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.

An analytic signal based accurate time-domain visco-acoustic wave equation from the Constant-Q theory

Geophysics ◽  
2021 ◽  
pp. 1-58
Author(s):  
Hongwei Liu ◽  
Yi Luo
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Time Domain ◽  
Seismic Waves ◽  
Heterogeneous Media ◽  
Relaxation Property ◽  
Analytic Signal ◽  
Acoustic Wave Equation ◽  
Real Component ◽  
Frequency Components

We present a concise time-domain wave equation to accurately simulate wave propagation in visco-acoustic media. The central idea behind this work is to dismiss the negative frequency components from a time-domain signal by converting the signal to its analytic format. The negative frequency components of any analytic signal are always zero, meaning we can construct the visco-acoustic wave equation to honor the relaxation property of the media for positive frequencies only. The newly proposed complex-valued wave equation (CWE) represents the wavefield with its analytic signal, whose real part is the desired physical wavefield, while the imaginary part is the Hilbert transform of the real component. Specifically, this CWE is accurate for both weak and strong attenuating media in terms of both dissipation and dispersion and the attenuation is precisely linear with respect to the frequencies. Besides, the CWE is easy and flexible to model dispersion-only, dissipation-only or dispersion-plus-dissipation seismic waves. We have verified these CWEs by comparing the results with analytical solutions, and achieved nearly perfect matching. Except for the homogeneous Q media, we have also extended the CWEs to heterogeneous media. The results of the CWEs for heterogeneous Q media are consistent with those computed from the nonstationary operator based Fourier Integral method and from the Standard Linear Solid (SLS) equations.

scholarly journals Modelling damped acoustic waves by a dissipation-preserving conformal symplectic method

2017 ◽  
Vol 473 (2199) ◽  
pp. 20160798 ◽  
Author(s):  
Wenjun Cai ◽  
Huai Zhang ◽  
Yushun Wang
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Acoustic Waves ◽  
Conservation Law ◽  
Heterogeneous Media ◽  
Numerical Dispersion ◽  
Discrete Version ◽  
Symplectic Method ◽  
Ode System ◽  
Strang Splitting

We propose a novel stable and efficient dissipation-preserving method for acoustic wave propagations in attenuating media with both correct phase and amplitude. Through introducing the conformal multi-symplectic structure, the intrinsic dissipation law and the conformal symplectic conservation law are revealed for the damped acoustic wave equation. The proposed algorithm is exactly designed to preserve a discrete version of the conformal symplectic conservation law. More specifically, two subsystems in conjunction with the original damped wave equation are derived. One is actually the conservative Hamiltonian wave equation and the other is a dissipative linear ordinary differential equation (ODE) system. Standard symplectic method is devoted to the conservative system, whereas the analytical solution is obtained for the ODE system. An explicit conformal symplectic scheme is constructed by concatenating these two parts of solutions by the Strang splitting technique. Stability analysis and convergence tests are given thereafter. A benchmark model in homogeneous media is presented to demonstrate the effectiveness and advantage of our method in suppressing numerical dispersion and preserving the energy dissipation. Further numerical tests show that our proposed method can efficiently capture the dissipation in heterogeneous media.

scholarly journals Analysis of Propagation and Distribution Characteristics of Leakage Acoustic Waves in Water Supply Pipelines

Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5450
Author(s):  
Yunfei Li ◽  
Yang Zhou ◽  
Ming Fu ◽  
Fan Zhou ◽  
Zhaozhao Chi ◽  
...  
Keyword(s):  
Acoustic Wave ◽  
Water Supply ◽  
Acoustic Waves ◽  
Simulation Analysis ◽  
Acoustic Signals ◽  
Detection Methods ◽  
Acoustic Analogy ◽  
Acoustic Wave Propagation ◽  
Source Characteristics ◽  
Water Supply Pipeline

Leakage detection methods based on the analysis of leakage acoustic signals provide an effective technical approach for detecting small leaks in water supply pipelines. From a technical perspective, the study of the propagation characteristics of acoustic waves generated by the leakage in the water supply pipeline is necessary for detecting the leak location on the basis of acoustic signals. In this study, a 3D transient leakage acoustic wave propagation equation was derived by combining the principles of fluid dynamics and Lighthill acoustic analogy theory. The propagation of the leakage-induced noise in water supply pipeline was modelled theoretically. We simulated the propagation of a leakage acoustic wave under different conditions for different target scenarios encountered in actual pipeline inspections. Specifically, we analysed the effect of different factors, such as the pipe size and acoustic source characteristics, on acoustic propagation. Finally, the simulated experiments were practically performed using a self-designed simulated water supply pipeline and self-developed spherical water supply pipeline detector to validate the simulation analysis. The results of this study provide a theoretical guidance and basis for the analysis of characteristics of leakage acoustic wave signals and the recognition of leakage conditions in water supply pipelines.

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