NUMERICAL STUDY OF FLOW AND HEAT TRANSFER OF SUPERFLUID HELIUM IN CAPILLARY CHANNELS

Abstract

Interdisciplinary Graduate School of Engineering Sciences, Kyushu University 39, Kasuga 816, Japan Received 23 May 1997 A modified two-fluid model is adopted to study flow and heat transfer of superfluid helium in a microchannel with a diameter as small as that of a superleak in a fountain effect pump. Variable properties of superfluid helium and energy dissipations due to the two-fluid mutual friction and the friction at the channel wall are fully taken into consideration. It is found that the normal fluid component flow is not trivial even in a channel with diameter of a micrometre, and that there exists an optimum diameter for the maximum mass flow rate. The flow of superfluid helium through a channel with different temperatures at the ends differs considerably from that of a Newtonian fluid. The strong dependence of the thermodynamic properties on temperature and pressure, as well as the internal-convection mechanism are found to be the causes of the unique flows. 0 1998 Elsevier Science Ltd. All rights reserved. Keywords: superfluid helium; superleak; heat transfer; internal-convection; numerical simulation; two-fluid model In recent years, superfluid helium (or He II) has found application in the development of space projects; it has been used to eliminate background thermal noises in the infrared telescope in space in order to maintain a very low temperature for the detector’s high sensitivity. In-orbit refilling with the coolant, a project called Space Tanker Plan’, has been suggested to refrigerate the He II open sys- tem. A mechanical pump is not appropriate for this purpose, since zero-gravitation in space and the very low vapour pressure of He II would cause cavitation that is destructive to the pump. Therefore, a non-mechanical pump called a fountain effect pump (or FEP)’ has been suggested which consists of only a porous element with microchannels, called superleak’, and an electric heater. The FEP is regarded as a pump of lower possibility of cavitation and of potentially high reliability. When He II is heated down- stream of the porous element, the superfluid component flows through the porous element, while the normal fluid still remains due to the viscosity. A few works have been published to study the FEP ana- lytically and experimentally3. To the author’s knowledge, however, only Snyder and Mord4 have presented numerical results of heat and fluid flow in a channel of small diameter (micrometres), simulating a superleak. Snyder and Mord developed a simple steady-state model to obtain tempera- ture and pressure profiles and compared the numerical results with their experiments. As will be shown in this paper, the model of Snyder and Mord could also be derived based on simplifications of a more accurate two-fluid modeP, and in particular the omis- sion of some terms in the enthalpy conservative equation as well as in the momentum equations. However, it is not evident whether these terms can be omitted for a channel of such a small diameter like a superleak. In the present study, a transient model is proposed, which consists of a full set of the two-fluid model momentum equations and an entropy transport equation in which the entropy generation due to the friction at the channel wall is taken into consideration. Steady-state results obtained with the present model are compared with those of Snyder and Mord. It is also interesting to show the existence of a normal fluid flow in the superleak and realize the role it plays in the flow and heat transfer, since it has been a gen- eral belief that no normal fluid flow would exist in such structures.