William Slaton

Evaporation–Condensation Effects on Resonant Photoacoustics of Volatile Aerosols

In determining the optical properties of the atmosphere, the measurement of light absorption by aerosols is particularly challenging, and yet it is important because of the influence of strongly absorbing black carbon on climate and atmospheric visibility. The photoacoustic method obtains aerosol light absorption in situ, without use of filters, by acoustic measurement of the heat generated from aerosol light absorption, and its transfer to the surrounding air. However, in the general case, volatile aerosols heated by light absorption may also cool by evaporation (mass transfer). In this paper, the limiting case of the photoacoustic response of a volatile aerosol is compared with that of a dry aerosol to further the understanding of the data obtained with photoacoustic instruments. While the theory of photoacoustics of volatile aerosols for low-frequency, nonresonant cells has already been developed, current methods employ high-frequency, acoustically resonant photoacoustic instruments for quantifying atmospheric aerosol light absorption and vehicle exhaust mass concentration associated with black carbon. In this paper, a complete theory of photoacoustics for volatile aerosols is developed that includes additional terms to allow for higher-frequency devices, large particles, and high particle densities. Numerical calculations are used to determine the limits of various approximations.

Working gases in thermoacoustic engines

The best working gases for thermoacoustic refrigeration have high ratios of specific heats and low Prandtl numbers. These properties can be optimized by the use of a mixture of light and heavy noble gases. In this paper it is shown that light noble gas-heavy polyatomic gas mixtures can result in useful working gases. In addition, it is demonstrated that the onset temperature of a heat driven prime mover can be minimized with a gas with large Prandtl number and small ratio of specific heats. The gas properties must be optimized for the particular application of thermoacoustics; it cannot be assumed that high specific heat ratio and low Prandtl number are always desirable.

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.

Acoustic power measurements of a damped aeroacoustically driven resonator

Strong self-sustained acoustic oscillations may occur in a gas pipe network under certain gas flow velocities within the network. The pipe network under consideration consists of a main pipe, with a variable mean airflow, with two closed coaxial side branches of variable but equal length joined to the main pipe. Coupling between resonant acoustic standing waves and instabilities of the shear layers separating the flow in the main pipe from the stagnant gas in the closed side branches leads to strong acoustic oscillations at a frequency corresponding to the half-wavelength acoustic mode defined by the total side-branch length. An acoustic damper consisting of a variable acoustic resistance and compliance is used to dissipate power from the resonating mode. The response of the aeroacoustically driven resonator to variable damping will be examined for different fluid flow regimes as well as side-branch geometries.

An aeroacoustically driven thermoacoustic heat pump

The mean flow of gas in a pipe past a cavity can excite the resonant acoustic modes of the cavity--much like blowing across the top of a bottle. The periodic shedding of vortices from the leading edge of the mouth of the cavity feeds energy into the acoustic modes which, in turn, affect the shedding of the next vortex. This so-called aeroacoustic whistle can excite very high amplitude acoustic standing waves within a cavity defined by coaxial side branches closed at their ends. The amplitude of these standing waves can easily be 20% of the ambient pressure at optimal gas flow rates and ambient pressures within the main pipe. A standing wave thermoacoustic heat pump is a device which utilizes the in-phase pressure and displacement oscillations to pump heat across a porous medium thereby establishing, or maintaining, a temperature gradient. Experimental results of a combined system of aeroacoustic sound source and a simple thermoacoustic stack will be presented.

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.

Shape factor characterization of fibrous media with a temperature gradient

Recent theoretical work generalizes thermoacoustic theory to random porous media [H. S. Roh et. al., J. Acoust. Soc. Am. 121(3), 1413–1422 (2007)]. Characteristics of the porous media, such as the tortuosity and dynamic shape factors for viscous and thermal effects, are introduced into the thermoacoustic wave equation and may be determined by suitable impedance measurements at zero temperature gradient. This theoretical approach may also be used to model fibrous media, such as fiberglass or steel wool. A new technique to determine the scaling factors for fibrous media utilizing a single‐step finite difference inversion of the thermoacoustic wave equation [R. Raspet et. al., J. Acoust. Soc. Am. 103(5), 2395–2402 (1998)] with zero temperature gradient will be presented. Roh et. al. predict that acoustic gain with a nonzero temperature gradient may be written in terms of these scaled cylindrical dissipation functions. The acoustic gain term may also be determined by suitable application of the single‐step fi...

Determining the Coefficient of Discharge for a Draining Container

The flow of fluids through open containers is a topic studied frequently in introductory physics classes. A fluid mechanics class delves deeper into the topic of fluid flow through open containers with holes or barriers. The flow of a fluid jet out of a sharp-edged orifice rarely has the same area as the orifice due to a fluid flow phenomenon known as the vena contracta. The area of a fluid jet out of an orifice is related to the actual area of the orifice by a value known as the coefficient of discharge, Cd. The purpose of this paper is to develop a mathematical model for a draining open container and an experimental method that will efficiently determine the coefficient of discharge for such a system. Prior work in physics education literature has developed a method for measuring the flow of a fluid out of an orifice using ultrasonic motion detectors. In this paper we present data that show our method can be used to find the coefficient of discharge within the expected literature values for sharp-edged ...

Aeroacoustic response of coaxial wall-mounted Helmholtz resonators in a low-speed wind tunnel

The aeroacoustic response of coaxial wall-mounted Helmholtz resonators with different neck geometries in a low-speed wind tunnel has been investigated. Experimental test results of this system reveal a strong aeroacoustic response over a Strouhal number range of 0.25 to 0.1 for both increasing and decreasing the flow rate in the wind tunnel. Aeroacoustic response in the low-amplitude range O(10(-3)) < Vac/Vflow < O(10(-1)) has been successfully modeled by describing-function analysis. This analysis, coupled with a turbulent flow velocity distribution model, gives reasonable values for the location in the flow of the undulating stream velocity that drives vortex shedding at the resonator mouth. Having an estimate for the stream velocity that drives the flow-excited resonance is crucial when employing the describing-function analysis to predict aeroacoustic response of resonators.