Modeling the dynamic response of pressures in a distributed helium refrigeration system

Abstract

A mathematical model is created of the dynamic response of pressures caused by flow inputs to an existing distributed helium refrigeration system. The dynamic system studied consists of the suction and discharge pressure headers and compressor portions of the refrigeration system used to cool the superconducting magnets of the Tevatron accelerator at the Fermi National Accelerator Laboratory. The modeling method involves identifying the system from data recorded during a series of controlled tests, with effort made to detect locational differences in pressure response around the four mile accelerator circumference. A review of the fluid mechanics associated with the system indicates linear time invariant models are suitable for the identification, particularly since the governing equations of one dimensional fluid flow are approximated by linear differential equations. An outline of the experimental design and the data acquisition system are given, followed by a detailed description of the modeling, which utilized the Matlab programming language and associated System Identification Toolbox. Two representations of the system are presented. One, a black box model, provides a multi-input, multi-output description assembled from the results of single input step function testing. This description indicates definite variation in pressure response with distance from the flow input location, and also suggests subtle differences in response with the input location itself. A second system representation is proposed which details the relation between continuous flow changes and pressure response, and provides explanation of a previously unappreciated pressure feedback internal to the system.