Numerical simulation of the flow in a toroidal thermosiphon

Buoyancy-driven flows are widespread in diverse engineering applications. Such flows have been studied in great detail theoretically, experimentally, and numerically. The prototype of passive, residual heat removal systems is the toroidal thermosiphon. The stability properties of such systems were first examined in detail by Creveling et al. in the mid-1970s, who reported flow reversals and instability in this geometry. Traditionally, however, the stability analysis of natural convection loops has been confined to one-dimensional calculations, on the argument that the flow would be monodimensional when the ratio between the radius of the loop and the radius of the pipe is much larger than 1. Nevertheless, accurate velocity measurements of the flow in toroidal loops have shown that the flow presents three-dimensional effects. In the present work we analyze the stability problem in a toroidal loop and then use computational fluid dynamics to evaluate the relative importance of these three-dimensional effects with regard to stability. We performed a series of high-fidelity numerical simulations using the spectral element code Nek5000. We compared the results to the available data and calculations performed with the code STAR-CCM+ 5.06. The results show a much richer dynamics than expected from either previous calculations or stability theory. The results also point to some outstanding issues in the RANS modeling of such flows.