Acoustic Reynolds Number Research Articles

Numerical investigation of acoustic streaming vortices in cylindrical tube arrays

Abstract Acoustic streaming has a significant effect on accelerating material mixing and flow field disturbance. To explore the characteristics of acoustic streaming in the cylindrical tube array field under the action of an acoustic wave, we derive the dimensionless acoustic streaming control equation and establish a numerical calculation model of acoustic streaming. The effects of acoustic incidence angle, acoustic Reynolds number, and Strouhal number on the acoustic streaming vortex flow field in the tube array were investigated. The numerical results show that with the change in acoustic parameters, the acoustic streaming in the tube array presents rich changes in the vortex flow field, and there are flow field phenomena such as shrinking, merging, tearing, and splitting of the vortex structure. Toward the walls of each tube, there is a strong acoustic streaming flow velocity. Besides, there is also a large streaming velocity on the interface of the adjacent acoustic streaming vortices. The inner streaming vortex structure in the acoustic boundary layer decreases with the increase in the acoustic Reynolds number, but the intensity of the inner streaming vortex and outer streaming vortex increases rapidly, and the disturbance effect of the flow field is enhanced. With the increase in the dimensionless acoustic frequency (or Strouhal number), although the structure and intensity of the inner streaming vortex decrease, the velocity gradient on the wall of the cylindrical tube increases, which is beneficial to destroy the flow boundary layer of the cylindrical tube wall and accelerate the instability of the wall flow field.

Simulation of acoustic oscillatory flows around a curvature controlled by a plasma actuator

In this study, simulations based on the three-dimensional compressible Navier–Stokes equations were conducted to clarify a control method with a plasma actuator to reduce the acoustic power loss in the oscillatory flow under acoustic excitation (acoustic oscillatory flow) in a curved duct. The acoustic power loss for the curved duct exceeds that for the straight duct, particularly at a high acoustic Reynolds number based on the amplitude of the velocity fluctuations in the duct. Flow control by a plasma actuator, which was installed near the curvature in the straight section, was applied to suppress the periodically occurring flow separation around the curvature, which leads to energy loss in the baseline flow. The plasma actuator was intermittently driven at the same frequency as the acoustic oscillatory flow. It was thus demonstrated in the present numerical simulations that the acoustic power loss around the curvature was reduced by the flow control with the plasma actuator. Furthermore, efficient control conditions for the number of plasma actuators and the driving voltage are discussed considering the power consumption of the plasma actuator, although the power efficiency of the control needs to be improved for actual application. Moreover, the relatively effective intermittent control conditions of the phase and duty ratio for the reduction of acoustic power loss are presented with the predicted flow fields around the curvature.

Effect of sound excitation on the flow field and convection heat transfer around a cylinder

The combination of experiment and numerical simulation, sound frequency and sound pressure level on the flow field, and heat transfer around a cylinder with two flow patterns are investigated. Flow patterns are periodic laminar flow (L3, Re0 = 100) and wake transition (TrW2, Re0 = 300), respectively. Sound frequency range f = 100–1000 Hz, and sound pressure level range SPL = 127–145 dB. Based on the influence of acoustic characteristics on the viscous boundary layer and thermal boundary layer of cylindrical wall, constructed a functional relationship between convection heat transfer and sound wave frequency and sound pressure level. Influenced by the acoustic action, the flow field force around the cylinder, the vortex street structure, the vortex size, and the length of the wake area may be changed. Acoustic action flow field excitation fluid particle velocity amplitude increased. As the sound pressure level increased, the amplitude of the fluid mass vibration velocity increased. From the experimental results, it can be seen that for the acoustic frequency effect, the heat transfer coefficient increases with increasing sound frequency. For the particle velocity amplitude effect, as the acoustic Reynolds number increases, the heat transfer coefficient increases and is 2.3 times higher than that without acoustic disturbance in the wake turning flow regime. In comparison with numerical and experimental results, the error is less than 15%, which meets the actual requirements of the project. It has been shown that sound waves can enhance the convective heat transfer around a cylinder in the cross-flow.

Derivation of a second-order acoustic wave equation in an air-saturated porous medium from a volume-averaged transport model

For propagation of high-amplitude acoustic waves in a rigid porous frame saturated by air, significant departures from a constant flow resistivity model have been observed. This departure can be modeled as a quadratic modification to the linear Darcy’s drag law, known as Forchheimer’s correction. To study the physical cause and relative significance of this nonlinear correction with respect to convective nonlinearity, a second-order acoustic wave equation is derived from volume-averaged equations of mass, momentum, and entropy conservation. Due to the scale separation between the wavelength and the porous structure, the particle velocity is approximated as the sum of irrotational macroscopic and incompressible microscopic fields. The porosity, tortuosity, and permeability are defined and incorporated into the macroscopic conservation equations. Porous drag terms are also derived in the macroscopic momentum equation for Darcy’s law and Forchheimer’s correction. Conservation equations for fluid parameter perturbations are obtained, and a second-order wave equation is derived. Dimensional analysis, in terms of the acoustic Reynolds number and Darcy number, describes the criteria for significant Forchheimer and convective nonlinearity. A case is obtained for a Westervelt-like equation for approximately progressive plane waves. These results inform modeling of nonlinearities for sound propagation in porous media under practical conditions.

ТЕОРЕТИЧЕСКИЙ АНАЛИЗ УРАВНЕНИЯ ДВИЖЕНИЯ ПРИМЕНИТЕЛЬНО К КОЛЕБАНИЯМ ТВЕРДОЙ ПОВЕРХНОСТИ В НЕСЖИМАЕМОЙ ЖИДКОСТИ

In this paper, the equation of motion is calculated as applied to vibrations of a solid surface in an incompressible fluid. The equation of motion was reduced to a dimensionless form, and its solution was obtained by the finite difference method. An analysis of the solution showed that when a solid surface vibrates in an incompressible fluid, a stationary flow is formed, the speed of which depends proportionally on the acoustic Reynolds number

Gas-liquid hydrodynamics and mass transfer in microreactors under ultrasonic oscillation

Integration of microreactors with ultrasound is a promising way to intensify gas-liquid mass transfer. The present study locally visualized and characterized the O2 mass transfer around Taylor bubbles flowing in a square microchannel reactor under ultrasonic oscillation. The effect of acoustic field on the gas-liquid hydrodynamics and mass transfer were investigated. A reciprocating phenomenon of the bubble contraction and expansion was observed, and the evolution of bubble length was found to be a periodic harmonic process. It was also revealed that the cavitation microstreaming generated by the bubble surface oscillation, as well as the periodic bubble length variation, could strongly modify and twist the recirculation loops in the liquid slug, thus intensify the mass transfer. As the bubble surface oscillation during the bubble formation was not as fierce as during the bubble flowing, the enhancement factors of mass transfer by the ultrasonic oscillation range from 1.04 to 1.85 for the formation and from 1.27 to 3.17 for the flowing stage. Semi-empirical equations were established to predict the overall mass transfer coefficient in terms of the acoustic power density and Reynolds number.

Knudsen number effects on the nonlinear acoustic spectral energy cascade.

We present a numerical investigation of the effects of gas rarefaction on the energy dynamics of resonating planar nonlinear acoustic waves. The problem setup is a gas-filled, adiabatic tube, excited from one end by a piston oscillating at the fundamental resonant frequency of the tube and closed at the other end; nonlinear wave steepening occurs until a limit cycle is reached, resulting in shock formation for sufficiently high densities. The Knudsen number, defined here as the ratio of the characteristic molecular collision timescale to the resonance period, is varied in the range Kn=10^{-1}-10^{-5}, from rarefied to dense regime, by changing the base density of the gas. The working fluid is Argon. A numerical solution of the Boltzmann equation, closed with the Bhatnagar-Gross-Krook model, is used to simulate cases for Kn≥0.01. The fully compressible one-dimensional Navier-Stokes equations are used for Kn<0.01 with adaptive mesh refinement to resolve the resonating weak shocks, reaching wave Mach numbers up to 1.01. Nonlinear wave steepening and shock formation are associated with spectral broadening of the acoustic energy in the wavenumber-frequency domain; the latter is defined based on the exact energy corollary for second-order nonlinear acoustics derived by Gupta and Scalo [Phys. Rev. E 98, 033117 (2018)2470-004510.1103/PhysRevE.98.033117], representing the Lyapunov function of the system. At the limit cycle, the acoustic energy spectra exhibit an equilibrium energy cascade with a -2 slope in the inertial range, also observed in freely decaying nonlinear acoustic waves by the same authors. In the present system, energy is introduced externally via a piston at low wavenumbers or frequencies and balanced by thermoviscous dissipation at high wavenumbers or frequencies, responsible for the base temperature increase in the system. The thermoviscous dissipation rate is shown to scale as Kn^{2} for fixed Reynolds number based on the maximum velocity amplitude, i.e., increasing with the degree of flow rarefaction; consistently, the smallest length scale of the steepened waves at the limit cycle, corresponding to the thickness of the shock (when present) also increases with Kn. For a given fixed piston velocity amplitude, the bandwidth of the inertial range of the spectral energy cascade decreases with increasing Knudsen numbers, resulting in a reduced resonant response of the system. By exploiting dimensionless scaling laws borrowed by Kolmogorov's theory of hydrodynamic turbulence, it is shown that an inertial range for spectral energy transfer can be expected for acoustic Reynolds numbers Re_{U_{max}}>100, based on the maximum acoustic velocity amplitude in the domain.

Acoustically driven oscillatory flow fields in a cylindrical resonator at resonance.

Generation and development of acoustic waves in an air-filled cylindrical resonator driven by a conical electro-mechanical speaker are studied experimentally and simulated numerically. The driving frequencies of the speaker are chosen such that a standing wave field is produced at each chosen frequency in the resonator. The amplitude of the generated acoustic (pressure) waves is measured along the axis of the resonator by a fast response piezo-resistive pressure transducer, while the radial distribution of the oscillatory axial velocities is measured at the corresponding velocity anti-node locations by a constant temperature hot-film anemometer. For the cases studied, the acoustic Reynolds number ranged between 20.0 and 60.0 and the flow fields were always found to be in the laminar regime. The flow field in the resonator is also simulated by a high-fidelity numerical scheme with low numerical diffusion. Formation of the standing wave and quasi-steady acoustic streaming are numerically simulated by solving the fully compressible form of the Navier-Stokes equations. The effects of the sound field intensity (i.e., input power to the speaker) and driving frequency on the standing wave field and the resultant formation process of the streaming structures are also investigated.

Numerical investigation on turbulent oscillatory flow through a jet pump.

A jet pump with an asymmetrical channel can induce a time-averaged pressure drop in oscillatory flow, which can effectively suppress Gedeon streaming in looped thermoacoustic engines. In this work, the flow characteristics and time-averaged pressure drop caused by a jet pump in turbulent oscillatory flow are investigated through numerical simulation. Through the analysis of the dimensionless governing equations, the emphasis is put on the effects of Womersley number and maximum acoustic Reynolds number on the performance of the jet pump. Meanwhile, the steady flow resistance coefficients are also measured numerically. The results indicate that the oscillatory flow resistance coefficients are relatively insensitive to Womersley number when it is less than 46. Moreover, the oscillatory flow resistance coefficients agree well with the steady state flow results, which validate the quasi-static assumption in turbulent oscillatory flow. However, further increasing Womersley number will lead to a reduction in the time-averaged pressure drop. The simulation method and results, as well as the hydrodynamic mechanism beneath the results, are presented and discussed in detail.

The effect of acoustic wave on the stability of stationary convective flow of binary fluid in a horizontal layer subjected to horizontal temperature and concentration gradients

The effect of acoustic wave propagating in the direction of temperature gradient on a stability of stationary plane-parallel flow of binary fluid, generated by horizontal temperature and concentration gradients in a horizontal layer is investigated for two types of thermal boundary conditions: perfectly conductive and adiabatic boundaries. The study is performed analytically for the longwave perturbations and numerically for finite-wavelength perturbations. Stability maps for fixed Prandtl number value Pr=0.01 and different values of Schmidt number and acoustic Reynolds number are obtained. The most dangerous instability modes and critical perturbation structure are discussed. Comparison with the case where acoustic wave is absent is performed. It is shown, that longwave perturbations are always stabilized by acoustic wave. Numerical investigation demonstrates, that acoustic wave also stabilizes the flow with respect to finite-wavelength perturbations when negative concentrational Grashof number is higher in modulus than certain value depending on acoustic wave intensity.

Evolution of intense narrowband noise beams

The main part of this work is focused on the experimental study of the evolution of acoustic beams with a narrowband spectrum at the input. The nonlinear interaction leads to initiation of new harmonics whose width increases with the harmonic number and a continuous power spectrum is formed at high frequencies. The experimental equipment enables us to study the beam propagation at large acoustic Reynolds numbers and analyze the spectral content of the field in a wide frequency band. For narrowband noise, the input field can be considered as a quasi-monochromatic signal with random amplitude and phase modulation. The amplitude-modulation suppression is observed for large Reynolds numbers as the wave propagates. Far from the sound transducer, the field on the sound transducer axis is a sequence of discontinuities with a universal behaviour between them. The locations of the discontinuities and their amplitudes and, hence, the statistical characteristics of the waves are determined by the phase fluctuations of the initial wave. It has been theoretically shown that the field spectrum at the discontinuous stage has a universal structure which is determined by the probability distribution of the initial wave frequency. It has been demonstrated experimentally that the theory describes sufficiently well the noise-signal spectrum form at the discontinuous stage.

Evolution of weak noise and regular waves on dissipative shock fronts described by the Burgers model

The interaction of weak noise and regular signals with a shock wave having a finite width is studied in the framework of the Burgers equation model. The temporal realization of the random process located behind the front approaches it at supersonic speed. In the process of moving to the front, the intensity of noise decreases and the correlation time increases. In the central region of the shock front, noise reveals non-trivial behaviour. For large acoustic Reynolds numbers the average intensity can increase and reach a maximum value at a definite distance. The behaviour of statistical characteristics is studied using linearized Burgers equation with variable coefficients reducible to an autonomous equation. This model allows one to take into account not only the finite width of the front, but the attenuation and diverse character of initial profiles and spectra as well. Analytical solutions of this equation are derived. Interaction of regular signals of complex shape with the front is studied by numerical methods. Some illustrative examples of ongoing processes are given. Among possible applications, the controlling the spectra of signals, in particular, noise suppression by irradiating it with shocks or sawtooth waves can be mentioned.

Autonomous propulsion of nanorods trapped in an acoustic field

Acoustic fields in a liquid medium can trap and suspend small particles at their pressure nodes. Recent measurements demonstrate that nanorods immersed in these fields generate autonomous propulsion, with their direction and speed controlled by both the particle’s shape and density distribution. Specifically, slender nanorods with an asymmetric density distribution about their geometric centre are observed to move steadily with their low density end leading the motion; particle geometry exerts an equally significant and potentially opposing effect. In this article, we investigate the physical mechanisms underlying this combined density/shape induced phenomenon by developing a simple yet rigorous mathematical framework for axisymmetric particles. This only requires solution of the (linear) unsteady Stokes equations, which can be performed numerically or analytically. The theory holds for all particle shapes, particle aspect ratios (length/width) and acoustic frequencies. It is applied to slender dumbbell-shaped particles and asymmetric nanorods – these provide model systems to investigate the competing effects governing propulsion. This shows that geometric and density asymmetries in the particle generate axial jets that can produce motion in either direction, depending on the relative strengths of these asymmetries and the acoustic Reynolds number (dimensionless frequency). Strikingly, the propulsion direction is found to reverse with increasing frequency, an effect that is yet to be reported experimentally. The general theory and mechanism described here enable thea prioridesign and fabrication of nano-motors in fluid for transport of small-scale payloads and robotic applications.

Using degenerate parametric interaction of intense acoustic beams to amplify weak signals

The paper considers the degenerate parametric interaction of an intense acoustic pumping beam and a weak signal beam at the subharmonic. The use of a special emitter system with independent signal emission at the harmonic and subharmonic made it possible to study the features of nonlinear interaction both for different amplitude levels and arbitrary phase relations of the fields at these frequencies. Just as predicted in the theory, the experiment showed that signal amplification at the subharmonic hardly occurs at all. It is shown that the use of odd field harmonics, which are absent for a zero amplitude of the signal wave, makes it possible to substantially increase the efficiency of isolating a weak signal wave. The interaction of beams for large and small acoustic Reynolds numbers of the signal wave is studied.

A Numerical Study on the Oscillating Flow Induced by an Acoustic Field around Coal Particles

In order to investigate the acoustically driven oscillating flow around coal particles in the power plant boiler, the two-dimensional, unsteady mass and momentum conservation equations for laminar flow in spherical coordinates are developed numerically. The velocity field, axial pressure gradient, shear stress, and flow separation angle on the particle surface are carefully analyzed with different values of acoustic Reynolds number and Strouhal number. The minimum frequency required for flow separation is also investigated with different SPL (sound pressure level). The axial pressure gradient, shear stress, and separation angle on the surface are proportional to the magnitude of the oscillating flow velocity at low frequency (~50 Hz). However, those physical quantities have different values at high frequency (~5000 Hz), due to the combined effect of curvature and the flow acceleration.

The effect of thermal boundary conditions on a stability of convective flow in a horizontal layer subjected to the longitudinal temperature gradient and acoustic wave

The effect of thermal boundary conditions on linear stability of stationary convective flow in a horizontal layer subjected to the longitudinal temperature gradient and propagating acoustic wave is studied. Two-dimensional shear instability and three-dimensional monotonic and oscillatory instabilities are analyzed. The stability maps for different acoustic Reynolds number values with respect to different perturbation types are obtained. The stabilization under the influence of acoustic wave at low Prandtl numbers is demonstrated. It takes place when two-dimensional shear or three-dimensional oscillatory instability modes are most dangerous. Three-dimensional monotonic mode is destabilized by acoustic influence. Energy analyses for two-dimensional and monotonic three-dimensional modes of instability is carried out.

Experimental study of the oscillatory velocity and temperature near a heated circular cylinder in an acoustic standing wave

Experiments were performed to characterize thermo-fluid interactions between oscillatory fluid motion and the heat transferred from a hot cylinder immersed in an acoustic standing wave. A stationary circular cylinder was mounted inside a water channel and immersed in a sinusoidal oscillatory flow. Particle Image Velocimetry and Planar Laser Induced Fluorescence were used to simultaneously capture the synchronous, time-dependent velocity and temperature fields around the cylinder. The vorticity generation and heat convection from the cylinder were found to significantly differ from those in comparable steady flows. Local time-dependent, phase-dependent and total heat transfer rates were obtained as a function of acoustic Reynolds number, Keulegan–Carpenter number and dimensionless frequency parameter. The results highlight the role of secondary vortical interaction on the heat transfer.

Heat transfer processes in parallel-plate heat exchangers of thermoacoustic devices – numerical and experimental approaches

This paper addresses the issues of heat transfer in oscillatory flow conditions, which are typically found in thermoacoustic devices. The analysis presented concerns processes taking place in the individual “channels” of the parallel-plate heat exchangers (HX), and is a mixture of experimental and numerical approaches. In the experimental part, the paper describes the design of experimental apparatus to study the thermal-fluid processes controlling heat transfer in thermoacoustic heat exchangers on the micro-scale of the individual channels. Planar Laser Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV) techniques are applied to obtain spatially and temporally resolved temperature and velocity fields within the HX channels. The temperature fields allow obtaining the local and global, phase-dependent heat transfer rates and Nusselt numbers, and their dependence on the Reynolds number of the oscillating flow. The numerical part of the paper deals with the implementation of CFD modelling capabilities to capture the physics of thermal-fluid processes in the micro-scale and to validate the models against the experimental data. A two-dimensional low Mach number computational model is implemented to analyse the time-averaged temperature field and heat transfer rates in a representative domain of the HXs. These are derived by integrating the thermoacoustic equations of the standard linear theory into a numerical calculus scheme based on the energy balance. The comparisons between the experimental and numerical results in terms of temperature and heat transfer distributions suggest that the optimal performance of heat exchangers can be achieved when the gas displacement amplitude is close to the length of hot and cold heat exchanger. Heat transfer coefficients from the gas-side can be predicted with a confidence of about 40% at moderate acoustic Reynolds numbers.

F104 積層メッシュの熱音響特性評価(OS10 外燃機関・廃熱利用技術)

An empirical equation is addressed for evaluating the oscillatory-flow resistance of regenerators consisting of stacked mesh screens. The empirical equation is expressed by a linear function of velocity amplitude and parameterized by acoustic Reynolds number Re_h and ωτ_v (ωis the angular frequency of acoustic wave, and τ_v is the viscous relaxation time given by effective pore radius). In the absence of axial temperature difference, the flow resistance of regenerator is determined from measurements of the acoustic field at ends of the regenerator. The measured resistance per unit length of the regenerator is compared to the prediction of the empirical equation. Through the experiments with air at atmospheric pressure, helium and argon gases with mean pressure of 0.45 MPa, the maximum deviation of the empirical equation is found to be 6 percent.

Numerical computation for parallel plate thermoacoustic heat exchangers in standing wave oscillatory flow

A simplified computational method for studying the heat transfer characteristics of parallel plate thermoacoustic heat exchangers is presented. The model integrates the thermoacoustic equations of the standard linear theory into an energy balance-based numerical calculus scheme. Details of the time-averaged temperature and heat flux density distributions within a representative domain of the heat exchangers and adjoining stack are given. The effect of operation conditions and geometrical parameters on the heat exchanger performance is investigated and main conclusions relevant for HX design are drawn as far as fin length, fin spacing, blockage ratio, gas and secondary fluid-side heat transfer coefficients are concerned. Most relevant is that the fin length and spacing affect in conjunction the heat exchanger behavior and have to be simultaneously optimized to minimize thermal losses localized at the HX-stack junctions. Model predictions fit experimental data found in literature within 36% and 49% respectively at moderate and high acoustic Reynolds numbers.