Pulsation-Amplitude-Dependent Flame Dynamics of High-Frequency Thermoacoustic Oscillations in Lean-Premixed Gas Turbine Combustors

2017 ◽  
Author(s):  
Frederik M. Berger ◽  
Tobias Hummel ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Heat Release ◽  
Gas Turbine ◽  
Growth Rates ◽  
High Frequency ◽  
Individual Growth ◽  
Mean Flow ◽  
Flame Dynamics ◽  
Pulsation Amplitude ◽  
The Mean ◽  
Thermoacoustic Oscillations

This paper presents the experimental investigation of pulsation-amplitude-dependent flame dynamics associated with transverse thermoacoustic oscillations at screech level frequencies in a generic gas turbine combustor. Specifically, the flame behavior at different levels of pulsation amplitudes is assessed and interpreted. Spatial dynamics of the flame are measured by imaging the OH* chemiluminescence signal synchronously to the dynamic pressure at the combustor’s face plate. First, linear thermoacoustic stability states, modal dynamics, as well as flame-acoustic phase relations are evaluated. It is found that the unstable acoustic modes converge into a predominantly rotating character in the direction of the mean flow swirl. Furthermore, the flame modulation is observed to be in phase with the acoustic pressure at all levels of the oscillation amplitude. Second, distributed flame dynamics are investigated by means of visualizing the mean and oscillating heat release distribution at different pulsation amplitudes. The observed flame dynamics are then compared against numerical evaluations of the respective amplitude-dependent thermoacoustic growth rates, which are computed using analytical models in the fashion of a non-compact flame-describing function. While results show a nonlinear contribution for the individual growth rates, the superposition of flame deformation and displacements balances out to a constant flame driving. This latter observation contradicts the state-of-the-art perception of root-causes for limit-cycle oscillations in thermoacoustic gas turbine systems, for which the heat release saturates with increasing amplitudes. Consequently, the systematic observations and analysis of amplitude-dependent flame modulation shows alternative paths to the explanation of mechanisms that might cause thermoacoustic saturation in high frequency systems.

Pulsation-Amplitude-Dependent Flame Dynamics of High-Frequency Thermoacoustic Oscillations in Lean-Premixed Gas Turbine Combustors

2017 ◽  
Vol 140 (4) ◽  
Author(s):  
Frederik M. Berger ◽  
Tobias Hummel ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Heat Release ◽  
Gas Turbine ◽  
Growth Rates ◽  
High Frequency ◽  
Individual Growth ◽  
Mean Flow ◽  
Flame Dynamics ◽  
Pulsation Amplitude ◽  
The Mean ◽  
Thermoacoustic Oscillations

This paper presents the experimental investigation of pulsation-amplitude-dependent flame dynamics associated with transverse thermoacoustic oscillations at screech level frequencies in a generic gas turbine combustor. Specifically, the flame behavior at different levels of pulsation amplitudes is assessed and interpreted. Spatial dynamics of the flame are measured by imaging the OH⋆ chemiluminescence (CL) signal synchronously to the dynamic pressure at the combustor's face plate. First, linear thermoacoustic stability states, modal dynamics, and flame-acoustic phase relations are evaluated. It is found that the unstable acoustic modes converge into a predominantly rotating character in the direction of the mean flow swirl. Furthermore, the flame modulation is observed to be in phase with the acoustic pressure at all levels of the oscillation amplitude. Second, distributed flame dynamics are investigated by means of visualizing the mean and oscillating heat release distribution at different pulsation amplitudes. The observed flame dynamics are then compared against numerical evaluations of the respective amplitude-dependent thermoacoustic growth rates, which are computed using analytical models in the fashion of a noncompact flame-describing function. While results show a nonlinear contribution for the individual growth rates, the superposition of flame deformation and displacement balances out to a constant flame driving. This latter observation contradicts the state-of-the-art perception of root-causes for limit-cycle oscillations in thermoacoustic gas turbine systems, for which the heat release saturates with increasing amplitudes. Consequently, the systematic observations and analysis of amplitude-dependent flame modulation shows alternative paths to the explanation of mechanisms that might cause thermoacoustic saturation in high frequency systems.

Amplitude-Dependent Damping and Driving Rates of High-Frequency Thermoacoustic Oscillations in a Lab-Scale Lean-Premixed Gas Turbine Combustor

2021 ◽  
Author(s):  
Thomas Hofmeister ◽  
Thomas Sattelmayer
Keyword(s):  
Flow Field ◽  
Gas Turbine ◽  
Limit Cycle ◽  
High Frequency ◽  
Mean Flow ◽  
Gas Turbine Combustor ◽  
Cfd Simulations ◽  
The Mean ◽  
Amplitude Dependency ◽  
Thermoacoustic Oscillations

Abstract This paper presents numerical investigations of the amplitude-dependent stability behavior of thermoacoustic oscillations at screech level frequencies in a lean-premixed, swirl-stabilized, lab-scale gas turbine combustor. A hybrid Computational Fluid Dynamics / Computational AeroAcoustics (CFD / CAA) approach is applied to individually compute thermoacoustic damping and driving rates for various acoustic amplitude levels at the combustors' first transversal (T1) eigenfrequency. Forced CFD simulations with the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations mimic the real combustor's rotating T1 eigenmode. An increase of the forcing amplitude over time allows observation of the amplitude-dependent flow field and flame evolution. In accordance with measured OH*-chemiluminescence images, a pulsation amplitude-dependent flame contraction is reproduced in the CFD simulations. At several amplitude levels, period-averaged flow fields are then denoted as reference states, which serve as inputs for the CAA part. There, eigenfrequency simulations with linearized flow equations are performed with the Finite Element Method (FEM). The outcomes are damping and driving rates as a response to the amplitude-dependency of the mean flow field. It is found that driving due to flame-acoustics interactions governs a weak amplitude-dependency, which agrees with experimentally based studies at the authors' institute. This disqualifies the perception of heat release saturation as the root-cause for limit-cycle oscillations in this high-frequency thermoacoustic system. Instead, significantly increased dissipation due to the interaction of acoustically induced vorticity perturbations with the mean flow is identified, which may explain the formation of a limit-cycle.

Amplitude-Dependent Damping and Driving Rates of High-Frequency Thermoacoustic Oscillations in a Lab-Scale Lean-Premixed Gas Turbine Combustor

2021 ◽  
Author(s):  
Thomas Hofmeister ◽  
Thomas Sattelmayer
Keyword(s):  
Flow Field ◽  
Gas Turbine ◽  
High Frequency ◽  
Mean Flow ◽  
Gas Turbine Combustor ◽  
Cfd Simulations ◽  
Root Cause ◽  
The Mean ◽  
Amplitude Dependency ◽  
Thermoacoustic Oscillations

Abstract This paper presents the numerical investigations of amplitude-dependent stability behavior of thermoacoustic oscillations at screech level frequencies in a lean-premixed, atmospheric, swirl-stabilized, lab-scale gas turbine combustor. A hybrid Computational Fluid Dynamics / Computational AeroAcoustics (CFD / CAA) approach is applied to individually compute thermoacoustic damping and driving rates for various acoustic amplitude levels at the combustors’ first transversal (T1) eigenfrequency. Harmonically forced CFD simulations with the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations mimic the real combustor’s rotating T1 eigenmode. A slow and monotonous increase of the forcing amplitude over time allows observation of the amplitude-dependent flow field and flame evolution. In accordance with measured OH*-chemiluminescence images, a pulsation amplitude-dependent flame contraction is reproduced in the CFD simulations, where acoustically induced backflow at the combustion chamber inlet is identified as the root-cause of this phenomenon. At several amplitude levels, period-averaged flow fields are then denoted as reference states, which serve as inputs for the CAA part. There, eigenfrequency simulations with linearized flow equations are performed with the Finite Element Method (FEM). The outcomes are damping and driving rates as a response to the amplitude dependency of the mean flow field, which combined give the net thermoacoustic growth rate. It is found that driving due to flame-acoustics interactions only governs a weak amplitude dependency, which agrees with prior, experimentally based studies at the authors’ institute. This disqualifies the perception of heat release saturation as the root-cause for limit-cycle oscillations — at least in this high-frequency thermoacoustic system. Instead, significantly increased dissipation due to the interaction of acoustically induced vorticity perturbations with the mean flow is identified, which may explain the formation of a limit-cycle.

Low-Order Modeling of Nonlinear High-Frequency Transversal Thermoacoustic Oscillations in Gas Turbine Combustors

2016 ◽  
Author(s):  
Tobias Hummel ◽  
Klaus Hammer ◽  
Pedro Romero ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Dynamical System ◽  
Gas Turbine ◽  
High Frequency ◽  
Linear Part ◽  
Combustion Noise ◽  
Dynamical System Theory ◽  
Flame Dynamics ◽  
The Impact ◽  
Thermoacoustic Oscillations ◽  
Low Order

This paper analyzes transversal thermoacoustic oscillations in an experimental gas turbine combustor utilizing dynamical system theory. Limit cycle acoustic motions related to the first linearly unstable transversal mode of a given 3D combustor configuration are modeled, and reconstructed by means of a low order dynamical system simulation. The source of nonlinearity is solely allocated to flame dynamics, saturating the growth of acoustic amplitudes, while the oscillation amplitudes are assumed to always remain within the linearity limit. First, a Reduced Order Model (ROM), which reproduces the combustor’s modal distribution and damping of acoustic oscillations is derived. The ROM is a low-order state-space system, which results from a projection of the Linearized Euler Equations (LEE) into their truncated eigenspace. Second, flame dynamics are modeled as a function of acoustic perturbations by means of a nonlinear transfer function. This function has a linear and a nonlinear contribution. The linear part is modeled analytically from first principles, while the nonlinear part is mathematically cast into a cubic saturation functional form. Additionally, the impact of stochastic forcing due to broadband combustion noise is included by additive white noise sources. Then, the acoustic and the flame system is interconnected, where thermoacoustic non-compactness due to the transversal modes’ high frequency is accounted for by a distributed source term framework. The resulting nonlinear thermoacoustic system is solved in frequency and time domain. Linear growth rates predict linear stability, while envelope plots and probability density diagrams of the resulting pressure traces characterize the thermoacoustic performance of the combustor from a dynamical systems theory perspective. Comparisons against experimental data are conducted, which allow the rating of the flame modes in terms of their capability to reproduce the observed combustor dynamics. Ultimately, insight into the physics of high-frequency, transversal thermoacoustic systems is created.

A Time-Domain Network Model for Nonlinear Thermoacoustic Oscillations

2008 ◽  
Author(s):  
Simon R. Stow ◽  
Ann P. Dowling
Keyword(s):  
Heat Release ◽  
Frequency Domain ◽  
Limit Cycle ◽  
Network Model ◽  
Time Domain ◽  
Acoustic Waves ◽  
Mean Flow ◽  
The Mean ◽  
The Time Domain ◽  
Thermoacoustic Oscillations

Lean premixed prevaporised (LPP) combustion can reduce NOx emissions from gas turbines, but often leads to combustion instability. Acoustic waves produce fluctuations in heat release, for instance by perturbing the fuel-air ratio. These heat fluctuations will in turn generate more acoustic waves and in some situations linear oscillations grow into large amplitude self-sustained oscillations. The resulting limit cycles can cause structural damage. Thermoacoustic oscillations will have a low amplitude initially. Thus linear models can describe the initial growth and hence give stability predictions. An unstable linear mode will grow in amplitude until nonlinear effects become sufficiently important to achieve a limit cycle. While the frequency of the linear mode can often provide a good approximation to that of the resulting limit cycle, linear theories give no prediction of its resulting amplitude. In previous work, we developed a low-order frequency-domain method to model thermoacoustic limit cycles in LPP combustors. This was based on a ‘describing function’ approach and is only applicable when there is a dominant mode and the main nonlinearity is in the combustion response to flow perturbations. In this paper that method is extended into the time domain. The main advantage of the time-domain approach is that limit-cycle stability, the influence of harmonics, and the interaction between different modes can be simulated. In LPP combustion, fluctuations in the inlet fuel-air ratio have been shown to be the dominant cause of unsteady combustion: these occur because velocity perturbations in the premix ducts cause a time-varying fuel-air ratio, which then convects downstream. If the velocity perturbation becomes comparable to the mean flow, there will be an amplitude-dependent effect on the equivalence ratio fluctuations entering the combustor and hence on the rate of heat release. Since the Mach number is low, the velocity perturbation can be comparable to the mean flow, with even reverse flow occurring, while the disturbances are still acoustically linear in that the pressure perturbation is still much smaller than the mean. Hence while the combustion response to flow velocity and equivalence ratio fluctuations must be modelled nonlinearly, the flow perturbations generated as a result of the unsteady combustion can be treated as linear. In developing a time-domain network model for nonlinear thermoacoustic oscillations an initial frequency-domain calculation is performed. The linear network model, LOTAN, is used to categorise the combustor geometry by finding the transfer function for the response of flow perturbations (at the fuel injectors, say) to heat-release oscillations. This transfer function is then converted into the time domain through an inverse Fourier transform to obtain the Green’s function, which thus relates unsteady flow to heat release at previous times. By combining this with a nonlinear flame model (relating heat release to unsteady flow at previous times) a complete time-domain solution can be found by stepping forward in time. If an unstable mode is present, its amplitude will initially grow exponentially (in accordance with linear theory) until saturation effects in the flame model become significant, and eventually a stable limit cycle will be attained. The time-domain approach enables determination of the limit-cycle. In addition, the influence of harmonics and the interaction and exchange of energy between different modes can be simulated. These effects are investigated for longitudinal and circumferential instabilities in an example combustor system and results are compared to frequency-domain limit-cycle predictions.

Low-Order Modeling of Nonlinear High-Frequency Transversal Thermoacoustic Oscillations in Gas Turbine Combustors

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Tobias Hummel ◽  
Klaus Hammer ◽  
Pedro Romero ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Dynamical System ◽  
Gas Turbine ◽  
High Frequency ◽  
Linear Part ◽  
Combustion Noise ◽  
Dynamical System Theory ◽  
Flame Dynamics ◽  
The Impact ◽  
Thermoacoustic Oscillations ◽  
Low Order

This paper analyzes transversal thermoacoustic oscillations in an experimental gas turbine combustor utilizing dynamical system theory. Limit-cycle acoustic motions related to the first linearly unstable transversal mode of a given 3D combustor configuration are modeled and reconstructed by means of a low-order dynamical system simulation. The source of nonlinearity is solely allocated to flame dynamics, saturating the growth of acoustic amplitudes, while the oscillation amplitudes are assumed to always remain within the linearity limit. First, a reduced order model (ROM) which reproduces the combustor's modal distribution and damping of acoustic oscillations is derived. The ROM is a low-order state-space system, which results from a projection of the linearized Euler equations (LEE) into their truncated eigenspace. Second, flame dynamics are modeled as a function of acoustic perturbations by means of a nonlinear transfer function. This function has a linear and a nonlinear contribution. The linear part is modeled analytically from first principles, while the nonlinear part is mathematically cast into a cubic saturation functional form. Additionally, the impact of stochastic forcing due to broadband combustion noise is included by additive white noise sources. Then, the acoustic and the flame system is interconnected, where thermoacoustic noncompactness due to the transversal modes' high frequency (HF) is accounted for by a distributed source term framework. The resulting nonlinear thermoacoustic system is solved in frequency and time domain. Linear growth rates predict linear stability, while envelope plots and probability density diagrams of the resulting pressure traces characterize the thermoacoustic performance of the combustor from a dynamical systems theory perspective. Comparisons against experimental data are conducted, which allow the rating of the flame modes in terms of their capability to reproduce the observed combustor dynamics. Ultimately, insight into the physics of high-frequency, transversal thermoacoustic systems is created.

Self-Excited High-Frequency Transverse Limit-Cycle Oscillations and Associated Flame Dynamics in a Gas Turbine Reheat Combustor Experiment

2021 ◽  
Author(s):  
Jonathan McClure ◽  
Frederik M. Berger ◽  
Michael Bertsch ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Heat Release ◽  
Combustion Chamber ◽  
Gas Turbine ◽  
Limit Cycle ◽  
High Frequency ◽  
Dynamic Pressure ◽  
High Amplitude ◽  
Limit Cycle Oscillations ◽  
Flame Dynamics ◽  
Auto Ignition

Abstract This paper presents the investigation of high-frequency thermoacoustic limit-cycle oscillations in a novel experimental gas turbine reheat combustor featuring both auto-ignition and propagation stabilised flame zones at atmospheric pressure. Dynamic pressure measurements at the faceplate of the reheat combustion chamber reveal high-amplitude periodic pressure pulsations at 3 kHz in the transverse direction of the rectangular cross-section combustion chamber. Further analysis of the acoustic signal shows that this is a thermoacoustically unstable condition undergoing limit-cycle oscillations. A sensitivity study is presented which indicates that these high-amplitude limit-cycle oscillations only occur under certain conditions: namely high power settings with propane addition to increase auto-ignition propensity. The spatially-resolved flame dynamics are then investigated using CH* chemiluminescence, phase-locked to the dynamic pressure, captured from all lateral sides of the reheat combustion chamber. This reveals strong heat release oscillations close to the chamber walls at the instability frequency, as well as axial movement of the flame tips in these regions and an overall transverse displacement of the flame. Both the heat release oscillations and the flame motion occur in phase with the acoustic mode. From these observations, likely thermoacoustic driving mechanisms which lead to the limit-cycle oscillations are inferred. In this case, the overall flame-acoustics interaction is assumed to be a superposition of several effects, with the observations suggesting strong influences from autoignition-pressure coupling as well as flame displacement and deformation due to the acoustic velocity field. These findings provide a foundation for the overall objective of developing predictive approaches to mitigate the impact of high-frequency thermoacoustic instabilities in future generations of gas turbines with sequential combustion systems.

High-Frequency Instability Driving Potential of Premixed Jet Flames in a Tubular Combustor due to Dynamic Compression and Deflection

2020 ◽  
Author(s):  
Payam Mohammadzadeh Keleshtery ◽  
Gerrit Heilmann ◽  
Christoph Hirsch ◽  
Lukasz Panek ◽  
Michael Huth ◽  
...  
Keyword(s):  
Heat Release ◽  
Growth Rates ◽  
High Frequency ◽  
Dynamic Compression ◽  
Thermal Power ◽  
Design Parameters ◽  
Flame Dynamics ◽  
Dynamics Models ◽  
The Impact ◽  
Driving Potential

Abstract Constructive interference of acoustic oscillations and combustion heat release can result in high-frequency thermoacoustic instabilities in gas turbine combustion chambers with strong pressure pulsations. They may cause component wear and limit the safe operating range of the engine. During the development of stable combustors the influence of design variables on the driving mechanisms of these instabilities is of particular interest. This paper studies the influence of design parameters on the linear growth rates of high-frequency thermoacoustic transverse modes in a tubular combustor of hexagonal cross-section equipped with 12 turbulent premixed jet burners. Two flame dynamics models are used, i. e. the dynamic compression and the deflection mechanisms, which have in the past been validated for turbulent swirl burners. To demonstrate the applicability as well as the shortfalls of these flame dynamics models the impact of different geometrical and flow parameters on the driving potential of high-frequency thermoacoustic modes are considered. A parameter variation study of thermal power, air excess ratio, diameter of the combustor and the radial position of jet burners was performed. The first transversal eigenmodes and eigenfrequencies were computed by solving the inhomogeneous Helmholtz equation with the flame driving source terms in the frequency domain using the finite element method. The required mean fields of temperature and heat release rate were obtained using a generic flame distribution scaled with respect to the experimental OH* chemiluminescence measurements. The resulting growth rates give a measure for the thermoacoustic driving potential.

A Time-Domain Network Model for Nonlinear Thermoacoustic Oscillations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Simon R. Stow ◽  
Ann P. Dowling
Keyword(s):  
Heat Release ◽  
Frequency Domain ◽  
Limit Cycle ◽  
Network Model ◽  
Time Domain ◽  
Acoustic Waves ◽  
Mean Flow ◽  
The Mean ◽  
The Time Domain ◽  
Thermoacoustic Oscillations

Lean premixed prevaporized (LPP) combustion can reduce NOx emissions from gas turbines but often leads to combustion instability. Acoustic waves produce fluctuations in heat release, for instance, by perturbing the fuel-air ratio. These heat fluctuations will in turn generate more acoustic waves and in some situations linear oscillations grow into large-amplitude self-sustained oscillations. The resulting limit cycles can cause structural damage. Thermoacoustic oscillations will have a low amplitude initially. Thus linear models can describe the initial growth and hence give stability predictions. An unstable linear mode will grow in amplitude until nonlinear effects become sufficiently important to achieve a limit cycle. While the frequency of the linear mode can often provide a good approximation to that of the resulting limit cycle, linear theories give no prediction of its resulting amplitude. In previous work, we developed a low-order frequency-domain method to model thermoacoustic limit cycles in LPP combustors. This was based on a “describing-function” approach and is only applicable when there is a dominant mode and the main nonlinearity is in the combustion response to flow perturbations. In this paper that method is extended into the time domain. The main advantage of the time-domain approach is that limit-cycle stability, the influence of harmonics, and the interaction between different modes can be simulated. In LPP combustion, fluctuations in the inlet fuel-air ratio have been shown to be the dominant cause of unsteady combustion: These occur because velocity perturbations in the premix ducts cause a time-varying fuel-air ratio, which then convects downstream. If the velocity perturbation becomes comparable to the mean flow, there will be an amplitude-dependent effect on the equivalence ratio fluctuations entering the combustor and hence on the rate of heat release. Since the Mach number is low, the velocity perturbation can be comparable to the mean flow, with even reverse flow occurring, while the disturbances are still acoustically linear in that the pressure perturbation is still much smaller than the mean. Hence while the combustion response to flow velocity and equivalence ratio fluctuations must be modeled nonlinearly, the flow perturbations generated as a result of the unsteady combustion can be treated as linear. In developing a time-domain network model for nonlinear thermoacoustic oscillations an initial frequency-domain calculation is performed. The linear network model, LOTAN, is used to categorize the combustor geometry by finding the transfer function for the response of flow perturbations (at the fuel injectors, say) to heat-release oscillations. This transfer function is then converted into the time domain through an inverse Fourier transform to obtain Green’s function, which thus relates unsteady flow to heat release at previous times. By combining this with a nonlinear flame model (relating heat release to unsteady flow at previous times) a complete time-domain solution can be found by stepping forward in time. If an unstable mode is present, its amplitude will initially grow exponentially (in accordance with linear theory) until saturation effects in the flame model become significant, and eventually a stable limit cycle will be attained. The time-domain approach enables determination of the limit cycle. In addition, the influence of harmonics and the interaction and exchange of energy between different modes can be simulated. These effects are investigated for longitudinal and circumferential instabilities in an example combustor system and the results are compared with frequency-domain limit-cycle predictions.

scholarly journals Dynamic Response of Fuel Nozzles for Liquid-Fueled Gas Turbine Combustors

1996 ◽  
Author(s):  
Mounir Ibrahim ◽  
Terry Sanders ◽  
Douglas Darling ◽  
Michelle Zaller
Keyword(s):  
Gas Turbine ◽  
Cone Angle ◽  
Outer Region ◽  
Test Fluid ◽  
Mean Flow ◽  
Spray Cone Angle ◽  
Spray Cone ◽  
Gas Turbine Combustors ◽  
The Mean ◽  
Piezoelectric Drive

To imitate resonances that might occur in the fuel delivery system of gas turbine combustors, the incoming liquid streams of two pressure swirl nozzles were perturbed using a piezoelectric driver. Frequencies of perturbations examined were from 3 to 20 kHz, and water was used as the test fluid. A video camera and a Phase Doppler Particle Analyzer (PDPA) were used to study the effect of perturbations on the mean flow quantities of the sprays. Various lighting arrangements were used for the video photography: back lighting, front lighting, a strobe synchronized with the input to the piezoelectric, and a laser sheet oriented along the midplane of the sprays. The study showed that the piezoelectric drive had an effect an the spray system at discrete frequencies. At these particular frequencies, by increasing the input voltage, it was found that the piezoelectric drive affected the atomization in the following ways: (1) the mean flow rate decreased, (2) the spray cone angle decreased, (3) the break up length decreased, (4) the peak of the spatial distribution of the mean droplet size decreased, and (5) the mean droplet sizes and velocities increased near the spray center line and decreased in the outer region of the spray. A hysteresis effect of the drive frequency on the spray cone angle was observed. The results indicated that more fundamental research is needed to gain an in-depth understanding of the physical processes induced in the spray by the piezoelectric drive.

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