Reply to: ‘‘Comments on the influence of wind and temperature gradients on sound propagation calculated with the two‐way wave equation’’ [J. Acoust. Soc. Am. 91, 498–500 (1992)]

1992 ◽  
Vol 91 (1) ◽  
pp. 501-504 ◽  
Author(s):  
L. Nijs ◽  
C. P. A. Wapenaar
Keyword(s):  
Wave Equation ◽  
Sound Propagation ◽  
Temperature Gradients

Pressure and Shock Waves in Bubbly Liquids

2015 ◽  
Author(s):  
Shahid Mahmood ◽  
Yungpil Yoo ◽  
Ho-Young Kwak
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Dispersion Relation ◽  
Sound Propagation ◽  
Relaxation Oscillation ◽  
Bubbly Flow ◽  
Gas Bubbles ◽  
Bubbly Liquid ◽  
Bubbly Liquids ◽  
Pressure Profiles

It is well known that sound propagation in liquid media is strongly affected by the presence of gas bubbles that interact with sound and in turn affect the medium. An explicit form of a wave equation in a bubbly liquid medium was obtained in this study. Using the linearized wave equation and the Keller-Miksis equation for bubble wall motion, a dispersion relation for the linear pressure wave propagation in bubbly liquids was obtained. It was found that attenuation of the waves in bubbly liquid occurs due to the viscosity and the heat transfer from/to the bubble. In particular, at the lower frequency region, the thermal diffusion has a considerable affect on the frequency-dependent attenuation coefficients. The phase velocity and the attenuation coefficient obtained from the dispersion relation are in good agreement with the observed values in all sound frequency ranges from kHz to MHz. Shock wave propagation in bubbly mixtures was also considered with the solution of the wave equation, whose particular solution represents the interaction between bubbles. The calculated pressure profiles are in close agreement with those obtained in shock tube experiments for a uniform bubbly flow. Heat exchange between the gas bubbles and the liquid and the interaction between bubbles were found to be very important factor to affect the relaxation oscillation behind the the shock front.

Sound Propagation in a Sheared Flow Based on Fluctuating Total Enthalpy as Generalized Acoustic Variable

2012 ◽  
Author(s):  
César Legendre ◽  
Gregory Lielens ◽  
Jean-Pierre Coyette
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Wave Operator ◽  
Sound Propagation ◽  
Acoustic Analogy ◽  
Linearized Euler Equations ◽  
Total Enthalpy ◽  
Continuity Equations ◽  
Computational Performance ◽  
Flow Variables

Noise propagation mechanisms in presence of a rotational flow are currently receiving some attention from the aircraft industry. Different methods are used in order to compute the acoustic wave propagation in sheared flows in terms of pressure perturbations (e.g. Linearized Euler Equations (LEE), Lilley’s and Galbrun’s equations). Nevertheless, they have drawbacks in terms of computational performance (high number of DOFs per node, inadequacies of classical numerical schemes like standard FE). In contrast with other studies, in this work, the fluctuating total enthalpy is selected as the main variable in order to describe the acoustic field, which obeys to a convected wave equation obtained by linearization of momentum (Crocco’s form), energy and continuity equations and with coefficients depending on flow variables. The resulting 3D convected wave operator is an extension of the Möhring acoustic analogy which is able to predict the sound propagation through rotational flows in the subsonic regime and is well adapted to FE discretization. A 2D convected wave equation is generated from the previous operator. This is followed by a numerical solution based on FEM with two types of boundary conditions: non reflecting BC and incident plane wave excitation. The numerical results are used to estimate the reflection coefficient generated by the shear flow. The new acoustic wave operator is compared to well-known theories of flow acoustics (Pridmore-Brown wave operator) and shows promising results. Finally additional development steps are presented so further improvements on the new operator can be carried out.

scholarly journals Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

1996 ◽  
Vol 118 (4) ◽  
pp. 622-629 ◽  
Author(s):  
K. J. Baumeister ◽  
K. L. Kreider
Keyword(s):  
Wave Equation ◽  
Steady State ◽  
Finite Difference ◽  
Frequency Domain ◽  
Sound Propagation ◽  
Time Dependent ◽  
Frequency Domain Method ◽  
Impedance Boundary ◽  
Frequency Domain Methods ◽  
Time Marching

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Diffraction Tomography I: The Wave-Equation

1980 ◽  
Vol 2 (3) ◽  
pp. 213-222 ◽  
Author(s):  
R. K. Mueller
Keyword(s):  
Wave Equation ◽  
Test Object ◽  
General Equation ◽  
Viscoelastic Medium ◽  
Perturbation Methods ◽  
Sound Propagation ◽  
Diffraction Tomography ◽  
Inhomogeneous Wave ◽  
General Wave ◽  
Inhomogeneous Wave Equation

A general wave equation for sound propagation in a viscoelastic medium is obtained. From this general equation an approximate inhomogeneous wave equation is derived by perturbation methods. Born's and Rytov's approximations are considered. The equation is finally brought into a form which provides transformation properties under rotation of the test object required for diffraction tomography.

Investigation of Fan Casing Aerodynamic Noise at the Blade Passing Frequency

2009 ◽  
Author(s):  
Jian-Cheng Cai ◽  
Da-Tong Qi ◽  
Fu-An Lu
Keyword(s):  
Wave Equation ◽  
Flow Rate ◽  
Sound Propagation ◽  
Numerical Study ◽  
Pressure Fluctuations ◽  
Sound Field ◽  
Noise Model ◽  
Aerodynamic Noise ◽  
Centrifugal Fan ◽  
Blade Passing Frequency

From our previous studies of fan casing vibroacoustics, it was found that noise caused by casing vibration was fairly small compared to its aeroacoustic counterpart. In the present work, a numerical study on the aerodynamic tonal noise of a centrifugal fan casing was carried out. A 3-D numerical simulation of turbulent unsteady flow on the whole impeller-volute configuration was performed using computational fluid dynamics (CFD) technique in order to obtain the pressure fluctuations on the casing wall which serve as aeroacoustic dipole sources. Three different flow rates were simulated: the best efficiency point (BEP), 1.382×BEP and the maximal flow rate (2.104×BEP). Fast Fourier Transform (FFT) was applied to the time series of pressure fluctuations to extract the blade passing frequency (BPF) component constituting the source term of the wave equation. Boundary element method (BEM) was used to solve the inhomogeneous frequency-domain wave equation. The influence of the casing on the sound field was taken into account in simulating the noise radiation by taking it as a rigid body. Results showed that the presence of the casing could greatly affect sound propagation. With the increase of flow rate, the radiated sound power rose drastically. The tonal blade noise was also investigated using Lowson’s formulation of rotor noise model, and the results showed that it’s smaller than the tonal casing noise.

Sign in / Sign up

Export Citation Format

Share Document