Superfluid helium forced flow in the Gorter-Mellink regime

A dimensional study of the momentum equations of superfluid helium is presented together with a parametric analysis of newly derived dimensionless numbers. The study is performed with a focus on the role of forced flows in the Gorter-Mellink regime. The dimensionless numbers are derived in such a way they become dependent solely on the total fluid velocity, heat flux, and thermophysical properties in order to facilitate their application to engineering problems where the velocity of the single fluid components might be difficult to measure directly. With a similar approach, a novel form of the superfluid Reynolds number is obtained. This form takes into account the velocity of a forced flow and allows to make considerations about the contribution of both forced flow and heat flux to the establishment of the ordinary turbulence in the normal fluid component. It is also presented a formula for a channel critical dimension at which the critical heat flux for the onset of superfluid turbulence causes ordinary turbulence too. •The role of forced flow in the Gorter-Mellink regime of He II is investigated.•Novel dimensionless numbers are derived as a function of macroscopic quantities only.•The pressure drop term becomes comparable to the mutual friction force in forced flow.•A novel superfluid Reynolds number is derived to include both forced and counter-flow.•A formula for critical characteristic dimension for the onset of turbulence is derived.