Ffowcs Williams And Hawkings Equation Research Articles

Investigation on the comparison analysis of the characteristics between the Forward and Backward curved fan system and the Improvement on flow/noise performances by optimizing blade angles in clothes dryers

Recently, the needs for clothes dryers are rapidly increasing due to the consumer's interest in convenience for time reducing and cleanliness like dust. The drying performance of these clothes dryers is greatly affected by the fan system. The fan system affects the flow performance and is related to drying time of clothes dryer. Also, the aerodynamic noise generated by the fan system in the dryer has a great influence on the overall noise of the machine. Because of these reasons, many manufacturers are conducting researches on improving the performance of the fan system in the dryers. The purpose of this study is to improve the flow & noise performance of a fan system in clothes dryer using CFD (Computational Fluid Dynamics) and acoustic analogy based on FW-H (Ffowcs-Williams and Hawkings) equation. The numerical analysis on the flow characteristics of the fan system is conducted by ANSYS FLUENT. The 3-dimesnsional incompressible RANS (Reynolds Averaged Navier-Stokes) equation is adopted as the governing equation and the SST k-ω model is used for turbulent model. The integral surface for FW-H equation to analyze the acoustic field is composed of the closed surfaces including the scroll. This study investigates more suitable fan for a dryer system by comparing the flow characteristics of a backward curved fan, already adopted to a dryer, with a new forward curved fan which has same diameter. To improve the flow performance, the blade angles have been tuned by the design optimization which is the response surface method for geometric parameters. As a result, the dryer with the forward curved fan, which had optimal blade angles, reduced the rotating speed with the same volume flow rate as the original fan. And finally it showed the much reduced noise level compared to the original fan when the dryer ran.

Marine propeller noise propagation within bounded domains

In the present work, we develop a new methodology to investigate the propagation of acoustic noise originating from a naval propeller, in a bounded marine environment. The propagation in a realistic environment is achieved by coupling the Ffowcs-Williams and Hawkings (FW-H) equation with the acoustic wave equation, overcoming some intrinsic limitations of the FW-H equation. First, the FW-H equation applied to the hydrodynamics field obtained from Large Eddy Simulation, accurately characterizes the propeller source in the acoustic near-field. Then, the propagation in the acoustic far-field is evaluated in an arbitrary domain by solving the acoustic wave equation. After validating the new proposed methodology, we investigate the propagation of the linear part of the noise generated by a naval propeller within a canal. The results show complex interaction between the noise source and the environment: the decay rate of the acoustic energy is strictly related to the distance of the source from the boundaries of the canal; local maxima and minima of the acoustic energy are observed resulting from the superposition of direct and reflected waves; the water–air interface introduces a peculiar asymmetry of the acoustic field associated with the interaction between the acoustic waves.

Computationally efficient, frequency-domain quadrupole corrections for the Ffowcs Williams and Hawkings equation

In the present article, frequency-domain formulations of quadrupole corrections are derived in a computationally efficient form for the Ffowcs Williams and Hawkings (FW-H) equation with permeable control surfaces. Quadrupole corrections effectively reduce spurious noise associated with hydrodynamic fluctuations passing across integral surfaces, originally derived for Formulation 1A of Farassat in the time domain. When a corresponding frequency-domain formulation is sought, however, difficulty arises as its Green’s function is written in a convective form and different from that of Formulation 1A. First, the mathematical framework of the convective FW-H equation is shown to be equivalent to Formulation 1A by applying a simple Galilean transformation for rectilinear motion. Then, a frequency-domain formulation is derived via a Fourier transform applied directly to the time-domain quadrupole correction forms. The results of the derived formulation agree precisely with the time-domain solutions, in the verification study of vortex convection, as well as non-uniform entropy convection, in which spurious noise can be effectively removed by the present quadrupole correction integrals.

Scaling properties of the Ffowcs-Williams and Hawkings equation for complex acoustic source close to a free surface

We perform a scaling analysis of the terms composing the Ffowcs-Williams and Hawkings (FWH) equation, which rules the propagation of noise generated by a rigid body in motion. Our analysis extends the seminal work of Lighthill (Proc. R. Soc. Lond.A, vol. 211, 1952, pp. 564–587) and the dimensional analysis of classical sources (monopole, dipole and quadrupole) considering all the FWH integral terms. Scaling properties are analysed in light of perfect/imperfect similarity when laboratory-scale data are used for full-scale predictions. As a test case we consider a hydrodynamic example, namely a laboratory-scale ship propeller. The data, obtained numerically in a previous study, were post-processed according to the scaling analysis presented herein. We properly scale the speed of sound to obtain perfect similarity and quantify the error with respect to the imperfect scaling. Imperfect similarity introduces errors in the acoustic response related both to the linear terms and to the nonlinear terms, the latter of great importance when the wake is characterized by robust and organized vorticity. Successively, we analyse the effect of a free surface, often present in hydrodynamic applications. We apply the method of images to the FWH equation. The free surface may generate a frequency-dependent constructive/destructive interference. The analysis of an archetypal acoustic field (monopole) provides robust explanation of these interference effects. Finally, we find that imperfect similarity and the absence of a free surface may introduce errors when model-scale data are used to obtain the full-scale acoustic pressure. The error is small for microphones placed in the near field and becomes relevant in the far field because of the nonlinear terms.

Analysis of spurious sound due to vortical flow through permeable surfaces

Aeroacoustic wave equations proposed by Lighthill and developed by Ffowcs-Williams and Hawkings (FW-H) have been widely used to analyze sound generated from turbulence and its interaction with solid surfaces, such as jet noise and airfoil noise. In engineering applications, the wave equation is usually solved by integral formulations derived by Farassat, where quadrupole volume sources outside permeable integral surfaces are usually ignored in subsonic flow. However, several existing studies have shown that the acoustic prediction result will be greatly contaminated by spurious sources due to vortical components crossing permeable integral surfaces. This paper analytically studies spurious source terms on permeable integral surfaces, and concludes that the convective FW-H equation is always exact to predict the aerodynamic noise because the material derivative and divergence operators in the monopole and dipole sources enable to automatically filter spurious sources located on the permeable integral surfaces. However, the formulations of Farassat fail to filter the spurious sound owing to replacing the spatial derivative by the temporal derivative. A three-dimensional convective frequency-domain version of the Kirchhoff integral formulation is developed to resolve this issue, because it does not use velocity fluctuations as the input variable. Numerical test cases are performed to validate the analytical result and the developed formulation.

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.

A two-dimensional solution of the FW-H equation for rectilinear motion of sources

In this paper, a subsonic solution of the two-dimensional Ffowcs Williams and Hawkings (FW-H) equation is presented for calculation of noise generated by sources moving with constant velocity in a medium at rest or in a moving medium. The solution is represented in the frequency domain and is valid for observers located far from the noise sources. In order to verify the validity of the derived formula, three test cases are considered, namely a monopole, a dipole, and a quadrupole source in a medium at rest or in motion. The calculated results well coincide with the analytical solutions, validating the applicability of the formula to rectilinear subsonic motion problems.

Coarse-resolution numerical prediction of small wind turbine noise with validation against field measurements

The noise emission and the power output from a small horizontal axis wind turbine is investigated using coarse-resolution computational fluid dynamics (CFD) simulations conducted with the commercial software STAR-CCM+®. The steady Reynolds-averaged Navier-Stokes (RANS) and transient delayed detached-eddy simulation (DDES) methodologies were used for the prediction of the flow field around the wind turbine. It is found that the DDES method with the Spalart-Allmaras turbulence model provides predictions of the wind turbine power that are in good conformance with available field measurements. The aeroacoustic calculations were performed using both the STAR-CCM+® acoustic model and an in-house code. The in-house code implemented both the permeable and impermeable formulations of the Ffowcs Williams and Hawkings (FW-H) equation. The predicted A-weighted sound pressure level (SPL) spectra, as well as the apparent SPL, obtained from the permeable formulation of the FW-H equation agree well with the wind turbine acoustic field measurements. It is found that the presence of the tower slightly decreases the wind turbine power output at all simulated incident wind speeds. It is also found that the presence of the tower leads to modifications of the SPL spectra at frequencies between about 300 and 1500 Hz.

Aeroacoustic Computation of Ducted-Fan Broadband Noise Using LES Data

Following large efforts to reduce tone noise during the last decades in modern high-bypass ratio turbofans, fan broadband noise reduction has become now an industrial priority. A hybrid computational method providing source-to-far-field predictions of broadband noise due to rotor-stator interaction is presented. The acoustic model is based on the loading term of the FWH (Ffowcs Williams and Hawkings) equation with a modal Green's function valid for an infinite annular duct, and a Kirchhoff approximation for the free-field radiation. The aerodynamic sources on the airfoils required by the model are expected to be directly issued from a LES (Large Eddy Simulation) computation. The method is applied to a simplified configuration tested in a laboratory rig. The first part of the study is concerned with the assessment of in- duct acoustic field. Usual assumptions about coherence and energy distribution between the acoustic modes are analyzed. PSD (Power Spectrum Density) are calculated through several ways. The second part is focused on the ability to generate an equivalent PSD by means of equivalent source distributions. The purpose is to validate a practical way for coupling LES with Computational Aero-Acoustics Euler solver, in order to include realistic geometry and mean flow effects.