Modeling the cooldown of cryocooler conduction-cooled devices

TL;DR

This paper presents a Python-based framework for modeling and estimating cooldown times of conduction-cooled cryogenic devices, aiding in design optimization for faster or slower cooldowns.

Contribution

It introduces a novel Python tool that models cooldown profiles using differential equations considering material properties and heat transfer mechanisms.

Findings

The framework accurately predicts cooldown times for conduction-cooled devices.

It enables design optimization by allowing parameter adjustments to control cooldown speed.

A case study demonstrates practical application with a superconducting magnet.

Abstract

Cryocooler conduction cooled devices can experience significant cooldown time due to lower available cooling capacity compares to convection cooled devices. Therefore, the cooldown time is an important design parameter for conduction cooled devices. This article introduces a framework developed in Python for calculating the cooldown profiles and cooldown time of cryocooler conduction-cooled devices such as superconducting magnets and accelerator cavities. The cooldown time estimation problem is essentially a system of ordinary first-order differential equations comprising the material properties (temperature dependent thermal conductivity and specific heat capacity) of the components intertwined with the prevailing heat transfer channels (conduction, radiation, and heat flow across pressed contacts) and the cryocooler capacity. The formulation of this ODE system is first presented. This ODE system is then solved using the in-built Python library odeint. A case study is presented comprising a small cryocooler conduction-cooled copper stabilized niobium-titanium magnet. The case study is supplemented with the Python script enabling the reader to simply tweak the device design parameters and optimize the design from the point of view of slow/fast cooldown.