Acoustics Module

By COMSOL, Inc.

Simulation Software for Analyzing Acoustics and Vibrations Pressure Acoustics Modeling pressure acoustics is the most common use of the Acoustics Module. It includes capabilities for modeling effects such as the scattering, diffraction, emission, radiation, and transmission of sound. Simulations run in the frequency domain employ the Helmholtz equation, whereas in the time domain, the classical scalar wave equation is used. In the frequency domain, both FEM and BEM are available, as well as hybrid FEM–BEM. In the time domain, time implicit (FEM) as well as time explicit (dG-FEM) formulations are available. There are many options to account for boundaries in acoustics models. For instance, a boundary condition can be added for a wall, or an impedance condition can be added for a porous layer. Ports can be used to excite or absorb acoustic waves at the inlet and outlet of waveguide structures using multimode expansion. This applies to ducts, periodic structures, or boundary couplings to lumped acoustic models. Sources like prescribed acceleration, velocity, displacement, or pressure can be applied on exterior or interior boundaries. Furthermore, radiation or Floquet periodic boundary conditions can be used to model open or periodic boundaries. The dG-FEM time-domain-based formulation can be run on a GPU for increased performance in, for example, wave-based room acoustic simulation scenarios. Time-domain simulations are further enhanced with dedicated tools for including general frequency-dependent impedance conditions and porous material data. The Acoustics Module can also be used to model pipe acoustics, computing the acoustic pressure and velocity in flexible pipe systems. Applications include HVAC systems, large piping systems, and musical instrument components such as organ pipes. Electroacoustics: Speakers and Microphones When modeling speakers and microphones, it is essential to consider acoustic–structure interaction, where the fluid pressure causes a fluid load on the solid domain, and the structural acceleration affects the fluid domain as a normal acceleration across the fluid–solid boundary. The Acoustics Module includes a variety of acoustic–structure interaction capabilities. For modeling transducers of all sorts, the capabilities included in the Acoustics Module are readily combined with functionality from the AC/DC Module, the MEMS Module, or the Structural Mechanics Module to create fully coupled multiphysics FEM models. This includes detailed modeling of magnets and voice coils in loudspeaker drivers or the electrostatic forces in condenser microphones and electrostatic speakers. In electro-vibroacoustic (i.e., electro-mechanical-acoustic or electroacoustic) transducer systems, it is easy to use lumped circuit models or two-port representations to simplify the electric and mechanical components. Both approaches are solved with a full two-way coupling. There are also features for extracting the lumped representations from full FEM models. In addition, the (linear) small signal behavior and nonlinear large signal dynamics can be modeled and analyzed. In miniature transducer systems, like mobile devices, condenser microphones, and hearing aid receivers, the important damping due to the thermoviscous boundary layer losses is included. There is also extensive functionality for modeling piezoelectric transducers of all kinds. Microacoustics For an accurate microacoustic analysis of acoustic propagation in geometries with small dimensions, losses associated with viscosity and thermal conduction need to be accounted for, particularly the losses in the viscous and thermal boundary layers. These effects are automatically included when running a thermoviscous simulation using the Acoustics Module, and are important for vibroacoustics modeling in miniature electroacoustic transducers like microphones, mobile devices, hearing aids, and MEMS devices. In particular, a dedicated acoustic slip-wall condition exists for modeling MEMS devices with very small dimensions or operating at low ambient pressures. For detailed transducer modeling, there are built-in multiphysics couplings between structures and thermoviscous acoustic domains. The software accounts for additional thermoviscous acoustics physics effects, including the full transition from adiabatic to isothermal thermodynamic behavior at very low frequencies. Local nonlinear effects, such as vortex shedding in microspeaker ports or perforates, can be captured in the time domain with the addition of the nonlinear governing terms. Elastic Waves and Ultrasound in Solids The propagation of sound in solids happens through small-amplitude elastic oscillations of the solid's shape and structure. These elastic waves are transmitted to surrounding fluids as ordinary sound waves. The Acoustics Module can be used to model the propagation of elastic waves in solids and porous materials, for single-physics or multiphysics applications, such as vibration control, nondestructive testing (NDT), or mechanical feedback. Application areas range from micromechanical devices to seismic wave propagation. Elastic wave propagation over large domains containing many wavelengths is solved using a higher-order dG-FEM time-explicit method, and is multiphysics enabled for couplings with fluids as well as piezoelectric materials. The full structural dynamics formulation accounts for the effects of shear waves as well as pressure waves. The coupled propagation of elastic and pressure waves in porous materials solving Biot's equations (the mixed p-u formulation) can be modeled both for isotropic and anisotropic porous materials. Ultrasound in Fluids Acoustic signals with frequencies that are too high to be audible to humans are classified as ultrasound. In fluids, this implies that ultrasonic waves have a short wavelength. Simulating ultrasound in fluids requires computing the transient propagation of acoustic waves in fluids over large distances. With the software, this simulation can be done in two ways: modeling wave propagation that includes a background flow or modeling the effects of high-power nonlinear acoustics. It is possible to solve for transient linear acoustics in a simulation that contains many wavelengths in a stationary background flow by modeling the convected wave equation. Applications include flowmeters and exhaust systems. For high-power nonlinear acoustics applications, the software is able to capture progressive wave propagation phenomena where the cumulative nonlinear effects surpass the local nonlinear effects. This includes modeling the formation and propagation of shocks. Applications include biomedical applications such as ultrasonic imaging and high-intensity focused ultrasound (HIFU). For both options, there are multiphysics capabilities available for fully coupling a model with elastic waves in structures and/or with piezoelectric materials. Aeroacoustics Using the Acoustics Module, computational aeroacoustics (CAA) simulations can efficiently be run with a decoupled two-step approach. First, the background mean flow is identified using either the CFD Module, flow imported in the CGNS format, or a user-defined flow profile; then, the acoustic propagation is solved for. For convected acoustics simulations, several finite element formulations are available, including linearized Navier–Stokes, linearized Euler, and linearized potential flow aeroacoustics simulations. There is also support for computing acoustic variations in pressure, density, velocity, and temperature in the presence of any stationary isothermal or nonisothermal background mean flow. The formulations readily account for convection, damping, reflection, and diffraction of acoustic waves by the flow. There is also functionality for fluid–structure interaction (FSI) analyses in the frequency domain with predefined couplings to elastic structures. Additionally, tools are available for modal source decomposition and for conducting modal transmission loss simulations in the context of duct acoustics, such as those found in turbofan engines. Flow-induced noise can be included in a pressure acoustics analysis by the addition of aeroacoustic flow sources using Lighthill's acoustic analogy with input from a transient large eddy simulation (LES), detached eddy simulation (DES), or a transient Reynolds-averaged Navier–Stokes (RANS) shear stress transport (SST) model with scale-adaptive simulations (SST-SAS) with the CFD model. Room Acoustics The Acoustics Module offers an array of tools for analyzing the acoustics of rooms, such as concert halls, recording studios, and office spaces. For instance, there are geometrical acoustics formulations like ray tracing, wave-based methods, and hybrid approaches. Methods can be used together to perform a broadband analysis of a listening space. The geometrical acoustics capabilities of the Acoustics Module can be used to analyze high-frequency systems where the acoustic wavelength is smaller than the characteristic geometric features. There are two methods available for this type of analysis: ray acoustics and acoustic diffusion. For ray acoustics, the trajectories, phase, and intensity of acoustic rays can be computed. Additionally, impulse responses, energy and level decay curves, and the classical objective room acoustic metrics can be calculated. An atmosphere attenuation material model is available to include the attenuation in air as a function of temperature, pressure, and relative humidity. Additionally, the module features integrated couplings that enable transitioning from wave-based simulation results to ray tracing, enabling the realistic modeling of sources, such as loudspeakers, based on both near-field and far-field computations. For acoustic diffusion, there is functionality for determining the sound pressure level distribution in coupled rooms and the reverberation times at different locations. The acoustics are modeled in a simplified way using a diffusion equation for the acoustic energy density. This method is well suited for quick analyses inside buildings and other large structures. Wave-based simulations can be performed efficiently using the Pressure Acoustics, Time Explicit interface, which can be run on multiple GPUs for increased performance. This physics interface is supported for all license types when using a single GPU, but it requires a floating network license when using multiple GPUs. Realistic models can be set up using dedicated tools to include general frequency-dependent impedance conditions of walls and boundaries. Modal and time-harmonic simulations of rooms can be performed using the Pressure Acoustics, Frequency Domain interface. Dedicated iterative solvers exist for modeling large problems. Underwater Acoustics Underwater acoustics covers a wide range of applications, including transducer design, sonar technology, and noise propagation and mitigation. The Acoustics Module offers a comprehensive set of tools for modeling phenomena that span multiple length scales, frequency ranges, and multiphysics effects. Full electroacoustic modeling capabilities as well as piezoelectric multiphysics capabilities are essential for modeling underwater transducers. Sound propagation over large distances can be modeled with the Ray Acoustics interface. The rays can propagate in graded media (depth-dependent material properties), which is necessary in underwater acoustics applications, and a dedicated ocean attenuation material model is available to capture attenuation when propagating over large distances and at high frequencies. Additionally, the module features integrated couplings that make it possible to transition from wave-based simulation results to ray tracing, enabling the realistic modeling of sources, such as a vibrating ship hull or underwater piling noise, based on both near-field and far-field computations. Moreover, use of the BEM or Kirchhoff–Helmholtz formulation in the software is essential for analyzing the acoustic signature, like target strength (TS), of underwater objects. Acoustic Streaming With the Acoustics Module, it is possible to simulate acoustic streaming that describes the physical process where an acoustic field can induce movement in a fluid. The module contains multiphysics capabilities for coupling acoustics and fluid flow in order to model acoustic streaming phenomena for pressure and thermoviscous acoustics. Acoustic streaming is a nonlinear phenomenon that occurs due to the nonlinearity of the Navier–Stokes equations. The Acoustics Module computes the forces, stresses, and boundary slip velocities that the acoustic field induces in a fluid to generate the streaming flow field. This phenomena is used widely in biotech and semiconductor processing and is important in microfluidics and lab-on-a-chip systems for applications such as particle handling, the mixing of fluids, and microfluidic pumps. Features and Functionality in the Acoustics Module Built-In User Interfaces The Acoustics Module provides built-in interfaces covering all of the application areas listed above. These interfaces define sets of domain equations, boundary conditions, initial conditions, predefined meshes, predefined studies with solver settings, and predefined plots and derived values. All of the modeling steps performed with these interfaces occur within the COMSOL Multiphysics® environment. Meshing and solver settings are handled automatically by the software, with options for manual editing. The COMSOL Multiphysics® workflow for building acoustics models with the acoustics interfaces is the same as for building a model with any other physics interface. In this way, it is easy to incorporate multiple physics into one acoustics model, and there are several multiphysics interfaces built into the Acoustics Module and accessible when combining with other add-on modules from the COMSOL product suite. Pressure Acoustics Interfaces For modeling pressure acoustics, there are multiple interfaces where the sound field is represented by a scalar pressure variable. The general-purpose interfaces, based on FEM, include the capability of solving in both the frequency and time domain. For transient models, nonlinear effects can be included and are based on the Westervelt equation. To efficiently solve large radiation and scattering problems, frequency-domain BEM is available that couples seamlessly with both the acoustic and structural finite-element-based interfaces. To efficiently solve large transient models, a specialized interface based on the discontinuous Galerkin finite element method and a time-explicit solver is available. This interface can be coupled to the corresponding time-explicit interface for elastic and piezoelectric waves. For pure acoustic simulations, the time-explicit solver can run in a single- or multi-GPU setup for improved performance. Using the interface for boundary mode analysis, allows for studying propagating modes in the cross sections of waveguides and ducts. High-Frequency Pressure Acoustics Two highly specialized interfaces are available for quick high-frequency acoustics analysis in the frequency domain. These interfaces are based on computing the Kirchhoff–Helmholtz integral and include one interface for scattering analysis and another interface for radiation analysis. High-frequency acoustics analysis can be used as a first step before moving on to a more computationally demanding analysis based on FEM or BEM. Elastic Waves Interfaces The Acoustics Module includes interfaces for modeling the propagation of linear elastic waves in solids, porous, and piezoelectric materials. These interfaces readily couple to fluid domains using a set of built-in multiphysics couplings. The Solid Mechanics interfaces have the capability of representing full elastodynamics and can be used for modeling elastic waves in solids in both the frequency and time domain. A Port boundary condition is specifically implemented to model and handle various propagating modes in elastic waveguide structures. The poroelastic interfaces are used for modeling poroelastic waves in porous materials. These waves result from the complex two-way interaction between acoustic pressure variations in the saturating fluid and the elastic deformation of the solid porous matrix. The poroelastic interfaces solve Biot’s equations in the frequency domain and include loss mechanisms from viscous losses (Biot), for modeling rocks and soils, as well as thermal and viscous losses (Biot–Allard), for sound-absorbing materials in air. Models are available for materials with isotropic or anisotropic porous and structural properties, which are relevant in, for example, fibrous porous materials. Two interfaces, based on a time-explicit discontinuous Galerkin formulation, can be used for modeling linear elastic waves in solid and piezoelectric domains. These interfaces can be coupled and are suited for efficiently modeling domains with several wavelengths. A dedicated Fracture boundary condition can be used to model two solids with nonideal bonding, for example, if the goal is to simulate the acoustic response of a defect or a delamination zone. In addition, these interfaces can be coupled with the time-explicit interfaces for pressure acoustics and the convected wave equation. Aeroacoustics Interfaces For modeling detailed convected acoustics, or flow-borne noise, a number of aeroacoustics interfaces are available in both the frequency and time domain. These interfaces are used for simulating one-way interaction of a background fluid flow with an acoustic field. There are different physics interfaces that solve the governing equations under various physical approximations. The flow can either be computed in COMSOL using the CFD Module, or it can be imported using the CGNS file format. The Linearized Navier-Stokes interfaces are used for solving for the acoustic variations in pressure, velocity, and temperature. This formulation is the most detailed; it accounts for boundary layer losses as well as damping of acoustic waves in turbulent flow regions. The Linearized Euler interfaces are used for computing the acoustic variations in density, velocity, and pressure in the presence of a stationary background mean flow that is well approximated by an ideal gas flow. Special boundary mode interfaces are available for computing propagating and nonpropagating modes in waveguides and ducts in the presence of a background flow. Modal source decomposition and modal transmission loss simulations in duct acoustics, such as turbofan engines, can be achieved using the dedicated port conditions available with the Linearized Potential Flow interface. Liners are modeled using either the classical Ingard–Myers condition or the Brambley impedance condition that accounts for a finite flow boundary layer. Ray Acoustics and Acoustic Diffusion Interfaces The Ray Acoustics interface is available for running simulations in the high-frequency limit, where the acoustic wavelength is much smaller than the characteristic geometric features. In addition, for quick analyses, the Acoustic Diffusion interface is available for solving the acoustic diffusion equation, also known as energy finite elements. The interfaces for ray acoustics and the acoustic diffusion equation are suited for modeling acoustics in rooms and concert halls. The Ray Acoustics interface can also be used in outdoor or underwater scenarios. The Ray Acoustics interface is used to compute the trajectories, phase, and intensity of acoustic rays. It includes the capabilities of impulse response analysis, showing the level decay curves and computed objective room acoustic metrics, such as early decay time (EDT), T 60 values, etc. In addition, a set of dedicated features makes it easy to define sources and receivers with spatial directivity. There are also built-in couplings between wave-based simulations of various sources (such as transducers) and ray tracing, which simplify setting up realistic sources based on both the near-field and far-field results. Flow-Induced Noise Combining the Acoustics Module and the CFD Module results in a hybrid aeroacoustic (CAA) method for modeling flow-induced noise. The computational method is based on the FEM discretization of Lighthill's acoustic analogy (wave equation). This formulation of the equations ensures that any solid (fixed or vibrating) boundaries are implicitly taken into account. Windowing is available to truncate the source domain in space. The functionality relies on coupling an SST-SAS, LES, or DES fluid flow simulation, using the CFD Module, to an aeroacoustic flow source for pressure acoustics, available in the Acoustics Module. Finite Element and Boundary Element Methods Most interfaces in the Acoustics Module are based on different versions of FEM. Interfaces based on BEM are available as well, and can be seamlessly combined with FEM-based interfaces. Hybrid FEM–BEM is very efficient for modeling acoustic–structure interaction involving vibrating structures. Applications for hybrid FEM–BEM include complex geometries of transducers (piezo or electromagnetic) where FEM is used to model the transducer (and its interior) and BEM is used to model the exterior acoustics. A BEM-based interface can be used to replace an FEM-based radiation condition or PML, as well as the FEM-based exterior-field calculations. Boundary Conditions and Sources for Pressure Acoustics There is a large variety of boundary conditions available for pressure acoustics, including hard walls and conditions for applying sources. There are radiation, symmetry, periodic, and port conditions for modeling open boundaries. Impedance conditions include models for different parts of the human ear and human skin, simple RCL circuit models, and more. In the time domain, frequency-dependent impedance conditions can be set up using dedicated tools based on a partial fraction approximation of the data. The options for modeling idealized sources include built-in options for monopole, dipole, and quadrupole point sources. Extensive functionality is also provided for modeling waveguides using multimode expansions in combination with port boundary conditions. Port boundary conditions are used to excite or absorb acoustic waves at the inlets and outlets of ducts. A lumped port condition allows a waveguide to be coupled to a lumped acoustic representation, such as a lumped-element circuit or a transfer-matrix model. Periodic port conditions enable efficient simulation of absorption, transmission, and scattering in periodic structures, including diffusers and acoustic metamaterials. Acoustic–Structure Interaction Interfaces The interfaces for acoustic–structure interaction apply to phenomena where the fluid pressure causes a load on the solid domain and the structural acceleration affects the fluid domain across the fluid–solid boundary. This is also known as vibroacoustics. The interfaces include the capability of solving in either the frequency or the time domain. The solids included in the simulations can be isotropic, anisotropic, porous, or piezoelectric. When the Acoustics Module is combined with the Structural Mechanics Module, the structural side of an acoustic–structure coupling can additionally include structural shells or membranes. The Acoustics Module can be combined with the Multibody Dynamics Module in order to include the effects of multiple moving rigid or flexible parts connected through various types of joints. For more advanced options, the Acoustics Module can be combined with the AC/DC Module or MEMS Module to analyze fluid–structure interaction involving electric or magnetic forces, such as in cases where solids have electrostrictive or magnetostrictive material properties. Thermoviscous Acoustics Interfaces In order to accurately model acoustics in geometries with small dimensions, it is necessary to include thermal conduction effects and viscous losses explicitly in the governing equations. Near walls, there are viscous and thermal boundary layers. In these layers, viscous losses due to shear and thermal conduction become important because of large gradients. The interfaces for thermoviscous acoustics include the capability to simultaneously model the effects of pressure, particle velocity, and acoustic temperature oscillations. Thermoviscous acoustics is, for example, used when modeling the response of small transducers like microphones and receivers, also known as microacoustics. A multiphysics coupling with thermoelasticity physics allows for detailed modeling of damping in MEMS applications, including detailed thin-film damping. This functionality is further enhanced with a dedicated acoustic slip-wall condition necessary for systems with very small dimensions or operating at low ambient pressures. The condition should be used for the slip-flow regime when the Knudsen number is in the range of 0.001