Phase Angle Model for Pulse Tube with Secondary Orifice Using Lumped-Element Electrical Network Analysis

Abstract

The pressure-flow phase angle is a key design parameter for optimizing pulse tube cryocooler performance. A high efficiency cryocooler requires an optimal phase angle that minimizes viscous dissipation losses in the regenerator and maximizes the acoustic power (PV) flow into the pulse tube. This will result in greater cooling capacity for a given amount of acoustic power delivered by the compressor. In a pulse tube cryocooler, the pressure-flow phase angle is driven by a combination of effects which include valve flow area, inertance tube size, and reservoir volume for a fixed working fluid flow rate. In this paper, the pressure-flow phase angle at the pulse tube is modeled using a simple lumped-element model RLC electrical network analysis. The RLC electrical network consists of a resistance component (R), an inertance component (L), and compliance component (C). The paper also addresses the effect of a secondary orifice (also referred to as a secondary valve) on the pressure-flow phase angle model. Phasor diagrams using vector representation are presented to visualize the direction and variation of the pressure-flow phase angle due to configuration changes in valves, inertance tubes, reservoir volumes, and working fluid flow rate. The model predictions will be compared to the established phase angle in-line theory method, as well as experimental results obtained with the Sierra Lobo pulse tube cryocooler developed under the NASA 2nd Generation Reusable Launch Vehicle Program.