A question of streaming
A glib comparison of the main types of regenerative cryo-cooler might assert that Stirling types function despite the realities of the heat exchange and flow processes, while thermo-acoustic and pulse-tube types function by virtue of those very same realities. The pulse-tube section sustains a substantial temperature gradient - up to 2000 K/m. This is less severe than the gradient encountered in the regenerator, but sufficient to create another unwelcome reality -thermal shorting of the productive thermodynamic cycle. Thus ‘streaming’, a steady secondary-flow phenomenon, comes under scrutiny.
Streaming is a response by the boundary layer to excitation by the free-stream. The established analytical picture (Schlichting 1955 and/ or White 1974) is for uniform temperature conditions. Specimen solutions are for simple-harmonic excitation. In the context of cryo-coolers the technical literature goes under the heading of thermo-acoustics. As the name implies, this combines elements of acoustic (linear wave) theory with thermodynamics. Reconciling the two areas is achieved with some compromise, possibly explaining why streaming intensity predicted under conditions of severe temperature gradient barely differs from the classic, uniform-density, uniform-temperature case.
Rott's work is representative. His 1974 formulation for the compressible case includes a term dt/dx, but the driving function does not reflect it. This is consistent with ...