Numerical simulation of thermal counterflow in superfluid helium: Investigating the effect of rotation and heat flux on the surface of the cylinder

This study focuses on the numerical simulation of the thermal counterflow of helium superfluid around a cylinder. To model helium superfluid behavior, two-fluid equations, incorporating the Gorter-Mellink mutual friction, were employed. The simulation utilized the PIMPLE (Pressure Implicit with Splitting of Operator) algorithm, which couples the velocities of the normal and superfluid components with pressure, thereby enhancing numerical stability. This approach made it possible to simulate the thermal counterflow around the rotating cylinder and heat flux on its surface, including both heating and cooling effects. The research aims to explore the impact of rotation and heat flux on separation angles, drag and lift forces, and in principle, the overall pattern of the flow. The primary objective is to gain a more profound insight into the behavior of superfluid helium and optimize its applications in both research and industrial contexts. The findings reveal that, in contrast to classical fluids, the influences of various factors do not adhere to a consistent rule. Rotation and cooling/heating were observed to significantly affect separation and the aerodynamic forces. However, the nature of this impact can vary across different scenarios. In some cases, rotation increases the separation angle, while in others, it completely eliminates separation. Consequently, the effect of rotation on the drag force coefficient exhibits substantial variation depending on the specific problem at hand. For instance, in one problem, the drag force coefficient increases from approximately 0.7 to about 1.4 due to rotation, whereas in another, it decreases from around 0.8 to approximately 0.1. Additionally, rotation leads to a drag force coefficient of approximately 1.3 in one specific scenario. Furthermore, this study has demonstrated that the rotation of the cylinder induces asymmetry in the mass flow rates of the components. For instance, in one case, the cylinder's rotation resulted in approximately 86 % of the superfluid component passing from one side of the cylinder.

Overall, cooling tends to reduce the separation angle and drag force coefficient, while heating has the opposite effect and increases them. For example, in one scenario, cooling causes the drag force coefficient to drop from 0.8 to about 0.1, whereas heating elevates above 1.6.