Thermoviscous Effects Research Articles

Contribution to the definition of a simple focusing test case and ONERA results for the two test cases of the sonic boom focusing predictions special session

For usual cruise flight conditions, the prediction of the sonic boom on ground caused by an aircraft flying supersonically can be predicted numerically by ray tracing codes according to the geometrical acoustics hypotheses. Such codes account for the non-linear and dissipative (thermoviscous and molecular relaxation) effects that occur during the propagation from flight level down to the ground by solving dissipative Burgers' equations along the rays, accounting for the evolution of the ray tube area. Such an approach is not applicable to predict the pressure waveform in the neighbourhood of a caustics that can be generated by the cusp of the focussing pressure wave generated under specific unsteady flight conditions of the aircraft. For such focussing conditions, the pressure waveform can be modelled by the Tricomi equations. The BANGV code has been used to predict the pressure waveforms in focussing conditions of the sonic boom focusing predictions special session of the 182nd ASA meeting. The results obtained for the two test-cases will be presented in this paper to be compared to other participants' results and contribute to the validation of numerical simulation methods of focussing boom.

On the acoustic effects of sonic crystals in heat exchanger arrangements

Heat exchangers can be found in a large number of technical systems and installations. They are usually operated in combination with other machines, such as axial fans, in order to remove or supply heat to a system. The heat exchanger can influence the existing flow field and thus lead to increased noise emission from fans located downstream of the heat exchanger. This can be observed, for example, in air conditioning units in which axial fans operate in combination with heat exchangers. Even though this mechanism is known, it is not yet understood how the heat exchanger affects the sound propagation of the sound produced by the downstream machine. For example, the heat exchanger may lead to a change in directional characteristics or specific frequencies may be attenuated. In order to better understand the interaction of the heat exchanger with the sound field, sound power measurements were carried out on various heat exchangers and the sound propagation was simulated numerically. It was shown that the sound attenuation due to the interaction with the periodic tube array is detectable in heat exchangers and that this leads to a sound reduction at the Bragg frequency. Based on its filling factor, the heat exchanger can reduce the sound propagation in certain frequency bands by up to 10 dB if the geometrirical properties are selected suitably. The simulations of a single unit cell confirm in very good agreement with the experimental results. This allows the conclusion that the approach presented in this paper is a cost-effective way to model acoustic effects of heat exchangers. Furthermore, sound attenuation effects by the heat exchanger were caused by thermoviscous effects on the cooling fins and dimensions of the heat exchanger housing.

Role of suction pressure in the stability of a gravity-driven thermoviscous liquid film flow down the interior surface of a cylinder.

This study aims to analyze the stability of a gravity-driven thin film flow in the heated/cooled interior surface of a vertical hollow cylinder. The model development involves simplifying the flow and energy equations using the usual thin-film approximation, where the average film thickness is considered to be much smaller than the radius of cylinder. A dispersion relation is then derived to study the temporal stability of the system in order to quantify the effect of various non-dimensional parameters present in the model, such as the thermoviscous number, Marangoni number, Biot number, and Bond number. Another non-dimensional parameter is introduced by considering an opposing suction pressure in the annulus region. The thermocapillary stress and the thermoviscous effect are shown to strongly affect the temporal stability of the flow. It is shown that although the suction pressure affects the velocity profile of the flow, it does not affect the temporal stability results. The suction pressure is then shown to have some effect on the spatiotemporal stability. Critical condition is presented for the transition between absolutely and convectively unstable systems, and parameter regimes are presented to quantify the effect of the above-mentioned parameters.

The impact of temperature and humidity variations on the resulting frequencies of metal flue pipes in pipe-organs: An analytical model

Pipe organs are probably the biggest existing instruments. Apart from positive organs that wheels can move, pipe organs remain in the same place where they have been installed and become parts of the buildings architecture that host them. Churches are the main venues for these instruments due to their important role in the liturgy. Unfortunately, these buildings, usually characterized by huge volumes, are hardly air-conditioned except during events, and temperature and humidity variations affect the pipes' sound. An analytical model has been developed for metal flue pipes to analyse the entity of the emitted-frequency variations. Temperature and humidity affect the dimensions of the pipe as well as air density and sound’s velocity. The model involved plane wave mode and air-jet analysis dynamics depending on the temperature and humidity of the flowed air. Thermo-viscous effect of air flowing into the pipe is also considered. Results have been compared to the spectral analysis of a metal flue pipe of an existing pipe organ located inside a church. Conclusions gather the differences between the results and explain the open opportunities for this research.

Underwater stealth metasurfaces composed of split-orifice–conduit hybrid resonators

The development of sound-absorbing materials for noise reduction in daily life has been a prolonged issue that also applies to a recognized need for submarine anechoic tiles to stay independent from SONAR (SOund NAvigation Ranging). Here, we present an underwater stealth metasurface that uses split-orifice–conduit (SOC) hybrid resonators to significantly reduce its acoustic reflectance. A theoretical analysis of SOC elements provides an approach to quantifying acoustic characteristics using the transfer matrix method in a single metasurface. The findings confirm that we can tune the absorption with respect to a resonating frequency by adjusting geometrical parameters. Utilizing a hybrid mechanism that enables easy access to coupled resonances, we obtain broadband absorption spectra even in the presence of a covariant sound speed profile in the deep sea and a thermoviscous effect on unit cells of the metasurface. Such a metasurface will provide a further step toward developing feasible underwater stealth technologies for submarines and remains to be experimentally demonstrated.

Full waveform inversion for bore reconstruction of woodwind-like instruments

The internal geometry of a wind instrument can be estimated from acoustic measurements. For woodwind instruments, this involves characterizing the inner shape (bore) but also the side holes (dimensions and location). In this study, the geometric parameters are recovered by a gradient-based optimization process, which minimizes the deviation between simulated and measured linear acoustic responses of the resonator for several fingerings through an observable function. The acoustic fields are computed by solving a linear system resulting from the 1D spectral finite elements spatial discretization of the wave propagation equations (including thermo-viscous effects, radiation and side holes). The “full waveform inversion” (FWI) technique exploits the fact that the gradient of the cost function can be computed by solving the same linear system as that of the direct problem but with a different source term. The gradient is computed with better accuracy and less additional cost than with finite-difference. The dependence of the cost function on the choice of the observed quantity, the frequency range and the fingerings used, is first analyzed. Then, the FWI is used to reconstruct, from measured impedances, an elementary instrument with 14 design variables. The results, obtained in about 1 minute on a laptop, are in excellent agreement with the direct geometric measurements.

Full-wave numerical simulation of nonlinear dissipative acoustic standing waves in wind instruments

A finite volume full-wave method is used to simulate nonlinear dissipative acoustic propagation in ducts with a circular cross-section. Thermoviscous dissipative effects, due to bulk viscosity and shear viscosity in the boundary layer adjacent to the duct walls, are also considered. The propagation is assumed to be axisymmetric, and two different geometries are considered: a straight cylindrical tube, and a cylindrical tube joined smoothly to a slowly-flaring bell. Of special interest is the study of the onset of standing waves in the nonlinear regime. The full-wave numerical scheme is particularly well-adapted for this purpose, as it is not necessary to impose boundary conditions at the open end of the duct. A simplified model of excitation is adopted, where the lips are replaced by a spring–mass system which behaves like a pressure valve with a single degree of freedom. The full system behaves as expected, with a feedback cycle established between the pressure valve and the air column. The simulation is validated successfully in the linear regime using a theoretical solution. It is shown that increasing the stiffness of the lips leads to discrete jumps in playing frequency, which is behaviour typical of brass instruments. In the nonlinear regime, shock formation is observed for sufficiently high amplitudes of oscillation, and the radiation of these shock waves by the open end of the ducts can be visualised in the time-domain, along with edge-diffraction effects. The formation and evolution of standing waves in the nonlinear regime, where the effect of these shocks is very noticeable, is also examined.

Asymptotic modeling of Helmholtz resonators including thermoviscous effects

We systematically employ the method of matched asymptotic expansions to model Helmholtz resonators, with thermoviscous effects incorporated starting from first principles and with the lumped parameters characterizing the neck and cavity geometries precisely defined and provided explicitly for a wide range of geometries. With an eye towards modeling acoustic metasurfaces, we consider resonators embedded in a rigid surface, each resonator consisting of an arbitrarily shaped cavity connected to the external half-space by a small cylindrical neck. The bulk of the analysis is devoted to the problem where a single resonator is subjected to a normally incident plane wave; the model is then extended using “Foldy’s method” to the case of multiple resonators subjected to an arbitrary incident field. As an illustration, we derive critical-coupling conditions for optimal and perfect absorption by a single resonator and a model metasurface, respectively.

Measurement and analysis of sound absorption by a composite foam

A composite foam consisting of open-cell metallic foam embedded with polyurethane foam is fabricated and evaluated for sound absorbing properties. The best performing composite foam increased the sound absorption by a factor of 6 (from .1 to .6) in the low frequency test range and by a factor of 2 (from .2 to .4) broadband compared to the original metallic foam. A lumped element model is used to predict and elucidate the absorption mechanisms for the composite, as well as for pure metallic foam and pure polyurethane foam. The model gives insight into the physical mechanisms that control acoustic absorption, including thermo-viscous effects at pore interfaces, structural damping effects due to foam elasticity, and coupling effects due to the interaction of air, metal, and polyurethane in the composite. Additionally, a simplified two parameter model was used to elucidate acoustic absorption trends for composite foams. The developed composite foams are advantageous for engineering and architectural applications where combined high stiffness and sound absorption are required.

A Transfer Matrix Model of the IEC 60318-4 Ear Simulator: Application to the Simulation of Earplug Insertion Loss

The IEC 60318-4 ear simulator is used to measure the insertion loss (IL) of earplugs in the ear canal of an acoustical test fixture (ATF) and is designed to represent an average acoustic impedance (in a reference plane) of the human ear. The ear simulator is usually modeled using a lumped parameter model (LPM) which has frequency limitations and inadequately accounts for the thermo-viscous effects in the simulator. The simulator numerical models that can better deal with the thermo-viscous phenomena often lack essential geometric details. Most related studies also suffer from the lack of experimental validation of the models. Therefore, a transfer matrix (TM) model of the IEC 60318-4 simulator is proposed based on a direct assessment of its geometric dimensions. Such a model is of particular interest for designing artificial ear simulators. The variability in the simulator impedance due to the geometric uncertainties is quantified using the Monte Carlo method. The TM model is validated using i) a finite element (FE) model of the simulator and ii) impedance measurements with a sound intensity probe. It is found to better describe the simulator impedance above 3 kHz compared to the LPM. The TM model is then coupled to a FE model of an occluded ATF ear canal to simulate the IL of an earplug in the frequency range [100 Hz, 10 kHz]. In the model, the simulator is considered as a cylindrical cavity terminated by an equivalent tympanic impedance which is determined from the TM model to simulate the sound pressure measured at the real microphone position (not at the reference plane) in the ATF ear canal. The simulated IL is validated against i) that obtained with a complete FE model of the corresponding system and ii) measurements using an ATF. The TM model is shown to better agree with the simulator FE model than the LPM above 6 kHz regarding the earplug IL simulated using this method.

Ultrathin Acoustic Metasurface Holograms with Arbitrary Phase Control

Holograms show great potential in optical or acoustical waves applications due to their capability to reconstruct images. In this paper, we propose a novel scheme to realize acoustic holograms based on an ultrathin metasurface with arbitrary phase control ability. Compared with the conventional imaging method, e.g., concave mirror, which has a bulky size and limited imaging effects, the acoustic metasurface comprises a single layer of Helmholtz-like elements that can largely reduce the complexity of production. With this ultrathin reflective metasurface, acoustic holograms are constructed through a subtle structure design for single and multiple focal imaging, while the potential thermoviscous effects are minimized. We further demonstrate that the metasurface has the capability of arbitrary phase control in a certain frequency range, where the reflected phase dispersion is linear. Our proposed ultrathin metasurface holograms would be very useful in numerous applications, such as acoustic sensing, medical imaging, and so on.

The sound of a pulsating sphere in a rarefied gas: continuum breakdown at short length and time scales

The pressure field of a pulsating sphere is a canonical problem in classical acoustics, used to illustrate the acoustic efficiency of a monopole source at continuum conditions. We consider the counterpart vibroacoustic and thermoacoustic problems in a rarefied gas, to investigate the effect of continuum breakdown on monopole radiation. Focusing on small-amplitude normal-to-boundary mechanical and heat-flux excitations, the perturbation field is analysed in the entire range of gas rarefaction and input frequencies. Numerical calculations are carried out via the direct simulation Monte Carlo method, and are used to validate analytical predictions in the free-molecular and near-continuum regimes. In the latter, the regularized thirteen moments model (R13) is applied, to capture the system response at states where the Navier–Stokes–Fourier (NSF) description breaks down. Comparing with the continuum inviscid solution, the results quantitate the dampening effect of gas rarefaction on source point-wise strength and acoustic power. At near-continuum conditions, the acoustic field is composed of exponentially decaying ‘compression’, ‘thermal’ and ‘Knudsen-layer’ modes, reflecting thermoviscous and higher-order rarefaction effects. With reducing rarefaction, the contributions of the latter two modes vanish, and the former degenerates into the ideal-flow inverse-to-distance decaying wave. Stronger attenuation is obtained with increasing rarefaction, where boundary sphericity results in a ‘geometric reduction’ of the molecular layer affected by the source. Notably, while the R13 model at low frequencies appears valid up to moderate gas rarefaction rates, both the NSF and R13 descriptions break down at common low Knudsen numbers at higher frequencies. Further study should therefore be carried out to extend the applicability of moment models to unsteady flows with short time scales.

Stability analysis of a gravity-driven thermoviscous liquid film flowing over a heated flat substrate.

Two-dimensional steady-state solutions and their stability analysis are presented for a gravity-driven thin film of a thermoviscous liquid. The governing equations and boundary conditions are simplified using the lubrication approximation. The analytically obtained film thickness evolution equation consists of various dimensionless parameters such as the Marangoni number, Biot number and thermoviscosity number. The viscosity of the liquid is assumed as an exponential function of temperature. The viscosity decreases within the liquid film as the temperature increases. Due to localized heating interfacial temperature gradients generate surface tension gradient which results into thermocapillary or Marangoni stress. The Marangoni stress opposes the fluid flow at the leading edge of heater leading to an increase in the film thickness locally. This locally thick structure becomes unstable beyond critical values of the parameters that leads to formation of rivulets in the transverse direction. Using the linear stability analysis it is found that the Marangoni stress and the thermoviscous effect have a destabilizing effect on the thin-film flow. At much higher values of the thermoviscosity number another mode of instability appears which is known as thermocapillary instability which leads to oscillating film profiles. For streamwise perturbations, the destabilizing effect of the thermoviscosity number for localized and uniform heating remains consistent.

Fabrication and measurement of a hybrid resonant gradient index metasurface at 40kHz

Over the past decade, gradient index metasurfaces(GIMs) have been voraciously studied for the numerous wave control capabilities that they facilitate. In this regard, a hybrid structure consisting of shunted Helmholtz resonators and a straight channel is often chosen as building blocks of the metasurface. Prior research, however, has primarily focused on GIMs that operate in the audible frequency range, due to the difficulties in fabricating such intricate structures at the millimeter and sub-millimeter scales, for ultrasonic applications. In this paper, we design, fabricate and experimentally realize a gradient index metasurface for airborne ultrasound at 40kHz. The fabrication of such a GIM is made possible by projection micro-stereolithography, an emerging additive manufacturing technique capable of micro-scale, high aspect-ratio features over a wide area. Simulations were first conducted to verify the metasurface design. Experiments were subsequently performed to corroborate the simulations and theory. The challenges faced by the thermoviscous effects, their usefulness in certain applications and optimal designs for minimal dissipation are discussed.

Time‐Asymmetric FORC Diagrams: A New Protocol for Visualizing Thermal Fluctuations and Distinguishing Magnetic Mineral Mixtures

AbstractFirst‐order reversal curves (FORCs) are nowadays routinely used to assess domain states and magnetostatic interactions of magnetic minerals. While a huge step forward from bulk magnetic measurements in terms of sample characterization, there is a missing link between the FORC diagrams and remanence behavior: FORC diagrams mainly reveal domain states, while remanence behavior is largely controlled by thermal activations. We present a new tool to visualize thermal fluctuations in so‐called time‐asymmetric (TA) FORC diagrams. TA‐FORCs differ from traditional FORCs in that they maintain the reversal field Ha for a longer time (minutes) than the FORC measurement field Hb (milliseconds). During this extended hold time, thermal activations cause some magnetic grains to change their magnetization, giving rise to an upward shift in the FORC diagram. The magnitude of this shift gives insight into the thermoviscous stability of the mineral and its remanence acquisition behavior. This not only allows to distinguish thermoviscous effects in FORC diagrams from magnetostatic (i.e., interactions/domain state related) effects but also provides a way to separate mixtures of magnetic minerals: two minerals with similar coercivity spectra that would totally overlap in traditional FORC diagrams show different upward shifts in TA‐FORC diagrams, which in some cases enable complete separation of the minerals visually. This effectively provides two independent FORC signatures for two magnetic constituents in a sample such as two grain populations of different grain sizes, grain shapes, and/or mineral.

Mixing enhancement in microchannels using thermo-viscous expansion by oscillating temperature wave

The aim of this paper is to use the thermo-viscous expansion-contraction effect to enhance mixing in microchannels. To do this, numerical simulation of chaos flow generated by periodic thermal boundary condition in a 2-D microchannel is considered.The main objectives are to evaluate the effect of Reynolds number, Strouhal number and thermal penetration length on chaotic mixing. The vorticity is used as a criteria evaluating the chaos. It is shown that thermo-viscous expansion-contraction effect can be used as aconsiderable potential mean for micro-scale chaotic mixingpotential mean for micro-scale chaotic mixing. The results show that, the vorticity generated by change of density and viscosity due to the temperature difference caused by periodic heat transfer at flow boundary is mainly a function of dimensionless flow velocity and film thickness.

Shock discontinuities: from classical to non-classical shocks

The possibility of shocks was first suggested by Stokes in 1848, but no consistent theory emerged for another almost 30 years. Indeed, severe criticism by Lord Kelvin and Lord Rayleigh led him to finally discard this idea. In the meantime, algebraic shock conditions had been derived by Rankine and Hugoniot, and their names have come to be associated with the shock conditions generally. As Thompson (Compressible-fluid dynamics, McGraw-Hill, New York, 1972) concludes, “Stokes’s claim to recognition for his discovery has been diverted by circumstance.” Starting with a brief discussion of these early developments, the present review paper will then concentrate on the important question of how to select from all formally possible solutions of the Rankine–Hugoniot jump relations those which are physically realizable solutions. This is at the core of the so-called admissibility problem. Of course, a necessary condition is provided by the second law of thermodynamics which states that the entropy must not decrease during adiabatic changes of state. For perfect gases, this requirement is also a sufficient condition to rule out “impossible” shocks. For fluids with an arbitrary equation of state and/or situations where in addition to thermoviscous effects, dispersive effects also come into play this is not the case in general. The selection of physically admissible solutions is then found to be a more delicate matter and may result in new types of shocks which differ distinctively from their classical counterparts and, therefore, are termed non-classical shocks.

Thermoviscous effect on sound propagation in acoustic metastructures

Thermoviscous dissipation plays an important role in sound propagation through acoustic metastructures for a variety of applications. The thermoviscous effects rely on the resonances in the structures of subwavelength features. Our analyses and numerical simulations reveal that thermoviscous dissipation can significantly reduce the transmission of sound waves through acoustic metastructures of hybrid resonances in certain scenarios even when the thickness of the viscous boundary layer is much smaller than the width of the slit in the structure [Jiang et al., J. Acous. Soc. Am. (2017)]. To further explore how the resonances affect the significance of the losses, we analyze and simulate sound propagation in acoustic metamaterials of various configurations, including a slit connected to one or multiple resonators at the side of the slit or at the end of the slit. We take into account both wall friction and thermoviscous diffusivity in both the slits and the resonators. The results are compared with that without the resonators to gain insight into the role of the resonances. Optimal designs for both minimal dissipation and maximal absorption are addressed.

Acoustic field of a pulsating cylinder in a rarefied gas: Thermoviscous and curvature effects

The impact of gas rarefaction on the acoustic field of a pulsating cylinder is studied for all Knudsen numbers. The continuum-limit far field exhibits thermoviscous exponential decay. Stronger attenuation occurs in the ballistic limit because of curvature-related geometric reduction of the affected layer.

Thermoviscous effects on sound transmission through a metasurface of hybrid resonances.

This letter analytically and numerically examines sound transmission through a metasurface of hybrid resonances in the presence of thermoviscous dissipation. The metasurface unit of a subwavelength thickness consists of a slit and series of sided resonators embedded in air. Both wall friction and thermoviscous diffusivity in the unit are taken into account. The results reveal that the dissipation has a weak influence on phases even when there is a large loss. The dissipation reduces the transmission by 28% when the thermoviscous boundary layer thickness is only around 2.3% of the slit width. Optimal designs for minimal dissipation are addressed.