Hawkings Equation Research Articles

A design methodology for quiet and long endurance MAV rotors

Over the last 10 years, the use of micro air vehicles has rapidly covered a broad range of civilian and military applications. While most missions require optimizing the endurance, a growing number of applications also require acoustic covertness. For rotorcraft micro air vehicles, combining endurance and covertness heavily relies on the capability to design new propulsion systems. The present paper aims at describing a complete methodology for designing quiet and efficient micro air vehicle rotors, ranging from preliminary aerodynamic prediction to aeroacoustic optimization to experimental validation. The present approach is suitable for engineering purposes and can be applied to any multirotor micro air vehicle. A fast-response and reliable aerodynamic design method based on the blade-element momentum theory has been used and coupled with an extended acoustic model based on the Ffowcs Williams and Hawkings equation as well as analytical formulations for broadband noise. The aerodynamic and acoustic solvers have been coupled within an optimization tool. Key design parameters include the number of blades, twist and chord distribution along the blade, as well as the choice of an optimal airfoil. An experimental test bench suitable for non-anechoic environment has been developed in order to assess the benefit of the new rotor designs. Optimal rotors can maintain high aerodynamic efficiency and low acoustic signature with noise reductions in the order of 10 dB(A).

Electrically Controlled Rotor Blade Vortex Interaction Airloads and Noise Analysis Using Viscous Vortex Particle Method

An electrically controlled rotor (ECR), also called a swashplateless rotor, replaces a swashplate with a trailing‐edge flap system to implement primary rotor control. To investigate the aerodynamic characteristics of an ECR in blade‐vortex interaction (BVI) condition, an analysis model based on the viscous vortex particle method, ECR blade pitch equation, and the Weissinger‐L lifting surface model is established. In this model, the ECR wake flow field vorticity is discretized as multiple vortex particles, and the vorticity‐velocity form of the Navier‐Stokes equation is solved to simulate the transport diffusion of the vorticity. The flap motion‐inducing blade‐pitch movement is obtained by solving the ECR blade‐pitch movement equation via the Runge–Kutta fourth‐order method. On the basis, BVI noise radiation of an ECR is evaluated using the Ffowcs Williams and Hawkings (FW‐H) equation. Based on the present prediction model, the aerodynamic and acoustic characteristics of a sample ECR in BVI condition are analyzed. The results show that since the BVI event of the ECR on the advancing side is mainly caused by the interaction between the flap tip vortex and the blade, the blade spanwise range of ECR BVI occurrence on the advancing side is smaller than that of the conventional rotor. In addition, the magnitude of the maximum sound pressure level on the advancing side as well as on the retreating side of the ECR is also different from that of the conventional rotor, which is consistent with the difference in the airloads between the ECR and conventional rotor. Furthermore, a study was performed to examine the effect of the pre‐index angle on the BVI‐induced airloads and noise. The amplitude of the impulsive airloads of the ECR on the advancing side is increased with the increase in pre‐index angle, while the amplitude of the impulsive airloads of the ECR on the retreating side is decreased. Indeed, when the pre‐index angle of the sample ECR is 8 degrees, the retreating‐side noise radiation lobe is almost disappeared. In addition, the different intensity of wake vorticity is the main reason for the differences of the BVI‐induced airloads and noise among the ECR with different pre‐index angles.

Some Peculiarities of Helicopter Main Rotor Aeroacoustic for Far-Field Observer

Mathematical models for helicopter rotor acoustics are usually based on the Ffowcs Williams–Hawkings (FW–H) equation. The level of rotor noise is determined by geometry (thickness noise) of a flying vehicle and distributed blade loading (loading noise). Initially, the FW-H equation was obtained from Euler’s equations and does not depend on the viscosity of flow. In the present work the UH-1H helicopter is considered as a test case for numerical CFD simulation and comparison to experimental data.

Aerodynamic Noise Simulation and Quadrupole Noise Problem of 600km/h High-Speed Train

The quadrupole aerodynamic noise is a difficult problem in numerical simulation of the aerodynamic noise. The Kirchhoff-Ffowcs Williams and Hawkings (K-FWH) equation method and the three-dimensional compressible Large Eddy Simulation (LES) method are adopted in this manuscript for aerodynamic noise accuracy simulation of 600km/h high-speed train. The influence of different distributions of penetrable integral surfaces on the results of far-field aerodynamic noise is discussed. The optimum combination form of penetrable integral surfaces is obtained. The aerodynamic noise of high-speed train considering quadrupole can be calculated efficiently and accurately by using the upstream body surface and wake area penetrable integral surface as sound source surface. The wake area penetrable integral surface should contain the main vorticity structure of the wake as far as possible and the surface vorticity amplitude should be insignificant. The contribution rate of the dipole and quadrupole to the total aerodynamic noise energy of high-speed train is different. The aerodynamic noise energy of the upstream measurement points is mainly dipole aerodynamic noise energy, while that of the downstream measurement points is mainly dipole and quadrupole noise energy. The method proposed in this manuscript is of great significance in the aerodynamic noise numerical simulation of 600km/h high-speed train.

Adaptability of Turbulence Models for Pantograph Aerodynamic Noise Simulation

This study was targeted at CX‐PG‐type Faiveley pantograph of high‐speed train and cylinders and analysed the fluctuating flow field around these objects by using the large eddy simulation (LES) model, the scale adaptive simulation (SAS) model, the improved delayed detached eddy simulation with shear‐stress transport‐kω (IDDES sst‐kω) model, the delayed detached eddy simulation with shear‐stress transport‐kω (DDES sst‐kω) model, and the delayed detached eddy simulation with realizable‐kε (DDES R‐kε) model. The space distributions of velocity, vorticity, and vortex structures were compared to investigate their performances on simulating fluctuating flow fields and computing aeroacoustic sources through Fourier transformation based on the surface fluctuating pressures. Furthermore, the far‐field radiated noise was calculated based on the Ffowcs Williams–Hawkings equation. Based on the computation precision of the five models, a feasible turbulent model was selected for simulating aerodynamic noise. The relative errors to the results from wind‐tunnel experiments of the sound pressure level (SPL) were obtained as 0.7%, 1.6%, 7.8%, 3.8%, and 12.1%, respectively, and the peak Strouhal numbers were obtained as 2.0%, 8.5%, 5.5%, 11.5%, and 51.0% for cylinder simulation. Moreover, the relative errors of SAS, IDDES sst‐kω, DDES sst‐kω, and DDES R‐kε models to the result from LES of SPL were respectively obtained as 2.3%, 4.5%, 5.6%, and 10.8% for pantograph. Thus, it is conclusive that none of the aforementioned models are comparable with the LES model with respect to the precision in the aeroacoustic simulation. However, SAS, IDDES sst‐kω, and DDES sst‐kω are practically competent with the LES model considering the numerical simulations with respect to the engineering computation precision. The numerical computation model was verified using the wind‐tunnel test results.

Numerical investigation of aerodynamic and acoustic characteristics of bionic airfoils inspired by bird wing

Airfoil is the basic element of fluid machinery and aircraft, and the noise generated from that is an important research aspect. Aiming to reduce the aerodynamic noise around the airfoil, this study proposes an airfoil inspired by the long-eared owl wing and another airfoil coupled with the bionic airfoil profile, leading edge waves, and trailing edge serrations. Numerical simulations dependent on the large eddy simulation method coupled with the wall-adapting local eddy-viscosity model and the Ffowcs Williams and Hawkings equation are conducted to compare the aerodynamic and acoustic characteristics of two types of bionic airfoils at low Reynolds number condition. The simulations reveal the dipole characteristic of acoustic source and sound pressure level distribution at various frequencies. Two types of bionic airfoils show lower noise compared with the conventional NACA 0012 airfoil with a similar relative thickness of 12%. Compared with the bionic airfoil, the average value of sound pressure level at the monitoring points around the bionic coupling airfoil is decreased by 9.94 dB, meanwhile the lift-to-drag ratio also keep higher. The bionic coupling airfoil exerts a suppression of sound pressure fluctuation on the airfoil surfaces, which result from that the range and size of separation vortices are reduced and the distance between vortices and airfoil surface are increased. The tube-shaped vortices in the wake of airfoil are effectively restrained and split into small scale vortices, which are important to cause less aerodynamic noise around the bionic coupling airfoil. Consequently, a novel bionic coupling airfoil is developed with the excellent aerodynamic and acoustic performance.

New Approach for Aerodynamic and Aeroacoustic Analysis of Actively Controlled Flaps Rotor

A new approach for aerodynamic and aeroacoustic analysis of actively controlled flaps (ACF) rotor is established to predict airloads and noise reduction. The approach is divided into three parts. The first is an unsteady aerodynamic model of the ACF described through a panel method, and the unsteady pressure under interaction of rotor tip vortex and ACF trailing-edge vortex, which are depicted through a viscous vortex particle method, are taken into account. The second is the influence of the ACF on trajectory of the wake and ACF trailing-edge vortex, which is carried out by a new imaged vortex model to capture blade-vortex interaction (BVI). The third is an aeroacoustic model coupled into the aerodynamic model by transmitting the unsteady pressure to Ffowcs Williams and Hawkings (FW-H) equation. The present approach is applied to AH-1G rotor, and the results show that the predicted unsteady airloads, high-speed impulsive (HSI), and BVI noise are compared favorably with experiment and Reynolds-averaged Navier–Stokes (RANS)/FW-H results. Finally, the variation of airload and noise reduction of ONERA Active Blade Concept rotor (ABC) is predicted and compared with experiment. It is shown that the present approach predicts the airload and noise reduction of the ACF with different phases and flap locations with good accuracy.

Numerical investigation into cavitation flow noise of hydrofoil using quadrupole-corrected Ffowcs Williams and Hawkings equation

Numerical investigation into cavitation flow noise of hydrofoil using quadrupole-corrected Ffowcs Williams and Hawkings equation

Numerical analysis of supersonic flows over an aft-ramped open-mode cavity

The characteristics of supersonic cavity flows were investigated using large eddy simulation together with the acoustic analogy method. A fifth-order hybrid compact-weighted essentially non-oscillatory scheme was applied to calculate the convective flux, and a sixth-order compact scheme was used for the viscous flux. Farassat's Formula 1A was used to solve the Ffowcs William–Hawkings equations to obtain the far-field acoustic pressure fluctuations. The effects of cavity configuration and flow Mach number on the pressure waves generated by the interaction of shear vortices and cavity were compared. The ramped rear-step of the cavity can increase the more-organized level of flow coherent structures, and decrease the static pressure distribution on the cavity bottom-wall. The attenuation of the interactions between the shear layer vortex and the aft-ramped wall of the cavity can reduce the feedback of pressure waves upstream. The energy of the main frequency significantly decreases for the far-field acoustics in the upstream flow over the ramped rear-step cavity. Thus, the effectiveness of noise reduction by the rear-ramp is considerable for the area upstream of the cavity for the present conditions, but it is not the case opposite to and downstream of the cavity. The present conclusions are valuable for evaluating the performance of noise suppression by cavities embedded in supersonic inflows in engineering applications.

A numerical study of transient flow around a cylinder and aerodynamic sound radiation

The fully 3D turbulent incompressible flow around a cylinder and in its wake at a Reynolds number Re = = 9×104 based on the cylinder diameter and Mach number M = 0.1 is calculated using Large Eddy Simulations (LES). Encouraging results are found in comparison to experimental data for the fluctuating lift and drag forces. The acoustic pressure in far-field is commutated through the surface integral formulation of the Ffowcs Williams and Hawkings (FWH) equation in acoustic analogy. Five different sound sources, the cylinder wall and four permeable surfaces in the flow fields, are employed. The spectra of the sound pressure are generally in quantitative agreement with the measured one though the acoustic sources are pseudo-sound regarding the incompressible flow simulation. The acoustic component at the Strouhal number related to vortex shedding has been predicted accurately. For the broad band sound, the permeable surfaces in the near wake region give qualitative enough accuracy level of predictions, while the cylinder wall surface shows a noticeable under-prediction. The sound radiation of the volumetric sources based on Lighthill tensors at vortex shedding is also studied. Its far-field directivity is of lateral quadrupoles with the weak radiations in the flow and cross-flow directions.

Effect of tip rake angle on the hydrodynamic characteristics and sound pressure level around the marine propeller

ABSTRACTThis paper presents the effect of the tip rake angle on the hydrodynamic characteristics and sound pressure level (SPL) around the ship propeller by Reynolds-Averaged Navier–Stokes solver. Tip rake angle may cause changes in tip vortex and hydrodynamic performance and noise level. The two-step Fflowcs Williams and Hawkings (FW-H) equations are used to calculate the pressure distribution, hydrodynamic characteristics as well as SPL at various points around the propeller. The DTMB4382 propeller is selected. The effects of the tip rake angle on the hydrodynamic and SPL around the propeller are investigated. Various numerical results such as SPL at different downstream points and different topside points of the propeller and hydrodynamic characteristics are presented and discussed. Main conclusion is found that when the positive or negative rake is increased the efficiency is slightly decreased and the SPL is also diminished.

Numerical Investigation into Effects of Viscous Flux Vectors on Hydrofoil Cavitation Flow and Its Radiated Flow Noise

In this study, cavitation flow around a hydrofoil and its radiated hydro-acoustic fields were numerically investigated, with an emphasis on the effects of viscous flux vectors. The full three-dimensional unsteady compressible Reynolds-averaged Navier–Stokes equations were numerically solved. The mass transfer model was adopted to model phase changes between liquid water and vapor. To resolve the numerical instability problem arising from the rapid changes in local density and speed of sound of the mixture, the preconditioning and dual-time stepping methods were employed. The filter-based turbulent model was applied to resolve the unstable cavitation flow field more accurately. In splitting the viscous terms, three approaches for dealing with viscous flux vectors were considered: the so-called viscous lagging, full viscous, and thin-layer models. Radiated hydro-acoustic waves were predicted by applying the Ffowcs Williams and Hawkings equations. The effects of the viscous flux vectors on the predicted flow fields and its radiated noise were then examined by comparing the hydro-dynamic forces, velocity distribution, volume fraction, far-field sound directivities, and sound spectrum of the three approaches. The results revealed that the thin-layer model can provide predictions as accurate as the full viscous model, but required less computational time.

Development and validation of a hybrid method for predicting helicopter rotor impulsive noise

Prediction of helicopter rotor impulsive noise is practically a very challenging task. This paper describes a hybrid method to predict rotor impulsive noise for both high-speed impulsive noise and blade–vortex interaction noise. The hybrid solver has been developed by combining the advantages of three different methods: (1) a computational fluid dynamics method based on Reynolds-averaged Navier–Stokes equations to account for the viscous and compressible effects near the blade; (2) a vorticity transport model to predict rotor wake system without artificial dissipation; and (3) an acoustic calculation method, based on Ffowcs-Williams Hawkings equation implemented to a permeable data surface. The developed hybrid solver is validated through available test data, for the cases of UH-1H model rotor, AH-1 Operational Loads Survey rotor, and Helishape 7A rotor. Peak sound pressure level of high-speed impulsive noise is accurately predicted with relative errors less than 7%. Additionally, acoustic waveform of blade–vortex interaction noise is well captured though it is sensitive to small changes in aerodynamic load. It is suggested that present hybrid method is versatile for the prediction of rotor impulsive noise with moderate computational cost.

Calculation of sound pressure level of marine propeller in low frequency

The research performed in this paper is carried out to calculate the sound pressure level of the marine propeller by Reynolds-Averaged Navier–Stokes solver in low frequencies band. Noise is generated by the induced trailing vortex wake and induced pressure pulses. The two-step Fflowcs Williams and Hawkings equations are used to calculate hydrodynamic pressure and its performance as well as sound pressure level at various points around the propeller. The directivity patterns of this propeller and accurate explanation of component propeller noise are discussed. Comparison of the numerical results shows good agreement with the experimental data.

A time-domain method for prediction of noise radiated from supersonic rotating sources in a moving medium.

This paper presents a time-domain method for noise prediction of supersonic rotating sources in a moving medium. The proposed approach can be interpreted as an extensive time-domain solution for the convected permeable Ffowcs Williams and Hawkings equation, which is capable of avoiding the Doppler singularity. The solution requires special treatment for construction of the emission surface. The derived formula can explicitly and efficiently account for subsonic uniform constant flow effects on radiated noise. Implementation of the methodology is realized through the Isom thickness noise case and high-speed impulsive noise prediction from helicopter rotors.

A numerical study on the effects of design parameters on the acoustics noise of a high efficiency propeller

PurposeA numerical study on the aerodynamic noise generation of a high efficiency propeller is carried out.Design/methodology/approachThree-dimensional numerical simulation based on Reynolds averaged N-S model is performed to obtain the aerodynamic performance of the propeller. Then, the result of the aerodynamic analysis is given as input of the acoustic calculation. The sound is calculated using the Farassat 1A which was derived from Ffowcs Williams–Hawkings equation and is compared with the measurements.FindingsMoreover, the fan is modified for noise reduction by changing its geometrical parameters such as span, chord length and torsion angle.Originality/valueThe variation trend of aerodynamic and acoustic are compared and discussed for different modification tasks. Some meaningful conclusions are drawn on the noise reduction of propeller.

A Ffowcs Williams and Hawkings formulation for hydroacoustic analysis of propeller sheet cavitation

A novel hydroacoustic formulation for the prediction of tonal noise emitted by marine propellers in presence of unsteady sheet cavitation, is presented. The approach is based on the standard Ffowcs Williams and Hawkings equation and the use of transpiration (velocity and acceleration) terms, accounting for the time evolution of the vapour cavity attached on the blade surface. Drawbacks and potentialities of the method are tested on a marine propeller operating in a nonhomogeneous onset flow, by exploiting the hydrodynamic data from a potential-based panel method equipped with a sheet cavitation model and comparing the noise predictions with those carried out by an alternative numerical approach, documented in literature. It is shown that the proposed formulation yields a one-to-one correlation between emitted noise and sheet cavitation dynamics, carrying out accurate predictions in terms of noise magnitude and directivity.

A numerical study of the effects of design parameters on the acoustics noise of a high efficiency propeller

A numerical study of a high efficiency propeller in the aerodynamic noise generation is carried out. Based on RANS, three-dimensional numerical simulation is performed to obtain the aerodynamic performance of the propeller. The result of the aerodynamic analysis is given as input of the acoustic calculation. The sound is calculated using the Farassat 1A, which is derived from Ffowcs Williams–Hawkings equation, and compared with the data of wind tunnel. The propeller is modified for noise reduction by changing its geometrical parameters such as diameter, chord width and pitch angle. The trend of variation between aerodynamic analysis data and acoustic calculation result are compared and discussed for different modification tasks. Meaningful conclusions are drawn on the noise reduction of propeller.

Acoustic Analogy for Multiphase or Multicomponent Flow

The Ffowcs Williams and Hawkings (FW-H) equation is widely used to predict sound generated from flow and its interaction with impermeable or permeable surfaces. Owing to the Heaviside function used, this equation assumes that sound only propagates outside the surface. In this paper, we develop a generalized acoustic analogy to account for sound generation and propagation both inside and outside the surface. The developed wave equation provides an efficient mathematical approach to predict sound generated from multiphase or multicomponent flow (MMF) and its interaction with solid boundaries. The developed wave equation also clearly interprets the physical mechanisms of sound generation, emphasizing that the monopole and dipole sources are dependent on the jump in physical quantities across the interface of MMF rather than the physical quantities on one-side surface expressed in the FW-H equation. The sound generated from gas bubbles in water is analyzed by the newly developed wave equation to investigate parameters affecting the acoustic power output, showing that the acoustic power feature concluded from the Crighton and Ffowcs Williams (C-FW) equation is only valid in a specific case of all bubbles oscillating in phase.

다중 투과면을 이용한 UH-1H 로터 블레이드의 제자리 비행 시 원방 소음 해석 연구

In this study, aero-acoustics in far-field is computed for the UH-1H rotor blade in hovering flight. A Chimera grid method is applied in this simulation to consider the blade motion and moving effects. Multi-permeable surfaces surrounding a blade are constructed to include the flow noise generated from the shock wave and the tip vortices. A computation is performed with three-dimensional Euler’s equations. An acoustic analogy code using the Kirchhoff approach to Ffowcs Williams and Hawkings equations is applied to efficient the noise prediction caused by volume noise sources in far-field. The high speed impulsive noise on the rotor blade is predicted and validated according to the permeable surface locations. It is confirmed that the noise source caused by the shock waves generated on the blade surface is a dominant factor in the far-field noise prediction.