Application of Particle Tracking Velocimetry to Thermal Counterflow and Towed-Grid Turbulence in Helium II

The superfluid phase of helium-4, known as He~II, is predominantly used to cool low-temperature devices. It transfers heat by a unique thermally driven counterflow of its two constituents, a classical normal fluid and an inviscid superfluid devoid of entropy. It also has potential use for economical reproduction and study of high Reynolds number turbulent flow due to the extremely small kinematic viscosity and classical characteristics exhibited by mechanically driven flow. A number of diagnostic techniques have been applied in attempts to better understand the complex behavior of this fluid, but one of the most useful, flow visualization, remains challenging because of complex interactions between foreign tracer particles and the normal fluid, superfluid, and a tangle of quantized vortices that represents turbulence in the superfluid. An apparatus has been developed that enables application of flow visualization using particle tracking velocimetry (PTV) in conjunction with second sound attenuation, a mature technique for measuring quantized vortex line density, to both thermal counterflow and mechanically-driven towed-grid turbulence in He~II. A thermal counterflow data set covering a wide heat flux range and a number of different fluid temperatures has been analyzed using a new separation scheme for differentiating particles presumably entrained by the normal fluid ("G2") from those trapped on quantized vortices ("G1"). The results show that for lower heat flux, G2 particles move at the normal fluid velocity vn, but for higher heat flux all particles move at roughly vn/2 ("G3"). Probability density functions (PDFs) for G1 particle velocity vp are Gaussian curves with tails proportional to |vp|⁻³, which arise from observation of particles trapped on reconnecting vortices. A probable link between G1 velocity fluctuations and fluctuations of the local vortex line velocity has been established and used to provide the first experimental estimation of c₂, a parameter related to energy dissipation in He~II. Good agreement between the length of observed G2 tracks and a simple model for the mean free path of a particle traveling through the vortex tangle suggests that flow visualization may be an alternative to second sound attenuation for measurement of vortex line density in steady-state counterflow. Preliminary PTV and second sound data in decaying He~II towed-grid turbulence shows agreement with theoretical predictions, and enables reliable estimation of an effective kinematic viscosity and calculation of longitudinal and transverse structure functions, from which information about the energy spectrum evolution and intermittency enhancement can be obtained.