Computational Aeroacoustic Simulations Research Articles

Multirotor drone noise: numerical approach for aeroacoustics and in-flight noise prediction

Nowadays, multirotor drone usage has become widespread for various purposes: amateur or professional videos, building inspection, civil security, military defense, etc. But this usage increase has also seen growing concerns about community noise annoyance in inhabited areas, acoustic detectability for security and military purposes, or remote wildlife monitoring. Predicting the drone noise can now be accurately achieved thanks to computational aeroacoustics (CAA). The present work deals with the aeroacoustic simulation and measurement of a quadcopter drone and in-flight condition prediction. The CAA simulation of a single rotor is first compared with test bench measurements in an anechoic room. Comparison for the full drone is then derived from this single-rotor comparison. Finally, the study is further extended to in-flight comparisons, in order to show that CAA simulation can help design quieter drones in real operating conditions.

Computational aeroacoustics of low-pressure axial fans installed in parallel

Abstract Ducted rotor-only Low-Pressure Axial (LPA) fans play an integral role in automotive thermal management of electric vehicles and are the primary source of noise from the underhood region. Multiple LPA fans are often placed in parallel in cooling packages of electric vehicles. There is little scientific work concerning aeroacoustics of ducted LPA fans operating in parallel. This work aims to address this gap through hybrid computational aeroacoustic simulations. Three-dimensional, full-annulus, transient simulations are done using the Delayed Detached Eddy Simulation (DDES) turbulence model. First, a numerical validation study is presented, where aerodynamic and aeroacoustic results from this work are compared to experimental results for a LPA fan issued by the European Acoustics Association (EAA). In the second part, aeroacoustic performance of two-fans placed in parallel is presented. A local diffusion zone is observed in the region where the two-fans are closest to one another. A previously unidentified vortex which envelopes the local diffusion zone is observed. For two-fans in parallel, the amplification of the acoustic spectrum scales in accordance to having two identical equally strong sound sources, i.e, by 6 dB. The scaling of the acoustic spectrum for two-fans in parallel in comparison to a single-fan suggests limited interaction between the acoustic field of the two-fans.

High-fidelity computational study of aerodynamic noise of side-by-side rotor in full configuration

This paper presents a numerical study of side-by-side rotor aircraft in full configuration during hover using high-fidelity computational fluid dynamics (CFD) and aeroacoustic simulations. CFD simulations are performed using HPCMP CREATE™-AV Helios, while acoustic calculations are conducted with PSU-WOPWOP. Overset structured grids are applied using the SA-DES turbulence model along with adaptive mesh refinement in the near- and off-body meshes. Four overlap cases at a specific collective pitch angle of 8° are considered. Results reveal a substantial influence of the fuselage on rotor performance, with improvement in the figure of merit being observed for each overlap configuration due to a partial ground effect. There is considerable increase in blade sectional thrust, pressure fluctuations, and noise levels seen in the 0% overlap configuration compared to the 25% overlap configuration. This increase is primarily due to the absence of rotor overlap, resulting in a lower induced velocity allowing for flow to travel upward, and reaching the rotor disk plane. The acoustic spectrum appears at all harmonics of the blade passing frequency for the 0% and 5% overlap configurations. In contrast, the acoustic spectrum is distinctly present only at even harmonics for the 15% and 25% overlap cases. A noise reduction benefit of 3-5 dBA is noticed in the full configuration cases having rotor overlap compared to the 0% overlap configuration. Acoustic destructive interference is observed in the directivity plot only for the 15% and 25% overlap configurations. Overall, this paper reveals that the fuselage has a significant impact on the performance, aerodynamics, and aeroacoustics of the side-by-side UAM vehicle in hover.

Analysis of Sound Propagation Behaviors for Supersonic Jet on Far Field Region by Computational Aero-Acoustics (CAA) Simulation

Noise emission is an essential issue for the aviation industry, as it harms health and induces various physiological responses. The noise generated by supersonic jets is very intense. It will cause fatigue and even damage the human hearing system in the surrounding area of jet operation. Besides, the experimental and prototyping cost for the jet model is prohibitive, and it is a vast project and process that takes a lot of time to run. The purpose of this study is to determine the sound propagation behaviours of a supersonic jet in the far-field region and to analyse the consequences of the velocity of a supersonic jet on sound propagation of supersonic jet by using computational fluid dynamics (CFD) and computational aeroacoustics (CAA) simulations. This study focused on the perspective of observing the distance of the receiver when receiving the sound propagation of a supersonic jet, the observed angle of the receiver when receiving the sound propagation of a supersonic jet, and the velocity of the supersonic jet. The CFD and CAA analyses were performed in transient state simulation and the 2-inch Acoustics Reference Nozzle (ARN2). The result shows that the overall SPL throughout the frequency is proportional to the jet velocity of the supersonic jet. However, the distance and angle of the receiver gave different results in sound propagation behaviour. The results also conclude that as the distance between the receiver and jet nozzle exit increases, the overall SPL trend will decrease throughout the frequency increase. As the vertical distance between the receiver and the axisymmetric line of the jet nozzle increases, the frequency of the receiver starts to observe will decrease.

Reducing the aerodynamic noise of the axial flow fan with perforated surface

In this study, the effect of utilizing a perforated surface as an innovative flow control method to reduce fan noise is numerically investigated. The case study consists of a shrouded axial flow fan with a perforated surface placed on its shroud behind the trailing edge. Using the LES model and FW-H analogy, the fan noise is determined in the frequency domain at a nominated location by performing computational aero-acoustic (CAA) simulations. In order to evaluate the penalty imposed on the aerodynamic performance by this control method, an aerodynamic simulation is performed using RANS equations and the k-ω SST turbulence model. The mentioned numerical models are experimentally validated. The results show that the coherent structures of the flow are disrupted, and the fan noise is reduced in the trailing edge area - an extremely noise-prone zone - thanks to the passive control method. The noise reduction values could potentially reach 6 dB specifically at the critical blade pass frequency, which significantly contributes to the overall noise produced by the fan. Moreover, it is shown that there are strong relationships between the Proudman, turbulence kinetic energy, and entropy indexes with the total aeroacoustic performance of the fan. In contradistinction to other applied methodologies, this control method does not impose any aerodynamic performance penalty, though it could be improved by around 1.5 % at the operating point.

Stochastic Noise Sources for Computational Aeroacoustics of a Vehicle Side Mirror

<div>The broadband aeroacoustics of a side mirror is investigated with a stochastic noise source method and compared to scale-resolving simulations. The setup based on an already existing work includes two geometrical variants with a plain series side mirror and a modified mirror with a forward-facing step mounted on the inner side. The aeroacoustic near- and farfield is computed by a hydrodynamic–acoustic splitting approach by means of a perturbed convective wave equation. Aeroacoustic source terms are computed by the Fast Random Particle-Mesh method, a stochastic noise source method modeling velocity fluctuations in time domain based on time-averaged turbulence statistics. Three RANS models are used to provide input data for the Fast Random Particle-Mesh method with fundamental differences in local flow phenomena. Results of aeroacoustics simulations excited by the Fast Random Particle-Mesh method based on well-matching RANS data are in good agreement to the scale-resolving simulations in the integral acoustic Delta on the side window induced by the different side mirror geometries. For relative levels in between the variations, the robustness of the Fast Random Particle-Mesh method can be shown with secondary influences on the choice of the integral length scale. Absolute levels are only achieved with an adaptation of the length scale from literature. Two different RANS models with a missing separation bubble on the mirror or an overestimated wake flow show a good agreement with the plain series side mirror. However, they fail at computing the Delta to the step variant due to the missing amplification of the local turbulent kinetic energy interacting with the step and downstream mirror surfaces. Computational aeroacoustics simulations excited by the Fast Random Particle-Mesh method method based on RANS data only needs 14% of the computational effort compared to the conventional hybrid RANS-LES approach. This reveals its enormous potential for aeroacoustic broadband noise optimization purposes.</div>

Noise assessment and low-noise flight path planning platform for urban air mobility

The rapidly emerging market of urban air mobility has raised considerable public concern about noise exposure and annoyance, which is likely to limit the development of future aerial transportation. This study presents a comprehensive approach to evaluate the flight noise of an urban air mobility vehicle under various operating conditions and to provide practical flight strategies for low-noise path planning. Two methods with different fidelity levels are considered and compared in evaluating sound sources. The first approach is based on an efficient semi-empirical model to predict the rotor noise and a boundary element method solver to account for the noise scattering from the vehicle fuselage. The second approach is based on high-fidelity computational aeroacoustic simulations considering a practical full-scale urban air mobility vehicle. Then, a Gaussian beam method is used to calculate the far-field sound propagation considering practical physical phenomena in complex environments, including sound refraction attenuation in the atmosphere and reflection from obstacles. A low-noise flight planning strategy is proposed using a heuristic method to optimize the vehicle flight path in realistic urban scenarios. The proposed methods should contribute to future green aerial transportation in low-altitude operations.

LibFastMesh: An optimized finite-volume framework for computational aeroacoustics

This paper presents an optimized framework for simulating aeroacoustic flow on unstructured meshes. The libFastMesh (LFM) framework is based on a low-dissipation finite–volume discretization, together with high-order explicit time integration, for direct computation of aeroacoustic fields. These methods were previously implemented in caafoam, an OpenFOAM-based solver developed by D'Alessandro et al. [1] to resolve aeroacoustic flows. The new framework is specifically developed from scratch to alleviate two of the main bottlenecks currently limiting the performance of OpenFOAM-based solvers at large scale: memory bandwidth and inter-node communication. Compact data structures and compute kernel fusion are employed to enhance cache utilization and re-use, respectively. Separate treatment of inter-process boundary cells, together with non-blocking MPI communication enable effective overlap between communication and flux computations. The accuracy and robustness of libFastMesh are established via simulations of well-established aeroacoustic flow benchmarks. Comparison to previous simulation results obtained with caafoam, and to DNS data serve to validate the code. Finally, the effectiveness of the aforementioned optimizations is demonstrated through rigorous analysis of the proposed solver performance in single-node and multi-node operation modes. The obtained results show that libFastMesh offers a speed-up of up to 20x with respect to the previously developed OpenFOAM-based solver, caafoam, in large-scale computations. Moreover, LFM is shown to scale extremely for cell-per-core ratios of less than 500. These results are particularly appealing given the highly resource-demanding nature of direct computational aeroacoustics (CAA). Consequently, LFM could be an extremely attractive tool for scientists who wish to conduct large-scale CAA simulations on modern, exascale architectures. Program summaryProgram Title: libFastMeshCPC Library link to program files:https://doi.org/10.17632/7w9fy2xtcf.1Developer's repository link:https://github.com/TRC-HPC/LFM_PublicLicensing provisions: GPLv3Programming language: C++Nature of problem: This software solves compressible Navier–Stokes equations. The adopted numerics and flow models allow to capture with high accuracy aerodinamically generated sound. The solver is also designed to take advantage of the massively parallel computing systems which are strictly required for facing real–life aeroacoustic problems.Solution method: The libFastMesh (LFM) framework is based on a low-dissipation finite–volume discretization, together with high-order explicit time integration, for direct computation of aeroacoustic fields on unstructured meshes. Convective terms can be approximated using either the Kurganov–Noelle–Petrova (KNP) scheme or Pirozzoli's energy conserving approach. Time integration is fully–explicit and relies on a low-storage, 4th order Runge–Kutta scheme. The solver is specifically developed to run efficiently on modern many-core CPUs, and at large-scale where it exhibits excellent strong scaling features. This is made possible thanks to several optimizations that alleviate memory bandwidth and inter-node communication bottlenecks.Additional comments: OpenFOAM-v2112+ is an installation prerequisite. Standard OpenFOAM pre-processing and post-processing tools, as well as mesh decomposition and reordering methods may be used with the solver.

Variations with Mach number for gust–airfoil interaction noise

The interaction of turbulence with airfoil is an important noise source in many engineering fields, including helicopters, turbofans, and contra-rotating open rotor engines, where turbulence generated in the wake of upstream blades interacts with the leading edge of downstream blades and produces aerodynamic noise. One approach to study turbulence–airfoil interaction noise is to model the oncoming turbulence as harmonic gusts. A compact noise source produces a dipole-like sound directivity pattern. However, when the acoustic wavelength is much smaller than the airfoil chord length, the airfoil needs to be treated as a non-compact source, and the gust–airfoil interaction becomes more complicated and results in multiple lobes generated in the radiated sound directivity. Capturing the short acoustic wavelength is a challenge for numerical simulations. In this work, simulations are performed for gust–airfoil interaction at different Mach numbers using a high-fidelity direct computational aeroacoustic (CAA) approach based on a spectral/hp element method verified by a CAA benchmark case. It is found that the squared sound pressure varies approximately as the fifth power of Mach number, which changes slightly with the observer location. This scaling law can give a better sound prediction than the flat-plate theory for thicker airfoils. Furthermore, another prediction method, based on the flat-plate theory and CAA simulation, has been proposed to give better predictions than the scaling law for thicker airfoils.

A Hybrid, Runtime Coupled Incompressible CFD-CAA Method for Analysis of Thermoacoustic Instabilities

Abstract Thermoacoustic instabilities in gas turbine engines are of increasing interest for design of future low-emission technology combustors. Numerical methods used to predict thermoacoustic instabilities often employ either fully compressible resource-intense computational fluid dynamics (CFD) simulations, or two-step approaches where source terms extracted from CFD simulations are supplied to subsequent computational aeroacoustics (CAA) simulations. This work demonstrates an analysis of self-excited thermoacoustic instabilities using a hybrid method based on runtime coupling of incompressible CFD and CAA simulations. A prior implementation for the computation of combustion noise through one-way coupling of CFD and CAA solvers has been extended to a two-way coupling that allows acoustics to influence the flow field. The resulting hybrid method couples acoustic and convective physical phenomena by using mean flow field quantities and the thermoacoustic energy source term obtained from the solution of the Navier–Stokes equations in the low Mach number limit as an input for the acoustic perturbation equations (APEs). The fluctuating acoustic quantities pressure and velocity obtained from the solution of the APE are in turn included in the solution of the low Mach number Navier–Stokes equations, influencing the convective dynamics of the flow field. The suitability of the present implementation to capture thermoacoustic feedback is demonstrated through analysis of the well-known self-excited instability observed in a Rijke tube. The results are presented and discussed in comparison with a fully compressible reference solution.

On identifying the deterministic components of propeller noise

This study focuses on methods of processing the noise data of propulsive propellers commonly found on ubiquitous multi-rotor flying vehicles. The noise signals recorded in experiments typically contain periodic tonal and random broadband components produced by the rotational motion of the propellers, the interaction between the propellers and turbulence, and other random factors. Factors such as unsteady rotational speed, manufacturing tolerance and flow disturbance can exist, leading to time-varying characteristics of the noise signals. In this work, we made assessments of methods to identify the deterministic components of the noise signals of propellers. Considering that the different noise patterns within two adjacent periods (due to the rotation) are similar, we applied averaging methods to remove the random components iteratively. A total of three methods were employed in this work: simple averaging, exponentially weighted moving averaging, and Kalman filter averaging. The exponentially weighted moving averaging method uses a constant weight while the weighting parameter based on the Kalman filter approach is iteratively adjusted. The methods are applied to synthesized signals and results from the computational aeroacoustic simulations, demonstrating the capabilities of removing the random components. Then, the averaging techniques are also applied to the experimental results, and some characteristics of the noise signals are identified.

An implicit p‐adaptive discontinuous Galerkin solver for CAA/CFD simulations

Abstract In the last decades flow simulations have become a routine practice in many industrial fields for the aerodynamic and noise prediction. Moreover, the ever increasing interest in simulating off‐design operating conditions promoted the development of high‐fidelity simulation tools to overcome the modeling and accuracy limits of standard industrial codes in predicting turbulent separated flows. The discontinuous Galerkin (DG) method is well suited for this class of simulations, but today DG‐based CFD and CAA (Computational AeroAcoustics) solvers cannot yet reach the computational efficiency of well‐established commercial codes. As a consequence, the present paper aims at exploiting some attractive strategies, such as the adaptation of the elemental polynomial degree (‐adaptation) and of the degree of exactness of quadrature rules, to enhance the computational efficiency of an implicit DG platform for CFD and CAA simulations. Moreover, a sponge layer non‐reflecting boundary treatment has been also implemented for CAA. The predicting capabilities of the method have been assessed on classical CAA and CFD test cases. The proposed adaptive strategy guarantees a significant reduction () of the computational effort for both CFD and CAA simulations, compared to uniform‐order discretizations, while not spoiling the high accuracy requested to an high‐fidelity simulation tool.

Zonal direct-hybrid aeroacoustic simulation of trailing edge noise using a high-order discontinuous Galerkin spectral element method

We present the extension of a discontinuous Galerkin framework to zonal direct-hybrid aeroacoustic simulations. This extension provides the ability to simultaneously perform a zonal large eddy simulation (LES), solving the compressible Navier–Stokes equations, and an acoustic propagation simulation, solving the acoustic perturbation equations. In doing so, the acoustic sources are exchanged without using the file system, and the bottleneck of I/O operations is avoided. This approach is well suited for large-scale simulations done in high-performance computing. The zonal LES uses the recently introduced recycling rescaling anisotropic linear forcing as a turbulent inflow method. We present a methodology to model the required Reynolds stresses based on the distribution of the turbulent kinetic energy obtained from solving the Reynolds-averaged Navier–Stokes equations. We show at the example of a turbulent flow over a flat plate and a NACA 64418 trailing edge simulation that the chosen model of the Reynolds stresses is valid. Direct-hybrid simulation results of a NACA 0012 airfoil, including tonal self-noise and a NACA 64418 trailing edge, demonstrate the presented approach’s applicability. This zonal direct-hybrid simulation approach shows great potential for efficient hybrid computational aeroacoustic simulations in high-performance computing.

Analysis of the sound sources of lean premixed methane–air flames

AbstractTwo investigations on the sound generation mechanisms of lean methane–air flames are reviewed and linked. A two‐step approach is used for the analysis. First, the compressible conservation equations are solved in a large‐eddy simulation formulation to compute the acoustic source terms of the reacting fluid. Second, the acoustic source terms are used in computational aeroacoustics simulations to determine the acoustic field by solving the acoustic perturbation equations. To identify the contributions of the different source terms to the overall sound emission of the flames different source term formulations are considered in the computational aeroacoustics simulations. The results of various flames of increasing complexity are shown: harmonically excited laminar flames, a turbulent jet flame, and an unconfined and a confined swirl flame. The results show that in general the heat release source alone does not determine the acoustic emission of the flame. Only the acoustic emission of the unconfined swirl flame could be computed by the heat release source. To accurately predict the phase and the amplitude of the sound emission of the other flames the acceleration of density gradients occurring at the flame front must be included in the considered set of source terms.

Infrasound Radiation From Impulsive Volcanic Eruptions: Nonlinear Aeroacoustic 2D Simulations

AbstractInfrasound observations are increasingly used to constrain properties of volcanic eruptions. In order to better interpret infrasound observations, however, there is a need to better understand the relationship between eruption properties and sound generation. Here we perform two‐dimensional computational aeroacoustic simulations where we solve the compressible Navier‐Stokes equations for pure‐air with a large‐eddy simulation approximation. We simulate idealized impulsive volcanic eruptions where the exit velocity is specified and the eruption is pressure‐balanced with the atmosphere. Our nonlinear simulation results are compared with the commonly used analytical linear acoustics model of a compact monopole source radiating acoustic waves isotropically in a half space. The monopole source model matches the simulations for low exit velocities ( m/s or where is the Mach number); however, the two solutions diverge as the exit velocity increases with the simulations developing lower peak amplitude, more rapid onset, and anisotropic radiation with stronger infrasound signals recorded above the vent than on Earth's surface. Our simulations show that interpreting ground‐based infrasound observations with the monopole source model can result in an underestimation of the erupted volume for eruptions with sonic or supersonic exit velocities. We examine nonlinear effects and show that nonlinear effects during propagation are relatively minor for the parameters considered. Instead, the dominant nonlinear effect is advection by the complex flow structure that develops above the vent. This work demonstrates the need to consider anisotropic radiation patterns and jet dynamics when interpreting infrasound observations, particularly for eruptions with sonic or supersonic exit velocities.

On the effects of anisotropic turbulence on leading edge noise

This paper presents an investigation on the broadband noise produced by the interaction of anisotropic turbulence with isolated aerofoils. Computational aeroacoustic simulations are performed using a synthetic turbulence method with a linearised Euler solver. A comprehensive and fundamental parameter study on leading edge noise is presented to assess the effects of aerofoil thickness, mean flow Mach number, and angle of attack in the presence of moderately anisotropic turbulence. To this end, the streamwise-to-transverse length scale ratio is varied from 0.33 to 3, which can be representative of the anisotropy in the fan wakes from aero-engines, grid-generated turbulence in open-jet wind tunnel experiments, and rotors ingesting turbulent boundary layers. Anisotropic turbulence presents a significant redistribution of the energy in the turbulence spectra in comparison with an isotropic baseline, which affects the resulting noise spectra. It has been found that the noise spectra are mainly influenced by the transverse velocity component for the examined anisotropic flows. The frequency at which the noise spectrum is at a maximum only relies on the mean flow speed and the axial length scale of the anisotropic turbulent flow. Noise reduction due to aerofoil thickness at high frequencies follows a linear trend, but the amount of noise reduction is sensitive to the anisotropy in the flow. It is shown that the contribution of the streamwise disturbances and length scale become increasingly important for thick aerofoils at high Mach numbers and for aerofoils at non-zero angle of attack.

Computational Aeroacoustic Investigation of Airfoil Cascades

At moderate Reynolds numbers and angles of attack, the Laminar Boundary Layer (LBL) becomes unstable on the surface of airfoils, and causes periodic vortex shedding, which means undesired tonal peaks in the spectrum of the emitted aeroacoustic noise along with increased vibration and decreased aerodynamic performance. In the past, numerous research campaigns focused on the LBL vortex shedding, including measurements and numerical simulations as well. The results of these investigation showed that, the formation of the LBL instability related to the presence of the laminar separation bubble. It was also shown that, the spectrum of the emitted noise has a multitonal behavior, and the scaling of the mean frequency with the free stream velocity has a ladder structure. Based on these results, the LBL instability is a complex phenomenon; however, in the preliminary design of axial flow turbomachines the prediction of the frequency of the vortex shedding is essential, therefore the use of semi-empirical formulas is usual to achieve this goal. The previous researches mostly focused on separated airfoils, however, in case of turbomachines, the blades form a cascade, which can significantly affect the aerodynamic of the airfoils, i.e. it can affect the behavior of the LBL instability as well. According to this, in the present paper the LBL instability of NACA 0012 cascades are investigated, using 2D computational fluid mechanics and aeroacoustics simulations. The investigation involves the variation of the angle of attack, the chord based Reynolds-number and the spacing. The results are compared to the semi-empirical Brooks-Pope-Marcolini model.

Entropy noise modelling in 2D choked nozzle flows

Entropy noise is produced when temperature fluctuations (entropy spots) are accelerated by the mean flow, through a nozzle or a turbine stage for instance. When it propagates outside the engine it contributes to community noise and may generate thermoacoustic instabilities when reflected back towards the combustor, hence the need for its modelling. Among all the inviscid models proposed in the literature, only the one developed by ONERA takes into account the 2D nature of the mean flow and the radial deformation of the entropy waves through the nozzle, which plays a crucial role in noise generation (Emmanuelli et al., J. Sound Vib., vol. 472, 2020, pp. 115163). This model has been validated in the subsonic regime and is extended in the present work to 2D supercritical configurations, without and with a normal shock in the diffuser. Modelled transfer functions are validated by comparison with reference data obtained with computational aeroacoustics simulations and excellent agreement is found between the simulations and the model. The contribution of the shear dispersion of the entropy wave to noise generation is evidenced and the failure of the quasi-1D models, which do not account for the radial deformation of the entropy fluctuations, is illustrated. Noise scattering through the nozzle is also investigated. The 2D model is found to correctly recover the simulated transmitted and reflected acoustic waves through the nozzle. Quasi-1D solutions are also found to collapse with the reference simulations, which indicates that 2D mean flow effects are negligible for the propagation of the acoustic waves through the nozzle.

Acoustic Relaxation Term for Damping and Forcing of Waves

An acoustic relaxation term for the momentum equation is introduced that can act as a damping or forcing term for pressure waves while leaving other modes untouched. This acoustic relaxation term can be seen as the acoustic variant of the eddy relaxation term previously introduced in other work, and therefore shares several important characteristics. Its damping behavior is shown to be favorably frequency selective; that is, application to a test case with spurious acoustics shows that, indeed, the acoustic relaxation term is able to remove these undesired oscillations while leaving the hydrodynamics untouched. Subsequently, the acoustic relaxation term is applied as a forcing to couple an acoustic signal into a computational aeroacoustics (CAA) simulation. The transfer function shows a desirable behavior. The acoustic relaxation term is able to damp or excite acoustic waves; in that way, it potentially enables the excitement of prescribed acoustics in the linearized equations, such as a linearized Euler or acoustic perturbation or, as is done in this paper, the Navier–Stokes equations.

Noise sources of an unconfined and a confined swirl burner

The sound sources of an unconfined and a confined swirl burner are investigated by a two-step approach. The Reynolds number based on the injector diameter downstream of the swirler is ReD = 8800 and the swirl number is S = 0.73. First, the conservation equations of a compressible fluid are solved to determine the flow field under reacting and non-reacting conditions. The solution determines the mean flow field and the source terms of the acoustic perturbation equations (APE). The contributions of the various sound sources are analyzed by solving the acoustic perturbation equations (APE) in a computational aeroacoustics (CAA) simulation for each of the source terms. For the unconfined swirl burner, the precessing vortex core (PVC) of the swirl flow is a dominant sound source in non-reacting flow, whereas in reacting flow the unsteady heat release dominates the sound field. This changes when the burner is confined. A self-excited instability occurs at the quarter-wave mode of the burner and further sources, i.e., the momentum source due to fluctuations of the pressure at the flame front and the energy source due to velocity fluctuations at the flame front, become important to accurately predict the sound pressure amplitude of the limit cycle.