He II heat transfer through random packed spheres: Pressure drop

• The permeability and shape factor for various random packs of spheres are reported.
• A pressure model is found to have a consistent friction factor in full turbulence.
• Higher resolution is achieved with pressure drop over the temperature drop results.

Heat flow induced pressure drop through superfluid helium (He II) contained in porous media is examined. In this experiment, heat was applied to one side of a He II column containing a random pack of uniform size polyethylene spheres. Measured results include steady state pressure drops across the random packs of spheres (nominally 35 μm, 49 μm, and 98 μm diameter) for different heat inputs. Laminar, turbulent, and transition fluid flow regimes are examined. The laminar permeability and equivalent channel shape factor are compared to our past studies of the temperature drop through He II in the same porous media of packed spheres. Results from the pressure drop experiments are more accurate than temperature drop experiments due to reduced measurement errors achieved with the pressure transducer. Turbulent results are fitted to models with empirically derived friction factors. A turbulent model considering only dynamic pressure losses in the normal fluid yields the most consistent friction factors. The addition of the laminar and turbulent heat flow equations into a unifying prediction fits all regimes to within 10%.