Cryogenic helium flow in adiabatic capillary tubes: Numerical insights into choked flow and superfluid behavior in Joule-Thomson cryocoolers

Abstract

The Joule-Thomson (J-T) effect, utilizing helium as the working fluid, is widely employed for refrigeration in the 1–4 K temperature range. The capillary tube, acting as a throttling element, plays a crucial role in providing flow resistance and regulating flow rates. However, critical information regarding helium flow in the capillary tube—such as the onset of choked flow, the existence of superfluid transition, and the dependence of flow rates and the cooling power on the geometric factors of the capillary tube and operating conditions—remains inadequately understood. This paper presents a numerical analysis investigating the flow dynamics and refrigeration characteristics of helium through adiabatic straight capillary tubes. The findings establish criteria for identifying the onset of choked flow and superfluid transition. Results indicate that helium flow within the capillary tube typically operates in the choked flow regime in practical applications. Should a superfluid transition occur, it takes place in the free expansion region outside the capillary tube, exerting minimal influence on the internal flow dynamics. Furthermore, sensitivity analysis identifies the inner diameter as a crucial parameter dictating the mass flow rate. Design guidelines are also provided for the optimal selection of capillary tubes in cryogenic applications.