We report a comprehensive study of turbulent superfluid 4He flow through a channel of square cross section. We study for the first time two distinct flow configurations with the same apparatus: coflow (normal and superfluid components move in the same direction), and counterflow (normal and superfluid components move in opposite directions). We realise also a variation of counterflow with the same relative velocity, but where the superfluid component moves while there is no net flow of the normal component through the channel, i.e., pure superflow. We use the second-sound attenuation technique to measure the density of quantised vortex lines in the temperature range 1.2 K ≲ T ≲ Tλ ≈ 2.18 K and for flow velocities from about 1 mm/s up to almost 1 m/s in fully developed turbulence. We find that both the steady-state and temporal decay of the turbulence significantly differ in the three flow configurations, yielding an interesting insight into two-fluid hydrodynamics. In both pure superflow and counterflow, the same scaling of vortex line density with counterflow velocity is observed, L∝Vcf2, with a pronounced temperature dependence; in coflow instead, the vortex line density scales with velocity as L ∝ V3/2 and is temperature independent; we provide theoretical explanations for these observations. Further, we develop a new promising technique to use different second-sound resonant modes to probe the spatial distribution of quantised vortices in the direction perpendicular to the flow. Preliminary measurements indicate that coflow is less homogeneous than counterflow/superflow, with a denser concentration of vortices between the centre of the channel and its walls.

The concept of "effective viscosity" v(eff) of superfluid helium, widely used to interpret decaying turbulence, is tested in the steady-state case. We deduce.eff from measurements of the vortex line density, L, in a grid flow. The scaling of L with velocity confirms the validity of the heuristic relation defining v(eff), epsilon =v(eff) (kappa L)(2), where epsilon is the energy dissipation rate and. the circulation quantum. Within 1.17-2.16K, v(eff) is consistent with that from decays, allowing for uncertainties in flow parameters. Numerical simulations of the two-fluid equations yield a second estimation of v(eff) within an order of magnitude with all experiments. Its temperature dependence, more pronounced in numerics than experiments, shows a crossover from a viscous-dominated to a mutual-friction-based dissipation as temperature decreases, supporting the idea that the effective viscosity of a quantum turbulent flow is an indicator of the dissipative mechanisms at play. Copyright (C) EPLA, 2014

We report an experimental study of turbulent pipe flow with superfluid 4 He as a working fluid, through smooth square ducts of width 7 and 10 mm, and 115 mm in length. The helium temperature is in the range 1:35 K < T < 2:16 K, which corresponds to varying the superfluid fraction respectively from 94% to 9%, that is, from a quasi-ideal to a quasi-viscous fluid. The flow is generated by a low temperature bellows capable of producing well controlled steady flow velocities up to 1 m/s in the duct. We have studied the case of a straight unobstructed duct, and measurements in the same duct with the addition of a grid are under progress. We have studied the dependence of the total length of quantized vortex lines per unit volume (a quantification of total vorticity per unit quantum circulation) as a function of mean velocity and also its decay as a function of time when the turbulence drive is suddenly stopped. Instructive comparisons with a previous experiment where the viscous component of helium was prevented from flowing through the channel are made, and interpretation of measurements based on existing and new models of quantum turbulence are suggested.

A flow source has been developed to generate turbulent superfluid flows in channels equipped for detection of quantised vortices. The source consists of a motor driven low temperature compressible volume capable of pushing or sucking superfluid He-4 into a flow channel. Detection is based on the attenuation of second sound caused by the presence of quantised vortex lines in the turbulent flow. In this paper we present the technical details of the apparatus, along with some raw data obtained during the first successful low temperature test. The test has been performed using the source to generate a flow into a channel whose ends have been blocked by superleaks to allow for the inflow and outflow of the superfluid component of helium only. This technique enables to determine the areal density of quantised vortex lines in the temperature range 1.3 to 2.1 K, with well controlled flow velocities between 0.01 and 30 cm/s.