NATURAL-CONVECTION IN LARGE HE-II BATHS

Natural convection is important in systems of large dimensions where h eated sections may develop over a significant length of the vertical b oundary. In superconducting magnetic energy storage (SMES) systems the postulated design includes baths 20 m high housing superconductive co ils. It is of interest to determine how natural circulation evolves in such a bath when a significant number of turns become normal, and wha t additional heat capacity is afforded by natural circulation. In this paper the circulation velocity resulting from the natural convection process is evaluated. A coupled set of energy, mass and momentum equat ions is solved in two dimensions. These equations are formulated using the two-fluid model, which describes He II as consisting of two inter penetrating fluids, the normal and superfluid. They are also solved fo r a one-fluid model treating He II as a single fluid. The two models a re compared to show that the two-fluid model illustrates the existence of a counterflow resulting from the motion of the two fluids with or opposite to the applied heat flux. A well established single-fluid num erical method, the marker and cell (MAC) method, has been adapted to s olve the two-fluid equations. Results indicate that natural convection cells in superfluid helium evolve in a fundamentally different way th an those in ordinary fluids, because of the counterflow that develops in the presence of temperature gradients.