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This paper reports a study of the ability of an improved LBM in replicating acoustic interaction. With a BGK model with two relaxation times approximating the collison term, the improved LBM is shown not only able to recover the equation of state, but also replicates the specific heat ratio, the fluid viscosity and thermal conductivity correctly. With these improvements, the recovery of full set of unsteady compressible Navier-Stokes equations is possible. Two complex aeroacoustic interaction problems, namely the interaction of three fundamental aeroacoustic pulses and scattering of short wave by a zero circulation vortex, are calculated. The LBM solutions are compared with DNS results. In the first case it has been shown that the improved LBM is as effective as the DNS in simulating aeroacoustic interaction of three pulses. Both methods obtain essentially same results using same truncated domains. In the scattering problem, LBM is able to replicate the directivity of scattered acoustic wave from the vortex but it does not accurately reproduce the symmetry as calculated using DNS.

The noise emitted from an axial fan has become one of the primary concerns for many industrial applications. This paper presents the work to predict the noise generation and investigate sound sources in a low speed axial fan. Computational fluid dynamics modeling is conducted using Scale Adaptive Simulation for the unsteady flow field. The sound predictions by the acoustic analogy are in good agreement with the experimental data. The results from this study show that the aerodynamic interaction between the blades and outlet vanes has a major contribution to the radiated noise spectrum. Two types of sources of narrowband humps are identified in the axial fan. The first is found at the leading edge of the blade tip, which is related to the interaction of coherent flow structures in the blade tip region. The second is found in the vicinity of the blade hub, which can be attributed to the recirculating flow and hub vortex. The noise below the frequency of 1500 Hz is mainly due to the blade-outlet vane aerodynamic interaction, manifested as the tonal sound at BPF and its harmonics, whereas above 1500 Hz the broadband component of sound is mainly related to the turbulent boundary layers.

The aerodynamic sound from bluff bodies is a practically important problem in various engineering applications. To control the aerodynamic noise, the sound emitted from a circular cylinder with and without a splitter plate in a Reynolds number (Re) of $3\times 10^4$ is studied using Ffowcs Williams and Hawkings (FW-H) acoustic analogy. The flow field is simulated by Detached Eddy Simulation (DES) approach to investigate the mechanism of the sound reduction using a splitter plate in a three-dimensional calculation. The predicted sound of the circular cylinder is compared with the experimental data from the literature, and a good agreement is achieved. The results from this study show that lift and drag fluctuations of the circular cylinder with the splitter plate are smaller than those of the no-splitter case. The Strouhal number related to vortex shedding with the splitter plate is slightly reduced compared to the unmodified circular cylinder due to the stretched shear layers. The pressure fluctuations in the wake are decreased by the splitter plate, resulting from the suppression of vortex shedding. The application of the splitter plate reduces the lift dipole which is the main sound source. It leads to a sound reduction of 13 dB.

Finding the sources of sound in large nonlinear fields via direct simulation currently requires excessive computational cost. This paper describes a simple technique for efficiently solving the multidimensional nonlinear Euler equations that significantly reduces this cost and demonstrates a useful approach for validating high order nonlinear methods. Up to 15th order accuracy in space and time methods were compared and it is shown that an algorithm with a fixed design accuracy approaches its maximal utility and then its usefulness exponentially decays unless higher accuracy is used. It is concluded that at least a 7th order method is required to efficiently propagate a harmonic wave using the nonlinear Euler equations to a distance of five wavelengths while maintaining an overall error tolerance that is low enough to capture both the mean flow and the acoustics.

Dispersion-relation-preserving (DRP) spatial differentiation schemes are investigated for staggered non-uniform finite-volume grid type. It is shown that the staggering improves the numerical accuracy and stability whether the grid is uniform or non-uniform. The effect of the non-uniformity in the grid on the optimization procedure of the schemes is discussed. The spatial differentiation schemes are tested for the aeroacoustic problems of monopole and quadrupole radiation, showing the effectiveness of the non-uniform grid and the optimized high-order scheme.

Inflow/Outflow conditions are formulated for time-harmonic waves in a duct governed by the Euler equations. These conditions are used to compute the propagation of acoustic and vortical disturbances and the scattering of vortical waves into acoustic waves by an annular cascade. The outflow condition is expressed in terms of the pressure, thus avoiding the velocity discontinuity across any vortex sheets. The numerical solutions are compared with the analytical solutions for acoustic and vortical wave propagation with and without the presence of vortex sheets. Grid resolution studies are also carried out to discern the truncation error of the numerical scheme from the error associated with numerical reflections at the boundary. It is observed that even with the use of exponentially accurate boundary conditions, the dispersive characteristics of the numerical scheme may result in small reflections from the boundary that slow convergence. Finally, the three-dimensional interaction of a wake with a flat plate cascade is computed and the aerodynamic and aeroacoustic results are compared with those of lifting surface methods.

In a recent paper (J. Computational Acoustics10 (2002) 387–405) Tam has claimed that the famous Lighthill Acoustic Analogy predicts the wrong flow field for the simple problem of the propagation of a normal shock. However, we show that Tam has misinterpreted the results of his analysis, and that when this error is corrected the results of the Acoustic Analogy are brought into exact agreement with the well-known Rankine–Hugoniot solution of the Euler equations.

We present in this paper a time-domain discontinuous Galerkin dissipation-free method for the transient solution of the three-dimensional linearized Euler equations around a steady-state solution. In the general context of a nonuniform supporting flow, we prove, using the well-known symmetrization of Euler equations, that some aeroacoustic energy satisfies a balance equation with source term at the continuous level, and that our numerical framework satisfies an equivalent balance equation at the discrete level and is genuinely dissipation-free. In the case of ℙ₁ Lagrange basis functions and tetrahedral unstructured meshes, a parallel implementation of the method has been developed, based on message passing and mesh partitioning. Three-dimensional numerical results confirm the theoretical properties of the method. They include test-cases where Kelvin–Helmholtz instabilities appear.

A detailed study on the accuracy and reflection behavior of nonreflection boundary conditions is presented. To this end, a selection of five distinct nonreflecting boundary conditions is evaluated and the mechanisms which dominate the reflection properties of boundary conditions are identified based on a rigorous quantification of reflection levels. It is shown that the reflection behavior is significantly affected by the incident angle. The relation between the boundary condition effectiveness and the incident angle is investigated and the reflection rates as a function of the incident angle are quantified. Furthermore, the obtained results are used to predict the reflections from boundary conditions in general applications. It is shown that these predictions are reliable for different test cases.

This study provides a computational insight into unsteady far-field and surface pressure developed by vortex interaction with multiple rigid bodies in lift conditions. Flows around a spinning cylinder and two cylinders in tandem were taken as simple but yet representative prototypes of flows around multi-element lifting devices. The unsteady Euler equations are solved in terms of propagating disturbances originating from deforming vortices in the mean flow developed in the neighborhood of cylinders. Numerical errors associated with the discretization and boundary conditions were kept small employing a high-order scheme with accurate nonreflecting boundary conditions. To model the interaction of vortices with rigid bodies using moderate amount of computational resources, we apply a single-grid approach and implement the bipolar coordinate transformation where applicable. We address here the amplification of sound by the mean flow with nonzero circulation, strong influence of vortex profile on the generated sound waves, and different degree of amplification of sound in lifting flows for localized and nonlocal vortices. We find that the flow about a cylinder not only amplifies the sound strength but it also shifts the sound directivity. Vortices deforming within the flow about cylinders placed in tandem and in the traverse layouts were examined.

This paper addresses the application of the spectral finite element (FE) method to problems in the field of computational aeroacoustics (CAA). We apply a mixed finite element approximation to the acoustic perturbation equations, in which the flow induced sound is modeled by assessing the impact of a mean flow field on the acoustic wave propagation. We show the properties of the approximation by numerical benchmarks and an application to the CAA problem of sound generated by an airfoil.

A high-order interior penalty discontinuous Galerkin method for the compressible Navier–Stokes equations is introduced, which is a modification of the scheme given by Hartmann and Houston. In this paper we investigate the influence of penalization and boundary treatment on accuracy. By observing eigenvalues and condition numbers, a lower bound for the penalization term μ was found, whereas convergence studies depict reasonable upper bounds and a linear dependence on the critical time step size. By investigating conservation properties we demonstrate that different boundary treatments influence the accuracy by several orders of magnitude, and propose reasonable strategies to improve conservation properties.

Due to the growing number of drones and unmanned aerial vehicles, the aeroacoustic noise radiated by airfoils in moderate Reynolds-number flows increasingly becomes the focus of interest. In the present paper, the flow-generated noise of two basic (a flat plate and a cambered plate) and two conventional (RAF6 and NACA 0012) airfoil profiles is investigated in an open-jet wind tunnel in the interval of Reynolds numbers between 60,000 and 140,000. The measurements were carried out with a phased array microphone. The measurement data were evaluated using frequency–domain beamforming and the analysis of variance statistical method. The results show that the emitted noise is nearly independent of the angle of attack but dependent on the airfoil geometry and the chordwise location.

The noise created when a firearm is fired has a lot of adverse effects on humans and the environment, so analyzing and attenuating this noise is essential. This study aimed to examine propellant flow and the sound generated by this flow using a hybrid computational fluid dynamics and computational aeroacoustics method. The compatibility of this numerical study was also validated by comparing it with the experimental result. The impact of critical parameters, such as the shape and number of baffles of the suppressor, was studied. Finally, the overpressure and acoustics results of different suppressors were compared with each other and with the unsuppressed condition. According to the result, the suppressor with curved baffles shows a better performance. When the exit pressure at the tip of suppressor compared to the initial inlet pressure to the suppressor the percentage drop in overpressure was 76.01%, 78.79% and 81.3% for the suppressor with one, three and five curved baffles, respectively. For condition without suppressor, 169.49dB of SPL was recorded. When using a suppressor without a baffle, this value was reduced to 162.13dB. For the suppressor with one, three and five curved baffles, the SPL value was 160.234dB, 159.43dB and 158.11dB, respectively. Generally, this study shows that the suppressor’s efficiency is directly proportional to its shape and number of baffles.

Airflow should be affected by ear, nose, etc, and aerodynamic sound could be brought when the human head and the airflow occurs at a relative speed movement. Because the drag force of the head is large, in cycling competitions and other high-speed sport the diversion hats should be worn. After the speed of airflow reaches to a certain speed, due to the strong airflow interference, the aerodynamic noise could be brought and it could greatly impact on the athletes to make action decisions. In this paper, computational fluid dynamics (CFD) method is used for solving the aerodynamic behavior of a human head under different air velocities, and the pressure on head surface and the airflow around the head are calculated. Then, the above-mentioned conditions of different aerodynamic sound are solved by the finite element/infinite element method (FEM/IFEM), the points in the canal entrance of the two ears are picked up for collecting the SPL spectral curves, and the sound distribution of the horizontal plane and the median plane are drawn. Previous studies showed that the aerodynamic noise brought by head spoiler is obvious at low frequencies, because the influence of the head, if the airflow speed is greater than a certain value, the aerodynamic noise could not only increase, but also should be substantially reduced. The results are useful for athlete diversion cap design and spatial hearing research in which the influence of the airflow should be considered.

This paper collects the state of the art and the tremendous progress that has been made in hybrid modeling of aeroacoustic sound. Hybrid modeling is defined such that flow and acoustics are modeled separate and connected by an aeroacoustic model. The contributions will be classified with respect to the aeroacoustic models being developed, covering Lighthill’s analogy, Ffowcs Williams and Hawkings, vortex sound, linearized Euler equations (LEE), and different perturbation equations modeling flow induced sound. Within each topic, specific applications, such as jet noise, aircraft noise, ground mobility, noise, fan noise and human phonation, are covered. We focus on the accomplishments and provide the authors’ contribution to aeroacoustic research. Eventually, a concise summary of the different methods and their capabilities is included.

A high-order large eddy simulation (LES) code based on the flux reconstruction (FR) scheme is further developed for supersonic jet simulation. The FR scheme provides an efficient and easy-to-implement way to achieve high-order accuracy on an unstructured mesh. The order of accuracy and the shock capturing capability of the solver are validated with the isentropic Euler vortex and Sod’s shock tube problem. A heated under-expanded supersonic jet case from NASA’s Small Hot Jet Acoustic Rig (SHJAR) database is used for validation. The turbulence statistics along the nozzle centerline and lip-line are examined. We predict the acoustic radiation with the Ffowcs Williams and Hawkings method, which is integrated with our solver. The far-field acoustic predictions show reasonable agreement with the experimental measurement in the upstream and downstream directions, where the shock-associated noise and the large-scale turbulent mixing noise are dominant, respectively.

The field of aeroacoustics has gained much attention since the well-known acoustic analogies were first published in the 1950s. In parallel, the continuous growth of computational resources has enabled researchers and engineers to investigate phenomena involving flow-induced noise or sound propagation effects related to arbitrary velocity fields. To describe the latter mentioned physical processes, Galbrun utilized a mixed Eulerian–Lagrangian framework to describe perturbations of the underlying fluid dynamics. While less known compared to the more common linearized Euler equations, Galbrun’s equation provides an original framework. Since its publication in 1931, a number of scholars have further developed the approach first proposed by Galbrun. This paper provides a review of the existing literature dedicated to the use of Galbrun’s equation by highlighting possible advantages of the underlying theory as well as difficulties when utilizing numerical methods for solving problems in time or frequency domain. Furthermore, this work intents to serve as a companion for researchers interested in the field of aeroacoustics and hydroacoustics associated with Galbrun’s equation.

In low Mach number aeroacoustics, the well-known disparity of scales allows applying hybrid simulation models using different meshes for flow and acoustics, which leads to a fast computational procedure. The hybrid workflow of the perturbed convective wave equation involves three steps: (1) perform unsteady incompressible flow computations on a subdomain; (2) compute the acoustic sources and (3) simulate the acoustic field, using a mesh specifically suited. These aeroacoustic methods seek for a robust, conservative and computational efficient mesh-to-mesh transformation of the aeroacoustic sources. In this paper, the accuracy and the application limitations of a cell-centroid-based conservative interpolation scheme is compared to the computationally advanced cut-volume cell approach in 2D and 3D. Based on a previously validated axial fan model where spurious artifacts have been visualized, the results are evaluated systematically using a grid convergence study. To conclude, the monotonic convergence of both conservative interpolation schemes is demonstrated. Regarding arbitrary mesh deformation (for example, the motion of the vocal folds in human phonation), the study reveals that the computationally simpler cell-centroid-based conservative interpolation can be the method of choice.

A series of direct numerical simulations (DNS) were conducted of turbulent jets issuing from acoustically lined pipe. The inclusion of the pipe in the simulations with a fully turbulent flow inside ensures that all possible noise generation mechanisms are represented. Earlier results from a similar pipe/jet configuration, albeit without acoustic liner treatment, showed contamination of the far field noise field by interior noise from the pipe. Therefore, here two key modifications were made. Firstly, the interior pipe walls were acoustically lined using an impedance condition. Secondly, the turbulent pipe inflow boundary condition was modified to reduce spurious noise introduced into the axisymmetric mode. The sound radiation from the pipe/jet configuration was analysed using a phased array source breakdown technique. It is demonstrated that the modification of the inflow boundary results in a strongly reduced contribution of the interior noise component to the farfield noise in the axisymmetric mode, while the acoustic liner is effective in reducing the interior noise contribution to farfield noise in the higher azimuthal modes. This enables the source breakdown analysis to extract the jet mixing noise contributions to the farfield much more clearly.