Thermo-viscous Boundary Layer Research Articles

Acoustic black hole combined with microperforated plate for a rectangular waveguide

The concept of an acoustic black hole (ABH) for anechoic termination of waveguides has been well-established and extensively studied. The fundamental principle underlying an ABH is the deceleration of acoustic waves, leading to the accumulation and subsequent absorption of acoustic energy within the thermoviscous boundary layer formed along the ribs forming its internal structure. The primary advantage of ABHs, in contrast to classical solutions, lies in their avoidance of porous or fibrous materials, rendering them suitable for deployment in challenging environments. While the majority of published works have focused on ABHs with circular cross-sections, recent advancements have demonstrated the effectiveness of the ABH effect also in waveguides with rectangular cross-sections. However, it has been revealed that these ABHs require very fine internal structure for optimal performance, posing challenges in manufacturing. This study addresses this issue by utilizing a microperforated plate to provide the necessary resistance. To model these ABHs, a simple mathematical model is proposed, enabling the optimization of their parameters. Subsequently, their performance is investigated through numerical experiments. The validity of the results is confirmed by comparing them with a detailed mathematical model, ensuring the accuracy and reliability of the proposed approach.

Synergetic effect of microfluidic flow and ultrasonication on chains pre-ordering in conjugated polymer solution

Multi-physical fields solution processing strategy provides a universal and facile way to prepare various conjugated polymer (CP) films and high-performance devices, whereas the hierarchical structures evolution and crystallization of the polymer chains are elusive particularly under the far-from-equilibrium state in solution. In this work, we employed a combined microfluidic flow and ultrasonication strategy (FU) for CP solution processing and found a pronounced synergetic effect of these fields in promoting the pre-ordering of chains in solution. This conformation order and anisotropy of the solution were revealed by using UV–Vis absorption, polarized optical microscopy (POM) and cryogenic transmission electron microscopy (Cryo-TEM) characterizations. A non-classical nucleation model for the conjugated polymer crystallization in the procedure of non-equilibrium solution processing was confirmed. The roles of microfluidic flow and ultrasonication on the chain aggregation and crystallization were addressed with the aim of a multi-physical simulation based on pressure acoustics streaming, fluid heat transfer and thermoviscous boundary layer impedance. Compared to pristine solutions, the FU strategy showed improved solution anisotropy and crystallization kinetics, substantially giving rise to a larger crystallinity in films and much increased mobilities for the organic field-effect transistor (OFET) devices by more than an order of magnitude. With an appropriate balance between the solvation and interchain interactions, the FU processing strategy is universal for regulation of chains conformation and aggregation in conjugated polymer solution.

Development of a thermo-pressure acoustic model and its application in modeling three-dimensional acoustofluidic systems

Theoretical modeling of acoustofluidic systems faces extreme challenges as the thickness of the thermoviscous boundary layer is very small compared to the microscale fluid dimensions. The classical pressure acoustic model overcomes these difficulties and is extensively used in simulating three-dimensional (3D) or large two-dimensional (2D) acoustofluidic systems. However, this model cannot be applied to thermoviscous acoustofluidics, as it does not consider energy conservation. Modeling thermoviscous acoustofluidic systems is, therefore, difficult and restricted to small 2D systems only. Here, we have developed a thermo-pressure acoustic model that can effectively simulate thermoviscous acoustofluidic systems. The model has been validated with the full model by performing numerical simulations for a small 2D acoustofluidic system for which capturing the acoustic boundary layer effect is feasible using the full model. After successful validation, we demonstrate that the thermo-pressure acoustic model can also be applied to studying 3D acoustofluidic systems.

Theory of pressure acoustics with thermoviscous boundary layers and streaming in elastic cavities.

We present an effective thermoviscous theory of acoustofluidics including pressure acoustics, thermoviscous boundary layers, and streaming for fluids embedded in elastic cavities. By including thermal fields, we thus extend the effective viscous theory by Bach and Bruus [J. Acoust. Soc. Am. 144, 766 (2018)]. The acoustic temperature field and the thermoviscous boundary layers are incorporated analytically as effective boundary conditions and time-averaged body forces on the thermoacoustic bulk fields. Because it avoids resolving the thin boundary layers, the effective model allows for numerical simulation of both thermoviscous acoustic and time-averaged fields in three-dimensional models of acoustofluidic systems. We show how the acoustic streaming depends strongly on steady and oscillating thermal fields through the temperature dependency of the material parameters, in particular the viscosity and the compressibility, affecting both the boundary conditions and spawning additional body forces in the bulk. We also show how even small steady temperature gradients ( ∼1 K/mm) induce gradients in compressibility and density that may result in very high streaming velocities ( ∼1 mm/s) for moderate acoustic energy densities ( ∼100 J/m3).

Grenzschichtdämpfung von Wanderwellen in einem dreidimensionalen passiven Finite Elemente Modell der Cochlea des Menschen

A passive three-dimensional model of the human cochlea is described and analysed in the present article. One of its features is the implementation of a thermo-viscous boundary layer as a physically approved mechanism of mechanical damping. The model is solved numerically with the finite element method in ANSYS® and the simulation results are analysed with the help of MATLAB®. In this way curves of the basilar membrane's amplitude, phase and velocity for frequencies between 1000Hz and 8000Hz are calculated. A traveling wave develops on the basilar membrane and is damped after reaching its frequency-dependent maximum due to the boundary layer damping. A plot of the frequency-to-space transformation can be obtained which fits to the experimental data found in the literature. Furthermore, the study shows an energy analysis of the simulation verifying the boundary layer damping as a relevant physical effect for 3D-models of the cochlea.

Acoustically sticky topographic metasurfaces for underwater sound absorption.

A class of metasurfaces for underwater sound absorption, based on a design principle that maximizes thermoviscous loss, is presented. When a sound meets a solid surface, it leaves a footprint in the form of thermoviscous boundary layers in which energy loss takes place. Considered to be a nuisance, this acoustic to vorticity/entropy mode conversion and the subsequent loss are often ignored in the existing designs of acoustic metamaterials and metasurfaces. The metasurface created is made of a series of topographic meta-atoms, i.e., intaglios and reliefs engraved directly on the solid object to be concealed. The metasurface is acoustically sticky in that it rather facilitates the conversion of the incident sound to vorticity and entropy modes, hence the thermoviscous loss, leading to the desired anechoic property. A prototype metasurface machined on a brass object is tested for its anechoicity, and shows a multitude of absorption peaks as large as unity in the 2-5 MHz range. Computations also indicate that a topographic metasurface is robust to hydrostatic pressure variation, a quality much sought-after in underwater applications.

Acoustic Modeling of Charge Air Coolers

The necessity of reducing CO2 emissions has lead to an increased number of passenger cars that utilize turbocharging to maintain performance when the internal combustion (IC) engines are downsized. Charge air coolers (CACs) are used on turbocharged engines to enhance the overall gas exchange efficiency. Cooling of charged air increases the air density and thus the volumetric efficiency and also increases the knock margin (for petrol engines). The acoustic properties of charge coolers have so far not been extensively treated in the literature. Since it is a large component with narrow flow passages, it includes major resistive as well as reactive properties. Therefore, it has the potential to largely affect the sound transmission in air intake systems and should be accurately considered in the gas exchange optimization process. In this paper, a frequency domain acoustic model of a CAC for a passenger car is presented. The cooler consists of two conical volumes connected by a matrix of narrow ducts where the cooling of the air takes place. A recently developed model for sound propagation in narrow ducts that takes into account the attenuation due to thermoviscous boundary layers and interaction with turbulence is combined with a multiport representation of the tanks to obtain an acoustic two-port representation where flow is considered. The predictions are compared with experimental data taken at room temperature and show good agreement. Sound transmission loss increasing from 5 to over 10 dB in the range 50–1600 Hz is demonstrated implying good noise control potential.

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.

Development and Analysis of Wall Models for Internal Combustion Engine Simulations Using High-speed Micro-PIV Measurements

The performance, efficiency and emissions of internal combustion (IC) engines are affected by the thermo-viscous boundary layer region and heat transfer. Computational models for the prediction of engine performance typically rely on equilibrium wall-function models to overcome the need for resolving the viscous boundary layer structure. The wall shear stress and heat flux are obtained as boundary conditions for the outer flow calculation. However, these equilibrium wall-function models are typically derived by considering canonical flow configurations, introducing substantial modeling assumptions that are not necessarily justified for in-cylinder flows. The objective of this work is to assess the validity of several model approximations that are commonly introduced in the development of wall-function models for IC-engine applications. This examination is performed by considering crank-angle resolved high-resolution micro-particle image velocimetry (µ-PIV) measurements in a spark-ignition direct-injection single cylinder engine. Using these measurements, the performance of an algebraic equilibrium wall-function model commonly used in RANS and LES IC-engine simulations is evaluated. By identifying shortcomings of this model, a non-equilibrium differential wall model is developed and two different closures are considered for the determination of the turbulent viscosity. It is shown that both wall models provide adequate predictions if applied inside the viscous sublayer. However, the equilibrium wall-function model consistently underpredicts the shear stress if applied in the log-layer. In contrast, the non-equilibrium wall model provides improved predictions of the near-wall region and shear stress irrespective of the wall distance and the piston location. By utilizing the experimental data, significant adverse pressure gradients due to the large vortical motion inside the cylinder (induced by tumble, swirl and turbulence) are observed and included in the non-equilibrium wall model to further improve the model performance. These investigations are complemented by developing a consistent wall heat transfer model, and simulation results are compared against the equilibrium wall-function model and Woschni’s empirical correlation.

Acoustic forces acting on particles and fluids in microscale acoustofluidics

Acoustofluidics relying on acoustic forces to handle fluids and particles in microfluidic systems has emerged as a useful tool for characterizing, focusing, separating, and sorting cells based on their acousto-mechanical properties. Here, we present recent advances in the theoretical understanding of acoustic forces on particles and fluids. In particular, we address the effects of thermoviscous boundary layers on acoustic scattering off sub-micron particles or droplets. Re-examining the far-field method of calculating acoustic radiation forces and torques, we show that exact non-perturbative expressions can be derived regardless of boundary layer dissipation. The necessary condition for moving the surface of integration from the particle surface to the far field, is the time-periodicity of the system rather than negligible boundary-layer dissipation. In the long-wavelength limit, this approach leads to particularly simple expressions for the force and torque acting on a particle in a thermoviscous fluid. ...

Fluid flow induced by periodic temperature oscillation over a flat plate: Comparisons with the classical Stokes problems

We delineate the dynamics of temporally and spatially periodic flow over a flat plate originating out of periodic thermoviscous expansion of the fluid, as a consequence of a thermal wave applied on the plate wall. We identify two appropriate length scales, namely, the wavelength of the temperature wave and the thermal penetration depth, so as to bring out the complex thermo-physical interaction between the fluid and the solid boundaries. Our results reveal that the entire thermal fluctuation and the subsequent thermoviscous actuation remain confined within a “thermo-viscous boundary layer.” Based on the length scales and the analytical solution for the temperature field, we demarcate three different layers, namely, the wall layer (which is further sub-divided into various sub-layers, based on the temperature field), the intermediate layer, and the outer layer. We show that the interactions between the pressure oscillation and temperature-dependent viscosity yield a unidirectional time-averaged (mean) flow within the wall layer opposite to the direction of motion of the thermal wave. We also obtain appropriate scalings for the time-averaged velocity, which we further substantiate by full scale numerical simulations. Our analysis may constitute a new design basis for simultaneous control of the net throughput and mixing over a solid boundary, by the judicious employment of a traveling temperature wave.

A quasi-one-dimensional model of thermoacoustics in the presence of mean flow

In thermoacoustic regenerators, the interaction of thermo-viscous boundary layers and axial temperature gradients causes a conversion from thermal energy to acoustic power or vice versa. In this paper, an improved analytical model for thermoacoustic boundary layer effects in the presence of mean flow is derived and analyzed. Previous formulations of the thermo-acoustic effect take into account effects of mean flow on acoustic propagation only implicitly, i.e. in as much as mean flow influences the mean temperature field. The new model, however, includes additional terms in the perturbation equations, which describe explicitly the interaction between steady mean flow and acoustics. For a parallel plate pore the three-dimensional thermoacoustic equations are derived and reduced to a transversally averaged system of differential equations by applying Green׳s function technique and suitable assumptions. The resulting one-dimensional perturbation equations are then solved numerically for two sets of boundary conditions to obtain the linear scattering matrix coefficients. The solutions, generated for a wide range of frequencies, can be applied in a low-order “network model” context to study the stability of thermoacoustic devices. The impact of mean flow on the thermoacoustic interaction is investigated and validated against full computational fluid dynamics simulations of laminar, compressible flow for one specific configuration. It is shown that at low frequencies (Womersley number <1) the new formulation predicts the acoustic behavior more accurately than the earlier formulations. Finally, the ideas and benefit of further improved and more complex models for higher Mach numbers are discussed.

Improved determination of the Boltzmann constant using a single, fixed-length cylindrical cavity

We report improvements to our previous (Zhang et al 2011 Int. J. Thermophys. 32 1297) determination of the Boltzmann constant kB using a single 80 mm long cylindrical cavity. In this work, the shape of the gas-filled resonant cavity is closer to that of a perfect cylinder and the thermometry has been improved. We used two different grades of argon, each with measured relative isotopic abundances, and we used two different methods of supporting the resonator. The measurements with each gas and with each configuration were repeated several times for a total of 14 runs. We improved the analysis of the acoustic data by accounting for certain second-order perturbations to the frequencies from the thermo-viscous boundary layer. The weighted average of the data yielded kB = 1.380 6476 × 10−23 J K−1 with a relative standard uncertainty ur(kB) = 3.7 × 10−6. This result differs, fractionally, by (−0.9 ± 3.7) × 10−6 from the value recommended by CODATA in 2010. In this work, the largest component of the relative uncertainty resulted from inconsistent values of kB determined with the various acoustic modes; it is 2.9 × 10−6. In our previous work, this component was 7.6 × 10−6.

First-principle simulation of the acoustic radiation force on microparticles in ultrasonic standing waves

The recent development in the field of microparticle acoustophoresis in microsystems has led to an increased need for more accurate theoretical predictions for the acoustic radiation force on a single microparticle in an ultrasonic standing wave. Increasingly detailed analytical solutions of this specific problem can be found in the literature [Settnes and Bruus, Phys. Rev. E 85, 016327 (2012), and references therein], but none have included the complete contribution from thermoviscous effects. Here, we solve this problem numerically by applying a finite-element method to solve directly the mass (continuity), momentum (Navier-Stokes), and energy conservation equations using perturbation theory to second order in the imposed time-harmonic ultrasound field. In a two-stage calculation, we first solve the first-order equations resolving the thermoviscous boundary layer surrounding the microparticle and with a perfectly matched layer as a non-reflecting boundary condition for the scattered waves. These first-order solutions are then used as source-terms for solving the time-averaged second-order equations [Muller et al., Lab Chip 12, 4617 (2012)] and in particular to determine the second-order time-averaged hydrodynamic stress on the particle surface. From this, we deduce the radiation force and compare it as a function of the physical parameters to existing analytical results.

A numerical study of microparticle acoustophoresis driven by acoustic radiation forces and streaming-induced drag forces

We present a numerical study of the transient acoustophoretic motion of microparticles suspended in a liquid-filled microchannel and driven by the acoustic forces arising from an imposed standing ultrasound wave: the acoustic radiation force from the scattering of sound waves on the particles and the Stokes drag force from the induced acoustic streaming flow. These forces are calculated numerically in two steps. First, the thermoacoustic equations are solved to first order in the imposed ultrasound field taking into account the micrometer-thin but crucial thermoviscous boundary layer near the rigid walls. Second, the products of the resulting first-order fields are used as source terms in the time-averaged second-order equations, from which the net acoustic forces acting on the particles are determined. The resulting acoustophoretic particle velocities are quantified for experimentally relevant parameters using a numerical particle-tracking scheme. The model shows the transition in the acoustophoretic particle motion from being dominated by streaming-induced drag to being dominated by radiation forces as a function of particle size, channel geometry, and material properties.

Determination of complex propagation constant, acoustic intensity, and acoustic power in an arbitrarily terminated pipe using laser Doppler anemometry

Microphones are widely used to determine acoustical parameters, such as the complex propagation constant and acoustic intensity and power, of sound fields. It is less common to use measurements of acoustic particle velocity for the same purpose. Precise measurement of acoustic particle velocity can be achieved using laser Doppler anemometry (LDA). Although this measurement technique requires optical access to the region of interest and the use of seeding particles, in some circumstances it can be less invasive and offer greater flexibility than measuring pressure fields with microphones. The focus of this research is to use LDA to determine the complex propagation constant, acoustic intensity, and power inside a constant cross-section circular pipe. The measured particle velocities are fit to a counterpropagating plane-wave model to determine the complex amplitudes and propagation constant. Other acoustic quantities, such as the radial-dependent acoustic intensity and the cross-sectional-averaged acoustic power, can then be calculated. The complex propagation constant is compared with the theoretical value based on thermoviscous boundary layer theory. The acoustic intensity and power are compared with numerical solutions to Rott’s wave equation. [Work supported by the Penn State Graduate Program in Acoustics.]

Saturation of the thermoacoustic separation of a binary gas mixture

Spoor and Swift have previously shown [Phys. Rev. Lett. 85, 1645–1649 (2000)] that sound waves can produce the separation of a binary mixture of gases in a duct. This phenomenon is caused by the conspiracy of two effects at the thermoviscous boundary layer: (i) oscillating temperature gradients drive thermal diffusion perpendicular to the direction of sound propagation; and (ii) viscosity sets up a time-averaged counterflow process. In order to assess the relevance and potential uses of this mechanism, it is important to determine the concentration gradient at which the separation process saturates. Here, it is shown that the saturation is determined primarily by ordinary diffusion and by a remixing flux due to the oscillatory motion. Both of these remixing processes are proportional to the concentration gradient, but only the latter process depends on the acoustics, being proportional to the squared volume flow rate and inversely proportional to the frequency. For He–Ar mixtures, saturation concentration gradients near 10%/m have been achieved, in agreement with detailed calculations of these processes. Evidence to date supports the possibility of more challenging separations, e.g., of isotopes. [Work supported by the DOE Office of Basic Energy Sciences.]

Modal surface impedances for two spheres in a thermoviscous acoustic medium

Two spherical bodies are submerged in an infinite thermoviscous fluid; one body is motionless and the other is vibrating at high frequency with a surface pattern that is axisymmetric with respect to the line joining the centers of the two spheres. Both bodies are sufficiently good conductors that their surface temperatures deviate insignificantly from the ambient temperature. The acoustic stress and velocity fields on the vibrating surface may be conveniently related by a modal surface impedance matrix based on field expansions in Legendre functions. This impedance matrix, which of course accounts for the presence of the motionless sphere, is here obtained from the field equations of Epstein and Carhart [J. Acoust. Soc. Am. 25, 553–565 (1953)] through the application of translational addition theorems for bispherical coordinates [Y. A. Ivanov, DiffractionofElectromagneticWavesonTwoBodies, NASA Tech. Trans. F-597 (1970)]. Impedance matrices for fluids that exhibit thermoviscous boundary layers of various thicknesses are compared with counterparts produced by the thin-boundary-layer model [A. D. Pierce, Acoustics (McGraw-Hill, New York, 1981)]. Special attention is devoted to the case when the motionless sphere is sufficiently large relative to the vibrating sphere that it approximates a rigid wall.

On the nature of the core-envelope boundary layer in a slowly rotating star

Abstract In this paper we discuss the large-scale meridional currents and differential rotation in the radiative envelope of a single, nonmagnetic, early-type star. Our solutions depend on the interaction between these large-scale motions and the small-scale baroclinic eddies, which are an ever-present feature of a stellar radiative zone. If one makes allowance for mean steady motions in a typical rotating star, then large eddy viscosities are necessary for the method to converge. We show that there exists a singular, thermo-viscous boundary layer at the interface between the convective core and the radiative envelope. Unless very unrealistic assumptions are made, this layer is not of the Ekman type.

Acoustical wave propagation in cylindrical ducts: Transmission line parameter approximations for isothermal and nonisothermal boundary conditions

Approximate expressions are given for the characteristic impedance and propagation wavenumber for linear acoustic transmission through a gas enclosed in a rigid cylindrical duct. These expressions are most complicated in the transition zone where the thermoviscous boundary layers are on the order of the tube radius. The approximations are accurate to within 1% for all frequencies and tube diameters except within the transition zone where the approximations are accurate to within 10%. A simple modification of the transmission line parameters is presented for the case where the tube walls are nonisothermal.