Two-dimensional model for tapered pulse tubes. Part 1: theoretical modeling and net enthalpy flow

Abstract

A two-dimensional model for the tapered pulse tube was proposed. Linearized conservation equations of mass, momentum and energy of the gas as well as the energy conservation equation of the tube wall were applied to the pulse tube. The mean temperature profile of the gas and the tube wall was obtained by assuming that the outer surface of the pulse tube wall is adiabatic. Axial profile of the mean temperature is linear when the dimensionless frequency is small, but it deviates significantly from linear profile when the dimensionless frequency is large. The effects of operating frequency, taper angle, displacement volume ratio and velocity phase angle between the ends of the pulse tube on net energy flow as well as the effect of the taper angle on the first-order axial velocity and temperature were shown.