DELTAE solves the one-dimensional wave equation based on the usual low-amplitude, `acoustic' approximation. It solves the wave equation in a gas or liquid, in a geometry given by the user as a sequence of segments, such as ducts, compliances, transducers, and thermoacoustic stacks or regenerators. A glance through the figures below will orient the reader to the range of cases that DELTAE can handle.
Figure I.1: Driven, lossy plane-wave resonator.
Figure I.2: Driven, radiating Helmholtz resonator.
Figure I.3: Duct network.
Figure I.4: Thermoacoustic refrigerator (Hofler style).
Figure I.5: Thermoacoustic refirgerator (TALSR style).
Figure I.6: Thermoacoustic refrigerator (Garrett and Hofler style).
Figure I.7: Beer Cooler
Figure I.8: Thermoacoustically driven orifice pulse-tube refrigerator.
A solution to the appropriate 1-d wave equation is found for each segment, with pressures and volumetric velocities matched at the junctions between segments. In stacks, the wave-equation solution is found simultaneously with that of the enthalpy-flow equation in order to find the temperature profile as well as the acoustic pressure. The enthalpy flow through stacks is determined by temperatures and/or heat flows at adjacent heat exchangers.
The user of DELTAE enjoys considerable freedom in choosing which variables are computed as `solutions.' For example, in a simple plane-wave resonator (the first example below), DELTAE can compute the input impedance as a function of frequency, or the resonance frequency for a given geometry and gas, or the length required to give a desired resonance frequency, or even the concentration in a binary gas mixture required to give a desired resonance frequency in a given geometry. Typically, a three to five dimensional solution vector is computed for reasonably complicated thermoacoustic engines, where heat-exchanger temperatures, heat and acoustic powers, efficiencies, etc. are typical solution elements of interest.
DELTAE does not include any nonlinear effects that arise at high amplitudes, so be cautious using it when Mach numbers or Reynolds numbers are too high. There are a number of other approximations used, which will be discussed below as we encounter them, and in more detail in Chapter V.