Abstract
Earth observation satellites require cryocoolers to cool down their infrared imagers at very low temperatures. Besides having very good thermodynamic performances, satellite cryocoolers are expected to generate as little vibrations as possible. In order to better understand vibration causes between 50 and 500 Hz, a precise model of the whole cryocooler is necessary. In the literature, two main modelling approaches for pulse tube cryocoolers exist: compressororiented models reduce the thermodynamic system to a linear mass-spring-damper system acting on compressor’s pistons; and thermodynamically oriented models aimed at understanding and predicting thermodynamic performances.In this paper, the mechanical behavior of the thermodynamic system is modelled. Assumptions concerning gas properties and thermodynamic behavior are made based on SAGE software simulations. A simplified Redlich Kwong equation is used. When necessary, polytropic coefficients were identified using simulation data, as were the time-averaged temperatures. The thermodynamic system is split into volumes, pipes and regenerators: conservation laws in volumes are integrated, dynamic mass and momentum conservation equations in pipes are solved using the method of characteristics and equations in regenerators are solved using a finite difference method. Three friction laws are used: one for straight pipes (Moody chart), another for wound pipes (White’s correlation) and a last one for porous media (Modified Ergun equation). Porosity is measured by weighing. The model is built to respect integral causality and propagation phenomena.The developed model is validated using experimental data. The simulations highlight the non-linear mechanical behavior of the thermodynamic system: a sinusoidal motion of the pistons induces a non-sinusoidal pressure in the compression chamber. Among other, first and second harmonics amplitudes are about 3% of fundamental pressure amplitude.This model can now be integrated into a global cryocooler model to predict compressor’s vibrations, power consumption or electrical harmonics. It could also be extended to predict vibrations from the thermodynamic system.
Highlights
For Earth observation purposes, satellites carry infrared cameras
An intermediate model based on conservation laws is developed. It is not aimed at predicting thermodynamic behavior or efficiency of the system, but rather reproduce the mechanical interaction between the compressor and the thermodynamic system at fundamental frequency and harmonics
Considering pressure gradient and friction to be negligible in the energy conservation equation (4.c), pressure as a function of volume as well as incoming and outgoing flow rate is obtained in equation (6)
Summary
For Earth observation purposes, satellites carry infrared cameras. In order to minimize the picture’s noise, focal planes must be cooled down at very low temperatures: typically between 150 K and 50 K. An intermediate model based on conservation laws is developed It is not aimed at predicting thermodynamic behavior or efficiency of the system, but rather reproduce the mechanical interaction between the compressor and the thermodynamic system at fundamental frequency and harmonics. Lopes summarizes in [8] the history and the aim of each component of the thermodynamic system: thanks to the inertance and the buffer, there is a phase shift between the flow and the pressure in the pulse tube. The aim of the regenerator is to store cold power in order to cool down the gas before entering in the pulse tube Ͳ Time average ܣComponent closer from compressor ܤComponent farther from compressor ܿ Combined ܲ Relative to pressure ݐPartial derivative with respect to time ݐݐTotal ܷ Relative to voltage ݔPartial derivative with respect to position ͲݔInlet position ܮݔOutlet position
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More From: IOP Conference Series: Materials Science and Engineering
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