Analytical, computational, and experimental study of thermoviscous acoustic damping in perforated micro-electro-mechanical systems with flexible diaphragm.

An analytical model for the damping and spring force coefficients of micro-electro-mechanical systems (MEMS) with a flexible diaphragm is developed. The model is based on the low reduced-frequency method, which includes thermal and viscous losses as well as inertial and compressibility effects. Specifically, the solutions are derived for circular MEMS with a clamped diaphragm with both open-edge and closed-edge boundaries. The deflection function of the circular clamped diaphragm is incorporated into the thermoviscous acoustic (TA) formulation to take into account the effect of the flexibility of the diaphragm. TA finite-element analysis (FEA) is also used to develop a computational model. The analytical results are in good agreement with the FEA results for a wide range of parameters and frequencies. The significance of the effect of the flexibility of the diaphragm on damping for actual MEMS is demonstrated. Measurements of the damping coefficient of circular MEMS are conducted for experimental validation of the presented model. The small difference between the experimental results and the results from the model (less than 6%) validates the accuracy of the presented model. The proposed analytical model can be applied to MEMS with various geometries and boundary conditions.

Thermo-viscous acoustic modeling of perforated micro-electro-mechanical systems (MEMS).

An analytical model based on the low reduced-frequency method is developed for the damping and spring force coefficients of micro-electro-mechanical systems (MEMS) structures. The model is based on a full-plate approach that includes thermal and viscous losses and hole end effects, as well as inertial and compressibility effects. Explicit analytical formulas are derived for damping and spring forces of perforated circular MEMS with open and closed edge boundary conditions. A thermo-viscous finite-element method (FEM) model is also developed for the numerical solution of the problem. Results for the damping and spring coefficients from the analytical models are in good agreement with the FEM results over a large range of frequencies and parameters. The analytic formulas obtained for the damping and spring coefficients provide a useful tool for the design and optimization of perforated MEMS. Specifically, it is shown that for a fixed perforation ratio of the back-plate the radius of the holes can be optimized to minimize the damping.

Acoustic end corrections for micro-perforated plates.

Micro-perforated plates (MPPs) are acoustically important elements in micro-electro-mechanical systems (MEMS). In this work an analytical solution for perforated plates is combined with finite element method (FEM) to develop formulas for the reactive and resistive end effects of the perforations on the plate. The reactive end effect is found to depend on the hole radius and porosity. The resistive end effect is found to depend on hole radius only. FEM is also used to develop an understanding of the loss mechanism that corresponds to the resistive end effects. The developed models can be used in optimization studies of the MEMS and MPPs.

Calculated wind noise for an infrasonic wind noise enclosure.

A simple calculation of the wind noise measured at the center of a large porous wind fence enclosure is developed. The calculation provides a good model of the measured wind noise, with a good agreement within ±5 dB, and is derived by combining the wind noise contributions from (a) the turbulence-turbulence and turbulence-shear interactions inside the enclosure, (b) the turbulence interactions on the surface of the enclosure, and (c) the turbulence-shear interactions outside of the enclosure. Each wind noise contribution is calculated from the appropriate measured turbulence spectra, velocity profiles, correlation lengths, and the mean velocity at the center, surface, and outside of the enclosure. The model is verified by comparisons of the measured wind noise to the calculated estimates of the differing noise contributions and their sum.

Infrasonic wind noise under a deciduous tree canopy.

In a recent paper, the infrasonic wind noise measured at the floor of a pine forest was predicted from the measured wind velocity spectrum and profile within and above the trees [Raspet and Webster, J. Acoust. Soc. Am. 137, 651-659 (2015)]. This research studies the measured and predicted wind noise under a deciduous forest with and without leaves. A calculation of the turbulence-shear interaction pressures above the canopy predicts the low frequency peak in the wind noise spectrum. The calculated turbulence-turbulence interaction pressure due to the turbulence field near the ground predicts the measured wind noise spectrum in the higher frequency region. The low frequency peak displays little dependence on whether the trees have leaves or not. The high frequency contribution with leaves is approximately an order of magnitude smaller than the contribution without leaves. Wind noise levels with leaves are very similar to the wind noise levels in the pine forest. The calculated turbulence-shear contribution from the wind within the canopy is shown to be negligible in comparison to the turbulence-turbulence contribution in both cases. In addition, the effect of taller forests and smaller roughness lengths than those of the test forest on the turbulence-shear interaction is simulated based on measured meteorological parameters.

Wind fence enclosures for infrasonic wind noise reduction.

A large porous wind fence enclosure has been built and tested to optimize wind noise reduction at infrasonic frequencies between 0.01 and 10 Hz to develop a technology that is simple and cost effective and improves upon the limitations of spatial filter arrays for detecting nuclear explosions, wind turbine infrasound, and other sources of infrasound. Wind noise is reduced by minimizing the sum of the wind noise generated by the turbulence and velocity gradients inside the fence and by the area-averaging the decorrelated pressure fluctuations generated at the surface of the fence. The effects of varying the enclosure porosity, top condition, bottom gap, height, and diameter and adding a secondary windscreen were investigated. The wind fence enclosure achieved best reductions when the surface porosity was between 40% and 55% and was supplemented by a secondary windscreen. The most effective wind fence enclosure tested in this study achieved wind noise reductions of 20-27 dB over the 2-4 Hz frequency band, a minimum of 5 dB noise reduction for frequencies from 0.1 to 20 Hz, constant 3-6 dB noise reduction for frequencies with turbulence wavelengths larger than the fence, and sufficient wind noise reduction at high wind speeds (3-6 m/s) to detect microbaroms.

Wind noise under a pine tree canopy.

It is well known that infrasonic wind noise levels are lower for arrays placed in forests and under vegetation than for those in open areas. In this research, the wind noise levels, turbulence spectra, and wind velocity profiles are measured in a pine forest. A prediction of the wind noise spectra from the measured meteorological parameters is developed based on recent research on wind noise above a flat plane. The resulting wind noise spectrum is the sum of the low frequency wind noise generated by the turbulence-shear interaction near and above the tops of the trees and higher frequency wind noise generated by the turbulence-turbulence interaction near the ground within the tree layer. The convection velocity of the low frequency wind noise corresponds to the wind speed above the trees while the measurements showed that the wind noise generated by the turbulence-turbulence interaction is near stationary and is generated by the slow moving turbulence adjacent to the ground. Comparison of the predicted wind noise spectrum with the measured wind noise spectrum shows good agreement for four measurement sets. The prediction can be applied to meteorological estimates to predict the wind noise under other pine forests.

Wind noise measured at the ground surface.

Measurements of the wind noise measured at the ground surface outdoors are analyzed using the mirror flow model of anisotropic turbulence by Kraichnan [J. Acoust. Soc. Am. 28(3), 378-390 (1956)]. Predictions of the resulting behavior of the turbulence spectrum with height are developed, as well as predictions of the turbulence-shear interaction pressure at the surface for different wind velocity profiles and microphone mounting geometries are developed. The theoretical results of the behavior of the velocity spectra with height are compared to measurements to demonstrate the applicability of the mirror flow model to outdoor turbulence. The use of a logarithmic wind velocity profile for analysis is tested using meteorological models for wind velocity profiles under different stability conditions. Next, calculations of the turbulence-shear interaction pressure are compared to flush microphone measurements at the surface and microphone measurements with a foam covering flush with the surface. The measurements underneath the thin layers of foam agree closely with the predictions, indicating that the turbulence-shear interaction pressure is the dominant source of wind noise at the surface. The flush microphones measurements are intermittently larger than the predictions which may indicate other contributions not accounted for by the turbulence-shear interaction pressure.

Improved prediction of the turbulence-shear contribution to wind noise pressure spectra.

In previous research [Raspet et al., J. Acoust. Soc. Am. 123(3), 1260-1269 (2008)], predictions of the low frequency turbulence-turbulence and turbulence-mean shear interaction pressure spectra measured by a large wind screen were developed and compared to the spectra measured using large spherical wind screens in the flow. The predictions and measurements agreed well except at very low frequencies where the turbulence-mean shear contribution dominated the turbulence-turbulence interaction pressure. In this region the predicted turbulence-mean shear interaction pressure did not show consistent agreement with microphone measurements. The predicted levels were often much larger than the measured results. This paper applies methods developed to predict the turbulence-shear interaction pressure measured at the ground [Yu et al., J. Acoust. Soc. Am. 129(2), 622-632 (2011)] to improve the prediction of the turbulence-shear interaction pressure above the ground surface by incorporating a realistic wind velocity profile and realistic turbulence anisotropy. The revised prediction of the turbulence-shear interaction pressure spectra compares favorably with wind-screen microphone measurements in large wind screens at low frequency.

Measurement of wind noise levels in streamlined probes.

This paper investigates the wind noise pressure spectra measured by aerodynamically designed devices in turbulent flow. Such measurement probes are often used in acoustic measurements in wind tunnels to reduce the pressure fluctuations generated by the interaction of the devices with the incident flow. When placed in an outdoor turbulent environment however, their performance declines noticeably. It is hypothesized that these devices are measuring the stagnation pressures generated by the cross flow components of the turbulence. Predictions for the cross flow contribution to the stagnation pressure spectra based on measured velocity spectra are developed, and are then compared to the measured pressure spectra in four different probe type devices in windy conditions outdoors. The predictions agree well with the measurements and show that the cross flow contamination coefficient is on the order of 0.5 in outdoor turbulent flows in contrast to the published value of 0.15 for measurements in a turbulent jet indoors.

Thermoacoustic power conversion using a piezoelectric transducer.

The predicted efficiency of a simple thermoacoustic waste heat power conversion device has been investigated as part of a collaborative effort combining a thermoacoustic engine with a piezoelectric transducer. Symko et al. [Microelectron. J. 35, 185-191 (2004)] at the University of Utah built high frequency demonstration engines for this application, and Lynn [ASMDC report, accession number ADA491030 (2008)] at the University of Washington designed and built a high efficiency piezoelectric unimorph transducer for electroacoustic conversion. The design presented in this paper is put forward to investigate the potential of a simple high frequency, air filled, standing wave thermoacoustic device to be competitive with other small generator technologies such as thermoelectric devices. The thermoacoustic generator is simulated using a low-amplitude approximation for thermoacoustics and the acoustic impedance of the transducer is modeled using an equivalent circuit model calculated from the transducer's mechanical and electrical properties. The calculations demonstrate that a device performance of around 10% of Carnot efficiency could be expected from the design which is competitive with currently available thermoelectric generators.

Thermoacoustic properties of fibrous materials.

The thermoacoustic properties of fibrous materials are studied using a computational fluid simulation as a test of proposed analytical models for propagation in porous materials with an ambient temperature gradient. The acoustic properties of porous materials have been understood in terms of microstructural models that approximate the material as an array of pores with empirical shape factors used to fit the pore theory to the material. An extension of these theories of acoustics to the thermoacoustic case with an ambient temperature gradient has been proposed by Roh et al. [J. Acoust. Soc. Am. 121, 1413-1422 (2007)] and a model based on Wilson's relaxation approximation for porous acoustics [J. Acoust. Soc. Am. 94, 1136-1145 (1993)] is proposed herein, but the predictions of these analytical models have not been tested successfully against measurements. Accurately characterizing the effects of the applied temperature gradient in a wide bandwidth laboratory setup have proven difficult; as a result, the authors conducted a numerical simulation of propagation within a fibrous geometry in order to test the predictions of the analytical models. The results for several fibrous samples show that the models yield a reliable prediction of thermoacoustic performance from the shape factors and relaxation times.

Low frequency wind noise contributions in measurement microphones.

In a previous paper [R. Raspet, et al., J. Acoust. Soc. Am. 119, 834-843 (2006)], a method was introduced to predict upper and lower bounds for wind noise measured in spherical wind-screens from the measured incident velocity spectra. That paper was restricted in that the predictions were only valid within the inertial range of the incident turbulence, and the data were from a measurement not specifically designed to test the predictions. This paper extends the previous predictions into the source region of the atmospheric wind turbulence, and compares the predictions to measurements made with a large range of wind-screen sizes. Predictions for the turbulence-turbulence interaction pressure spectrum as well as the stagnation pressure fluctuation spectrum are calculated from a form fit to the velocity fluctuation spectrum. While the predictions for turbulence-turbulence interaction agree well with measurements made within large (1.0 m) wind-screens, and the stagnation pressure predictions agree well with unscreened gridded microphone measurements, the mean shear-turbulence interaction spectra do not consistently appear in measurements.

Parallel capillary-tube-based extension of thermoacoustic theory for random porous media.

Thermoacoustic theory is extended to stacks made of random bulk media. Characteristics of the porous stack such as the tortuosity and dynamic shape factors are introduced into the thermoacoustic wave equation in the low reduced frequency approximation. Basic thermoacoustic equations for a bulk porous medium are formulated analogously to the equations for a single pore. Use of different dynamic shape factors for the viscous and thermal effects is adopted and scaling using the dynamic shape factors and tortuosity is demonstrated. Comparisons of the calculated and experimentally derived thermoacoustic properties of reticulated vitreous carbon and aluminum foam show good agreement. A consistent mathematical model of sound propagation in a random porous medium with an imposed temperature is developed. This treatment leads to an expression for the coefficient of the temperature gradient in terms of scaled cylindrical thermoviscous functions.

Infrasonic wind-noise reduction by barriers and spatial filters.

This paper reports experimental observations of wind speed and infrasonic noise reduction inside a wind barrier. The barrier is compared with "rosette" spatial filters and with a reference site that uses no noise reduction system. The barrier is investigated for use at International Monitoring System (IMS) infrasound array sites where spatially extensive noise-reducing systems cannot be used because of a shortage of suitable land. Wind speed inside a 2-m-high 50%-porous hexagonal barrier coated with a fine wire mesh is reduced from ambient levels by 90%. If the infrasound wind-noise level reductions are all plotted versus the reduced frequency given by f*L/v, where L is the characteristic size of the array or barrier, f is the frequency, and v is the wind speed, the reductions at different wind speeds are observed to collapse into a single curve for each wind-noise reduction method. The reductions are minimal below a reduced frequency of 0.3 to 1, depending on the device, then spatial averaging over the turbulence structure leads to increased reduction. Above the reduced corner frequency, the barrier reduces infrasonic noise by up to 20 to 25 dB. Below the corner frequency the barrier displays a small reduction of about 4 dB. The rosettes display no reduction below the corner frequency. One other advantage of the wind barrier over rosette spatial filters is that the signal recorded inside the barrier enters the microbarometer from free air and is not integrated, possibly out of phase, after propagation through a system of narrow pipes.

Theory of inert gas-condensing vapor thermoacoustics: propagation equation.

The theory of acoustic propagation in an inert gas-condensing vapor mixture contained in a cylindrical pore with wet walls and an imposed temperature gradient is developed. It is shown that the vapor diffusion effects in the mixture are analogous to the heat diffusion effects in the thermoacoustics of inert gases, and that these effects occur in parallel with the heat diffusion effects in the wet system. The vapor diffusion effects can be expressed in terms of the thermoviscous function F(lambda) used in the theory of sound propagation of constant cross-section tubes. As such, these results can be extended to any shape parallel-walled tube. The propagation equations predict that the temperature gradient required for onset of sound amplification in a wet-walled prime mover is much lower than the corresponding temperature gradient for an inert gas prime mover. The results of a measurement of the onset temperature of a simple demonstration prime mover in air with a dry stack and with a stack wetted with water provide a qualitative verification of the theory.

Theory of inert gas-condensing vapor thermoacoustics: transport equations.

The preceding paper [J. Acoust. Soc. Am. 112, 1414-1422 (2002)] derives the propagation equation for sound in an inert gas-condensing vapor mixture in a wet-walled pore with an imposed temperature gradient. In this paper the mass, enthalpy, heat, and work transport equations necessary to describe the steady-state operation of a wet-walled thermoacoustic refrigerator are derived and presented in a form suitable for numerical evaluation. The requirement that the refrigerator operate in the steady state imposes zero mass flux for each species through a cross section. This in turn leads to the evaluation of the mass flux of vapor in the system. The vapor transport and heat transport are shown to work in parallel to produce additional cooling power in the wet refrigerator. An idealized calculation of the coefficient of performance (COP) of a wet-walled thermoacoustic refrigerator is derived and evaluated for a refrigeration system. The results of this calculation indicate that the wet-walled system can improve the performance of thermoacoustic refrigerators. Several experimental and practical questions and problems that must be addressed before a practical device can be designed and tested are described.

Application of an acoustic backscatter technique for characterizing the roughness of porous soil.

An acoustic backscatter technique proposed by Oelze et al. [J. Acoust. Soc. Am. 109, 1826-1832 (2001)] was used to characterize the roughness of porous soil surfaces. Roughness estimation errors are minimized when the effective flow resistivity of the porous soil is high, e.g., above 300,000 mks Rayls/m. Four soil plots were constructed by roughening soil with farming implements. Three plots were sealed using Saran powder dissolved in methyl ethyl ketone (MEK) and then covered to prevent further weathering. A fourth plot was left in the open and exposed to rainfall, which also acted to seal the surface and further change the roughness. In sealing the surface the effective flow resistivity of the surface was increased above 300,000 mks Rayls/m, which is typical for weathered agricultural surfaces. The roughness power spectra of the soil surfaces were measured by acoustic backscatter and alternatively by a laser profiler. Regression analysis was used to approximate each roughness power spectrum versus roughness wave number with a best-fit line. The best-fit line was used to calculate the rms height and the correlation length of the rough surface by integrating the approximate roughness power spectrum over a range of roughness wave number values. The range of roughness wave number values defines the roughness length scales used in the statistical calculations. High-roughness wave numbers correspond to smaller length scales of roughness and low-roughness wave numbers correspond to larger length scales of roughness. Over certain ranges of roughness wave number values the statistics from the acoustic backscatter and laser profiler measurements is in good agreement. However, as the low-cutoff roughness wave number is decreased and the high-cutoff roughness wave number is increased, agreement between the laser and acoustic techniques diminishes.

Modification of sonic boom wave forms during propagation from the source to the ground.

A number of physical processes work to modify the shape of sonic boom wave forms as the wave form propagates from the aircraft to a receiver on the ground. These include frequency-dependent absorption, nonlinear steepening, and scattering by atmospheric turbulence. In the past two decades, each of these effects has been introduced into numerical prediction algorithms and results compared to experimental measurements. There is still some disagreement between measurements and prediction, but those differences are now in the range of tens of percent. The processes seem to be understood. The present understanding of sonic boom evolution will be presented along with experimental justification.