Numerical investigation of combined forced flow and counterflow effects in superfluid helium around a cylinder using the two-fluid model

Purpose This study investigates the behaviour of superfluid helium (He-II) around a two-dimensional cylinder under cryogenic conditions. To understand different aspects of the problem, three scenarios are examined pure thermal counterflow around a heated cylinder, forced flow past an adiabatic cylinder and combined forced and thermal counterflow. This study aims to understand the non-classical flow behaviour, its effect on drag and the complex interactions between the components of He-II. Design/methodology/approach The two-fluid model with the Gorter–Mellink mutual-friction assumption is used and solved with the finite volume method in OpenFOAM. Simulations are carried out at three Reynolds numbers (Re = 2, 20, 40) and a range of specific heat fluxes (0–40 W/m2) to capture the flow and drag characteristics under different conditions. Findings In pure thermal counterflow conditions, the flow is purely radial. In forced flows without heat flux, vortex formation and separation resemble classical fluids, but the two-fluid nature of the flow delays separation and reduces drag. In combined flows, increasing heat flux initially increases drag due to asymmetry; higher fluxes restore symmetry and reduce drag. These behaviours are quantified by a new non-dimensional parameter, β. Originality/value Existing literature indicates that the combined influence of thermal counterflow and forced flow in He-II around bluff bodies has not been previously examined. The present work fills the gap by establishing the first detailed analysis of mixed-flow behaviour in He-II. It offers new insights directly relevant to cryogenic systems.