Hawkings Formulation Research Articles

Aerodynamic sound generation in thermoviscous fluids: A canonical problem revisited

Although the Lighthill–Curle acoustic analogy theory is formally exact, the presence of linear source terms related to viscous stresses and non-isentropic density changes makes it unsuitable for studying aerodynamic sound generation in low Reynolds number thermoviscous flows. Here we use an extension of the Ffowcs Williams and Hawkings formulation, with thermoviscous effects explicitly included, to find an analytical solution to the canonical problem of sound radiation from a circular cylinder immersed in a viscous heat-conducting fluid and rotating sinusoidally about its axis. Existing published solutions are compared and an earlier null result is explained. The new analysis reveals the dominant source of sound at low Mach numbers to be unsteady viscous dissipation rather than Reynolds-stress quadrupoles, unless the fluid parameter B=αc2/cp is zero.

Numerical prediction of propeller-induced noise in open water and ship behind conditions

In this article, the underwater noise of non-cavitating propellers is investigated using a boundary element method (BEM) coupled with the Ffowcs Williams–Hawkings (FW–H) formulation in the presence of the hull. The propeller is mounted on the vessel with an infinite plane assumed at the design draft to consider the free surface or tunnel wall effect. The hydrodynamic BEM solves the flow field for the analysis of propeller performance, then the time-dependent surface pressures are taken as the known noise sources for the FW–H equation in the form proposed by Farassat. The hull geometry and its disturbance to the medium are considered by solving the boundary integral equations, and the half-space medium is modeled by adding an additional term to the full space Green’s function for an image body beyond the infinite plane. The propeller performance in open water condition is first investigated to validate BEM predictions against experimental measurements. Along with the overall noise patterns in the flow field, decay rates of noise with the distance from the propeller and limited influence of the linear noise terms of the FW–H equation are discussed. Afterward, the propeller-induced hull pressure fluctuations are investigated, and the time history of acoustic pressures shows reasonable agreement with experimental measurements. Direct noise from the propeller, its scattered noise by the hull, and their sums as the total noise are discussed. This study identifies the dominating noise source around the hull, which could provide a basis for the noise control strategy for a ship propulsion system.

Numerical Assessment of Open-Rotor Noise Shielding with a Coupled Approach

In this work, scattering and shielding of the tonal noise from contrarotating open rotors by surrounding parts are investigated. The computational tool chain is based on unsteady Reynolds-averaged Navier–Stokes simulations providing permeable integration surface data for a Ffowcs Williams and Hawkings-type evaluation (“Sound Generated by Turbulence and Surfaces in Arbitrary Motion,” Philosophical Transactions of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol. 264, No. 1151, 1969, pp. 321–342), which is coupled with a fast multipole boundary-element method to account for shielding by the airframe. The effect of a background mean flow is taken into account by applying a Lorentz transform to the boundary-element problem and using the Möhring analogy instead of the Ffowcs Williams and Hawkings formulation to obtain the incident acoustic field. Validation of the Möhring/boundary-element coupling method is shown on the basis of a model contrarotating open rotor with shielding geometries and a mounting pylon. The tool chain is then applied to a full-scale open-rotor engine installed in different aircraft tail configurations (T tail, L tail, and U tail) to assess their influence on flyover and lateral noise in takeoff conditions.

Performance and Noise Prediction of Marine Propeller Using Numerical Simulation

One of the phenomenon appears on operation of marine propeller is noise. It could reduce performance of the propeller. In this study, numerical simulation is used to predict hydrodynamic performance and noise around non cavitation propellers. The formulation of RANS (Reynold Averaged Naiver Stokes) with turbulence model k-ω SST (Shear Stress Transport) and FWH (Ffowcs Williams–Hawkings formulation) is applied on the simulation. The noise is expressed in time-domain acoustic analogy as well as finite volume, and it is predicted at different receiver positions. The performance of propeller is predicted by MRF technique (Multiple Reference Frame). The 3D model of B-series propeller with diameter of D = 250 mm, blade number Z = 4, pitch diameter ratio P/D = 1, and area ratio Ae/Ao = 0.55 is simulated on various advance coefficients (J). Propeller rotation is simulated in range of 7.5 rps - 29rps and Re = 6.95x104– 3.36x106

The role of compressibility in computing noise generated at a cavitating orifice

The computational fluid dynamics calculation can be accomplished by solving either compressible or incompressible Navier–Stokes equations to determine the flow-field variables of the noise source. The proper assumption depends on both the physical situation and the Mach number. Although in cavitating devices usually we are dealing with low Mach number flow, cavitation is an acoustic phenomenon that can be affected by compressibility. Cavitation behaves acoustically as a monopole and it is mentioned by some researchers that incompressible solution is sufficient to study the dipole sources. However, in order to study the monopole (and quadrupole) sources a compressible solution may be required. In this study, the role of compressibility in computing noise generated at a cavitating single-hole orifice was investigated using large eddy simulation and Ffowcs Williams–Hawkings formulation. The fluid zone downstream of the orifice where the cavitation occurs was evaluated as the acoustic source which generates sound. Time-accurate solutions of the flow-field variables on source surfaces were obtained from both compressible and incompressible flow simulations. Three cases of cavitation were studied and the sound pressure signals far downstream of the orifice were computed by the Ffowcs Williams–Hawkings formulation. For a developed cavitation regime at low frequencies, there is a big discrepancy between the computed values of sound pressure level from compressible and incompressible simulations, and at higher frequencies greater than 6 kHz, both simulation methods provide almost the same values for sound pressure levels. For a super cavitation regime, both compressible and incompressible simulations provide similar values for sound pressure levels at frequencies greater than 2 kHz. The results of this work demonstrate that the compressibility has a significant role in terms of computing noise generated at a cavitating orifice and cannot be ignored, especially when the noise generated by developed cavitation regimes at low frequencies is investigated.

Acoustic Prediction of LAGOON Landing Gear: Cavity Noise and Coherent Structures

Detached-eddy simulations of the LAGOON landing gear configuration are performed using different unstructured meshes. One mesh is generated based on available experimental and numerical data, and based on this first mesh, a second one is carefully designed to improve the solutions in regions of strong unsteadiness. Results are presented in terms of steady and unsteady hydrodynamic data as well as noise predictions, which are performed using the Ffowcs-Williams and Hawkings formulation. Numerical results show good agreement with experimental data available in the literature. A wavelet transform analysis demonstrates that the sound generation in the cavity is an intermittent process that leads to strongly varying amplitudes of the surface pressure and the far-field noise radiation. A proper orthogonal decomposition is employed to identify coherent energetic structures responsible for the cavity tones. Finally, it is shown how the local flow topology affects the impingement of these coherent structures on the cavity.

Noise investigation of a cavitating orifice: use of cfd simulation and ffowcs williams–hawkings (fw-h) formulation to gain insight into acoustics condition

In piping systems, hydrodynamic cavitation is well known for its destructive capabilities such as generation of intense noise. The investigation of the effect of the cavitation on acoustic pressure fluctuations and resonance frequencies provides much information about the geometry of the cavitation area, the propagation and the damping characteristics of the cavitation medium. The acoustical effects of cavitation caused by a water flow through a single-hole orifice have been investigated by using Computational Fluid Dynamics (CFD) and Ffowcs Williams–Hawkings (FW-H) formulation. The fluid zone downstream of the orifice where the cavitation happens considered as acoustic source. Time-accurate solutions of the flow-field variables are obtained from large eddy simulation (LES). Two cavitation regimes are investigated and for each regime, the sound pressure signals far downstream of the orifices are computed by applying the Ffowcs Williams–Hawkings (FW-H) formulation. From the results, it can be concluded that the spectral characteristics of the sound pressure fluctuations are influences by the cavitation condition. The super cavitation condition generates significantly more noise than the developed cavitation condition. Moreover, the results demonstrate that a combination of LES and FW-H formulation is a promising tool for acoustical study of cavitating orifices.

Noise predictions of the advanced noise control fan model using lattice Boltzmann method and Ffowcs Williams–Hawkings analogy

The lattice Boltzmann method (LBM) is applied to simulate the complete three-dimensional transient flow and noise generated on the Advanced Noise Control Fan (ANCF) geometry. The ANCF is a model developed by NASA Glenn composed by a rotor–stator system enclosed by a duct. The experimental noise spectra provided by NASA at 30 microphones around the fan are used to validate the results obtained with the LBM. Overall, the predicted sound spectra pattern and the main tonal frequencies agree well with the noise measurements; in terms of tonal noise levels, the agreement varies depending on the frequency and microphone position. The noise at the 30 microphone positions is also computed by employing the porous Ffowcs Williams and Hawkings (FW–H) formulation with noise sources located on two integral surfaces placed at the ANCF openings. The good agreement obtained between the sound levels calculated with the FW–H formulation and those computed by the LBM show that the FW–H analogy may be applied in place of the LBM numerical simulation. In addition, the FW–H formulation is applied to compute the sound generation with sources located on different physical surfaces of the ANCF model such as the rotor, stator, hub, and nacelle, procedure known as noise source breakdown. A comparison of the FW–H results applied on different surfaces of the ANCF model with the noise computed by the LBM shows that most of the tonal noise levels observed at the far-field microphones (predicted by the LBM simulation) correspond to the noise sources generated on the stator vane surfaces. Such a study of the noise sources breakdown also evidences the interaction effect between the rotor and the stator, whose mechanism is the main contributor to the tonal noise generation content.

Noise radiated by low-Reynolds number flows past a hemisphere at Ma = 0.3

Flows past a hemisphere and their noise generation are investigated at the Reynolds numbers (Re) of 1000 and 5000. The Mach number is 0.3. The computational method of the flows is large eddy simulation. The noise is computed using the Ffowcs Williams and Hawkings Formulation 1C (F1C). An integral surface with an open end is defined for the F1C. The end surface is removed to reduce the numerical contamination that is introduced by vortices passing this surface. However, the contamination cannot be completely reduced since a discontinuity of the flow quantities still exists at the open surface boundary. This problem is solved using a surface correction method, in which a buffer zone is set up at the end of the integral surface. The transformation of flow structures due to Re is explored. Large coherent structures are observable at low Re, whereas they diminish at high Re. A large amount of small-scale turbulent vortices occur in the latter case. It is found that these characteristics of the flows have an important influence on the noise generation in regard to the noise spectra. In the flows studied in this work, the fluctuating pressure on the walls is a negligible noise contributor as compared with the wake.

On the Extrapolation of Acoustic Waves from Flow Simulations with Vortical out Flow

Feri Farassat was one of the pioneers of the use of the Ffowcs Williams & Hawkings formulation of Lighthill's acoustic analogy as a way to extrapolate radiated waves from simulations of unsteady flows. Current computational limits mean that volume source terms are often neglected, causing inaccurate acoustical predictions when entropy fluctuations or vorticity pass across the extrapolation surface. The derivation of the Ffowcs Williams–Hawkings equation is modified to allow the equivalent surface sources to be distributed over a transition layer of finite thickness rather than being confined to a single layer, in order to reduce the effect of vorticity exiting the computational domain.

Experimental and Numerical Investigation of Turbulence-Airfoil Noise Reduction Using Wavy Edges

A passive leading-edge treatment based on sinusoidal serrations aimed at reducing turbofan interaction noise has been recently studied in the framework of a European project (FLOCON). The turbulence-airfoil interaction mechanism is achieved using a turbulence grid located upstream of an isolated NACA airfoil tested in the Institute of Sound and Vibration Research anechoic open jet wind tunnel. The experimental setup with several airfoils designed and manufactured by ONERA is first presented with main acoustic results, highlighting the sound power level reductions obtained for all studied flow speeds (about 3–4 dB reduction) without altering the aerodynamic performances (as shown by available measurements and Reynolds-averaged Navier–Stokes calculations). The experimental investigations are supplemented by numerical predictions in order to assess the acoustic performances of the serrations. The method described in the second part of the paper is based on a computational aeroacoustics code solving the nonlinear Euler equations applied to the disturbances and is coupled to a Ffowcs-Williams and Hawkings formulation. Convection effects are achieved from a Reynolds-averaged Navier–Stokes solution or approximated by a fully uniform flow. The upstream turbulence is synthesized by means of a stochastic model and injected into the computational domain through an adapted boundary condition. It is first validated in two and three dimensions against academic flat-plate configurations by comparison with Amiet solutions (exact in such cases). Finally, three-dimensional computations are applied to FLOCON configurations. The present methodology is shown to reproduce the measured spectra and far-field directivities with a reasonably good precision. Radiated sound level attenuation due to the serrations versus frequency is fairly well assessed too.

Aeroacoustic Integrals Accelerated by Fast Multipole Method

The calculation of acoustic field solutions due to aeroacoustic sources is performed for a large number of observer locations. Sound is predicted by a hybrid method that uses direct calculation for near-field source computations and the Ffowcs Williams―Hawkings equation as the acoustic analogy formulation. The integrations of surface dipole and volume quadrupole source terms appearing in the Ffowcs Williams―Hawkings formulation are accelerated by a three-dimensional wideband multilevel adaptive fast multipole method. The three-dimensional wideband fast multipole method presented here applies a plane-wave expansion formulation with fast spherical filtering and interpolation and diagonal translation for calculations in the high-frequency regime and a partial-wave expansion formulation with rotational―coaxial translation in the low-frequency regime. The method is described for the solution of a three-dimensional Green's function that incorporates convective effects. The sound generated by the unsteady flow past a cylinder in the proximity of a NACA0012 airfoil is studied and the interaction of both geometries is analyzed for different cylinder positions. The developed numerical capability allows the analysis of each noise source individually. Therefore, the effects of dipoles and quadrupoles for each configuration are investigated. Results for acoustic field solutions obtained by the accelerated Ffowcs Williams―Hawkings formulation are up to 2 orders of magnitude faster than with the conventional computation of Ffowcs Williams―Hawkings equation.

Acoustic Analogy Formulations Accelerated by Fast Multipole Method for Two-Dimensional Aeroacoustic Problems

The calculation of acoustic field solutions due to aeroacoustic sources is performed for a large number of observer locations. Sound generation by vortex shedding is computed by a hybrid method and an accurate two-dimensional direct calculation, and the results are compared. The hybrid approach uses direct calculation for near-field source computations and the Ffowcs-Williams―Hawkings equation as the acoustic analogy formulation. The integrations of surface dipole and volume quadrupole source terms appearing in the Ffowcs-Williams―Hawkings formulation are accelerated by a wideband multilevel adaptive fast multipole method. The wideband multilevel adaptive fast multipole method presented here applies a plane-wave expansion formulation for calculations in the high-frequency regime and a partial-wave expansion formulation in the low-frequency regime. The method is described in detail for the solution of a two-dimensional Green's function that incorporates convective effects. The method presented in this work is applied to two-dimensional calculations. However, it can be easily extended to three-dimensional calculations of surface monopole and dipole source terms and volume quadrupole source terms. Results for acoustic field solutions obtained by the accelerated Ffowcs-Williams―Hawkings formulation are 2 orders of magnitude faster when compared with the direct computation of the Ffowcs-Williams―Hawkings equation.

Aerodynamic/Acoustic Analysis for Main Rotor and Tail Rotor of Helicopter

A simulation method for full helicopter configuration is constructed by combining an unsteady Euler code and an aero-acoustic code based on the Ffowcs-Williams and Hawkings formulation. The flow field and helicopter noise are calculated using a moving overlapped grid system, and the mutual effect of main rotor and tail rotor are studied for the helicopter in hover or forward flight. In the hovering flight calculation, the tip vortex of the tail rotor is dragged by the induced flow of the main rotor, and the detailed phenomena of the flow pattern are captured well. In the forward-flight calculation, noises from the main rotor and tail rotor are predicted to show tail rotor noise for both self noise and the interaction noise with the main-rotor wake. Comparison of noise magnitude shows the relative importance of tail rotor noise according to flight conditions.

Analysis and optimization of aerodynamic noise in a centrifugal compressor

The numerical methods for the performance analysis and the noise prediction of the centrifugal compressor impeller are developed, which are coupled with the optimization design methodology consisting of response surface method, statistical approach, and genetic algorithm. Navier–Stokes equations with the two-equation ( k – ω ) turbulence model are applied to calculate impeller aerodynamic characteristics, and Ffowcs Williams–Hawkings formulation and boundary element method are used to predict the impeller aerodynamic noise on the basis of impeller flow field results. The computational codes are verified through the comparison of measured data. The quadratic response surface model with D-optimal three-level factorial experimental design points is constructed to optimize the impeller geometry for the advanced centrifugal compressor, and it is shown that the quadratic model exhibits a reasonable fitting quality resulting in the impeller blade design with the high performance and the low far-field noise level. The influences of selected design variables and their mutual interactions as well as the effects of various objective functions and constraints on the impeller performance and the impeller noise are also examined as a result of the optimization process.

Development of hybrid method for the prediction of underwater propeller noise

Noise reduction and control is an important problem in the performance of underwater acoustic systems and in the habitability of the passenger ship for crew and passenger. Furthermore, sound generated by a propeller is critical in underwater detection and it is often related to the survivability of the vessel especially for military purpose. This paper presents a numerical study on the non-cavitating and blade sheet cavitation noises of the underwater propeller. A brief summary of numerical method with verification and results are presented. The noise is predicted using time-domain acoustic analogy. The flow field is analyzed with potential-based panel method, and then the time-dependent pressure and sheet cavity volume data are used as the input for Ffowcs Williams–Hawkings formulation to predict the far-field acoustics. Noise characteristics are presented according to noise sources and conditions. Through this study, the dominant noise source of the underwater propeller is analyzed, which will provide a basis for proper noise control strategies.

원심압축기의 공력소음 저감에 관한 설계연구 Part I : 성능해석 및 소음예측

The objective of this research is to suggest anoise prediction method for a centrifugal compressor. It is focused on the Blade Passing Frequency component which is regarded as the main part of the rotating impeller noise. Navier-Stokes solver is used to simulate the flow-field of the centrifugal compressor, and the time-dependent pressure data are calculated to perform the near-field noise prediction by using Ffowcs Williams - Hawkings formulation. Indirect Boundary Element Method is applied to consider the noise propagation effect. Pressure fluctuations of the inlet and the outlet in the centrifugal compressor impeller are presented and the sound pressure level prediction results are compared with the experimental data.

Modeling the aeroacoustics of axial fans from CFD calculations

The main source of aeroacoustic noise in axial fans is the distribution of the fluctuating, unsteady, aerodynamic forces on the blades. Numerical simulations were carried out with the CFD code (NUMECA), first with steady flow conditions to validate the aerolic performances (pressure drop as a function of flow rate) of the simulated six-bladed axial fans. Simulations were then made with unsteady flows to compute the fluctuating force distributions on the blades. The turbulence was modeled either with the Baldwin–Lomax model or with the K-epsilon model (extended wall function). The numerical results were satisfactory both in terms of numerical convergence and in terms of the physical characteristic of the forces acting on the blades. The numerical results were then coupled into an in-house aeroacoustics code that computes the farfield radiated noise spectrum and directivity, based on the Ffowcs-Williams Hawkings formulation, or alternatively, on the simpler Lowson model. Results compared favorably with data obtained under nonanechoic conditions, based upon ISO 5801 and ISO 5136 standards.

PREDICTION OF NON-CAVITATING UNDERWATER PROPELLER NOISE

Non-cavitation noise of underwater propeller is numerically investigated. The main purpose is to analyze non-cavitation noise in various operating conditions with different configurations. The noise is predicted using time-domain acoustic analogy and boundary element method. The flow field is analyzed with potential-based panel method, and then the time-dependent pressure data are used as the input for Ffowcs Williams–Hawkings formulation to predict the farfield acoustics. Boundary integral equation method is also considered to investigate the effect of ducted propeller. Sound deflection and scattering effect on the duct is considered with the BEM. The governing equations are based on the assumption that all acoustic pressure is linear. A scattering approach is applied in which the acoustic pressure field is split into the known incident component and the unknown scattered component. Noise prediction results are presented for single propeller and ducted propeller in non-uniform flow conditions similar to real situation. The investigation reveals that the effect of a duct on the acoustic performance propeller is small in the far field under non-cavitating situations since the noise directivities of single and ducted propellers are almost the same. Only the high order BPFs are influenced by the existence of the duct.

ヘリコプタのブレード/渦干渉騒音の解析

Two types of prediction tools for helicopter noise have been developed under the cooperative research between Advanced Technology Institute of Commuter Helicopter Ltd. (ATIC) and National Aerospace Laboratory (NAL) . One of them is a combined method of CAMRAD II, interpolation code for blade motion and wake geometry, aerodynamic code of 3D unsteady Euler solver, and aeroacoustic code based on Ffowcs Williams and Hawkings (FW-H) formulation. The other consists of CAMRAD II, 3D unsteady Euler solver using moving overlapped grid method, and FW-H code. The acoustic waveform of Blade-Vortex Interaction (BVI) noise predicted by the former tool is in good agreement with the experimental data of 1/7-scale model AH-1 Operational Loads Survey (OLS) rotor. This method is applied to investigate the effect of blade-tip shape on the intensity of BVI noise. As a result, it is shown that anhedral and swept-forward tip shapes effectively reduce the BVI noise of OLS rotor in a descent flight condition. The predicted Effective Perceived Noise Level (EPNL) of a helicopter is also compared with the experimental data obtained by ATIC and reasonable correlation is obtained. The latter tool successfully predicts the distinct spikes in the BVI wave-form of ATIC model rotor tested in German-Dutch Wind Tunnel (DNW) . In the comparison of measured and calculated carpet noise contours, reasonable agreement is obtained. The present tools are expected to be useful for the design of low-noise helicopters in the future.