction in wake vortices and the near-zero-impedance of the boundary fundamentally suppress the acoustic pressure fluctuation above the bluff body surface. Finally, large broadband suppression of aerodynamic pressure and 7.3 dB reduction in the average acoustic pressure level are realized with the periodic acoustic metasurface. The greater the porosity of the square cavities, the smaller the fluctuating pressure amplitude. This work provides a new idea for the complete control of the aerodynamic pressure in a high-speed flow field and shows a great engineering application prospect.

Response of Autoignition-Stabilized Flames to One-Dimensional Disturbances: Intrinsic Response

Abstract Burning carbon-free fuels such as hydrogen in gas turbines promises power generation with reduced greenhouse gas emissions. A two-stage combustor architecture with an autoignition-stabilized flame in the second stage allows for efficient combustion of hydrogen fuels. However, interactions between the autoignition-stabilized flame and the acoustic field of the combustor may result in self-sustained oscillations of the flame front position and heat release rate, which severely affect the stable operation of the combustor. We study one such 'intrinsic' mode of interaction wherein acoustic waves generated by the unsteady flame travel upstream and modulate the incoming mixture resulting in flame front oscillations. In particular, we study the response of an autoignition-stabilized flame to upstream traveling acoustic disturbances in a one-dimensional configuration. We first present a numerical framework to calculate the response of autoignition-stabilized flames to acoustic and entropy disturbances in a one-dimensional combustor. The flame response is computed by solving the energy and species mass balance equations. We validate the framework with compressible direct numerical simulations. Lastly, we present results for the flame response to upstream traveling acoustic perturbations. The results show that autoignition-stabilized flames are highly sensitive to acoustic temperature fluctuations and exhibit a characteristic frequency-dependent response. Acoustic pressure and velocity fluctuations constructively or destructively superpose with temperature fluctuations, depending on the mean pressure and relative phase between the fluctuations. The findings of the present work are essential for understanding the intrinsic feedback mechanism in combustors with autoignition-stabilized flames.

Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure

We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogeneity in the temporal recurrence patterns at all relevant time scales. We demonstrate the potential of the proposed method when applied to empirical data, namely time series of acoustic pressure fluctuations from a turbulent combustor. Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots. Furthermore, it contributes to a better distinction between stable operation and near blowout states of combustors.

Suppression of thermoacoustic instability by targeting the hubs of the turbulent networks in a bluff body stabilized combustor

Abstract

Study of a thermoacoustic-Stirling engine connected to a piston-crank-flywheel assembly.

This paper deals with the theoretical description of self-sustained oscillations resulting from the coupling of a piston-crank-flywheel assembly with a thermoacoustic-Stirling prime mover. The governing equations of the piston-flywheel motion are coupled to those of the thermoacoustic system, which is described in the time domain through a rational differential operator relating acoustic pressure fluctuations inside the cavity to the piston's velocity. As a result, the complete device is described by means of a fourth-order nonlinear dynamical system and solved numerically. The dynamical behavior of the system is studied as a function of the temperature difference along the thermoacoustic unit, and it is shown that the regime of stable rotations of the flywheel appears through a saddle-node bifurcation above a threshold value of the temperature difference. Moreover, the simulation results show good agreement with experiments.

Numerical simulation of leakage flow field and acoustic characteristics for safety valve

Aiming at the internal leakage problem of spring type nuclear safety valve at the sealing surface, the flow field and sound field characteristics at the leakage height of 0.5mm between the valve disc and the valve seat sealing surface were studied, and the numerical simulation was carried out based on large eddy simulation(LES) and mohring acoustic analogy method, and compare the effects of acoustic wall pressure fluctuation(AWPF) and turbulent wall pressure fluctuation(TWPF) as the excitation source on the external sound field of the valve. The simulation results show that: the change gradient of velocity field and pressure field at the leakage port of safety valve is significant and form vortices of different sizes. The small-scale vortices are mainly in the leakage port, while the large-scale vortices mainly exist in the flow channel; When the valve is leaking, the noise is mainly dominated by high-pressure injection noise, its spectrum curve shows wide-band characteristics, and the external noise of the valve is mainly caused by AW P F. The above research results can provide a theoretical basis for the safety valve online detection method.

Separation of convective and acoustic pressure fluctuations on the front side window of DrivAer model based on pellicular mode decomposition

When a car is driven at high speed, the total pressure fluctuations on the side window include convective pressure fluctuation and acoustic pressure fluctuation, which have different generation mechanisms, transmission characteristics and efficiency. In order to understand the aerodynamic noise transmission mechanisms through the side window and calculate the aerodynamic noise accurately inside the car, it is necessary to separate these two kinds of pressure fluctuations. Based on the existing full-size DrivAer model, the pellicular mode decomposition theory proposed in recent years was investigated. With this approach, the two pressure fluctuations from a compressible CFD calculation acting on the side window were separated successfully. Through comparison with the pressure data obtained with the improved wavenumber decomposition approach, the reliability and accuracy of the pellicular mode decomposition approach for solving the acoustic pressure fluctuation was validated. Moreover, in comparison with wavenumber decomposition, the pellicular mode decomposition can be applied easily to any surface with arbitrary shape, even the surface curved in 3D. Further advantage of this approach is the ability to reconstruct the pressure field of convective and acoustic components individually at any frequency, which can help to understand the characteristics of these two pressure components. Disadvantage is however the handling of a large number of numerically computed pellicular modes, which is limited in principle by the implementation of finite element method. As a consequence, a reliable convective pressure fluctuation is difficult to be acquired directly with this approach.

Wind noise source characterization and transmission study through a side glass of DrivAer model based on a hybrid DES/APE method

Based on a DrivAer model with notchback, the characteristics of convective and acoustic pressure fluctuations on the side window, as well as their contributions to interior noise were studied. Firstly, a full-size DrivAer clay model was produced with a real glass set on the front left window, and the rest parts with thick clay. In this way, the side glass becomes the exclusive transmission path for the exterior convective and acoustic pressures into acoustic cabin inside. In this study, the acoustic pressure fluctuation on the side window surface was calculated by solving the acoustic perturbation equation (APE) based on the calculation results of convective pressure fluctuation with the incompressible Detached Eddy Simulation (DES). Furthermore, with the convective and acoustic pressure fluctuations as power inputs, the interior noise was calculated with Statistical Energy Analysis (SEA). The calculated interior noise level shows good agreement with the tested results in the wind tunnel, which indirectly validates the reliability of the calculated acoustic pressures with APE method. The contributions of the convective and acoustic pressure fluctuations to the interior noise show that the acoustic pressure fluctuation takes much higher transmission efficiency than the convective one, especially at the high frequency range above the coincidence frequency of the glass, the contribution of acoustic pressure fluctuation is absolutely dominant.

Effect of flame surface area of downward propagating flames induced by single and double laser irradiation on transition to parametric instability

The single laser irradiation ( SLI ) method was adopted to develop a double laser irradiation ( DLI ) method to investigate the effects of laser-induced structures of downward-propagating flames in a tube on the transition from primary acoustic instability to parametric instability . Previously, the SLI method was effectively used to study the interaction between acoustic oscillation and flame structure by controlling the shape of the flame front. The deformed cellular structure (either concave or convex) of the SLI -induced flame can transition from primary acoustic instability to parametric instability under certain conditions. We conducted experiments in the same combustion tube with C 2 H 4 /O 2 /CO 2 mixtures using both SLI and DLI for comparison. The DLI method forms double cellular structures, while SLI only forms single cellular structures on the flames. It was found that the DLI method was more effective than SLI in generating transition to parametric instability under same total laser power. Furthermore, a linear relationship was found between the area of the deformed structure (irrespective of its dimension) and the corresponding growth rate of acoustic pressure fluctuation during the propagation of the deformed flame. SLI - and DLI -induced deformed structures having the same deformed surface area demonstrate the same growth rate of thermo-acoustic instability regardless of the difference in ( ak ) 2 , where a is the amplitude and k is the wavenumber of the deformed structures, respectively. This factor described in the velocity coupling mechanism is important to reveal the growth rate of thermo-acoustic instability due to the variation in the flame surface area. The results revealed that the actual flame surface area, rather than ( ak ) 2 of the laser-induced downward-propagating flame structure, determines the transition in the presence of nonhomogeneous cell distribution induced by SLI and DLI . The total deformed surface area is a more comprehensive criterion for transition to parametric instability.