Thermoviscous Effects Research Articles

Effect of Hilbert Fractal Acoustic Metamaterials on Ventilation Noise Control

Abstract Ventilation noise control devices often involve a trade-off between their size and ventilating performance, which limits the ability to reduce low-frequency sound in high-ventilation conditions. To address this challenge, the present study explores the use of Hilbert fractal-based design in ventilated metamaterials for improved acoustic performance. The sound transmission loss (STL) of these metamaterials is compared to that of a simple expansion chamber, which serves as the base case. Various parameters, including Hilbert order (O), channel width (K), ventilated space (l), unit cell thickness (H), and the number of unit cells (N) are investigated. Initially, the transfer matrix method evaluates STL without considering thermoviscous effects, which are later incorporated in numerical simulations and impedance tube experiments. The parametric study reveals that increasing the Hilbert curve order decreases the fundamental frequency, while a higher K value increases it. Additionally, more unit cells enhance STL but reduce its broadband nature. Through the finite element method, band diagrams and eigenmodes of Hilbert and base configurations indicate that increased Hilbert orders result in more bands and correspondence between transmission loss spectra and band gaps. The study also identifies dipole resonance modes in the Hilbert structure, which induce a negative effective bulk modulus that contributes to STL. Real-time performance testing in a twin reverberation chamber demonstrates that the Hilbert structure achieves a 5-dB improvement in STL compared to the base configuration across the 700- to 1400-Hz range. These findings are essential for achieving broadband low-frequency noise reduction while allowing airflow.

Shape optimized acoustic metagratings for anomalous refraction under strong thermoviscous effects

The recent development of microacoustic metagratings opens up promising possibilities for manipulating acoustic wavefronts passively, particularly in applications such as flat acoustic lenses and ultra-high frequency ultrasound imaging. The emergence of two-photon polymerization has made it feasible to precisely manufacture microscopic structures, as required when metagratings are scaled to MHz frequencies in airborne ultrasound. Nevertheless, the downsizing process presents another hurdle as the increased thermoviscous effects result in substantial losses that must be considered during the design phase. In this study, we propose two designs for microacoustic metagratings that refract a normally incident wave towards –35 ° at 2 MHz, consisting of single-body and two-body meta-atoms. The designs are created by employing shape optimization techniques that incorporate the linearized Navier–Stokes equations in every iteration starting from a neutral geometry. This ensures that the evolution of geometric key features responsible for anomalous refraction fully accounts for thermoviscous effects, as would be the case during evolution in nature where the full set of physics is always active. Subsequently, we experimentally evaluate the effectiveness of these metagratings by employing a capacitive micromachined ultrasonic transducer as the sound source and an optical microphone as the detector, covering a frequency range from 1.8 to 2.2 MHz. Our findings confirm the single-body geometry reported in the literature and show an alternative geometry for two-body design, showcasing the successful utilization of two-photon polymerization for manufacturing microscopic acoustic metamaterials.

Numerical study of thermo-viscous effects in acoustic materials using linearized Navier-Stokes equations

Acoustic materials, characterized by small-scale structures, require a detailed understanding of dissipation effects within the viscous and thermal boundary layers where most of the dissipation takes place. Despite the prevalent assumption of lossless or isentropic conditions in many applications, a comprehensive study of regions where thermal and viscous losses occur is crucial, particularly in scenarios where wall-induced losses are significant. Bridging this gap, the study aims to investigate these losses in various structures to guide the development of innovative acoustic materials. To achieve this objective, the Linearized Navier-Stokes Equations (LNSE) solver from the finite element software COMSOL is employed to determine the absorption coefficients and to identify predominant regions of thermal and viscous losses. The model is validated using experimental and published data. The study effectively reveals specific regions where these losses significantly dominate, highlighting their critical influence on acoustic material performance. Although the structures are simplified to 2D models to balance physical details with computational feasibility, the ability to identify dominant loss regions marks a significant contribution to the field and paves the way to refine the design of acoustic materials.

An equivalent source method for acoustic problems with thermoviscous effects.

This paper presents an equivalent source method (ESM) for analyzing sound propagation in small-scale acoustic structures with thermoviscous effects. The formulations that describe the thermal, viscous, and acoustic modes for thermoviscous acoustic problems are introduced. The concept of ESM is then applied to solve these formulations, resulting in an efficient numerical computation and implementation procedure. Based on two different strategies, the obtained ESM formulations are coupled at the boundary using the isothermal, non-slip, and null-divergence conditions. The coupling based on the first strategy is efficient for solving thermoviscous acoustic problems with few matrices required. However, this procedure faces the evaluation of the tangential derivatives of the boundary velocity. Coupling the ESM formulations directly for each component of the total particle velocity at the boundary has no such problem, which leads to the second strategy. However, it entails a larger memory usage compared to the former. Additionally, the coupled finite element method (FEM)-ESM formulations based on the above strategies are developed for acoustic-structural interaction. The validity of the presented ESM formulations is demonstrated through benchmark examples, and that of the coupled FEM-ESM formulation is illustrated by the numerical analysis of a simplified microphone.

Interactive demo of Openwind, an online tool for simulating the acoustic response of wind instruments

Openwind is a Python library (free and open source) dedicated to the simulation of wind instruments. It allows the calculation of the acoustic response in the frequency domain (impedance or admittance) or in the time domain (impulse response), from the geometry of the instrument (main bore, side holes, and valves). The wave propagation model can take into account thermo-viscous effects, non-uniform temperature, multiple radiation conditions through boundary conditions, etc. It is also possible to simulate the sound of brass, reed, and flute instruments. Discretization is done in space with 1D spectral finite elements and in time with energy consistent finite differences. The sensitivity of the instrument to design parameters can be calculated and visualized. A graphical interface, freely available online (https://demo-openwind.inria.fr), gives the possibility to perform frequency domain simulations without coding. It is mainly used by students (in science or musicology) and instrument makers (hobby, student, or professional). With this interface, it is easy to observe the effect of a geometric modification on the acoustic response (resonance frequency, mode shape, etc.) or a change in temperature or radiation conditions. The numerical aspects (mesh, order, etc.) are set automatically and can be further refined using the Python library.

Investigation on unsteady fluid flow around an oscillating sphere-A numerical and analytical approach

This article presents the Investigation on unsteady fluid flow around an oscillating sphere-A Numerical and Analytical approach. The analytical expressions for angular velocity and temperature of the fluid around an oscillating sphere have been obtained in form of Bessel functions with suitable assumed boundary conditions. The numerical results in terms of angular velocity, temperature and pressure distribution for various values of the material parameters have been obtained using R-K method of 6th order with shooting methods with the help of MATHEMATICA ND solver. The influence of thermo-viscous flow parameters on angular velocity, temperature, pressure and drag on the boundary have been presented in form of tables and graphs. It may be noticed that the thermo-viscous effects are more predominant in the flow region around the boundary of the oscillating sphere. The R-K method with shooting method is the most powerful and elegant method to solve the governing equations related to the fluid dynamics problems. This method gives the accurate and valid results of highly complex coupled governing equations. The analytical results obtained are validated with this method in the present problem. The results obtained by this method gives more accurate, stable and converging to the analytical results. The numerical solutions of governing equations of present work have been obtained are compared with the existing analytical results and are found to be in excellent agreement. The present theoretical work will be hope fully for the better understanding of researchers and scientists and also it is useful in chemical and nuclear industries.

Analytical method for studying acoustic fields radiated by general spherical sound sources in thermoviscous fluids.

The study of acoustic radiation from spherical sound sources plays a crucial role in understanding the thermoviscous effects in practical acoustic problems. However, finding a general solution of acoustic radiation from spherical sound sources in thermoviscous fluids remains a formidable challenge. To advance this issue, an analytical method is developed in this paper to calculate the acoustic field radiated by spherical sound sources with the isothermal boundary condition and arbitrary velocity boundary condition. The developed method is utilized to present the solutions of the acoustic field generated by an oscillating sphere and a general spherical sound source, and the accuracy and validity of these solutions are verified through analytical and numerical methods.

Experimental Investigation of Thermoacoustics and High-Frequency Combustion Dynamics with Band Stop Characteristics in a Pressurized Combustor

In combustor systems, thermoacoustic instabilities may occur and must be avoided for reliable operation. An acoustic network model can be used to predict the eigenfrequencies of the instabilities and the growth rate by incorporating the combustion dynamics with a flame transfer function (FTF). The FTF defines the interconnection between burner aerodynamics and the rate of combustion. In the current study, the method to measure the FTF in a pressurized combustor is explored. A siren unit, mounted in the fuel line, induced a fuel flow excitation of variable amplitude and high maximum frequency. This was performed here for pressurized conditions at 1.5 bar and 3 bar and at a thermal power of 125 kW and 250 kW. In addition to the experimental investigation, a 1-D acoustic network model approach is used. In the model, thermoviscous damping effects and reflection coefficients are incorporated. The model results compare well with experimental data, indicating that the proposed method to determine the FTF is reliable. In the approach, a combination of an FTF with a band stop approach and a network modeling approach was applied. The method provides a good match between experimentally observed behavior and an analytical approach and can be used for instability analysis.

Superwavelength self-healing of spoof surface sonic Airy-Talbot waves

Self-imaging phenomena for nonperiodic waves along a parabolic trajectory encompass both the Talbot effect and the accelerating Airy beams. Beyond the ability to guide waves along a bent trajectory, the self-imaging component offers invaluable advantages to lensless imaging comprising periodic repetition of planar field distributions. In order to circumvent thermoviscous and diffraction effects, we structure subwavelength resonators in an acoustically impenetrable surface supporting spoof surface acoustic waves (SSAWs) to provide highly confined Airy-Talbot effect, extending Talbot distances along the propagation path and compressing subwavelength lobes in the perpendicular direction. From a linear array of loudspeakers, we judiciously control the amplitude and phase of the SSAWs above the structured surface and quantitatively evaluate the self-healing performance of the Airy-Talbot effect by demonstrating how the distinctive scattering patterns remain largely unaffected against superwavelength obstacles. Furthermore, we introduce a new mechanism utilizing subwavelength Airy beam as a coding/decoding degree of freedom for acoustic communication with high information density comprising robust transport of encoded signals.

The acoustic streaming effects and transmission mechanisms of a micro-cavity acoustic black hole structure with an abrupt cross-section

This paper investigates the acoustic streaming effects (ASEs) and mechanisms behind the transmittance of sound in a metallic micro-cavity acoustic black hole (ABH) structure with an abrupt cross-section and examines the sound field flow characteristics inside the micro-cavity ABH under the sound excitation, such as the velocity, acceleration and pressure fields. And the sound transmission mechanisms are characterized by the ASEs which can be obtained by solving Navier–Stokes equations. The numerical results show that the sharp increase in the velocity and acceleration at the ABH tip position is the main reason for the focusing of the sound energy. And the dramatic increase in the tip cross-section reduces the acoustic streaming velocity, which is the main reason for the attenuation of the sound energy. Additionally, the thermoviscous effect of the acoustic boundary layer can also dissipate the low-frequency sound energy. The sound insulation experiment shows that the proposed micro-cavity ABH structure has a sound transmission loss (STL) of over 15[Formula: see text]dB in the low-frequency regime. This research reveals the mechanisms of the ASE’s work on the sound transmission properties of the micro-cavity ABH and provides new insight into low-frequency sound wave suppression. The ABH structure proposed in this paper has excellent strength, bearing capacity and long lifecycle, so it can be applied in the construction industry through its integrated design of structure and performance.

A Two-Way Coupled Model of Visco-Thermo-Acoustic Effects in Photoacoustic Trace Gas Sensors

We introduce the first two-way coupled model for the thermo-viscous damping of a mechanical structure (such as quartz tuning fork) that is forced by the weak acoustic and thermal waves generated when a laser source periodically interacts with a trace gas. The model is based on a Helmholtz system of thermo-visco-acoustic equations in the fluid, together with a system of equations for the temperature and the displacement of the structure. These two subsystems are coupled across the fluid-structure interface via several conditions. With this model, the user specifies the geometry of the structure and the viscous and thermal parameters of the fluid, and the model outputs an effective damping parameter and a signal strength that is proportional to the concentration of the trace gas. This new model is a significant improvement over existing one-way coupled models in which damping effects are incorporated via a priori laboratory measurements. Analytical solutions derived for an annular structure show reasonable agreement between the one-way and two-way coupled models at higher ambient pressures. However, at low ambient pressure the one-way coupled model does not adequately capture thermo-viscous effects.

Thermo-viscous influence on the mechanical seal performance in a reactor coolant pump (RCP)

The mechanical seal performance in reactor coolant pump (RCP) is of great importance for the efficient and safe operation of primary loop in nuclear power plant. The sealing medium filling inside the seal encounters strong thermal gradient. In this paper, thermo-viscous effect on sealing characteristics with two typical mechanical seal faces, namely the tapered-end-face and wave-tilt-dam, is numerically studied, by introducing the temperature-viscosity equation according to the real physical properties of the sealing medium. Performance of mechanical seal with two different temperature-viscosity equations are compared. In addition, the influence of thermo-viscous effect on cavitation is also analyzed. It is revealed that the temperature-viscosity variation significantly influences the internal flow field, temperature field, two-phase distribution, and the opening force as well. With low base film thickness, the temperature difference will reduce 58% as considering the thermal effect on viscosity, and the difference in leakage may be as high as 43%. Also, the prediction of cavitation under small film thickness indicates that the thermo-viscous effect decreases the cavitating area. This work contributes to the mechanical seal design and performance prediction by assessing the thermal influences on viscosity of seal medium, and meanwhile revealing the effect on the possible cavitation event.

The Role of Thermoviscous and Thermocapillary Effects in the Cooling and Gravity-Driven Draining of Molten Free Liquid Films

We theoretically considered two-dimensional flow in a vertically aligned thick molten liquid film to investigate the competition between cooling and gravity-driven draining, which is relevant in the formation of metallic foams. Molten liquid in films cools as it drains, losing its heat to the surrounding colder air and substrate. We extended our previous model to include non-isothermal effects, resulting in coupled non-linear evolution equations for the film’s thickness, extensional flow speed and temperature. The coupling between the flow and cooling effect was via a constitutive relationship for temperature-dependent viscosity and surface tension. This model was parameterized by the heat transfer coefficients at the film–air free surface and film–substrate interface, the Péclet number, the viscosity–temperature coupling parameter and the slope of the linear surface tension–temperature relationship. A systematic exploration of the parameter space revealed that at low Péclet numbers, increasing the heat transfer coefficient and gradually reducing the viscosity with temperature was conducive to cooling and could slow down the draining and thinning of the film. The effect of increasing the slope of the surface tension–temperature relationship on the draining and thinning of the film was observed to be more effective at lower Péclet numbers, where surface tension gradients in the lamella region opposed the gravity-driven flow. At higher Péclet numbers, though, the surface tension gradients tended to enhance the draining flow in the lamella region, resulting in the dramatic thinning of the film in the later stages.

Theory and modeling of nonperturbative effects in thermoviscous acoustofluidics.

A theoretical model of thermal boundary layers and acoustic heating in microscale acoustofluidic devices is presented. Based on it, an iterative numerical model is developed that enables numerical simulation of nonlinear thermoviscous effects due to acoustic heating and thermal advection. Effective boundary conditions are derived and used to enable simulations in three dimensions. The theory shows how friction in the viscous boundary layers causes local heating of the acoustofluidic device. The resulting temperature field spawns thermoacoustic bulk streaming that dominates the traditional boundary-driven Rayleigh streaming at relatively high acoustic energy densities. The model enables simulations of microscale acoustofluidics with high acoustic energy densities and streaming velocities in a range beyond the reach of perturbation theory, and is relevant for design and fabrication of high-throughput acoustofluidic devices.

Transition from Boundary-Driven to Bulk-Driven Acoustic Streaming Due to Nonlinear Thermoviscous Effects at High Acoustic Energy Densities.

Acoustic streaming at high acoustic energy densities E_{ac} is studied in a microfluidic channel. It is demonstrated theoretically, numerically, and experimentally with good agreement that frictional heating can alter the streaming pattern qualitatively at high E_{ac} above 400 J/m^{3}. The study shows how as a function of increasing E_{ac} at fixed frequency, the traditional boundary-driven four streaming rolls created at a half-wave standing-wave resonance transition into two large streaming rolls. This nonlinear transition occurs because friction heats up the fluid resulting in a temperature gradient, which spawns an acoustic body force in the bulk that drives thermoacoustic streaming.

An implementation of a finite difference time domain method for second-order nonlinear acoustic equations

The framework of the numerical scheme presented in this talk is that of the finite-difference time-domain (FDTD) method published by Sparrow and Raspet [J. Acoust. Soc. Am. 90, 1991]. The method is fourth-order in space and second-order in time when propagating in homogeneous media. Our implementation resides in a Cartesian coordinate system and is meant to be used in inhomogeneous media. In the neighborhood of inhomogeneities the FDTD method is reduced to second-order in space. Of interest to our applications is the simulation of infinite domains, which is achieved using the perfectly matched layer (PML). The particular PML implementation we consider is one that was designed to absorb linear acoustic waves neglecting thermoviscous effects. In this talk, we will give an overview of our FDTD implementation and show one- and two-dimensional examples to illustrate performance in heterogeneous media that include changes in material properties and scattering objects.

Instabilities of intrinsic thermoacoustic modes in a thermoacoustic waveguide with anechoic terminations

A recent study [H. Hao and F. Semperlotti, Phys. Rev. B 104, 104303 (2021)] investigated the dynamic behavior of an infinite one-dimensional (1D) thermoacoustic waveguide (TAWG) and illustrated its ability to sustain nonreciprocal and near zero-index sound propagation behavior; these properties can be very beneficial in the design of acoustic devices, including acoustic diodes, amplifiers, and cloaks. Nevertheless, it is critical to realize that when this concept is implemented in a finite-length waveguide, dynamic instabilities may occur and either drastically reduce or completely hinder the ability of the TAWG to control and manipulate sound. In this work, we uncover and investigate the occurrence of either evanescent or intrinsic thermoacoustic (ITA) modes in a 1D TAWG with anechoic terminations. The stability analysis clearly distinguishes these two types of evanescent modes and highlights their different origin rooted in either acoustic or thermoviscous effects. Numerical results reveal that ITA modes in anechoic-terminated TAWG are strictly connected to the acoustic-driven evanescent modes, and evolve towards unstable modes as the TA coupling strength is increased. This study may have important implications for the practical design of novel acoustic manipulating devices enabled by TA coupling elements. The conclusions drawn in this study may also shed lights on the effective suppression of instabilities in TAWGs.

Aeroacoustic simulation of transient vortex dynamics subjected to high-intensity acoustic waves

The transient vortex dynamics within a microsecond-level acoustic cycle were numerically investigated when an orifice–cavity structure, which is a unit component of an acoustic liner, was subjected to high-intensity acoustic waves. Three-dimensional vortex-acoustic coupling fields were determined by solving the compressible linearized Navier–Stokes equations (LNSEs) and considering the nonlinear thermoviscous effect around the micro-orifice. First, the LNSE results were well validated by literature results in terms of the sound absorption coefficient, reflection coefficient, acoustic resistance, acoustic reactance, acoustic impedance, and the spatial features of acoustically induced vortex structures. Subsequent cross correlation analysis demonstrated that attenuated standing-waves were generated inside the back cavity when the incident acoustic wave propagated across the orifice. Aeroacoustic energy analysis revealed that the periodic production of vortex kinetic energy contributed more to the sound attenuation in the orifice structure than the viscous dissipation effect. Then, the acoustically induced vortex dynamics were characterized in terms of a phase-dependent evolution process, and the formation, convection, and dissipation regions were classified. Finally, dynamic mode decomposition analyses were conducted to extract the dominant vortex structures by determining their frequency spectra. The dominant modes contained large-scale vortices around the orifice, while the high-order modes contained a series of small-scale vortices toward the upstream incident tube and downstream cavity.

Aerodynamic sound generation in thermoviscous fluids: A canonical problem revisited

Although the Lighthill–Curle acoustic analogy theory is formally exact, the presence of linear source terms related to viscous stresses and non-isentropic density changes makes it unsuitable for studying aerodynamic sound generation in low Reynolds number thermoviscous flows. Here we use an extension of the Ffowcs Williams and Hawkings formulation, with thermoviscous effects explicitly included, to find an analytical solution to the canonical problem of sound radiation from a circular cylinder immersed in a viscous heat-conducting fluid and rotating sinusoidally about its axis. Existing published solutions are compared and an earlier null result is explained. The new analysis reveals the dominant source of sound at low Mach numbers to be unsteady viscous dissipation rather than Reynolds-stress quadrupoles, unless the fluid parameter B=αc2/cp is zero.

Thermoacoustic effects on the propagation of non-planar sound in a circular duct

This paper examines thermoacoustic effects on the propagation of non-planar sound in a circular duct subjected to an axial temperature gradient. Of particular concern are thermoviscous diffusive effects, which are taken into account by the boundary-layer approximation in a framework of the linear theory. For disturbances expanded into Fourier and Fourier–Bessel series in the azimuthal and radial directions, respectively, the pressure in each mode is described by a one-dimensional, dispersive wave equation, if non-diffusive propagation is assumed. When the diffusive effects are included, each radial mode is coupled to the other radial modes through the boundary layer. Focusing on a single azimuthal and radial mode only, the dispersion relation for the propagation along an infinite duct of a uniform gas is first derived. Effects of the temperature gradient are then examined by solving boundary-value problems for a duct of finite length in four typical cases. Assuming that the wall temperature increases exponentially along the duct, eigenfrequencies and decay rates in the lowest axial mode are obtained as well as axial distributions of the sound pressure and the axial velocity in the duct. The frequency and the decay rate increase as the temperature ratio at both ends becomes higher. It is found from the acoustic energy equation that the dispersion combined with the diffusion acts to reduce the damping and that the temperature gradient makes little contribution to the production of the energy. However, it is unveiled that the non-uniformity in temperature yields thermoacoustic sound confinement in the vicinity of the cold end.