Vortex dynamics and scaling in turbulent counterflowing helium II

Swanson, Charles E.; Donnelly, Russell J.

doi:10.1007/bf00683692

Cited by 39 publications

(23 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A comprehensive review of the numerous models to describe the threshold of the T 1 instability is clearly beyond the scope of this paper; however, it is worth referring to a few of them to illustrate the level of controversy and, sometimes, confusion about this transition. For instance, the critical superfluid velocity V c of the T 1 instability is predicted to have either no dependence on the pipe diameter or channel hydraulic diameter d [7][8][9] dependence with or without a logarithmic correction [11,12] or a d −1 dependence with a logarithmic correction [13][14][15][16][17][18][19] or, at last, a pure d −1 dependence [20][21][22]. The models that predict no dependence on the diameter clearly overestimate the critical velocity but all the others reach reasonable degrees of agreement with some subsets of experimental data.…”

Section: A Critical Velocities In Superfluid Counterflowsmentioning

confidence: 99%

Disproportionate entrance length in superfluid flows and the puzzle of counterflow instabilities

2017

View full text Add to dashboard Cite

Systematic simulations of the two-fluid model of superfluid helium (He-II) encompassing the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) mutual coupling have been performed in two-dimensional pipe counterflows between 1.3 and 1.96 K. The numerical scheme relies on the lattice Boltzmann method. A Boussinesq-like hypothesis is introduced to omit temperature variations along the pipe. In return, the thermomechanical forcings of the normal and superfuid components are fueled by a pressure term related to their mass-density variations under an approximation of weak compressibility. This modeling framework reproduces the essential features of a thermally driven counterflow. A generalized definition of the entrance length is introduced to suitably compare entry effects (of different nature) at opposite ends of the pipe. This definition is related to the excess of pressure loss with respect to the developed Poiseuille-flow solution. At the heated end of the pipe, it is found that the entrance length for the normal fluid follows a classical law and increases linearly with the Reynolds number. At the cooled end, the entrance length for the superfluid is enhanced as compared to the normal fluid by up to one order of magnitude. At this end, the normal fluid flows into the cooling bath of He-II and produces large-scale superfluid vortical motions in the bath that partly re-enter the pipe along its sidewalls before being damped by mutual friction. In the superfluid entry region, the resulting frictional coupling in the superfluid boundary layer distorts the velocity profiles toward tail flattening for the normal fluid and tail raising for the superfluid. Eventually, a simple analytical model of entry effects allows us to re-examine the long-debated thresholds of T 1 and T 2 instabilities in superfluid counterflows. Inconsistencies in the T 1 thresholds reported since the 1960s disappear if an aspect-ratio criterion based on our modeling is used to discard data sets with the strongest entry effects. Furthermore, it is observed that entry effects can spuriously reproduce the signature of a T 2 transition with a normal flow remaining laminar.

show abstract

Section: A Critical Velocities In Superfluid Counterflowsmentioning

confidence: 99%

Disproportionate entrance length in superfluid flows and the puzzle of counterflow instabilities

2017

View full text Add to dashboard Cite

show abstract

“…Only temperature oscillations with angular frequencies greater than ~ will propagate in a wavelike manner described by Eq. (12). In our case, single pulses of 200 p.sec length were used, so the principal angular frequency of the second sound was ~o~, = 31,400 see -1.…”

Section: Coefficients Formentioning

confidence: 99%

Attenuation of second sound in bulk flowing He II

Holmes

Sciver

1992

J Low Temp Phys

View full text Add to dashboard Cite

New measurements of second sound attenuation in bulk fowing He H are reported which extend to a region of higher Reynolds number An expression for the attenuation explicitly containing the quantum vortex line density is developed which allows comparison with vortex line density data taken by other means. A bellows driven experimental apparatus is used to produce bulk flow velocities of O to I m/sec in a channel of 4.064 mm square internal cross section. Second sound pulses are produced by applying a square voltage pulse 200 izs width and variable height to a strain gauge heater. The second sound pulses are detected with thin film sensors mounted 56 and 119 mm downstream. The velocity-dependent attenuation, measured as a function of bulk flow velocity at 1.5, 1.8, and 2.OK, is compared with data from other researchers. The attenuation, and thus the vortex line density, appears to follow a gradual transition from laminar to turbulent behavior Current theories do not account for the presence of quantized vortices in bulk flowing He II, where (~n --iSs) : O, and thus do not explain the observed second sound attentuation in this regime.

show abstract

“…Swanson & Donnelly have applied scaling theory to the equations of motion of vorticies [9]. They find that the exponent in F m is 3 at very low v ns but increases with v ns to approximately 3.6 at very high v sn .…”

Section: Supporting Evidence and Limitationsmentioning

confidence: 98%

Critical Velocities for HE II

Snyder

2004

AIP Conference Proceedings

View full text Add to dashboard Cite

We propose a model to calculate the mass and heat flow of He II in a pipe connecting two baths. The each bath is maintained at constant temperature and pressure. The chemical potential difference is nonzero. When the velocities of the normal and superfluid components are above the critical value, the Gorter-Mellink equations provide a good approximation. These equations have unique solutions and the method is straightforward. When the velocities are below critical, the Landau equations are appropriate. These equations have no steady state solution when the chemical potential is nonzero. The equations do not specify how to find the velocity of the superfluid component and it is not clear how to determine when the flow is above or below the critical velocity. The model envisages two flow regimes in different parts of the flow path. One regime is above critical and is a solution of the Gorter-Mellink equations. It brings the chemical potential difference to zero. The remainder of the flow path is below critical with no gradient of chemical potential. There is a change in the profile of the superfluid component where the transition of flow regimes occurs and this allows a conservation of mass and heat flow.

show abstract

Vortex dynamics and scaling in turbulent counterflowing helium II

Cited by 39 publications

References 27 publications

Disproportionate entrance length in superfluid flows and the puzzle of counterflow instabilities

Disproportionate entrance length in superfluid flows and the puzzle of counterflow instabilities

Attenuation of second sound in bulk flowing He II

Critical Velocities for HE II

Contact Info

Product

Resources

About