FERMILAB -TM-2782 -TD Modeling the cooldown of cryocooler conduction -cooled devices

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FERMILAB-TM-2782-TD

Modeling the cooldown of cryocooler conduction-cooled

devices

Ram C. Dhuley

Fermi National Accelerator Laboratory, Batavia, IL 60510, USA

Email: rdhuley@fnal.gov

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.

1. Introduction

Cryocooler conduction-cooled devices operating near 4 K such as small superconducting magnets

[1] and accelerator cavities [2-7] are fast gaining popularity as an alternative to the devices

convectively cooled by liquid or supercritical helium. Such devices are inherently safer to build

and operate as they lack liquid/supercritical helium around their insulation vacuum spaces, which

drastically mitigates the dangers associated with a sudden loss of this vacuum [8-11]. Due to small

cooling capacity of the cryocooler, however, conduction-cooled devices can have very long

periods of cooldown from room temperature to the base temperature near 4 K. The design of

thermal conduction links between the cryocooler and the device, therefore, needs to consider the

device cooldown time in addition to the system performance at the base temperature.

FERMILAB-TM-2782-TD

This note introduces a script written in Python that enables visualization of the cooldown profile

(temperature vs. time at various physical locations of the system) and estimation of cooldown time

for cryocooler conduction-cooled devices. The inputs are cryocooler capacity (generally provided

by a cryocooler manufacturer) and thermal properties of material used to construct the device

(usually obtained from the NIST cryogenic material properties database [12], literature on thermal

contacts [13,14], and other sources [15]). A system of ODEs comprising time dependent heat

transfer equations (with conduction, radiation, contact heat transfer terms) is first formulated and

then solved using the Python odeint library [16].

2. Methodology for estimating cooldown profile and time

The flowchart in figure 1 graphically represents the methodology. The process starts with

documenting temperature dependent material properties (thermal conductivity, specific heat

capacity, emissivity, and contact resistance), followed by formulation of the time dependent heat

transfer equations (a system of first-order ODEs), then writing down the conduction and radiation

heat transfer terms as functions of temperature, and finally solving the system of ODE.

Further details of this methodology is provided in following case study by applying it to a small

superconducting magnet conduction-cooled to a two-stage cryocooler.

Figure 1. A flowchart for calculating cooldown profile and time of cryocooler conduction-cooled

devices.

3. Case study

The methodology presented in the preceding section is illustrated using a small conduction-cooled

superconducting magnet. The magnet is a solenoid with a warm bore, wound using copper

stabilized niobium-titanium superconductor. The solenoid is mechanically coupled using copper

thermal links to the 4 K stages of two-stage pulse tube cryocoolers. The solenoid is enclosed in an

aluminum thermal shield that is conduction-cooled to the 45 K stages of the same two-stage

cryocoolers. The thermal shield is wrapped with multilayer insulation to reduce ambient radiation

heat leak. The entire cold is enclosed in a vacuum chamber to cut down convection heat transfer

between the two. More details of the magnet system under consideration can be found in [17, 18].

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摘要：

FERMILAB-TM-2782-TDModelingthecooldownofcryocoolerconduction-cooleddevicesRamC.DhuleyFermiNationalAcceleratorLaboratory,Batavia,IL60510,USAEmail:rdhuley@fnal.govAbstract.Cryocoolerconductioncooleddevicescanexperiencesignificantcooldowntimeduetoloweravailablecoolingcapacitycomparestoconvectioncooledd...

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FERMILAB -TM-2782 -TD Modeling the cooldown of cryocooler conduction -cooled devices

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