Azimuthal Mode Research Articles

Experimental study on acoustic and flame responses in an annular combustor under azimuthal force

This study investigates the flame dynamics of an annular combustor under various azimuthal acoustic forces. The experimental platform was applied to external azimuthal acoustic force through four loudspeakers installed on the wall outside the plenum. Experiments were conducted with an equivalence ratio of Ф = 0.71 and a combustion power of P = 9.5 kW. Therein, four loudspeakers were used to precisely control the acoustic pressure amplitude, spinning ratio, and spinning direction, which stimulated the first-order standing mode, spinning modes, and second-order standing mode acoustic mode of the plenum, respectively. Our analysis of flame dynamics and acoustic response characteristics was based on different azimuthal modes, combined with dynamic mode decomposition (DMD) of the flame image sequence and acoustic pressure signal. The results corroborate the consistency between the acoustic field quaternion analysis and the flame image sequence DMD results despite varied external forcing conditions. Specifically, the characteristics of the flame vary by the applied forces. Moreover, DMD results indicate that the flame structure of the eigenfrequency mode is asymmetrical in spinning modes and tilts in the direction of the pressure gradient.

Model of Faraday waves in a cylindrical container with force detuning

Recent experiments by Shao et al. [“Surface wave pattern formation in a cylindrical container,” J. Fluid Mech. 915, A19 (2021)] have revealed complex wave dynamics on the surface of a liquid bath in a vertically vibrated cylindrical container that are related to the presence of a meniscus on the container sidewall. We develop a corresponding theoretical model for this system by detuning the driving acceleration of the container, which results in an inhomogeneous Mathieu equation that governs the wave dynamics whose spatial structure is defined by the mode number pair (n,m), with n and m the radial and azimuthal mode numbers, respectively. Asymmetric m≠0 modes are unaffected by the detuning parameter, which is related to the meniscus shape and satisfy a homogeneous Mathieu equation with the shape of the instability tongues computed by the Floquet theory. The Poincaré–Lindstedt method is used to compute the instability tongues for the axisymmetric m=0 modes, which have a lower threshold acceleration and larger bandwidth that depend upon the detuning parameter. Our model results explicitly show how the shape of the meniscus and spatial structure of the wave determine the temporal response and are in good agreement with prior experimental observations for both pure modes and mixed modes.

Gain in efficiency of jet receptivity to acoustic disturbances with increasing nozzle-lip thickness

The gain in efficiency of the receptivity of jets to acoustic disturbances as the nozzle lip is thicker is investigated using numerical simulations. For that, axisymmetric acoustic pulses are introduced in jets with Blasius laminar boundary-layer profiles at Mach numbers $M=0.4$ , 0.6, 0.9 and 1.3 for nozzle-lip thicknesses between 1 % and 93 % of the nozzle radius. They are located on the jet axis or outside the jet with incidence angles $\varphi$ between $5^{\circ }$ and $90^{\circ }$ with respect to the downstream direction. Instability waves develop in the jet shear layer after the acoustic disturbances hit the nozzle. In all cases except for $\varphi \geq 75^{\circ }$ , their amplitudes and hence the efficiency of the jet receptivity to the disturbances increase with the nozzle-lip thickness. The gains in efficiency are greater for a pulse inside the jet, generating upstream-travelling pressure waves resembling guided jet waves, than for a pulse outside the jet, producing free-stream sound waves. In the second case, the gains are significant for $\varphi =5^{\circ }$ and decrease with the incidence angle, especially for $\varphi >30^{\circ }$ . Moreover, the gains are stronger for a higher Mach number, and roughly double between $M=0.4$ and $1.3$ , thus reaching, for a pulse inside the jet, values close to 6 between the thinnest and thickest lips. Finally, according to additional simulations for $M=0.9$ , the gains in receptivity efficiency do not change appreciably when different azimuthal mode numbers of the acoustic disturbances, widths of the pulse and shapes of the boundary-layer profile are considered.

Superresolution and analysis of three-dimensional velocity fields of underexpanded jets in different screech modes

Time-resolved (TR), three-dimensional (3D) velocity fields of screeching, underexpanded jets are estimated using non-time-resolved particle image velocimetry and simultaneous TR microphone measurements. Specifically, we aim to reconstruct TR 3D velocity fluctuation fields associated with the A2, B, and C modes of a screeching jet using a linear regression model and to analyze screech dynamics of these modes. The linear regression model is constructed on the basis of a linear relationship between the velocity and acoustic fields. Three nozzle pressure ratios (NPRs) of 2.30, 2.97, and 3.40 are employed. The dominant azimuthal modes for three cases are investigated using azimuthal Fourier coefficients of the acoustic data obtained by the azimuthal array of eight microphones placed near the nozzle exit. The dominant azimuthal modes at NPRs of 2.30, 2.97, and 3.40 are m=0, 1, and 1, respectively. The first two proper orthogonal decomposition (POD) modes in these azimuthal modes are dominant at all NPRs and are associated with screech. 3D velocity fluctuation fields associated with screech are reconstructed from these leading POD modes of the acoustic data. The reconstructed 3D velocity fluctuation fields at NPRs of 2.97 and 3.40 exhibit two helical structures with opposite rotation directions. The present results demonstrate that, in the B mode, the flapping structure exhibits random clockwise and counterclockwise rotations over an extended time domain, while maintaining a consistent direction within short time domains. In addition, in the C mode, two helical structures with opposite rotation directions, as well as the flapping structure, are observed. Published by the American Physical Society 2024

Spectral proper orthogonal decomposition analysis of a spatially developing underexpanded round jet at Re = 45 000

This study conducts a comprehensive analysis of the coherent structures within a spatially developing underexpanded axisymmetric jet at a Reynolds number of 45 000, utilizing high-fidelity implicit large eddy simulations (iLES) in conjunction with spectral proper orthogonal decomposition (SPOD). In the frequency–wavenumber space, the global SPOD analysis identifies three distinct coherent structures, corresponding to three different mechanisms, namely, Kelvin–Helmholtz (KH), Orr, and lift-up. Their salient characteristics are discussed in detail. Local SPOD analysis further explores the streamwise evolution of these coherent structures, revealing that the influence of KH mechanism is confined to the near field, while the lift-up mechanism persists and dominates the energy content beyond the potential core, with the streaks of azimuthal wavenumbers one and two being the most energetic. The reconstruction of turbulent kinetic energy (TKE) and Reynolds shear stress from SPOD modes is assessed, and the first few azimuthal modes with low wavenumbers and frequencies are found crucial for capturing the dominant features of the flow. It is found that only the m = 0 and m = 1 modes contribute to the TKE at the centerline. The Reynolds shear stress reconstruction quality is comparable to TKE, but with a negligible contribution from the m = 0 mode. The azimuthal mode m = 1 captures the slope of the actual Reynolds shear stress profile in the vicinity of centerline, while m = 2 and higher modes capture the peak location of the actual profile.

Optical communication in a turbulent atmosphere via the orbital angular momentum of a laser beam. II. Symbol error rate in a data line

A numerical simulation is applied to study the symbol error rate (SER) in an optical communication system with data modulation by the orbital angular momentum (OAM) of an optical beam propagating through a turbulent atmosphere. In this case, the OAM is calculated from pre-recorded powers of azimuthal modes, while the complex modes are the coefficients of expansion of the wave field of the beam into spiral harmonics. The SER is calculated as a function of turbulence conditions for the LG1 and LG4 beams and data line lengths, as well as the number of receiving channels (number of recorded powers of azimuthal modes) and size of the input aperture of the receiving telescope. It is shown that the range of angular harmonics can be optimized to diminish the SER. It is found that knowing the probability density of OAM fluctuations, with a pre-determined average OAM and its variance, we can estimate the SER without conducting special numerical tests.

Parametric oscillations of the sessile drop

Waves are formed on the surface of a sessile drop driven through substrate vibrations oriented at a slanting angle from the normal. A mathematical model is derived, which leads to an infinite system of coupled Mathieu equations governing the wave dynamics that are solved using Floquet theory. The spatial structure of the waves is described by the mode number pair $[\ell,m]$ , where $\ell$ and $m$ are the polar and azimuthal mode numbers, respectively. Limiting cases corresponding to horizontal and vertical vibrations are discussed with predictions agreeing well with prior literature. We focus our results on three drop motions – (1) harmonic $[1,1]$ rocking mode, (2) harmonic $[2,0]$ pumping mode, and (3) subharmonic rocking $[1,1]$ mode – as they depend upon the slanting angle, static contact angle, and contact-line conditions, which we assume to be either pinned or freely moving with fixed contact angle. New theoretical predictions are tested through experiments over a range of parameters, showing good agreement.

Bondi-Hoyle-Lyttleton accretion around the rotating hairy Horndeski black hole

Modeling of the shock cone formed around a stationary, hairy Horndeski black hole with Bondi-Hoyle-Lyttleton (BHL) accretion has been conducted. We model the dynamical changes of the shock cone resulting from the interaction of matter with the Horndeski black hole, where the scalar field and spacetime have a strong interaction. The effects of the scalar hair, the black hole rotation parameter, and the impacts of the asymptotic speed have been examined, revealing the influence of these parameters on the shock cone and the trapped QPO modes within the cone. Numerical calculations have shown that the hair parameter significantly affects the formation of the shock cone. As the absolute value of the hair parameter increases, the matter in the region of the shock cone is observed to move away from the black hole horizon. The rate of matter expulsion increases as h/M changes. After h/M < -0.6, a visible change in the physical structure of the shock cone occurs, ultimately leading to the complete removal out of the shock cone. On the other hand, it has been revealed that the asymptotic speed significantly affects the formation of the shock cone. As h/M increases in the negative direction and the asymptotic speed increases, the stagnation point moves closer to the black hole horizon. When the value of the hair parameter changes, the rest-mass density of the matter inside the cone decreases, whereas the opposite is observed with the asymptotic speed. Additionally, the formed shock cone has excited QPO modes. The deformation of the cone due to the hair parameter has led to a change or complete disappearance of the QPOs. Meanwhile, at asymptotic speeds of V ∞/c < 0.4, all fundamental frequency modes are formed, while at V ∞/c = 0.4, only the azimuthal mode is excited, and 1:2:3:4:… resonance conditions occur. No QPOs have formed at V ∞/c = 0.6. The results obtained from numerical calculations have been compared with theoretical studies for M87*, and it has been observed that the possible values of h/M found in the numerical simulations are consistent with the theory. Additionally, the results have been compared with those for the GRS 1915+105 black hole, and the hair parameters corresponding to the observed frequencies have been determined.

Suppression of Azimuthal Combustion Instability Using Perforated Liner Under Symmetry Breaking

Symmetry breaking occurring in annular combustors shows different stability patterns due to the formation of nondegenerate modes with different frequencies. This also brings about more profound complexity for control methodology. This paper presents a three-dimensional analytical model to investigate how to control nondegenerate azimuthal modes by modifying the wall boundary conditions of a multiburner annular combustor. The stability of the system can be evaluated by solving the eigenvalue of the dispersion relation equation derived in this study. Results show that changes in the parameters of the perforated liner cause different performance in nondegenerate modes due to frequency splitting. Meanwhile, the asymmetric perforated liner alters the original asymmetry of the annular combustor, inducing a shift in the nature of nondegenerate modes when significant symmetry breaking exists. Furthermore, variations of pressure amplitude in the backing cavity lead to diverse acoustic energy dissipation and even distinct stability patterns under two types of azimuthally nonuniformly perforated liner. Overall, this paper presents a new methodology for suppressing nondegenerate azimuthal modes under symmetry breaking by utilizing a perforated liner in an annular combustor. Additionally, a clear understanding of the evolution behavior of nondegenerate modes is also provided by studying their stability behavior and energy dissipation.

Dynamic three-dimensional measurement and analysis of rotating polygons

Rotating polygons are geometric patterns formed spontaneously by the free surface of a rotating fluid driven by a rotating disk at the bottom of a partially filled cylindrical container. Most previous studies mainly predict the number of polygon apexes as a function of disk rotation speed and initial fluid depth. We propose to experimentally characterize this three-dimensional instability by means of highly accurate measurements of the free surface height using Fourier transform profilometry. For a given initial height of 26 mm in a cylindrical cavity of radius 140 mm, these measurements enabled us to not only revisit quantitatively the previous analysis in the fully developed regime but also extend the analysis to the spin-up regime (starting from rest). This latter regime has not been explored. In addition, we describe the mixed-mode regime at the boundary between two clearly established polygons. Thanks to precise space-time resolved surface height measurements, we propose a decomposition of each azimuthal mode that provides valuable information on the growth and dynamics of rotating polygons and can, therefore, serve as a basis for future numerical simulations and theoretical models.

Intermittency transition to azimuthal instability in a turbulent annular combustor

We experimentally study the transition from a state of combustion noise to azimuthal thermoacoustic instability in a laboratory-scale turbulent annular combustor. This combustor has sixteen swirl-stabilized burners to facilitate continuous and spatially distributed combustion along the annular region. Our approach involves simultaneous measurement of CH* chemiluminescence emission of the flame using two high-speed cameras and the acoustic pressure fluctuations using eight piezoelectric pressure transducers mounted on the backplane of combustor. We observe that the transition from combustion noise to azimuthal instability occurs through mode shifting, where the system switches from a longitudinal mode to an azimuthal mode as the equivalence ratio is decreased. Throughout this progression, the combustor exhibits various dynamical behaviors, including intermittency, dual-mode instability, standing azimuthal instability, and beating azimuthal instability. These dynamical states are determined from the acquired pressure signals by decomposing the acoustic pressure fluctuations into clockwise (CW) and counterclockwise (CCW) waves, enabling a reconstruction of the amplitude of acoustic pressure fluctuations, nature angle, (anti-)nodal line location, and spin ratio. The global heat release response is then examined during various dynamical states, contrasting their behavior at different non-dimensional time steps by phase-averaging the fluctuations of the heat release rate over the acoustic pressure cycle. Distinctive flame behaviors were observed based on the direction of pressure wave propagation, showcasing characteristic CCW spinning, standing, and CW spinning heat release patterns. Moreover, our examination of relative phase distributions during various dynamical states, computed by analyzing the phase of heat release rate fluctuations across all burners with respect to one burner, reveals the emergence of diverse patterns in the interaction of neighboring flames influenced by acoustic field.

Localization of acoustical sources rotating in the cylindrical duct using a sparse nonuniform microphone array

The Doppler effect caused by the rotation of turbine fans brings significant challenges to the identification of fan noise sources inside the nacelle. Current methods of rotating source localization inside the cylindrical duct are executed with tough requirements for the microphone array mounted on the duct wall, which includes a fair enough number of microphones and equal-space distribution of each microphone in the azimuthal direction. A methodology based on nonuniform measurements and duct spin modes superposition (NMDMS) is proposed to identify rotating sources with high spatial resolution and few side lobes even near cut-on frequencies, which requires much fewer microphones and no uniform distribution of each microphone in the circumference. The sparsity in the azimuthal domain of the duct field generated by multiple rotating sources is verified theoretically, after which the azimuthal mode in each duct cross-section is reconstructed by the inhomogeneous measurements through the orthogonal matching pursuit (OMP) method. Followed by the identification of mode amplitude in the rotation frame, the sound pressure distribution as well as the axial acoustic velocity distribution on the source plane is reconstructed through duct modes summation. Numerical simulations and experiments are implemented to validate the method. Localization results indicate that rotating sources identification using the proposed method could not only save more than half the microphones without requirements of equal-space distribution but obtain good accuracy of localization and remarkably fewer side lobes.

Rossby wave instability and substructure formation in 3D non-ideal MHD wind-launching discs

ABSTRACT Rings and gaps are routinely observed in the dust continuum emission of protoplanetary discs (PPDs). How they form and evolve remains debated. Previous studies have demonstrated the possibility of spontaneous gas rings and gaps formation in wind-launching discs. Here, we show that such gas substructures are unstable to the Rossby wave instability (RWI) through numerical simulations. Specifically, shorter wavelength azimuthal modes develop earlier, and longer wavelength ones dominate later, forming elongated (arc-like) anticyclonic vortices in the rings and (strongly magnetized) cyclonic vortices in the gaps that persist until the end of the simulation. Highly elongated vortices with aspect ratios of 10 or more are found to decay with time in our non-ideal magnetohydrodynamic (MHD) simulation, in contrast with the hydro case. This difference could be caused by magnetically induced motions, particularly strong meridional circulations with large values of the azimuthal component of the vorticity, which may be incompatible with the columnar structure preferred by vortices. The cyclonic and anticyclonic RWI vortices saturate at moderate levels, modifying but not destroying the rings and gaps in the radial gas distribution of the disc. In particular, they do not shut-off the poloidal magnetic flux accumulation in low-density regions and the characteristic meridional flow patterns that are crucial to the ring and gap formation in wind-launching discs. Nevertheless, the RWI and their associated vortices open up the possibility of producing non-axisymmetric dust features observed in a small fraction of PPDs through non-ideal MHD, although detailed dust treatment is needed to explore this possibility.

Dominant duct azimuthal acoustic mode detection considering failed wall-installed microphones with amplitude or phase measurement biases

Reliable duct mode detection results are essential for aero-engine health condition monitoring and low-noise design. Harsh aero-engine measurement environments may cause biases in amplitude and phase measurements due to the failure of wall-mounted microphones, which will decrease the performance of advanced sparse representation algorithms for duct mode detection. In this paper, two strategies to detect the duct mode with the failed microphones are proposed. An optimization problem is constructed considering the low-rankness of theoretical array measurement and row-sparsity of the failed microphone measurements. The Strategy 1 is based on the recovery of the theoretical array measurement. The recovered array measurement can be further used to detect the duct mode via the sparsity-induced duct mode detection algorithm (generalized minimax-concave penalty in this paper). With the simulation, the Strategy 1 can not recover the theoretical array measurement completely. The Strategy 2 is based on the removal of the failed microphone measurements. With the simulation and experiment, it turns out that the Strategy 2 can detect the interested mode accurately.

Causal analysis among azimuthal Fourier modes in linear plasma based on multivariate time series models

This study investigates the causal relationships among azimuthal Fourier modes in linear plasma turbulence using multivariate time series models. We elucidate the dynamics of mode interactions in magnetized plasmas by employing the vector autoregressive model and Granger causality analysis. Our analysis, based on data from the plasma assembly for nonlinear turbulence analysis, reveals significant variations in causality with changing pressure conditions. Modes form weakly coupled clusters at lower pressures, while higher pressures lead to stronger coupling and larger clusters. The impulse response function further provides insights into the temporal propagation and nature of influences between modes. These findings enhance the understanding of spatial pattern formation in magnetized plasmas and offer a quantitative framework for analyzing plasma turbulence dynamics.

Effect of the magnetic field strength on the argon plasma characteristics of a helicon plasma source with a two-turn flat-loop antenna

New plasma applications in advanced fields, such as fundamental nuclear fusion research, require high-density, large-diameter plasma with a strong and non-uniform magnetic field. A helicon plasma (HP) source using a flat-type antenna is expected to be one of the promising methods for such applications. In this study, we developed an HP source with a two-turn flat-loop antenna connected to a 30 kW radio frequency power supply in the Compact Test Plasma device. In the argon plasma generation experiment with various magnetic fields, HP generation was observed for the first time in this device. The electron density was calculated from the dispersion relation with the magnetic field strength at 45 cm from the antenna surface, assuming a fundamental radial mode and an azimuthal mode of $m=0$ . The electron density expected from the experimental result was approximately in the same range as the calculation result by a factor of 2.3 to 3.5. In addition, the magnetic field strength and shape around the antenna are important factors in the plasma properties. This plasma source has been installed in the pilot GAMMA PDX-SC, which is under development for nuclear plasma research, and it contributes to the study of the HP generation process.

A simple method improving acoustic mode identification capability based on genetic algorithms

This letter develops a simple approach of duct mode identification and reconstruction based on genetic algorithms, which can extend the azimuthal mode order range compared to the conventional method based on the (spatial) discrete Fourier transform. The underlying principle is reconstructing the dominant mode from the modal identification forward model through optimization by exploiting the sparsity of the mode amplitude vector. The performance is experimentally demonstrated for detections of one and two azimuthal modes under noisy conditions with nondominant modes. Overall, the proposed genetic-algorithm-based framework for solving acoustic inverse problems is beneficial to duct acoustic testing, particularly design evaluations of fan blades and acoustic liners for aeroengines.

Large Eddy Simulation and Acoustic Analysis of Combustion Instability in an Annular Combustor with Low-Swirl Flames.

Self-excited combustion instability in an annular combustor with low-swirl flames is studied with a combination of large eddy simulation (LES) and acoustic solvers. Acoustic analysis with a Helmholtz solver provides an estimate of frequencies and modal structures in the annular combustor. LES gives detailed modal dynamics for specific instability modes. Combustion instabilities in the annular combustor including longitudinal, spinning, and standing modes are successfully captured in a single LES. Numerical results show that the instability modes are not constant; they switch among these modes randomly and rapidly. The flow oscillates back and forth in phase with the largest pressure amplitude located near the outlet of the injectors for the longitudinal mode. The azimuthal instability oscillates in the 1A2L mode of the annular system. In the spinning mode, the pressure antinodes move forward while the modal structure keeps constant. For the standing mode, the locations of pressure antinodes are fixed in the annular combustor and the fluctuations at the pressure antinodes keep out of phase. The near-zero value of the mean spin ratio indicates that the dominant azimuthal mode is the standing mode. The azimuthal modes captured by LES are in good agreement with that predicted by Helmholtz solver in terms of frequency and modal structure. The maximum deviation of the predicted frequency is less than 5%. This adds values before the low-swirl injector is placed into the actual annular combustor.

Longitudinal and azimuthal thermoacoustic modes in a pressurized annular combustor with bluff-body-stabilized methane-hydrogen flames

Longitudinal and azimuthal thermoacoustic modes in a pressurized annular combustor with bluff-body-stabilized methane-hydrogen flames

Mean azimuthal flow of puff in pipe flow

The mean azimuthal flow of puff, a key structure of the subcritical transition in pipe flow, is studied numerically and theoretically in this Letter. It is revealed that the mean azimuthal velocities (MAVs) are governed by the least stable azimuthal modes at the far downstream and upstream, respectively. At the upstream near-wall region, the statistical period between the direction reversals of the area-averaged MAV becomes longer with the increase in the Reynolds number (Re), illustrating the same trend as the lifetime of puffs. At Re = 2300, the puff splitting is found to be inhibited when MAV is suppressed, and the facilitating mechanism of MAV on the puff splitting is explained in terms of the enhancement effect of MAV on the downstream disturbance kinetic energy: it elongates the central high-kinetic-energy region of puff, whose extended downstream part may grow further to generate a new puff.