Acoustic Reynolds Number Research Articles

Acoustic Properties of Porous Coatings for Hypersonic Boundary-Layer Control

Numerical simulations are performed to investigate the interaction of acoustic waves with an array of equally spaced two-dimensional microcavities on an otherwise flat plate without external boundary-layer flow. This acoustic scattering problem is important in the design of ultrasonic absorptive coatings for hypersonic laminar flow control. The reflection coefficient, characterizing the ratio of the reflected wave amplitude to the incident wave amplitude, is computed as a function of the acoustic wave frequency and angle of incidence, for coatings of different porosities, at various acoustic Reynolds numbers relevant to hypersonic flight. Overall, the numerical results validate predictions from existing theoretical modeling. In general, the amplitude of the reflection coefficient has local minima at some specific frequencies. A simple model to predict these frequencies is presented. The simulations also highlight the presence of resonant acoustic modes caused by coupling of small-scale scattered waves near the coating surface. Finally, the cavity depth and the porosity are identified as the most important parameters for coating design. Guidelines for the choice of these parameters are suggested.

Behavior of intense acoustic noise at large distances

Propagation of intense acoustic noise waves is investigated in the case of a nonplanar geometry. It is shown that, at large distances from the source, where the nonlinear effects become negligible, the spectrum of such waves has a universal self-similar shape. The amplitude of the spectrum is determined by a single constant D∞ = D∞(ɛ, R0) (the spectrum steepness at zero-valued argument) whose value depends on two dimensionless parameters: the inverse acoustic Reynolds number ɛ and the dimensionless radius R0. It is shown that the plane of dimensionless parameters (ɛ, R0) can be divided into four regions, so that, within each of them, the quantity D∞ is described by a universal function of these parameters. The numerical factors of these parameters are found from numerical simulations.

Estimation of heat transfer coefficients in oscillating flows: The thermoacoustic case

The classical linear thermoacoustic theory is integrated through a numerical calculus with a simple energy conservation model to allow estimates of the optimal length of thermoacoustic heat exchangers and of the magnitude of the related heat transfer coefficients between gas and solid walls. This information results from the analysis of the temperature and heat flux density distributions inside a thermally isolated thermoacoustic stack. The effects of acoustic amplitude, plate spacing, plate thickness and Reynolds number on the heat transfer characteristics are examined. The results indicate that a net heat exchange between the acoustically oscillating gas and the solid boundary takes place only within a limited distance from the stack edges. This distance is found to be an increasing function of the plate spacing in the range (0 ⩽ y 0/ δ κ ⩽ 2), becoming constant for y 0/ δ κ ⩾ 2. The calculated dimensionless convective heat transfer coefficients, the Nusselt numbers, between gas and solid wall are comparable to those evaluated from classical correlations for steady laminar flow revised under the “Time-Average Steady-Flow Equivalent” (TASFE) and “root-mean-square Reynolds number” (RMSRe) models. Numerical results agree with measurements of the heat transfer coefficient found in literature to within 20%.

Heat transfer of heat exchangers in a standing wave thermoacoustic cooler

Standing wave thermoacoustic coolers require heat exchangers to move heat in and out of the working gas. Within most finned-tube type heat exchangers, heat is transferred from the oscillating gas to a liquid flowing through the tubes. Experiments were performed to evaluate the thermal performance of heat exchangers immersed in a standing wave thermoacoustic cooler. The gas-side convection heat transfer coefficient was calculated from the measured data, and compared to steady flow heat transfer model predictions. A simple relation between the Reynolds number in steady flow and the time dependent acoustic Reynolds number was obtained. The results suggest that substituting this relation into known steady flow correlations may yield accurate predictions of the heat transfer coefficient in oscillating flow.

Resonance gas oscillations in closed tubes: Numerical study and experiments

Periodic gas oscillations in closed tubes are investigated experimentally and numerically. At resonance, these oscillations are accompanied by shock waves traveling back and forth along the tube. Results of gas temperature and pressure measurements are reported. It is found that the gas temperature changes substantially along the tube. A two-dimensional numerical model of turbulent gas oscillations is developed and verified by a comparison with experiments. It is found that the experimental data of temperature and pressure inside the resonance tube are well correlated by the numerical model. Using the numerical model, turbulence and acoustic streaming at resonance are investigated. It is shown that the direction of gas streaming at resonance is opposite to that in nonresonant oscillations. A parametric investigation of resonant flow is performed in terms of the tube parameter ε, acoustic Reynolds number Rea and dimensionless tube length Λ. In particular, it is found that the normalized pressure amplitude, as well as other flow characteristics, are functions of a single parameter E=Rea1/3/Λ. Useful correlations for flow characteristics are proposed in terms of tube dimensionless parameters.

ANALYSIS OF THERMAL SLIP IN OSCILLATING RAREFIED FLOW USING DSMC

In this study, the nonequilibrium effects at the stagnation wall in one-dimensional unsteady microflow responding to the external sinusoidal oscillation are investigated. The fluctuating behavior of the rarefied medium is simulated by employing the unsteady DSMC method under various conditions with different acoustic Reynolds and Knudsen numbers. As a result, it is found that the nonequilibrium effect exists at the stagnation wall, especially when the gas density number is small. Due to such a nonequilibrium effect found in a fluctuating medium, the Knudsen number representing system size becomes a more important system parameter than the acoustic Reynolds number even for the constant excitation frequency. Also, the validity of the well-known Maxwell-Smoluchowski relation and its higher-order modifications are tested by comparing the heat fluxes from these relations with the direct DSMC result.

Inception of Turbulence in the Stokes Boundary Layer Over a Transpiring Wall

In this work, the onset of turbulence inside a rectangular chamber is investigated, with and without side-wall injection, in the presence of an oscillatory pressure gradient. Two techniques are used to define the transition from laminar to turbulent regimes: statistical analysis and flow visualization. Calibrated hot film anemometry and a computer data acquisition system are used to record and analyze acoustical flow data. Four classifications of flow regimes are reported: (a) laminar, (b) distorted laminar, (c) weakly turbulent, and (d) conditionally turbulent. Despite numerous attempts to promote turbulence, a fully turbulent flow does not develop at any of the driving frequencies tested. Statistical measurements reveal that a periodic drop in standard deviation of axial velocity fluctuations always occurs, indicating relaminarization within each cycle. Transition between flow regimes is assessed from the standard deviation of velocity data correlated as a function of the acoustic Reynolds number ReA. Under predominantly laminar conditions, the standard deviation is found to vary approximately with the square of the acoustic Reynolds number. Under turbulent conditions, the standard deviation becomes almost directly proportional to the acoustic Reynolds number. Inception of turbulence in the oscillatory flow with side-wall injection is found to be reproducible at the same critical value of ReA≅200.

PARTICLE IRREGULARITY AND AGGREGATION EFFECTS IN AIRBORNE SUSPENSIONS AT AUDIO- AND LOW ULTRASONIC FREQUENCIES

In the inertial regime of frequency-radius space, irregularity and aggregation of particles can result in values of acoustic attenuation that are significantly different from those predicted by assuming separated smooth spherical particles. Data obtained previously from suspensions of alumina particles and olivine sand in air at audio-frequencies, together with new data obtained at low ultrasonic-frequencies in suspensions of glass beads and silica flour, are compared with predictions. It is shown that neither a coupled phase theory modified to allow for non-spherical shapes nor effective radius theories are able to account for these data. Qian [21] has suggested that suspensions may be treated as fractal media and used the acoustic Reynolds number as the fractal dimension in modifying scattering theory. A new fractal modification of multiple-scattering theory for acoustic attenuation is derived. The theory uses ωτv(ω is the angular acoustic frequency, τvis the dynamic relaxation time of the particles) as a fractal scale. It requires an empirical determination of the difference between the fractal dimension of the measured suspension and that of a hypothetical suspension of spheres with the same particle size distribution. However, values obtained at a single frequency also enable fits with data at other frequencies. The new fractal modification of scattering theory is found to enable better agreement with measured attenuation as a function of concentration for irregular particles than an effective radius model. Also, the fractal modification is able to predict the observed frequency dependence at a given concentration rather better than effective radius approaches. Moreover, the fractal approach is found to enable discrimination between the effects of particle irregularity and aggregation.

A NOVEL INVESTIGATION OF THE OSCILLATORY FIELD OVER A TRANSPIRING SURFACE

The flowfield character is investigated inside a long rectangular chamber in the presence of time-harmonic pressure waves. The chamber is designed with multiple interchangeable sections for the purpose of controlling the length and therefore the system's natural frequency. Pressure waves are induced externally at variable frequencies by means of a Scotch-yoke mechanism theoretically capable of imparting pure oscillatory motions. In characterizing the internal flowfield, velocity measurements are acquired inside a principal test section that can accommodate flat blocks of solid carbon dioxide (i.e., dry ice). As solid CO2sublimates, a flow of gaseous carbon dioxide is generated at the bottom of the principal section and enters the chamber in the transverse direction. The resulting generalized Stokes layer formed above the transpiring surface exhibits several features associated with oscillatory flows over impermeable surfaces, including an overshoot in the velocity amplitude in the vicinity of the transpiring wall known as Richardson's annular effect. Quantitative pressure and velocity measurements are in agreement with theoretical predictions obtained from recent models of the oscillatory field over transpiring surfaces. The acoustic Reynolds number based on the Stokes layer thickness increases linearly with increasing Scotch-yoke frequency except in the neighborhood of the system's natural frequency. Near resonance, a sharp non-linear increase in the acoustic Reynolds number is noted. Furthermore, both acoustic pressure and velocity amplitudes increase with the driving frequency in a manner that is consistent with current theories. Since the sublimation rate of dry ice can be expressed in a similar mathematical form to the regression rate at the burning surface of solid propellants, this experiment constitutes a cold flow simulation of the internal flowfield in solid rocket motors.

New models and measurements concerning sound attenuation in concentrated airborne suspensions

In the inertial regime of frequency-radius space, irregularity and aggregation of particles can result in values of acoustic attenuation that are significantly different from those predicted by assuming separated smooth spherical particles. Data obtained previously from suspensions of alumina particles and olivine sand in air at audio frequencies, together with new data obtained at low ultrasonic frequencies in suspensions of glass beads and silica flour, are compared with predictions. It is shown that neither a coupled-phase theory modified to allow for nonspherical shapes nor effective radius theories are able to account for these data. Qian [Phys. Rev. E 53(3), 2304–2306 (1996)] has suggested that suspensions may be treated as fractal media and used the acoustic Reynolds number as the fractal dimension in modifying scattering theory. A new fractal modification of multiple scattering theory for acoustic attenuation is derived. The theory uses ωτv (ω is the angular acoustic frequency, τv is the dynamic relaxation time of the particles) as a fractal scale. Fitted values of fractal dimension obtained at a single frequency are found to enable fits with data at other frequencies. Moreover, the fractal approach is found to enable discrimination between the effects of particle irregularity and aggregation. [Work supported by EPSRC (UK).]

Propagation of N-Waves Caused by Temperature Variation of a Wall

The weakly nonlinear propagation of waves, which are generated in a half-space filled with a perfect gas through the heat addition, is studied from the standpoint of nonlinear acoustics. The wall temperature varies sinusoidally only during a half cycle. The result of analysis shows that the weak flow is induced at the outer edge of the thin boundary layer adjacent to the wall and thereby an acoustic wave is radiated to the outer wave region. The wave behavior in a far field can exactly be settled by solving Burgers equation. At a high acoustic Reynolds number, with the aid of the so-called equal-areas rule, it is shown that the entire wave profile develops into an N-wave with a long tail. In the farther far field, the tail diminishes and so the wave is reduced to an ordinary N-wave.

A calculation of the flow resistivity in intermediate flow regime

Many of the acoustic properties of fibrous materials can be modeled and predicted with the aid of appropriate empirical formulas. Among the input parameters that are required by such types of macroscopic models, the flow resistivity is a very well-established quantity in the literature, as usually this parameter is measured in steady Poiseuille flow conditions, i.e., at comparatively low flow speeds. One major concern with respect to such a parameter is the question of its possible frequency dependence. From a theoretical point of view, we have examined to which extent the capilar pore approximation can be utilized in intermediate flow regimes. The tendency towards lower values of flow resistivity for increasing acoustic Reynolds number also appears in all samples studied. And only the greater density samples, for the tested frequencies, were found in the flow regime of Poiseuille. However, if we want to obtain the value of the flow resistivity, for any sample, the employed experimental procedure makes it possible by a relationship between the experimental values and those of the Biot function. The value of the flow resistivity in different dynamical flow regimes to that of Poiseuille can be obtained.

Soot suppression by acoustic oscillated combustion

The soot suppression of acetylene diffusion flames by applying acoustic oscillation was studied experimentally. The soot emission decreased by increasing the sound pressure level and lowering the frequency of the acoustic oscillation. The efficiency of soot suppression can be related with acoustic Reynolds number, Re ∗. The result showed that the efficiency of soot suppression exceeded 90% in a region of Re ∗ > 3000. The flame temperature increased by applying the acoustic oscillation. It is considered that the acoustic oscillation enhanced the mixing of the fuel gas and surrounding gas, consequently, the high flame temperature caused the re-oxidation of soot particles.

Effect of dispersion factors on decay regimes of short waves in a gas-saturated porous medium

A linear analysis of the evolution of small fast-oscillating perturbations in a porous medium saturated with a viscous gas is carried out within a wide range of acoustic Reynolds and Peclet numbers.

Attenuation and Distortion of a Compression Wave Propagating in a High-Speed Railway Tunnel.

When a high-speed railway train enters a tunnel, a compression wave is generated ahead of the train and propagates along the tunnel. The attenuation and distortion of the compression wave were measured in three Shinkansen tunnels and the results were compared with the numerical values calculated using a second-order TVD scheme. The strength of a compression wave is exponentically attenuated with distance as it propagates along the tunnel in both slab and ballast track tunnels, and the attenuation in the ballast track tunnel is considerably larger than that in the slab track tunnel. In the slab track tunnel, the compression wave is steepened as it propagates, while it spreads in the ballast track tunnel. The criterion for judgment whether the compression wave is steepend or spreads is expressed by the value of acoustic Reynolds number of about 10∼15.

An investigation of heat and mass transfer in oscillating flows at high acoustic reynolds numbers

Heat transfer in an oscillating flow at high acoustic Reynolds number has been investigated using the mass-transfer analogy. Subliming naphthalene has been used in the experiments. In these experiments the acoustic Reynolds number was varied over a range from well below the values where acoustically generated turbulence is expected to occur to values above the anticipated transition value. A mass transfer (or heat transfer) rate increasing with Reynolds number, as would be expected with a turbulent flow, is observed, but beginning at Reynolds numbers an order of magnitude below the expected turbulent transition values and continuing with the same form to values well above the transition Reynolds number.

Direct numerical simulation of acoustic/shear flow interactions in two-dimensional ducts

The interaction between an imposed monochromatic, time-dependent acoustic disturbance and a steady mean shear flow in a two-dimensional duct is studied using direct numerical simulation. Unlike previously reported numerical results, the long-time acoustic response is captured through implementation of accurate nonreflecting boundary conditions. Below a certain cutoff frequency, the acoustic field is a nearly planar traveling wave propagating axially along the duct. Above this cutoff frequency, oblique waves are generated due to both acoustic refraction and cross-stream dependent source oscillation, leading to an alternating pattern of higher acoustic pressures at the wall and the centerline, downstream of the disturbance source. At resonant conditions, the growth of the oblique wave, which is nearly transverse, dominates the axial wave, leading to a phase change of 180 deg after their interaction. The thickness of the acoustic boundary layer and its response to imposed disturbances are also in good agreement with theory. These results are consistent with previously published theoretical predictions and represent their first numerical verification. Nomenclature #00 = reference speed of sound, also reference velocity Cp = constant pressure specific heat, temperature independent et = internal energy per unit volume h = duct half-width i, j,k = coordinate directions in Cartesian tensor notation L = computational length of duct M = mean flow Mach number Pr = Prandtl number p = pressure qj = heat flux vector component in the jth direction Re = acoustic Reynolds number in the calculation Rec = duct Reynolds number T = temperature t = time variable uk -• velocity component in the &th coordinate direction

Attenuation and Distortion of a Compression Wave Propagating in a High-Speed Railaway Tunnel.

Compression waves generated by a high-speed train entering a tunnel were measured in three Shinkansen tunnels and the results were compared with the numerical values calculated using the TVD scheme. The strength of a compression wave is exponentially attenuated with distance as it propagates along the tunnel in both slab and ballast track tunnels, and the attenuation in the ballast track tunnel is considerably larger than that in the slab track tunnel. In the slab track tunnel, the compression wave is steepened as it propagates, while it spreads in the ballast track tunnel. The criterion for judgment whether the compression wave is steepened or spreads is expressed by the value of acoustic Reynolds number of about l0∼15.

Weakly nonlinear waves and acoustic streaming produced by a vibrating strip flush with a plane wall

The weakly nonlinear propagation of a two‐dimensional wave, which is radiated into a half‐space from a sinusoidally vibrating strip mounted on a plane wall, is studied theoretically. It is supposed that the wavelength of radiated waves is of the same order as the width of the strip, and that the acoustic Reynolds number is sufficiently large. The entire propagation process, from generation of sound to the stage where the amplitude of a sawtooth wave is saturated, is analyzed in the leading‐order approximation. In a near field, linear wave theory is valid to first approximation. The asymptotic form of its time‐averaged acoustic intensity can have sidelobes in addition to a central lobe. Acoustic streaming occurs near the strip in the next order, whose flow pattern differs according to a normalized frequency which is less or greater than a critical frequency. In the far field, a simple‐wave equation is exactly solved and the subsequent evolution into the sawtooth wave is examined using the equal‐areas rule. These two‐dimensional waves may be regarded as cylindrical waves with directivity. At greater distances, the amplitude saturation becomes independent of direction.

Two-dimensional weak shock-vortex interaction in a mixing zone

The interaction between a vortex or a pair of vortices and a shock is studied by using two-dimensional direct numerical simulation. The deformation of the shock structure is analyzed and the mechanisms leading to the formation of triple points are underscored. It is shown that they are related to the appearance of pressure gradients in the direction parallel to the shock resulting from the shock-vortex interaction. A distribution of an inert chemical species, i.e., mixture fraction, is prescribed within the vortex. From its time evolution, one analyzes the coupling between the response of the shock to the disturbance and the change in mixing rate. Modifications of the maximum of the scalar gradient are observed in the direction perpendicular to the shock and also, to a smaller extent, in the direction parallel to the shock. Nomenclature A(s) = stretching function of the mesh a,b,c,d = coefficients of the FADE scheme D = diffusion coefficient of the inert chemical species L = reference length of the problem M = Mach number N = total number of grid points in streamwise direction P = pressure Pr = Prandtl number q, qr = mesh stretching ratio and stretching rate R = radius of the vortex Re = acoustic Reynolds number (r, ft) = polar coordinates s = position on the uniform mesh