On the boundary conditions for acoustic waves at a solid–solid or fluid–solid interface

1994 ◽  
Vol 95 (1) ◽  
pp. 40-44 ◽  
Author(s):  
Bruno Bianco ◽  
Andrea Cambiaso ◽  
Tullio Tommasi
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Solid Interface

scholarly journals Atmospheric radiation boundary conditions for the Helmholtz equation

2018 ◽  
Vol 52 (3) ◽  
pp. 945-964 ◽  
Author(s):  
Hélène Barucq ◽  
Juliette Chabassier ◽  
Marc Duruflé ◽  
Laurent Gizon ◽  
Michael Leguèbe
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Acoustic Waves ◽  
Numerical Study ◽  
Outgoing Wave ◽  
Atmospheric Radiation ◽  
Angle Of Incidence ◽  
Radiation Boundary Conditions ◽  
Radiation Boundary ◽  
Dirichlet To Neumann Map

This work offers some contributions to the numerical study of acoustic waves propagating in the Sun and its atmosphere. The main goal is to provide boundary conditions for outgoing waves in the solar atmosphere where it is assumed that the sound speed is constant and the density decays exponentially with radius. Outgoing waves are governed by a Dirichlet-to-Neumann map which is obtained from the factorization of the Helmholtz equation expressed in spherical coordinates. For the purpose of extending the outgoing wave equation to axisymmetric or 3D cases, different approximations are implemented by using the frequency and/or the angle of incidence as parameters of interest. This results in boundary conditions called atmospheric radiation boundary conditions (ARBC) which are tested in ideal and realistic configurations. These ARBCs deliver accurate results and reduce the computational burden by a factor of two in helioseismology applications.

Experimental Investigation of Thermoacoustic Instabilities for a Model Combustor With Varying Fuel Components

2011 ◽  
Author(s):  
X. Y. Zhang ◽  
H. Zhang ◽  
M. Zhu
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Thermal Power ◽  
Supply System ◽  
Dynamic Processes ◽  
Combustion Instabilities ◽  
Thermoacoustic Instabilities ◽  
Instability Modes ◽  
Syngas Combustion ◽  
Fuel Components

In this study, a combustion facility was constructed that includes a flexible fuel supply system to produce synthesis gas using a maximum of three components. The rig with lean premixed burner is able to operate at up to 5 bars. The length of the inlet plenum and the outlet boundary conditions of the combustion chamber are adjustable. Experiments were carried out under a broad range of conditions, with variations in fuel components including hydrogen, methane and carbon monoxide, equivalence ratios, thermal power and boundary conditions. The dynamic processes of self-excited combustion instabilities with variable fuel components were measured. The mechanisms of coupling between the system acoustic waves and unsteady heat release were investigated. The results show that instability modes and flame characteristics were significantly different with variations in fuel components. In addition, the results are expected to provide useful information for the design and operation of stable syngas combustion systems.

Mimetic finite-difference coupled-domain solver for anisotropic media

Geophysics ◽  
2021 ◽  
Vol 86 (1) ◽  
pp. T45-T59
Author(s):  
Harpreet Sethi ◽  
Jeffrey Shragge ◽  
Ilya Tsvankin
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Model Building ◽  
Fluid Layer ◽  
Anisotropic Media ◽  
Horizontal Displacement ◽  
Solid Boundary ◽  
Ocean Bottom ◽  
Solid Interface ◽  
And Inversion

Accurately modeling full-wavefield solutions at and near the seafloor is challenging for conventional single-domain elastic finite-difference (FD) methods. Because they treat the fluid layer as a solid with zero shear-wave velocity, the energy partitioning for body and surface waves at the seafloor is distorted. This results in incorrect fluid/solid boundary conditions, which has significant implications for imaging and inversion applications that use amplitude information for model building. To address these issues, here we use mimetic FD (MFD) operators to develop and test a numerical approach for accurately implementing the boundary conditions at a fluid/solid interface. Instead of employing a single “global” model domain, we partition the full grid into two subdomains that represent the acoustic and elastic (possibly anisotropic) media. A novel split-node approach based on one-sided MFD operators is introduced to distribute grid points at the fluid/solid interface and satisfy the wave equation and the boundary conditions. Numerical examples demonstrate that such MFD operators achieve stable implementation of the boundary conditions with the same (fourth) order of spatial accuracy as that inside the split-domain interiors. We compare the wavefields produced by the MFD scheme with those from a more computationally expensive spectral-element method to validate our algorithm. The modeling results help analyze the events associated with the fluid/solid (seafloor) interface and provide valuable insights into the horizontal displacement or velocity components (e.g., recorded in ocean-bottom-node data sets). The developed MFD approach can be efficiently used in elastic anisotropic imaging and inversion applications involving ocean-bottom seismic data.

scholarly journals Standing Waves in One-Dimensional Resonator Containing an Ideal Isothermal Gas Affected by the Constant Mass Force

2017 ◽  
Vol 42 (2) ◽  
pp. 263-271
Author(s):  
Anna Perelomova
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Standing Waves ◽  
Ideal Gas ◽  
Excess Pressure ◽  
Mass Force ◽  
Constant Mass ◽  
Total Field ◽  
One Dimensional ◽  
Isothermal Gas

Abstract The study is devoted to standing acoustic waves in one-dimensional planar resonator which containing an ideal gas. A gas is affected by the constant mass force. Two types of physically justified boundary conditions are considered: zero velocity or zero excess pressure at both boundaries. The variety of nodal and antinodal points is determined. The conclusion is that the nodes of pressure and antinodes of velocity do not longer coincide, as well as antinodes of pressure and nodes of velocity. The entropy mode may contribute to the total field in a resonator. It is no longer isobaric, in contrast to the case when the external force is absent. Examples of perturbations inherent to the entropy mode in the volume of a resonator are discussed.

scholarly journals The Effects of Piezoelectricity on the Interaction of Waves in Fluid-Loaded Poroelastic Half-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Vishakha Gupta ◽  
Anil K. Vashishth
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Constitutive Equations ◽  
Vertical Component ◽  
Amplitude Ratios ◽  
Governing Equations ◽  
Solid Interface ◽  
Interaction Of Waves ◽  
Electric Potentials

The effects of piezoelectricity on the interaction of waves at fluid-poroelastic interface are studied. The constitutive equations and governing equations are formulated and their solution is obtained. The boundary conditions are described at fluid-solid interface. The effects of various parameters on the angle of refraction, amplitude ratios, displacements, electric potentials, and vertical component of slowness are studied numerically for a particular model. The results obtained are in agreement with the general laws of physics.

scholarly journals The scattering of sound waves by a vortex: numerical simulations and analytical solutions

1994 ◽  
Vol 260 ◽  
pp. 271-298 ◽  
Author(s):  
Tim Colonius ◽  
Sanjiva K. Lele ◽  
Parviz Moin
Keyword(s):  
Boundary Conditions ◽  
Analytical Solutions ◽  
Acoustic Waves ◽  
Stokes Equations ◽  
Spatial Differentiation ◽  
Navier Stokes ◽  
Sound Waves ◽  
Navier Stokes Equations ◽  
Refraction Effect ◽  
Approximate Analytical Solutions

The scattering of plane sound waves by a vortex is investigated by solving the compressible Navier–-Stokes equations numerically, and analytically with asymptotic expansions. Numerical errors associated with discretization and boundary conditions are made small by using high-order-accurate spatial differentiation and time marching schemes along with accurate non-reflecting boundary conditions. The accuracy of computations of flow fields with acoustic waves of amplitude five orders of magnitude smaller than the hydrodynamic fluctuations is directly verified. The properties of the scattered field are examined in detail. The results reveal inadequacies in previous vortex scattering theories when the circulation of the vortex is non-zero and refraction by the slowly decaying vortex flow field is important. Approximate analytical solutions that account for the refraction effect are developed and found to be in good agreement with the computations and experiments.

Three Dimensional Thermoacoustic Oscillation in a Premix Combustor

2001 ◽  
Author(s):  
S. Akamatsu ◽  
A. P. Dowling
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Linear Equations ◽  
Three Dimensional ◽  
Total System ◽  
Mean Flow ◽  
Modal Coupling ◽  
Rate Of Heat Release ◽  
Flow Through ◽  
Combustion Processes

A theory is developed to describe high frequency three-dimensional thermoacoustic waves in a simplified geometry representing a typical premix combustor. The theory considers linear modes of frequency ω and circumferential mode number m i.e. proportional to eiωt+imθ. The radial and axial dependence is determined for a cylindrical combustor. Simple geometries are investigated systematically to analyze the effect of different inlet boundary conditions to the combustion chamber on the frequency of oscillation and on the susceptibility to instability, both near and away from the cut-off frequencies. The model includes a one-dimensional mean flow, radial mode coupling and idealized combustion processes, which are added in stages to build up an understanding of the complicated acoustics of the premix combustor geometry. It is demonstrated that the flow through the premix ducts provides a frequency-dependent boundary condition at combustor inlet and causes modal coupling. Generalized linear equations of conservation of mass, momentum and energy, together with boundary conditions, are solved to identify the eigenfrequencies, ω, of the total system. Then Real ω determines the frequency of the oscillation, while Imaginary ω indicates the growth rate of the disturbance. It is found that strong resonant peaks in the pressure waves exist close to the cut-off condition for acoustic waves and that the relationship between the unsteady rate of heat release and the flow significantly influences the instability of oscillation.

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