An internal streaming instability in regenerators

Various oscillating-wave thermodynamic devices, including orifice and feedback pulse tube refrigerators, thermoacoustic-Stirling hybrid engines, cascaded thermoacoustic engines, and traditional Stirling engines and refrigerators, utilize regenerators to amplify acoustic power (engines) or to pump heat acoustically up a temperature gradient (refrigerators). As such a regenerator is scaled to higher power or operated at lower temperatures, the thermal and hydrodynamic communication transverse to the acoustic axis decreases, allowing for the possibility of an internal acoustic streaming instability with regions of counterflowing streaming that carry significant heat leak down the temperature gradient. The instability is driven by the nonlinear flow resistance of the regenerator, which results in different hydrodynamic flow resistances encountered by the oscillating flow and the streaming flow. The instability is inhibited by several other mechanisms, including acoustically transported enthalpy flux and axial and transverse thermal conduction in the regenerator solid matrix. A calculation of the stability limit caused by these effects reveals that engines are immune to a streaming instability while, under some conditions, refrigerators can exhibit an instability. The calculation is compared to experimental data obtained with a specially built orifice pulse tube refrigerator whose regenerator contains many thermocouples to detect a departure from transverse temperature uniformity.