Exploration of thermal counterflow in He II using particle tracking velocimetry

Abstract

Flow visualization using PIV (particle image velocimetry) and particularly PTV (particle tracking velocimetry) has been applied to thermal counterflow in He II for nearly two decades now, but the results remain difficult to interpret because tracer particle motion can be influenced by both the normal fluid and superfluid components of He II as well as the quantized vortex tangle. For instance, in one early experiment it was observed (using PTV) that tracer particles move at the normal fluid velocity v n , while in another it was observed (using PIV) that particles move at v n /2.Besides the different visualization methods, the range of applied heat flux investigated by these experiments differed by an order of magnitude. To resolve this apparent discrepancy and explore the statistics of particle motion in thermal counterflow, we have applied the PTV method to a wide range of heat flux at a number of different fluid temperatures. In our analysis, we introduce a scheme for analyzing the velocity of particles presumably moving with the normal fluid separately from those presumably influenced by the quantized vortex tangle. Our results show that for lower heat flux there are two distinct peaks in the streamwise particle velocity PDF (probability density function), with one centered at the normal fluid velocity v n (named "G2" for convenience) while the other is centered near v n /2 ("G1"). For higher heat flux there is a single peak centered near v n /2 ("G3"). Using our separation scheme we show quantitatively that there is no size difference between the particles contributing to G1 and G2. We also show that non-classical features of the transverse particle velocity PDF arise entirely from G1, while the corresponding PDF for G2 exhibits the classical Gaussian form. The G2 transverse velocity fluctuation, backed up by second sound attenuation in decaying counterflow, suggests that large scale turbulence in the normal fluid is absent from the two peak region. We offer a brief discussion of the physical mechanisms that may be responsible for our observations, revealing that G1 velocity fluctuations may be linked to fluctuations of quantized vortex line velocity, and suggest a number of numerical simulations that may reveal the underlying physics in detail.

Fully Coupled Two-Fluid Dynamics in Superfluid He4 : Anomalous Anisotropic Velocity Fluctuations in Counterflow

“…The value of ∆v n,x increases with V n , keeping ∆v n,x > ∆v n,y . These results are consistent with the PTV experiments [33,34]. The present values are less than those of the experiments.…”

“…Marakov et al visualized the velocity profile of the normal fluid by using He * 2 molecules [30], and the characteristic energy spectra were analyzed [31,32]. A particle tracking velocimetry (PTV) experiment provides insights on statistical properties and indicated that the velocity fluctuations of the normal fluid are anisotropic in contrast to classical fluid [33,34]. The result implies that QT makes the normal fluid fluctuate anisotropically.…”

Characterizing vortex tangle properties in steady-state He II counterflow using particle tracking velocimetry

“…Recently, we studied particle motion in thermal counterflow across a wide heat flux range using PTV, and found that, indeed, particles moving under the influence of relatively high heat flux, to which we give the name G3, are constantly affected by both the normal fluid and vortex lines. However, for relatively low heat flux, we devised a scheme for analyzing the kinematics of particles entrained by the normal fluid, to which we give the name G2, separately from those trapped on vortices, which we call G1 [18]. Using this separation scheme, we proposed a simple estimation of the mean free path of G2 particles through the vortex tangle, we showed that G1 velocity fluctuations are likely caused by fluctuations of the local vortex line velocity, and we showed that power-law tails in transverse particle velocity probability density functions (PDFs) are due entirely to G1.…”

Dynamics of turbulent plugs in a superfluid He4 channel counterflow

“…Recent advances in the experimental techniques, including flow visualization [22][23][24] , as well as increasing computing power, renewed the interest to the spatial inhomogeneity due to presence of channel walls 19,[25][26][27][28][29][30][31] and spatially-resolved investigations of the transient behavior in the thermal counterflow 32 . The latter work showed that the vortex tangle that eventually fills the whole channel, grows starting from a number of remnant vortex rings.…”