Ffowcs Williams-Hawkings Equation Research Articles

Numerical research on the rotor “super blade/vortex interaction noise” generation mechanism in helicopter roll maneuver state

To explore the evolution law of rotor vortex and aeroacoustic characteristics during helicopter roll maneuver flight, numerical simulations were conducted in different roll rates based on the high-precision computational fluid dynamics method and the Ffowcs Williams-Hawkings equation. Initially, we verified the collective pitch increased test and the blade/vortex interaction (BVI) test cases. The comparison results show that the constructed method can capture the aerodynamic characteristics of rotor transient maneuvering states and has reliable predictive capability for BVI noise. Then, the aeroacoustic characteristics analyses of different right roll rates was performed. It was found that in the right roll state, multiple vortices merge and develop into a higher-intensity “supervortex system” near the 75° azimuth angle, triggering “superblade/vortex interaction noise” (Super-BVI) upon collision with the subsequent blade, with a maximum increase in the overall sound pressure level (OASPL) of approximately 16 dB. Next, numerical simulations were carried out for different left roll rates, and it was found that the maximum sound pressure (pmax) and maximum OASPL (OASPLmax) have linear and logarithmic relationships with roll rate, respectively. This law holds for both left- and right-roll states. Finally, four cases of specific roll angles were conducted for comprehensive comparison studies. It was found that transient roll maneuvers intensify the interaction strength on the rolling side while weakening the interaction strength on the other side, which is closely linked to the formation mechanism of “Super-BVI noise.”

Effect of model scale and airflow velocity on aerodynamic noise prediction for high-speed train leading car and bogie

Predicting noise from the actual train model by numerical simulation and wind tunnel testing requires appropriate corrections based on reduced model scale and airflow velocity. This paper utilises the Improved Delayed Detached Eddy Simulation method (IDDES) in conjunction with the Ffowcs Williams-Hawkings equation (FW-H) for simulating flow fields and predicting noise. The subdomain models of high-speed train head and leading bogie were used to investigate the effects of the model scale ratio (λ) and the airflow velocity ratio (γ) on the aerodynamic noise. The results show that compared with the baseline condition (case0), only reducing the model scale (case1) will lead to an increase in local viscous flow, thereby weakening the flow velocity and surface pressure fluctuation intensity in the bogie region, and the overall noise level is slightly reduced, with a difference of less than 1 dB. However, as expected, there is a significant frequency shift in the noise spectra. For case2, the model scale and the airflow velocity are reduced simultaneously to ensure the same Strouhal number, and the vortex structure and sound source distribution characteristics are closer to case0. The noise spectra have no frequency shift, but the noise level is reduced by 60 log10(γ).

Swirling Flow Effects on the Aeroacoustic Signature of an Aerospike Nozzle

Abstract Supersonic nozzles are not always operated at design conditions. The total pressure, temperature and velocity distributions at the nozzle inlet plane are often characterized by inhomogeneities, conditions dictated by the operating regime of the turbine or combustion chamber. In particular, a swirling flow motion can be induced by these components. While homogeneous inflow conditions are well documented for a large range of supersonic nozzles, data on the aeroacoustics of supersonic swirling jets is scarce. Large Eddy Simulations are deployed to simulate the swirling flow of a non-ideally expanded three-dimensional, cold, axisymmetric aerospike nozzle at a Nozzle Pressure Ratio (NPR) = 3. Three swirl numbers are considered and compared with the baseline case. Near-field acoustic analyses are completed by far-field acoustic computations based on the Ffowcs Williams-Hawkings (FWH) equation. Swirling flow shortens the potential core of the jet and leads to an annular shock cell length increase. Two-point space-time cross-correlations of pressure data acquired in the annular shear layer indicate an enhancement of the azimuthal modes. Similar cross-correlations in the circular jet shear layer further downstream show that screech tones are suppressed. Power spectral density of the radial velocity at monitoring points in the vicinity of the nozzle trailing edge allows to identify the oscillation modes of the annular shock-cell structure. The far-field spectra exhibit lower mixing noise with increasing swirl number. The global SPL decreases while the nozzle thrust remains at 99% of the baseline thrust at low swirl numbers.

Experimental Study and Numerical Simulation of Radiated Noise from Unmanned Underwater Vehicle

Abstract This paper focuses on the research of the radiation noise of underwater unmanned vehicle (UUV), which is one of the most important indicators for evaluating the performance of underwater unmanned equipment. Integrating experimental study and numerical calculations, this paper investigates the underwater radiated noise characteristics and hydrodynamic properties of the propeller of UUV. Firstly, an open-water radiated noise experiment is conducted. To ensure the accuracy of acoustic test, the UUV are held stationary during the experiment. Then, the hydrodynamic performance of a propeller in a steady flow field is calculated using Computational Fluid Dynamics (CFD). Finally, the noise in the unsteady flow field is calculated using the Ffowcs Williams-Hawkings (FW-H) equation. The results show that the propeller, as the main noise source when the UUV is working, exhibits distinct characteristic line spectra in the frequency response curve. By comparing the numerical and experimental results, it was found that the overall trend of the sound pressure level is similar. But the line spectrum characteristics of the numerical results between 100 and 400 Hz are more obvious, mainly because the simulation model is more idealized compared to the experimental tests. The study further examines the hydrodynamic characteristics, propeller noise, and directional characteristics of UUV under different operating conditions.

STUDY OF AERODYNAMIC NOISE OF PROPELLER CONSIDERING THE INFLUENCE OF BOUNDARY SURFACE USING CFD METHOD

This article focuses on the aerodynamic and acoustic characteristics of both an isolated propeller model and a propeller - boundary surface model. The study uses the Reynolds-averaged Navier-Stokes (RANS) method combined with Computational Fluid Dynamics techniques to analyze the flow field and wake flow behind the propeller and to determine its basic aerodynamic coefficients. The pressure on the surface of the propeller and boundary surface is used as input for the noise calculations. An acoustic analogy method, based on the Farassat 1A formulation derived from the Ffowcs Williams-Hawkings (FW-H) equation, is employed to calculate the propagation of noise from the surfaces of the propeller and boundary surface to designated positions (microphones). The research results lead to some significant conclusions drawn by the authors.

Computational fluid dynamics driven surrogate model to predict hydrodynamic and acoustic properties of propeller boss cap fins

A novel method is proposed to predict the hydrodynamic and acoustic properties of propeller boss cap fins (PBCF) based on computational fluid dynamics (CFD) and surrogate models. The propulsive performance and radiated noise of the B-series propeller equipped with PBCF under open-water and hull-propeller coupling conditions are predicted and analyzed. The transient calculations are performed to generate accurate sample data for the surrogate model based on the Unsteady Reynolds Averaged Navier–Stokes and Ffowcs Williams–Hawkings equations. The response surface, polynomial, and Kriging models are used to learn sample data and output predictions. The relationship between inputs and outputs can be established from local data, which enables to obtain arbitrary response results in the global range. The hydrodynamic performance and radiated noise are compared for configurations with and without PBCF. PBCF improves the open-water efficiency by more than 1.5% at medium to high advance velocities. For the self-propulsion efficiency, over 5% improvement is achieved under ideal working conditions. In addition, PBCF has a directional effect on the radial and axial radiated noise, with better noise reduction in the axial direction. The difference between the axial and radial spectrums is significant, especially near the first blade passing frequency.

A formulation for numerically computing sound at moving observers based on frequency-domain Ffowcs Williams-Hawkings equation

A formulation for numerically computing sound at moving observers based on frequency-domain Ffowcs Williams-Hawkings equation

Aerodynamic and aeroacoustic characterization of an axial fan using Adaptive Mesh Refinement (AMR) based CFD and CAA

This work focuses on numerical analysis of a low-pressure axial fan using Computational Fluid Dynamics (CFD) and Computational Aeroacoustics (CAA) methods. These simulations are performed with the commercial software Hexagon's Cradle scFLOW. The investigation focuses on flow prediction using incompressible Large Eddy Simulation (LES), and acoustic propagation based on the Ffowcs Williams-Hawkings (FW-H) equation. We present a method to evaluate the mesh resolution for LES and a mesh refinement approach to resolve strong flow interactions, particularly near the tip-gap region. Both the aerodynamic and aeroacoustics performance of the fan are compared to experimental measurements for model validation. The pressure rise, velocity profiles and surface pressure fluctuations are captured well. Similarly, the sound propagation results are in good agreement with the experimental measurements. At low-mid frequencies, the blade passing frequencies and subharmonic peaks are captured, and at high frequencies, the broadband energy content is underpredicted, but still reasonably correlated. Additionally, a discussion regarding the mesh quality for LES is presented.

Numerical study on aerodynamic and aeroacoustic characteristics of sinusoidal wavy square cylinders

This paper numerically investigates the influences of amplitude and wavelength of sinusoidal wavy square cylinders on aerodynamic performance and noise reduction by large eddy simulation along with the Ffowcs Williams–Hawkings equation. The results show that the mean drag, lift fluctuation, and far-field noise of wavy cylinders are all reduced compared to the straight counterpart. The far-field noise of wavy cylinders varies monotonically with amplitude in a specific range but not with wavelength. The case with the largest amplitude demonstrates a significant tonal noise reduction of 47 dB/Hz, while a tonal noise reduction of 23 dB/Hz is observed for the case with the largest wavelength. To explore the mechanisms of noise reduction, the characteristics of a flow field are analyzed. It is found that wavy cylinders attenuate the transverse oscillation of a shear layer and produce more three-dimensional coherent structures in the wake. The wake region is significantly extended due to the delayed vortex shedding, and the mutual interaction between shear layers is remarkably weakened along the entire span. The spanwise coherence is attenuated in a similar way. These lead to the suppression of wall pressure fluctuations and turbulence fluctuations in the wake, which are closely related to far-field noise radiation.

The influence of jet on aerodynamic noise in the pantograph area at different sinking heights

The influence mechanism of jet on aerodynamic noise control in the pantograph region at different sinking heights was numerically studied using an Improved Delayed Detached Eddy Simulation (IDDES) model and the Ffowcs Williams-Hawkings (FW-H) equation. Active flow control was achieved by setting jet slots at the leading edge of the cavity to predict the noise generated by the jet itself. The results showed that in the pantograph region with a sinking height of 500 mm, the shear layer was lifted by the jet, which prevented high-speed turbulence caused by flow separation from entering the cavity. Therefore, the model with jet control device reduced the overall far-field noise on the side of the pantograph by 1.6 ∼ 3.9 dB. Through flow field analysis, for the pantograph region where flow separation occurs in the front of the cavity, the jet needs to lift the shear layer enough to cross the front of the pantograph and prevent flow separation, thereby reducing the aerodynamic noise. For the pantograph region without flow separation in the front of the cavity, the jet may introduce additional noise sources, deteriorating the aerodynamic noise in the pantograph region.

Effects of propeller boss cap fins on hydrodynamics and flow noise of a pump-jet propulsor

As an underwater thruster, the pump-jet propulsor (PJP) exhibits low radiation noise but generates significant line spectral noise in the low-frequency band. In this paper, we equipped the PJP hub with two types of propeller boss cap fins (PBCF): one fixed and the other rotating with the rotor. The hybrid large eddy simulation and Reynolds-averaged Navier–Stokes method, along with the Ffowcs Williams-Hawkings (FW-H) equation, are employed to systematically analyze the hydrodynamics, exciting force, flow noise, and flow field of PJPs. The results indicate that the fixed PBCF improves the hydrodynamic performance and reduces the exiting force, raising the rotor's thrust coefficient by 9.22%–14.99%. The fixed PBCF also modifies the characteristics of line spectrum noise but causes an increase in the flow noise. The rotating PBCF increases the rotor's thrust coefficient by 2.03%–3.15%, decreasing both exciting force and line spectrum noise. For instance, at the advance coefficient of 0.8, its sound pressure level at the rotor frequency drops to 49.6%. Additionally, the rotating PBCF increases the pressure of the hub wake and effectively reduces the hub vortices' strengths. This paper provides a theoretical foundation for designing PJPs that enhance concealment and minimize vibrations and noise.

Numerical approach for the simulation of flow-induced noise around a structure with complex geometry: High-speed train bogie in a cavity

The bogie region is a significant source of aerodynamic noise on high-speed trains. Owing to its complex geometry and flow field, numerical simulations using computational fluid dynamics are especially challenging. The main challenge is to achieve a grid with adequate resolution, especially in the boundary layer, while ensuring computational affordability. This challenge is addressed here by employing a hybrid grid, integrating a structured hexahedral mesh near solid surfaces with an unstructured polyhedral mesh in the remaining volume. To limit the number of cells in the boundary layer region, the delayed detached eddy simulation method is adopted. Additionally, to achieve a further reduction in the cell count, the Reynolds number of the model is decreased by scaling down the model size and lowering the inflow speed. The hybrid grid generation and numerical settings are guided by validated simulations of flow over cylinders. A grid sensitivity study, conducted with a simplified half-width bogie model, reveals the meshing requirements for the full-width model. Aerodynamic results highlight the rear section of the cavity and bogie as primary noise sources, emphasizing the critical role of the detached shear layer from upstream components. Time-resolved surface pressure data are input into the Ffowcs Williams–Hawkings equation for far-field noise calculation. The results indicate that the sound energy is concentrated below 200 Hz in the full-scale model, with the cavity contributing more than the bogie. This study provides a practical numerical approach for simulating a structure with complex geometry, offering insights for realistic model simulations.

Acoustic optimization of a tee via a Helmholtz resonant cavity and noise prediction via a genetic algorithm coupled with the grey model

As a key local component in heating, ventilation and air conditioning (HVAC) systems, the acoustic characteristics of the tee largely determine the indoor acoustic environment quality. The aim of this study was to determine the impact of the Helmholtz resonant cavity (HRC) on the tee noise and sound transmission loss (STL). The noise was predicted using the Ffowcs Williams-Hawkings (FW-H) equation and large eddy simulation (LES), and an analysis was conducted on four design variables: the cavity width, cavity height, outlet flow ratio, and hole width. The results indicated that increasing the hole width had a positive effect on reducing the noise of the tee. HRC could result in a tee peak noise attenuation up to 34.81 dB. In addition, based on grey model (GM) and genetic algorithm (GA) theory, the noise of the Helmholtz resonant tee (HRT) was predicted, and a noise prediction formula for resonant cavity structure paraments was derived. This study provides a new perspective for optimizing the STL of the tee and a simplified prediction method for low-noise tee design.

Aerodynamic noise reduction of high-speed pantograph by introducing planar jet on leeward surface of panhead

Combining the improved delayed detached eddy simulation (IDDES) model and Ffowcs Williams-Hawkings (FW–H) equation, the potential of panhead leeward-side jet in pantograph aerodynamic noise control is numerically investigated. A typical double-strip pantograph is used as the baseline model. Two identical planar jets are arranged on the leeward side of the two strips to achieve active flow control. The results show that the planar jet can reduce the aerodynamic drag of the upstream strip and suppress its lift fluctuation, while the jet does not produce equivalent level of positive effects on the downstream strip. Benefiting from the suppression of lift fluctuation of the upstream strip, the far-field noise of the model equipped with jet achieves a 7 dB reduction in the main direction of panhead lift fluctuation, and the noise on the pantograph side is also reduced by 1–2 dB. The flow-field analysis reveals that the planar jet pushes the coherent flow structures in the panhead's wake downstream, which makes the high-intensity flow-field fluctuation away from the upstream strip. The absence of the positive effect of the jet on wake flow modification of the downstream strip can be attributed to the distinct inflow conditions of the two strips.

Research on finite element model of rotor aerodynamicnoise in hovering state

The helicopter has been widely used in many fields, and the rotor aerodynamic noise has gradually attracted attention. The non-homogeneous wave equation, Ffowcs Williams-Hawkings equation (FW-H equation) derived from hydrodynamic N-S equation, combined with RANS turbulence simulation, was used to simulate the sound field of NACA0012 airfoil-shape model in hovering state. On this basis, by changing the thickness and camber of the blade, the aerodynamic noise of the rotor under different airfoil profile thickness and camber is calculated. The results show that the change of airfoil thickness and camber will affect the aerodynamic noise of the rotor in hovering state.

Numerical investigation on cavitation and induced noise reduction mechanisms of a three-dimensional hydrofoil with leading-edge protuberances

In this work, a National Advisory Committee for Aeronautics 66 hydrofoil with leading-edge protuberances is designed. The large eddy simulation combined with the Schnerr–Sauer cavitation model is used to obtain a satisfactory result as compared with the experimental measurement, integrating the permeable Ffowcs Williams–Hawkings equation for cavitation-induced noise analysis. It is found that the special leading-edge geometric structure deflects the incoming flow, creating two counter-rotating streamwise vortices at the peak shoulders. These lead to upwash and downwash effects and alter the pressure distribution on the suction side. The low pressure localized in the trough facilitates the advancement of the leading-edge cavitation while severely limiting the spanwise development of the cloud cavity, shortening the cavitation evolution by about 20% and reducing the maximum cavitation volume by about 35%. Analysis using the vorticity transport equation indicates that different vorticity transport equation splitting terms play dominant roles at different stages of cavitation evolution. Although the cavitation induces disturbances in the primary vortex, the effect is limited. Acoustic simulation shows that the bionic structure can reduce the total sound pressure level by 7.8–8.3 dB. The spherical noise reduction is not as effective as expected due to the similar cavitation volume acceleration processes of the two hydrofoils. However, the pressure fluctuation caused by the collapse of the cloud cavity is reduced by cavitation suppression, which reduces the linear noise. In addition, the protuberances suppress the generation of large-scale vortex systems and transform them into smaller ones, resulting in reduced spanwise correlation and coherence of the shedding vortices. This is a critical factor in noise reduction. Finally, we hypothesize that the unstable noise reduction is related to the streamwise vortices in the trough regions. These vortices increase the momentum exchange within the boundary layer, affecting its stability and weakening the acoustic feedback loop.

Analysis of blade noise with different root boundary conditions considering fluid-structure interaction effect

It is of certain importance for noise reduction to investigate the relationship between the aeroacoustic characteristics of blade and root boundary conditions when considering the fluid-structure interaction (FSI) effect. In this study, a set of precise dynamic models and two-way FSI calculation methods are developed to predict the dynamic load and response of blades more accurately. The natural frequency inaccuracy of the blade model is kept within 5% by comparing the results of the modal test using the ploy-reference time domain method and adopting the sensitivity analysis method with the blade beam stiffness as the modification parameter. Besides, based on the numerical results from the computational fluid dynamics method considering the FSI effect, the aeroacoustic characteristics of blades with different root boundary conditions are analyzed by adopting the Ffowcs Williams-Hawkings equations. The aeroacoustic characteristics of the NACA blade in hover are thoroughly discussed, with emphasis on the impact of different root boundary conditions on rotation noise. The result demonstrates that, the sound pressure level (SPL) difference of loading noise can reach 1.4 dB between blades with various root boundary conditions, while the SPL difference of thickness is only 0.4 dB.

Rotor aeroacoustic response to an axisymmetric turbulent boundary layer

The acoustic response of a five-bladed rotor to an axisymmetric turbulent boundary layer at the tail end of a body of revolution (BOR) is investigated numerically to elucidate the physical sources of acoustics, particularly the role of coherent structures in sound generation. The BOR is at a length-based Reynolds number of $1.9 \times 10^6$ and free-stream Mach number of 0.059. Two rotor advance ratios, $1.44$ and $1.13$ , are considered. The turbulent boundary layer on the nose and midsection of the BOR is computed using wall-modelled large-eddy simulation, whereas that in the acoustically important tail-cone section is wall-resolved. The radiated acoustic field is calculated using 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, spectral humps near multiples of the blade-passing frequency and accompanying valleys are captured. They are shown to be caused by correlated blade unsteady-loading dipole sources and their constructive and destructive interference as a result of successive blades cutting through the same coherent structures. The latter undergo rapid growth in the decelerating tail-cone boundary layer before their interaction with the rotor. The acoustic radiation is dominated by the outer region of the blade owing to a combination of larger blade chord-length, inflow turbulence intensity and blade speed. The numerical results also correctly predict the effect of the rotor advance ratio on the acoustic field. A mixed free-stream/convection Mach-number scaling successfully collapses the sound pressure spectra at the two advance ratios.

Development and Application of Open Rotor Discrete Noise Prediction Program Using Time-Domain Methods

The aerodynamic noise of an open rotor is one of the critical challenges that must be considered in its design and application. FODNOPP, a program specifically programmed to predict the aerodynamic discrete noise of single- and counter-rotating open rotors (such as propellers, propfans, and rotorcraft rotors) at subsonic, transonic, and supersonic helical blade tip speeds, has recently been developed by the first author. This program is composed of four prediction codes, namely code a1, code a2, code b, and code c, each based on Farassat-derived formulations Formu 1-RTE, Formu 1A, Formu 1-Sph, and Formu 3, providing time-domain solutions to the Ffowcs Williams–Hawkings equation. Four verification examples for both propeller low-speed flight noise and counter-rotating propfan take-off noise are presented, along with an application case for transonic helical tip speed counter-rotating propfan cruise noise. The results demonstrate the accuracy of FODNOPP in calculating the noise for these verification cases. And in the counter-rotating propfan cruise noise case, the maximum harmonic sound pressure level of the rear propfan is 5.5 dB higher than that of the front propfan. FODNOPP can be referred to as a comprehensive design tool, and it offers valuable guidance for engineering design focused on rotor-related noise reduction.

Aerodynamic noise characteristics of a centrifugal fan in high-altitude environments.

In high-altitude areas, the air is thin and the atmospheric pressure is low, which can affect the performance of centrifugal fans and aerodynamic noise. In this paper, steady and unsteady simulations of a centrifugal fan flow field are performed at altitudes of 0, 1000, 2000, 3000, 4000, and 5000 m, and the Ffowcs Williams-Hawkings equation is used to predict the aerodynamic noise of the fan. The results indicate that the tonal and broadband noise generated by the fan decrease with increasing altitude, and the A-weighted sound pressure level of each frequency band of the fan decreases when the air volume is held fixed. The maximum sound power level Lwmax, sound pressure pulsation interval, and total noise sound pressure level Lp decrease linearly with increasing altitude. For every 1000 m increase in altitude, Lwmax and Lp decrease by 0.45 dB and 1.05 dB respectively. The fan noise characteristics, performance parameters, and human auditory perception are the main factors that affect the establishment of fan noise standards in high-altitude areas.