Mass flow and entropy production in choked 4He gas flow through micro-orifices

Abstract

Micro-orifice is a critical component in cryogenic refrigeration systems that determines the mass flow rate and total cooling power. However, a sophisticated model to accurately predict mass flow rates, especially for helium (He) below its maximum inversion temperature, where its properties differ significantly from those of an ideal gas, is lacking. This study investigated the mass flow characteristics and entropy production of ⁴He gas flow in micro-orifices using computational fluid dynamics (CFD) simulations. Various conditions, including upstream temperatures, upstream pressures, and downstream pressures, were analyzed and compared with the predictions from the Maytal model. Our results show that entropy production due to velocity and temperature gradient fluctuations plays a significant role in determining flow rates. Under upstream conditions of 15 K, 0.7 MPa, and a 20 μm diameter, the entropy increase coefficient (δ) is 0.083. Neglecting this entropy production leads to an overprediction of the mass flux by 39.8 %. A modified Maytal model that accounts for entropy production yields predictions in better agreement with CFD simulations, with a maximum deviation of less than 6.3 %. This work highlights the critical role of entropy production in ⁴He gas flow through micro-orifices and offers guidance for selecting micro-orifices in cryogenic applications.