Craig J. Hickey

Choosing Biot parameters for modeling water-saturated sand

The work of Chotiros [J. Acoust. Soc. Am. 97, 199–214 (1995)] has stimulated renewed interest in detecting the Biot type II (slow) P wave for the purpose of ocean bottom characterization. Chotiros postulates that total internal reflection of the type I (fast) P wave can occur at a water–sediment interface and that the observed refracted energy below the critical angle is associated with the type II (slow) P wave. The choice of parameters used in the Biot theory to model these observations is discussed. Two major differences between the parameter set proposed by Chotiros and previous parameter sets for sandy sediments exist. First, the value for the unjacketed bulk modulus, Kr, is about five times less than the bulk modulus for quartz crystals, which is commonly used. This value is obtained by equating it to a value of effective grain modulus measured by Molis and Chotiros [J. Acoust. Soc. Am. 91, 2483(A) (1992)]. Second, the value for the frame bulk modulus, Kb, obtained by fitting to measured values of t...

The effect of evaporation-condensation on sound propagation in cylindrical tubes using the low reduced frequency approximation

In order to better understand the effects of water on sound attenuation in porous materials, Mao [J. Acoust. Soc. Am. 104, 664–670 (1998)] has investigated sound propagation in a gas–water vapor mixture contained in a cylindrical tube. He used the Rayleigh eigenmode calculation to evaluate the high and low frequency limits of attenuation in an air-filled tube with wet walls. However, he was unable to obtain a general analytical expression and the interpretation of the limits is difficult because of their complexity. The formulation of the problem presented in this paper parallels the “low reduced frequency method” of Tijdeman [J. Sound Vib. 39, 1–33 (1975)]. In contrast to the earlier results, an analytical solution for the propagation constant is obtained which allows for calculation of attenuation over a broad frequency range. The simple expressions obtained in the small and large shear wave number limits provide useful insight into the behavior of the gas–water vapor mixture.

Measurements of two types of dilatational waves in an air-filled unconsolidated sand

This study consists of laboratory measurements of dilatational waves propagating through an air-filled unconsolidated sand. One excitation technique consists of a loudspeaker suspended in the air above the packing of sand. A second excitation technique uses a mechanical shaker in contact with the sand. The transmitted signals are received using microphones and geophones located at various depths within the sand. An interpretation based on measured phase speeds indicates that the transmitted energy from the suspended loudspeaker source is partitioned primarily but not exclusively into the type-II dilatational wave. This wave attenuates rapidly and is only detected at depths of less than about 15 cm for this particular sample. At the deeper depths the detected signal is associated with the type-I dilatational wave. The mechanical shaker produces only a type-I dilatational wave. Both the geophone and microphone sensors can detect both types of dilatational waves.

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.

Wind-induced ground motion

Wind noise is a problem in seismic surveys and can mask the seismic signals at low frequency. This research investigates ground motions caused by wind pressure and shear stress perturbations on the ground surface. A prediction of the ground displacement spectra using the measured ground properties and predicted pressure and shear stress at the ground surface is developed. Field measurements are conducted at a site having a flat terrain and low ambient seismic noise. Triaxial geophones are deployed at different depths to study the wind-induced ground vibrations as a function of depth and wind velocity. Comparison of the predicted to the measured wind-induced ground displacement spectra shows good agreement for the vertical component but significant underprediction for the horizontal components. To validate the theoretical model, a test experiment is designed to exert controlled normal pressure and shear stress on the ground using a vertical and a horizontal mass-spring apparatus. This experiment verifies the linear elastic rheology and the quasi-static displacements assumptions of the model. The results indicate that the existing surface shear stress models significantly underestimate the wind shear stress at the ground surface and the amplitude of the fluctuation shear stress must be of the same order of magnitude as the normal pressure. Measurement results show that mounting the geophones flush with the ground provides a significant reduction in wind noise on all three components of the geophone. Further reduction in wind noise with depth of burial is small for depths up to 40 cm.

Impedance and Brewster angle measurement for thick porous layers

For thin nonlocally reacting porous layers, a method derived from the work of Chien and Soroka [J. Sound Vib. 43, 9–20 (1975)] has been used to localize the pole of the reflection coefficient located at an angle close to grazing incidence and to measure the surface impedance at this angle. A very simple experimental setup is used to obtain measurements on materials with large flow resistivity, at frequencies larger than 1 kHz, using samples with areas on the order of 1 m2. This method is used in the present work to measure the surface impedance of acoustically thick porous layers of Ottawa sand and glass beads. There is good agreement between the measurements and predicted values. The method is also applied to study the effects of surface sealing. Sealing is modeled as a thin screen of higher flow resistivity at the surface. Reasonable agreement between the measured and predicted additional flow resistance is obtained.

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.

The effect of the physical properties of the tube wall on the attenuation of sound in evaporating and condensing gas–vapor mixtures

An investigation of sound propagation in an air-water vapor mixture contained in a cylindrical tube with wet walls was recently completed [Hickey et al., J. Acoust. Soc. Am. 107, 1126-1130 (2000)]. A generalization to include the heat flux at the tube wall is presented here. The attenuation of sound in air-water vapor mixtures can be affected by the thermal properties of the tube wall. The controlling parameter is epsilons, which is a proportionality constant that relates the heat flux per degree Kelvin for the substrate to that of the gas mixture. For a given amount of heat, provided by expansion and rarefaction of the working fluid, different substrates will undergo different temperature excursions. These temperature swings at the boundary change the vapor pressure of the condensate and thus reduce the diffusion of vapor to and from the boundary resulting in a reduction of the attenuation.

Acoustic-to-seismic transfer function at the surface of a layered outdoor ground

The ratio of the surface soil particle velocity to the surface acoustic pressure is termed the acoustic to seismic transfer function. Measurements of this transfer function typically show several maximum and minimum in the frequency range between 50-500 Hz. The magnitude of this transfer function can be explained in light of the porous nature of the ground surface .The ground is modeled as a poro-elastic layer overlying a non-porous substrate. The boundary conditions at the air/porous soil and the porous soil/non- porous substrate interfaces are applied to setup the acoustic-to-seismic coupling problem. In the porous layer, up an downing going Biot Type I, II compressional and shear plane waves are allowed. In the non-porous elastic substrate down going compressional and shear plane waves are allowed. Using the Biot characteristics equations and these boundary conditions the steady state frequency dependent acoustic to seismic transfer function is calculated. Layer depths, Type I, and shear wave speeds are determined from a shallow seismic refraction survey. Soil density, air porosity and permeability are determined from other measurements. The calculated transfer functions are compared to that measured on several outdoor grounds.

The effect of mass transfer on sound propagation in cylindrical tubes using the low reduced frequency approximation

The theory for sound propagation in a gas/vapor mixture contained in a cylindrical tube is investigated. The tube is assumed to have a rigid wall covered by a thin film of water. This thin film of water acts as a source/sink for the mass and the heat associated with the vapor. This problem has been previously solved in the high‐ and low‐frequency limits using the Rayleigh eigenmode method [Y. Mao and J. M. Sabatier, J. Acoust. Soc. Am. 96, 3254(A) (1994)]. However, the interpretation of these results is limited by their complexity. This formulation of the problem parallels the low reduced frequency approximation work of Tijdeman [J. Sound Vib. 39, 1–33 (1975)]. In contrast to the earlier results an easily interpreted analytical solution for the propagation constant is obtained. The parameters governing the propagation of the sound waves are the shear wave number, Prandtl number, Schmitt number, and the reduced frequency. The limits of small and large shear wave number provide useful insight into the behav...