Bonnie Andersen

Helmholtz-like resonators for thermoacoustic prime movers

In a thermoacoustic prime mover, high acoustic output power can be achieved with a large-diameter stack and with a cavity with a large volume attached at the open end of the resonator containing the stack. The combination of resonator and cavity makes the device Helmholtz-like, with special characteristics of the resonant frequencies and quality factor, Q. Analysis of its acoustic behavior based on a model of a closed bottle presents features that are useful for the development of such prime movers for energy conversion from heat to sound. In particular, the arrangement produces in the cavity a high sound level, which is determined by the Q of the system. Comparison with a half-wave resonator type of prime mover, closed at both ends, shows the advantages of the Helmholtz-like device.

Comparing clarinet grunt and squeak notes to transitions in coupled oscillators

Under certain circumstance, a clarinet can cause an undesired squeak or grunt note. A squeak note is the clarinet shifting to a higher register—a higher set of harmonics—while a grunt note is the clarinet shifting to a lower register. One might hypothesize that such changes occur naturally in the clarinet over time. Analysis of such transitions with waterfall plots reveals a similarity to transitions made with thermoacoustically-driven coupled oscillators. For coupled oscillators, transitions can occur when the resonance of one oscillator passes through that of the other. This suggests that the cause of the undesired transitions in the clarinet are the result of one resonance (possibly the reed, which is affected by the embouchure) passing through that of the resonance of the other (likely the bore) rather than the clarinet itself relaxing to a different register as a function of time. Notes played on an artificially-blown clarinet in the second register were shown to be stable over several minutes. This ...

Qualitative analysis of mode transitions in bottle-shaped resonators with waterfall plots

A closed bottle-shaped resonator consists of the coupled neck and cavity. Such a system yields avoided crossings where the resonance of the neck matches that of the cavity when one bottle dimension is varied. Self-sustained oscillations within the bottle are generated thermoacoustically. Mode transitions were previously observed to occur at the same position within a few millimeters when a piston controlled with a translation stage was moved with a manual control to adjust the cavity length. The dominant mode was recorded using a power spectrum of the signal measured with a pressure sensor. In this study, the piston motion is automated and eight neck/cavity combinations were tested at three different piston speeds and at various input powers. The input powers were adjusted to just above thermoacoustic onset and not to exceed thermal limits of the materials used. Waterfall plots allow the visualization of the time evolution of the power spectrum where intensity is plotted both as a function of time and fre...

Acoustic frequency splitting in thermoacoustically driven coupled oscillators

Frequency splitting, or level repulsion, occurs near the point where two resonant modes of coupled oscillators intersect as one parameter is varied such that the resonance of one passes through the resonance of the other. A thermacoustic stack, which provides internal self-sustained oscillations, placed inside the neck of a closed bottle-shaped resonator can set up standing waves of the coupled neck-cavity system. The neck behaves as a quarter-wave resonator because it is closed at the top of the bottle and open at the bottom where it is attached to the cavity. The cavity being closed at the bottom and mostly closed near the neck behaves as a half-wave resonator. A one-dimensional wave equation with appropriately applied boundary conditions is used to generate solutions of the coupled neck-cavity system. These solutions reveal mode splitting near the intersections of the uncoupled neck and cavity modes. Thermoacoustic engines with bottle-shaped resonators were tested while varying one of three geometric p...

Using helium as the working fluid in thermoacoustic engines

The efficiency of thermoacoustic engines can be improved by using helium as the working fluid because it reduces viscous losses, has a higher thermal conductivity and speed of sound. The engine in this study has a bottle-shaped resonator. The neck consists of a brass cylinder, closed at the top end and a copper cylinder, open at both ends, with copper mesh screens heat exchangers between them (ID of 1.91 cm and total length of 5.24 cm). A small amount of steel wool (20 mg) functions as the stack. The neck opens into an aluminum cavity (10 cm long with an ID of 4.13 cm). A combination of two types of heat-shrink tubing and Teflon were used to connect the brass and copper pieces. The engine was evacuated of air and backfilled with helium as much as the setup would tolerate. Using an input power of 14.8 W over intervals of 0.5–3 h, it was observed that the frequency decreased in time, indicating that the helium was leaking out slowly. From the frequency data, the volume fraction of helium was calculated, ind...

Using helium as the working fluid to improve efficiency of high-frequency thermoacoustic engines

Previous work on thermoacoustic engines with bottle-shaped resonators has been done to improve performance by varying geometric parameters, using air as the working fluid. This study is focused on transitioning from air to helium for the working fluid to further improve device performance. The theoretical ratio of efficiencies was derived for the two operating fluids. The existing engine was redesigned for evacuating the air and introducing helium into the resonator and six different types of heat shrink tubing used to hold the heat exchangers in place were tested for effectiveness with a vacuum and ease of removal. The optimal stack masses for this engine operating with air and helium were theoretically estimated and tested with air using six different stack masses from 50 to 62 mg. The resonator had a cavity with a length of 10 cm and ID of 4.13 cm and a neck with a length of 2.62 cm and ID of 1.91 cm and used steel wool for the stack material. The engine was supplied 12 W from a heating element applied above the hot heat exchanger in the neck. The engine was allowed to run for 40 s after the temperature had reached a steady state and the acoustic pressure at the bottom of the cavity was measured. The optimal amount of stack in air was found to be 56 mg, and the acoustic pressure was 206 Pa, Pk-Pk. The adhesive heat shrink tubing was found to be the most effective for use with helium and ease of removal.

Hysteresis of mode transitions with varying cavity length of bottle-shaped thermoacoustic prime movers

Hysteresis behavior has been observed in transition regions to higher resonant modes of a bottle-shaped thermoacoustic prime mover (neck: 5.39 cm long, 1.91 cm ID; variable cavity with a sliding piston: up to 38 cm long, 4.76 cm ID). The neck and cavity regions behave as coupled resonators. A variable cavity with a sliding piston was constructed to study the nature of the device as the cavity length is varied. The dominant mode of operation depends on the length of the cavity, favoring successively higher modes as the cavity length increases, occurring roughly where the higher mode overlaps with the fundamental frequency of the neck region, but do not transition to lower modes at the same cavity length when shortened. Three transitions to higher modes were observed. The hysteresis was studied as a function of input power (12.0-16.5 W) and stack volume filling factor (3.0-4.9%). Preliminary results indicate that the transition region occurs shallower in the cavity and the hysteresis widens as the input pow...

Dissonant resonant modes of bottle‐shaped thermoacoustics engines.

A key component of a standing‐wave thermoacoustic engine is the resonator. A simple half‐wave resonator is not ideal, due to the loss of energy to the higher harmonics. Cylindrical resonators with regions with differing cross sections have been shown to have overtones that are not harmonics of the fundamental. For resonators composed of two adjoining concentric cylinders with two different radii, the half‐wave resonant harmonics that would be present if the radii were equal are altered. In particular, it is shown that the cylinder with the smaller radius that opens into the larger cylinder has a quarter‐wave resonator effect, while the larger‐radius cylinder has a half‐wave resonator effect. Graphs of the resonant frequencies, found numerically, plotted as a function of one geometric parameter of the resonator, show that the frequencies bend toward the asymptotes created by these quarter‐wave and half‐wave influences and that where the asymptotes cross is where the dissonance is the greatest. Experimental...

Effects of heat exchanger size on gain of thermoacoustic prime mover.

Thermoacoustic standing wave prime movers are discussed as self‐sustained oscillators whose initial growth pattern of oscillation followed by amplitude limitation can be modeled by the Van der Pol equation. The best fit solutions offer quantitative comparisons of terms related to the energy supplied to the system and the losses. This study on engines near 2.6‐kHz oscillations suggests that information on performance of the device is contained within the first second of oscillations. The Van der Pol equation is used to compare the performance of three hot heat exchangers. The hot heat exchangers used copper wire mesh with 40×40, 60×60, and 80×80 wires/in. The engine with the 40×40 mesh has a higher gain term and smaller loss term than either the 60×60 or the 80×80, as expected, since it has the largest wire diameter and the largest open area. The gain term for the three heat exchangers increases linearly with increasing surface area of the mesh in contact with the air in the resonator. This is evidenced in the build‐up of the oscillations, in agreement with the Van der Pol equation.