Dimensionless Analysis for Regenerator Design

Regenerative heat exchangers represent a crucial component in the design of single and multi-stage cryocoolers. Both the heat transfer and fluid dynamics that occur in the regenerator influence its performance significantly and can only be modeled adequately by solving the coupled mass, energy, and momentum conservation equations. Because of the inherent sophistication required, numerical solutions describing regenerator performance require substantial computational time in order to converge which limits their utility with respect to optimization and design. This report investigates the extrapolation of the performance of a regenerator from a known base case to conditions removed from the base case using a simple, analytical model that is based on running a few simulations in REGENv3.2 at conditions near the base case and correlating the results in terms of the key dimensionless parameters. The analytical model can be used for accelerated parametric study and optimization of a pulse tube cryocooler; the process of fitting an extrapolating function to the REGENv3.2 results must be accomplished periodically as the optimization process moves away from the base case. In this paper, the correlating functions are discussed and the methodology is demonstrated. The base case performance is determined using REGENv3.2 and the extrapolated performance, using the correlating functions, is compared to the performance at the same condition predicted directly by REGENv3.2. Correlations are developed to predict the mass flow rate and phase at the warm end of the regenerator, as well as the heat exchanger ineffectiveness and pressure drop.