Useful scaling parameters for the pulse tube

A set of dimensionless scaling parameters for use in correlating performance data for Pulse Tube Refrigerators is presented. The dimensionless groups result after scaling the mass and energy conservation equations, and the equation of motion for an axisymmetric, two-dimensional ideal gas system. Allowed are viscous effects and conduction heat transfer between the gas and the tube wall. The scaling procedure results in reducing the original 23 dimensional variables to a set of 11 dimensionless scaling groups. Dimensional analysis is used to verify that the 11 dimensionless groups obtained is the minimum number needed to describe the system. The authors also examine 6 limiting cases which progressively reduce the number of dimensionless groups from 11 to 3. The physical interpretation of the parameters are described, and their usefulness is outlined for understanding how heat transfer and mass streaming affect ideal enthalpy flow