1) Field of Invention
This invention relates to acoustic resonators which are designed to provide the specific harmonic phases and amplitudes required to predetermine the waveform of extremely large acoustic pressure oscillations, having specific applications to acoustic compressors.
2) Description of Related Art
It is well known in the field of acoustics that when acoustic pressure amplitudes are finite compared to the medium's undisturbed ambient pressure, the resulting nonlinear effects will generate sound waves at harmonics of the fundamental frequency. We will hereafter refer to these nonlinearly generated sound waves as harmonics.
For both traveling and standing waves, the presence of high amplitude harmonics is associated with the formation of shock waves, which severely limit a wave's peak-to-peak pressure amplitude. Shock formation requires harmonic amplitudes that are significant relative to the amplitude of the sound wave at the fundamental frequency. We will hereafter refer to these as high relative amplitude harmonics.
For finite amplitude traveling waves, the harmonic relative amplitudes will depend primarily on the nonlinear properties of the medium. For finite amplitude standing waves occurring in a resonant cavity the harmonic relative amplitudes will likewise depend on the medium, but also are strongly influenced by the resonator's boundary conditions. The boundary conditions of the resonator are determined by the geometry of the walls and by the acoustical properties of the wall material and the fluid in the resonator.
As explained in U.S. Pat. No. 5,319,938, acoustic resonators can now be designed which provide very large and nearly sinusoidal pressure oscillations. FIG. 1 shows the waveform of a sinusoidal pressure wave. A sinusoidal wave is pressure symmetric implying that P.sub.+ = P.sub.- , where P.sub.+ and P.sub.- are the maximum positive and negative pressure amplitudes respectively. If a sinusoidal pressure oscillation is generated in a resonator having an ambient pressure P.sub.0, then (P.sub.0 + P.sub.+ ) cannot exceed 2P.sub.0, since otherwise the pressure symmetry would require that (P.sub.0 - P.sub.- ) be less than zero absolute, which is impossible. Thus, the maximum peak-to-peak pressure a sinusoidal oscillation can provide is 2P.sub.0. This ignores any changes in the ambient pressure caused by nonlinear processes driven by the acoustic pressures.
The '938 patent provides shock-free waves by preventing formation of high relative amplitude harmonics. However, there are acoustic resonator applications where the resulting sinusoidal waveforms present a limitation. For example, resonators used in acoustic compressors must at times provide compressions requiring P.sub.+ to be larger than P.sub.0 by a factor of 3 or more. An acoustic compressor used in low-temperature Rankine-cycle applications may require P.sub.+ to exceed 215 psia for a P.sub.0 of only 70 psia. The acoustic wave needed to fit these conditions would require an extreme pressure asymmetry (about the ambient pressure P.sub.0) between P.sub.- and P.sub.+.
Previously, the generation of resonant pressure-asymmetric waves presented specific unsolved problems. For a waveform to deviate significantly from a sinusoid, it must contain high relative amplitude harmonics. These harmonics would normally be expected to lead to shock formation, which can critically limit peak-to-peak pressure amplitudes as well as cause excessive energy dissipation.
Resonant acoustic waves have been studied theoretically and experimentally. With respect to the present invention, these studies can be grouped into two categories: (i) harmonic resonators driven off-resonance, and (ii) anharmonic resonators driven on-resonance.
A resonator is defined as "harmonic" when it has a set of standing wave mode frequencies that are integer multiples of another resonance frequency. For the following discussions only longitudinal resonant modes are considered. Harmonically tuned resonators produce shock waves if finite amplitude acoustic waves are excited at a resonance frequency. For this reason harmonic resonator studies which examine non-sinusoidal, non-shocked waveforms focus primarily on waveforms produced at frequencies off-resonance. Driving a resonator off-resonance severely limits the peak-to-peak pressure amplitudes attainable.
The following references are representative of the harmonic resonator studies: (W. Chester, "Resonant oscillations in closed tubes," J. Fluid Mech. 18, 44-64 (1964)), (A. P. Coppens and J. V. Sanders, "Finite-amplitude standing waves in rigid-walled tubes," J. Acoust. Soc. Am. 43, 516-529 (1968)), (D. B. Cruikshank, Jr., "Experimental investigations of finite-amplitude acoustic oscillations in a closed tube," J. Acoust Soc. Am. 43, 1024-1036 (1972)) and (P. Merkli, H. Thoman, "Thermoacoustic effects in a resonance tube," J. Fluid Mech. 70, 1161-177 (1975))
A resonator is defined as "anharmonic" when its does not have a set of standing wave mode frequencies that are integer multiples of another resonance frequency. Studies of anharmonic resonators driven on-resonance are usually motivated by applications in which the elimination of high relative amplitude harmonics is necessary. For example, thermoacoustic engine resonators require high amplitude sine waves, and thus are designed for the greatest possible reduction of harmonic amplitudes. An example of such a study can be found in the work of D. Felipe Gaitan and Anthony A. Atchley (D. F. Gaitan and A. A. Atchley, "Finite amplitude standing waves in harmonic and anharmonic tubes," J. Acoust. Soc. Am. 93,2489-2495 (1993)).
Gaitan and Atchley provide anharmonic resonators by using geometries with sections of different diameter. The area changes occurred over a distance that was small compared to the length of the resonator. As explained in U.S. Pat. No. 5,319,938 this approach tends to provide significant suppression of the wave's harmonics, thus providing sinusoidal waveforms.
In summary, those resonators driven on-resonance at finite amplitudes either produced sinusoidal waves or shock waves. Resonators driven off-resonance resulted in very low peak-to-peak pressure amplitudes.
The ability to provide high peak-to-peak pressure amplitude, non-sinusoidal, unshocked waves of a desired waveform would represent a significant advance for high compression acoustic resonators. Such waveforms require high relative amplitude harmonics to exist when the resonator is excited at a resonant frequency.
Consequently, there exists a need for resonators that can synthesize unshocked waveforms at high pressure amplitudes.