Ffowcs Williams-Hawkings Equation Research Articles

Study on Influential Mechanism of Trailing Edge Sweep Angle on Aerodynamic Noise of a Centrifugal Air Compressor

As the main noise source in the hydrogen fuel cell system, the noise level of the centrifugal air compressor greatly affects the comfort of the hydrogen fuel cell vehicle, and can be effectively reduced by optimizing the trailing edge sweep angle of the blade. In this paper, the computational fluid dynamics model was used to study the influence of the trailing edge sweep angle on the aerodynamic performance and flow characteristics of a centrifugal air compressor for vehicle fuel cells. The Ffowcs Williams–Hawkings equation and the computational fluid dynamics–boundary element coupling method were adopted to calculate the dipole source strength on the surface of the blade and the radiated aerodynamic noise, respectively, under the different trailing edge sweep angles. The results showed that the trailing edge sweep could lead to an increase in pressure ratio as well as isentropic efficiency, and a decrease in the intensity of flow separation. Meanwhile, the sound pressure level of the compressor under each working condition could be effectively reduced by the trailing edge sweep. When the rotation speed was 80,000 r·min−1 and the blade trailing edge sweep angle was 15°, the sound pressure level of the radiated aerodynamic noise was 5.8 dBA lower than that without sweep.

Numerical Simulation Study of Aerodynamic Noise in High-Rise Buildings

In order to study the aerodynamic noise on the surfaces of high-rise buildings under the action of strong winds, this paper numerically simulated the sound pressure field on the surface of a high-rise building using the large-eddy simulation method combined with the acoustic analog method of FW-H (Ffowcs Williams–Hawkings) equation and obtained the intensity radiation distribution of sound pressure on the surface of the building to further identify the area with the maximum sound pressure intensity of the noise radiation and thus achieve the purpose of locating noise source. The accuracy of the numerical simulation results for aerodynamic noise obtained in this paper was then verified by comparing with the acoustic wind tunnel experimental results. The locations of noise source obtained by numerical simulation and acoustic wind tunnel experiment were in good agreement. The sound pressure intensity pulsation time course was measured by the acoustic wind tunnel experiment, and the noise sound pressure level spectrum of each part of the building surface was obtained by fast Fourier transform (FFT). Furthermore, the spectral characteristics of the noise sound pressure level were analyzed. The results of the sound pressure level spectrum of aerodynamic noise obtained from the numerical simulation were compared with the acoustic wind tunnel experimental results, which were found to be very similar. The analysis of the sound pressure level spectrum of aerodynamic noise on the building surface reveals that the numerical simulation results in the middle- and high-frequency bands of the spectrum are in good agreement with the acoustic wind tunnel experimental results, but there is a difference between those in the low-frequency bands and the acoustic wind tunnel experimental results. The microphone array used to locate the noise source in the acoustic wind tunnel was found to suffer non-eliminable measurement errors, which might be a potential reason for a reasonably slight difference between the experimental and numerical simulation results. The background noise in the low-frequency band of the acoustic wind tunnel sound pressure level spectrum was relatively large, while there was basically no background noise in the numerical simulation. This paper shows that the numerical simulation method combined with large-eddy simulation and acoustic analogy (FW-H) can calculate the aerodynamic noise intensity at various points on the surfaces of high-rise buildings and reasonably predict the location of sound source. In addition, the numerical simulation results are similar to the acoustic wind tunnel experimental results in most frequency bands.

Nonharmonic Control of the Blade-Vortex Interaction Noise of Electrically Controlled Rotor

Electrically controlled rotor, also known as swashplateless rotor, represents an active rotor system that, due to the use of a trailing edge flap system instead of a swashplate, not only enables primary control but also conveniently reduces the blade-vortex interaction (BVI) noise of the rotors through active control. The effect of nonharmonic inputs on the control of the BVI noise of electrically controlled rotors based on their unique trailing edge flap systems has been investigated in this paper. To this end, an analytical model for the vortex interaction-induced load and noise of electrically controlled rotor is first established based on the viscous vortex particle method, the Weissinger-L blade model, and the Ffowcs Williams-Hawkings (FW-H) equation. On this basis, a simulation study of flap nonharmonic control for BVI noise reduction in electrically controlled rotors is carried out. According to the mechanism of the BVI in electrically controlled rotors, the second quadrant flap nonharmonic control is used to reduce the advancing side BVI noise, and the effects of different control waveforms and amplitudes on the peak value and directivity of the BVI noise of the sample electrically controlled rotors are analyzed to reveal the noise reduction mechanism of flap nonharmonic control. Subsequently, the effect of the third quadrant flap nonharmonic control on BVI noise on the retreating side of the sample electrically controlled rotors is investigated. The results show that flap nonharmonic control has little effect on miss distance and that it controls BVI noise mainly by reducing the wake vortex strength on the advancing and retreating sides, which may lead to an increase in rotor noise in other regions; the noise reduction effect of flap nonharmonic control for different blade preindex angles indicates that suitable preindex angles coupled with flap nonharmonic control help optimally reduce noise.

Airframe noise predictions using the Ffowcs Williams-Hawkings equation

This paper considers potential sources of error when using the Ffowcs Williams-Hawkings equation to make predictions of airframe noise, which entails a relatively low-speed, uniform incoming flow encountering geometry of varying complexity. Numerical simulations are used to investigate several model problems where Ffowcs Williams-Hawkings integration surfaces are placed on solid surfaces as well as in the flow. Comparisons with the pressure obtained directly from the simulations reveal that when solid surfaces are used, the acoustic calculations can produce erroneous results in upstream directions and when scattering bodies block the line of sight from observers to the source. Using solid surface input data implies ignoring all volumetric source effects, which include noise generation as well as flow effects. Nonuniform flow alone, such as is found in a steady boundary layer, was not found to be a significant source of error, so the amplitude and phase changes induced by turbulent eddies in massively separated flow regions is speculated to be the primary cause of the error.

Effects of slat track on the flow and acoustic field of high-lift devices

Most of the published works related to noise generation in high-lift devices only consider clean idealized geometries, whereas real aircraft wings contain important parts called the slat tracks that connect the slat and the main wing. To investigate the effects of slat tracks on the ambient flow and noise, simulations are performed for wings based on the 30P30N airfoil. Two configurations are considered, i.e., the 30P30N wing with and without a slat track. Improved detached-eddy simulation is carried out to compute the unsteady near-field flow. The far-field noise propagation is calculated using the Ffowcs Williams-Hawkings equation. The results show that the installation of the slat track has observable effects on the aerodynamic and aeroacoustic performances of the high-lift devices. The maximum lift coefficient of the high-lift device and the stall angle of attack is reduced. Low-frequency broadband noise radiated from the main wing is significantly increased and the directivity of the overall sound pressure level is changed due to the slat track. The far-field noise from the configuration with the slat track displays noticeable sensitivity to the angle of attack. The slat track has an amplification effect on the high-pressure fluctuation on the main wing, especially at a small angle of attack. This leads to nearly 10 dB in the far-field noise based on the discussed wing section. To reveal the relative noise mechanism, vortical structures near the slat track, large-scale spanwise flows above the main wing, and the vortex dynamics are investigated. A spiral vortex pair is captured as the most important flow structure. It is generated in the spanwise direction by the interaction of slat wakes with the boundary layer on the upper surface of the main wing. The pressure fluctuations on the main wing are highly correlated with this flow structure, which cannot be ignored for the study of noise in a real aircraft.

Aeroacoustic prediction based on large-eddy simulation and the Ffowcs Williams\u2013Hawkings equation

A hybrid noise computation method is presented in this paper. Large-eddy simulation with wall-model equation is proposed to compute the flow field. With a stress-balanced wall-model equation, the near-wall computation cost of large eddy simulation was effectively reduced. The instantaneous flow variables obtained by the large-eddy simulation were used to compute the noise source terms of the Ffowcs Williams–Hawkings equation. The present method was investigated with two test cases: a single cylinder at Re = 10,000 and a rod-airfoil at Re = 480,000. The flow quantities and aeroacoustic characteristics were compared with the reference data. The mean velocity profiles and spectra of the flow fluctuations were consistent with data from the literature. When compared with the reference data, the noise computation error was less than 3 dB. The computation results demonstrate the present wall-modeled large eddy simulation is efficient for the noise computation of complex vortex shedding flows.

LES investigation of cavitation harmonic tone around a Delft twist-11 hydrofoil

In this paper, a hybrid CHA approach, including the LES approach and the permeable Ffowcs Williams-Hawkings (PFW–H) equation, is adopted to predict the cavitating flow and its induced noise around a Delft Twist-11 hydrofoil. The predicted hydrodynamic result shows good agreement with the measured one. A simplified equation for pseudo-thickness noise is proposed, indicating a close relationship between pseudo-thickness noise and cavity volume fluctuation. With this simplified equation, the characteristic of pseudo-thickness noise and its connection with cavitation evolution are discussed. The hydroacoustic result indicates that the cavitation noise around a twisted hydrofoil is mainly contributed by the pseudo-thickness term. Moreover, the harmonic characteristic of pseudo-thickness noise is observed, which is mainly controlled by the collapse of the separated cavity, the accelerated growth of the attached cavity, and the collapse of the primary U-shaped cavity. Finally, with the assistance of wavelet transform and bispectrum analysis, the inducement of tone at 1st harmonic is attributed to the collapse of the primary U-shaped cavity, which can simultaneously raise a significant interaction coupling of tones at low-order harmonics to strengthen the tones at high-order harmonics. Our work reveals the relationship between cavitation harmonic tones and cavitation structure, which is helpful for the understanding of hydroacoustic mechanism.

Application of High-Order WENO Scheme in the CFD/FW–H Method to Predict Helicopter Rotor Blade–Vortex Interaction Tonal Noise

The accurate prediction of helicopter rotor blade–vortex interaction (BVI) noise is challenging. This paper presents an implementation of the seventh-order improved weighted essentially non-oscillatory (WENO-Z) scheme for predicting rotor BVI noise using a high-resolution numerical method based on the Reynolds-averaged Navier–Stokes and the Ffowcs Williams–Hawkings equations. The seventh-order improved WENO-Z scheme is utilized to minimize the inherent numerical dissipation of the reconstruction method in the monotone upstream-centered scheme for conservation laws (MUSCL), thereby improving the rotor wake resolution and the BVI noise-prediction accuracy. The three-layer dummy cell method is used to ensure that the flux at the boundary maintains seventh-order accuracy. The effectiveness of the flow solver and the acoustic solver is validated using the Helishape-7A rotor and the UH-1H rotor, respectively. The flow field and BVI noise characteristics of the OLS rotor obtained from the fifth- and seventh-order WENO-Z schemes are compared with that of the third-order MUSCL for coarse and fine background grids. The wake resolution, noise-prediction accuracy, and computational cost of the three schemes are compared. The results show that the high-order WENO scheme provides higher accuracy for flow field simulation and BVI noise prediction than the MUSCL, but the computational cost of the WENO scheme increases substantially as the grid resolution increases. However, the WENO scheme can predict BVI using a coarser grid than the MUSCL. The computational cost of the WENO scheme is relatively low under the same flow field simulation resolution.

Numerical Investigation on the Aerodynamic Noise Generated by a Simplified Double-Strip Pantograph

In order to understand the mechanism by which a pantograph can generate aerodynamic noise and grasp its far-field characteristics, a simplified double-strip pantograph is analyzed numerically. Firstly, the unsteady flow field around the pantograph is simulated in the frame of a large eddy simulation (LES) technique. Then the location of the main noise source is determined using surface fluctuating pressure data and the vortex structures in the pantograph flow field are analyzed by means of the Q-criterion. Based on this, the relationship between the wake vortex and the intensity of the aerodynamic sound source on the pantograph surface is discussed. Finally, the far-field aerodynamic noise is calculated by means of the Ffowcs Williams-Hawkings (FW-H) equation, and the contribution of each component to total noise and the frequency spectrum characteristics are analyzed. The results show that on the pantograph surface where vortex shedding or interaction with the wake of upstream components occurs, the pressure fluctuation is more intense, resulting in strong dipole sources. The far-field aerodynamic noise energy of the pantograph is mainly concentrated in the frequency band below 1500 Hz. The peaks in the frequency spectrum are mainly generated by the base frame, balance arm and the rear strip, which are also the main contributors to the aerodynamic noise.

Aeroacoustic interaction between owl-inspired trailing-edge fringes and leading-edge serrations

The silent flight achieved by owls is attributed to their unique wing morphologies, characterized by leading-edge (LE) serrations, trailing-edge (TE) fringes, and a velvet-like surface. The specific morphological effects of LE serrations and TE fringes on aeroacoustic performance have been widely studied, but the LE–TE aeroacoustic interaction remains poorly understood. This paper describes a simulation-based study of the aeroacoustic characteristics of owl-inspired TE fringes and their interplay with LE serrations by combining large-eddy simulations of unsteady near-field flow structures with the Ffowcs Williams–Hawkings equation for sound radiation. Using owl-inspired LE serrated and TE fringed wing models, it is verified that TE fringes enable a pronounced high-frequency sound reduction at angles of attack (AoAs) of 5–15° while achieving comparable aerodynamic performance to a clean model. The near-field vortex dynamics, pressure distributions, and velocity spectra reveal that TE fringes suppress flow separation and vortex shedding in the vicinity of the TE, consequently reducing local velocity fluctuations and far-field overall sound pressure levels. Furthermore, the combination of TE fringes and LE serrations enables a remarkable reduction in overall sound pressure levels at all AoAs, and their aeroacoustic interplay is responsible for stabilizing velocity fluctuations over the suction surface, which suppress both low- and high-frequency sound. Our results demonstrate that TE fringes are a robust sound reduction device in resolving the trade-off between aerodynamic force production and sound reduction, while LE serrations and TE fringes complement one another as an effective noise-reducing biomimetic design.

Numerical research on the influence of sail leading edge shapes on the hydrodynamic noise of a submarine

As a protruding part of submarine surfaces, sails will produce large hydrodynamic noise under the impact of water flow. To reduce the noise generated by the sail, the effects of different sail leading edges on the submarine flow field and hydrodynamic noise are investigated. Combining the WMLES S-Omega turbulence model and the Ffowcs Williams-Hawkings equation, the flow field and hydrodynamic noise of submarines are numerically simulated. The simulation results are compared with the experimental data. Good comparative results reveal the accuracy and performance of the employed numerical method. Subsequently, the computational fluid dynamics (CFD) code Fluent is used to simulate the variations in the flow field and hydrodynamic noise with different sails. The results show that the hydrodynamic noise of submarines can be effectively suppressed by changing the leading edge of the sail, and the sound pressure level can be dropped by 4.69 dB.

LES Investigation of the noise characteristics of sheet and tip leakage vortex cavitating flow

In the present paper, cavitation noise induced by sheet cavity and tip leakage vortex cavity (TLVC) together generated by a NACA0009 hydrofoil are numerically investigated with Ffowcs Williams-Hawkings (FW-H) equations. Large eddy simulation (LES) combined with Schnerr-Sauer cavitation model is utilized and a satisfactory result is obtained as compared with the referenced experimental measurements. It is found that even though the volume of TLV cavity is much smaller than that of sheet cavity, their acoustic levels are comparable to each other. A close relationship is indicated between cavity evolutions and their radiated noises, which vary periodically for both sheet and TLV cavities. Moreover, intense sound pulses of pseudo-thickness and pseudo-loading noise are observed especially during the collapse process. It is indicated that the rise in far field pressure and action of the dilatation term inside the cavities may trigger the collapse of both kinds of cavities in the flow, resulting in sound impulses. It is worth mentioning that in agreement with previous investigations, high pressure distribution and jets at the ends of sub-TLVCs are noted to have a close relationship with the collapse of sub-TLVCs. Noise generated by sheet cavity is higher than that generated by TLV cavity at the dominant Strouhal number of 0.74, with relatively high values of both pseudo-thickness and pseudo-loading noises at the dominant Strouhal number. While noise of TLV cavitating flow has acoustic energy concentrated at either low Strouhal numbers or high Strouhal numbers for the two terms, respectively.

A Computational Study on the Aeroacoustics of a Multi-Rotor Unmanned Aerial System

The noise generated by a quadrotor biplane unmanned aerial system (UAS) is studied computationally for various conditions in terms of the UAS pitch angle, propellers rotating velocity (RPM), and the UAS speed to understand the physics involved in its aeroacoustics and structure-borne noise. The k-ω SST turbulence model and Ffowcs Williams-Hawkings equations are used to solve the flow and acoustics fields, respectively. The sound pressure level is measured using a circular array of microphones positioned around the UAS, as well as at specific locations on its structure. The local flow is studied to detect the noise sources and evaluate the pressure fluctuation on the UAS surface. This study found that the UAS noise increases with pitch angle and the propellers’ rotating velocity, but it shows an irregular trend with the vehicle speed. The major source of the UAS noise is from its propellers and their interactions with each other at small pitch angle. The propeller and CRC-3 structure interaction contributes to the noise at large pitch angle. The results also showed that the propellers and structure of the UAS impose unsteadiness on each other through a two-way mechanism, resulting in structure-born noises which depend on the propeller RPM, velocity and pitch angle.

Study of a FWH-based permeable-surface formulation for propeller hydroacoustics

This paper investigates the use of the permeable surface integral formulation based on the Ffowcs Williams–Hawkings Equation to predict the noise field generated by marine propellers. After derivation of the integral formulation, first, in the framework of potential flows, its main features are discussed for case-studies that allow a straightforward interpretation of the results achieved. Then, issues related to the use of pseudo-compressible, performance-oriented CFD solvers to detect the sources of sound over the permeable surface of integration are carefully examined. Among them, the occurrence of undesired boundary reflection effects and the strategies for their mitigation are discussed. The end-cap problem, open vs closed surface strategies, placement/sizing of the permeable surface and CFD grid topology suitability for hydroacoustic purposes are further topics considered in the paper. In order to provide guidelines and best practices for FWH permeable-surface hydroacoustics, the strategic choices made in determining the numerical predictions are discussed in detail. As one of the most interesting outcomes of the numerical investigation, it has been proven that accurate noise predictions are achievable through tailored CFD grid stretching capable of avoiding boundary reflections, an issue affecting hydroacoustics more than hydrodynamics.

Acoustics of rotor ingesting an axisymmetric turbulent boundary layer

The noise generation by a five-bladed rotor ingesting an axisymmetric turbulent boundary layer at the tail end of a body of revolution (BOR) is investigated numerically at Reynolds number of 1.9 × 106 based on the BOR length and free-stream Mach number of 0.059. The turbulent boundary layer on the nose and midsection of the BOR is computed using wall-modeled LES whereas that in the acoustically important tail-cone section under a strong adverse pressure gradient is wall resolved. The radiated acoustic field is calculated based on the Ffowcs Williams-Hawkings equation. The computed flow statistics and sound pressure spectra agree well with the experimental measurements at Virginia Tech. In addition to broadband turbulence-ingestion noise, haystacking spectral peaks near the blade passing frequency and its harmonics are well captured and related to correlated blade interactions with coherent turbulence structures. The accuracy of the classical Sears theory for rotor-noise prediction is evaluated using the upwash velocity field from the LES. The theory is shown to predict well the sound pressure levels at low to mid-frequencies including the haystacking peaks but less accurately at higher frequencies. The spatial and frequency characteristics of blade unsteady-loading dipoles and their correlations are investigated, and the appropriate Mach number scaling for the ingestion noise is identified.

Numerical study on hydrodynamic performance and flow noise of a hydrofoil with wavy leading-edge

Flow control based on bionics provides new research ideas for noise reduction. As one of the flow control methods, the wavy leading edge (WLE) inspired by the leading edge tubercles of the humpback whale is proposed in this paper. The hydrodynamic performance and flow noise of a National Advisory Committee for Aeronautics 0020 hydrofoil subjected to three WLEs are numerically investigated. A hybrid numerical method of large eddy simulation combined with the Ffowcs Williams–Hawkings equation is adopted to obtain the unsteady flow properties and predict the far-field noise. At a Reynolds number of 3.05 × 105, the simulation results show that the addition of WLEs can reduce the lift coefficient fluctuation but will increase the drag coefficient slightly. In addition, the WLE can reduce the OverAll Sound Pressure Level of the hydrofoil by up to 7.28 dB. The analysis of the flow features shows that the WLE can reduce the pressure fluctuation on the hydrofoil surface, which is directly beneficial to the noise reduction. Moreover, the WLE enhances the spanwise flow of the hydrofoil, produces streamwise vortices, and reduces the spanwise coherence coefficient at both the leading edge and trailing edge.

A time-domain inverse method for the localization and quantification of unsteady rotating loading sources

Analysis of aerodynamic loading noise generated by unsteady rotating forces is of great significance in aeroacoustics research. However, it is still difficult to obtain the position and strength information of unsteady rotating loading sources in practice. In this paper, a time-domain inverse method for the localization and quantification of unsteady rotating loading sources is proposed, based on the Farassat integral solution of the Ffowcs Williams-Hawkings equation with the monopole and quadrupole source terms being neglected. In this method, the analytical direct model that relates the unsteady rotating forces to the radiated sound field is first discretized, and then the unsteady rotating forces are reconstructed from the measured pressures via a time-domain inversion procedure. Different from the previous inverse aeroacoustic methods, the proposed method can reconstruct the time histories of the three components of the unsteady rotating forces in the Cartesian coordinate system, thereby accurately locating the source positions and quantitatively estimating the source strengths in a real-time way. Numerical simulations with two unsteady rotating point forces and experiments with the rotating blades of an unmanned aerial vehicle examine the validity of the proposed method.

Noise attenuation of quadrotor using phase synchronization method

The annoying noise produced by the rotors of multi-rotor aircraft can bring severe disturbance to the residents. Hence, it is essential to reduce the noise level of multi-rotor aircraft for its further development. In this paper, an attempt is made that applying the phase synchronization method to the multi-rotor aircraft for noise reduction, and the feasibility and potential are explored by the means of simulations. Firstly, the aerodynamic noise prediction model is established by combining the free wake method and the Ffowcs Williams-Hawkings equation. On this basis, the multi-island genetic optimization algorithm is employed to obtain the optimal phase angles which can minimize the noise level at the objective positions. Then, the noise attenuation simulations of the quadrotor at a single observation and a finite region are studied with different advance ratios, and the noise attenuation mechanism is analyzed. Finally, the noise reduction benefits of the square quadrotor and the diamond quadrotor are compared. The simulation results show that, for the observation plane 5 m below the vehicle, through employing the phase synchronization method, the noise level of a single observation point can be reduced by up to 30 dB, and the noise level of the forward quarter can be reduced by up to 12 dB. Therefore, it can be confirmed that the phase synchronization method shows an excellent noise attenuation potential for quadrotor.

Numerical and experimental study on spectrum and temporal coherence analyses of flow noise caused by sinusoidal vertical motion of sonobuoy

Flow noise caused by sinusoidal vertical motion of the sonobuoy reduces the signal-to-noise ratio (SNR) of the recorded signal. Therefore, understanding the physical properties of the flow noise is important for improving the working performance of the sonobuoy. The present work is dedicated to investigate the characteristics of the flow noise of sonobuoy generated from vertical motion based on the combination of numerical calculations and experimental results. The flow noise of the hydrophone under time varying stream velocity is predicted using a hybrid computational fluid dynamics (CFD)-Ffowcs Williams-Hawkings (FW–H) equation technique. The flow noise calculated with the hybrid computational method is in good agreement with that analyzed by the experimental measurement and empirical formula. The numerical calculation results of the flow noise under time-varying stream velocity condition reveal that the spectrum and temporal coherence of the flow noise exhibit the periodic changes same as that of the stream velocity. These analyses and conclusions are verified by experimental data. The study in this paper will contribute to signal processing of the sonobuoy and thus improving SNR of the measure signal.

Effect of hydrofoil leading edge waviness on hydrodynamic performance and flow noise

This paper provides a numerical investigation into the effect of the wavy leading edge on the flow structures and noise of a hydrofoil. NACA0012 hydrofoils with straight and wavy leading edges (denoted by SLE and WLE, respectively) are simulated. The simulations are performed using the large eddy simulation approach to obtain the near-field unsteady flow properties and the Ffowcs Williams–Hawkings equation to predict far-field noise. The numerical results at Reynolds number of 2.5×105 show that the fluctuating amplitude of the lift and drag coefficient decreases after the wavy structure is applied to the leading edge, and the flow field around the hydrofoil is changed due to the streamwise vortices generated in each trough by the pressure gradient of the leading edge. In addition, the wavy leading edge can effectively reduce or even eliminate the tonal noise of the foil without significantly changing the noise directivity. Moreover, the effect of inlet velocities on noise reduction is studied with three different velocities(1, 2.5, and 4.8 m/s). It is found that at the higher velocity of the three, the WLE has a better inhibition effect on lift fluctuation and a better noise reduction effect.