Search results for "quantum turbulence"
showing 10 items of 18 documents
Refrigeration bound of heat-producing cylinders by superfluid helium
2019
In this paper we go ahead in our studies on refrigeration of nanosystems by superfluid helium, as an appealing subject for future applications to computers or astronautical precision nanodevices. We first recall the effective thermal conductivity in laminar counterflow superfluid helium through arrays of mutually parallel cylinders and we discuss the conditions for the appearance of quantum turbulence around the heat-producing cylinders. We then consider the cooling of an array of heat-producing cylindrical nanosystems by means of superfluid-helium counterflow. We discuss the upper bound on heat removal set by avoidance of quantum turbulence and avoidance of phase transition to normal He I,…
K-ϵ-L model in turbulent superfluid helium
2020
We generalize the K−ϵ model of classical turbulence to superfluid helium. In a classical viscous fluid the phenomenological eddy viscosity characterizing the effects of turbulence depends on the turbulent kinetic energy K and the dissipation function ϵ, which are mainly related to the fluctuations of the velocity field and of its gradient. In superfluid helium, instead, we consider the necessary coefficients for describing the effects of classical and quantum turbulence, involving fluctuations of the velocity, the heat flux, and the vortex line density of the quantized vortex lines. By splitting the several fields into a time-average part and a fluctuating part, some expressions involving t…
Refrigeration of an Array of Cylindrical Nanosystems by Flowing Superfluid Helium
2016
We consider the refrigeration of an array of heat-dissipating cylindrical nanosystems as a simplified model of computer refrigeration. We explore the use of He II as cooling fluid, taking into account forced convection and heat conduction. The main conceptual and practical difficulties arise in the calculation of the effective thermal conductivity. Since He II does not follow Fourier’s law, the effective geometry-dependent conductivity must be extracted from a more general equation for heat transfer. Furthermore, we impose the restrictions that the maximum temperature along the array should be less than (Formula presented.) transition temperature and that quantum turbulence is avoided, in o…
Effective thermal conductivity of helium II: from Landau to Gorter–Mellink regimes
2014
The size-dependent and flux-dependent effective thermal conductivity of narrow channels filled with He II is analyzed. The classical Landau evaluation of the effective thermal conductivity of quiescent He II is extended to describe the transition to fully turbulent regime, where the heat flux is proportional to the cubic root of the temperature gradient (Gorter–Mellink regime). To do so, we use an expression for the quantum vortex line density L in terms of the heat flux considering the influence of the walls. From it, and taking into account the friction force of normal component against the vortices, we compute the effective thermal conductivity as a function of the heat flux, and we disc…
Contribution of the normal component to the thermal resistance of turbulent liquid helium
2015
Previous results for the velocity profile of the normal component of helium II in counterflow are used to evaluate the viscous contribution to the effective thermal resistance. It turns out that such a contribution becomes considerably higher than the usual Landau estimate, because in the presence of vortices, the velocity profile is appreciably different from the Poiseuille parabolic profile. Thus, a marked increase in the contribution of the normal component to the thermal resistance with respect to the viscous Landau estimate does not necessarily imply that the normal component is turbulent. Furthermore, we examine the influence of a possible slip flow along the walls when the radius of …
Vortex diffusion and vortex-line hysteresis in radial quantum turbulence
2014
Abstract We study the influence of vortex diffusion on the evolution of inhomogeneous quantized vortex tangles. A simple hydrodynamical model to describe inhomogeneous counterflow superfluid turbulence is used. As an illustration, we obtain solutions for these effects in radial counterflow of helium II between two concentric cylinders at different temperatures. The vortex diffusion from the inner hotter cylinder to the outer colder cylinder increases the vortex length density everywhere as compared with the non-diffusive situation. The possibility of hysteresis in the vortex line density under cyclical variations of the heat flow is explored.
Effective thermal conductivity of superuid helium: Laminar, turbulent and ballistic regimes
2016
Abstract In this paper we extend previous results on the effective thermal conductivity of liquid helium II in cylindrical channels to rectangular channels with high aspect ratio. The aim is to compare the results in the laminar regime, the turbulent regime and the ballistic regime, all of them obtained within a single mesoscopic formalism of heat transport, with heat flux as an independent variable.
Non-classical Velocity Statistics in Counterflow Quantum Turbulence
2014
In this work we analyse the statistical distribution of turbulent superfluid velocity components in a He II counterflow channel, via two-dimensional numerical simulations pre- sented in past studies. The Probability Density Functions (PDFs) of the superfluid velocity components are investigated at lengthscales smaller than the average intervortex spacing, for varying vortex densities and different wall-normal distances. The results obtained con- firm the non-classical signature of quantum turbulence already observed in past numerical studies.
Non-equilibrium temperature of well-developed quantum turbulence
2009
Abstract A non-equilibrium effective temperature of quantum vortex tangles is defined as the average energy of closed vortex loops. The resulting thermodynamic expressions for the entropy and the energy in terms of the temperature of the tangle are confirmed by a microscopic analysis based on a potential distribution function for the length of vortex loops. Furthermore, these expressions for the entropy and energy in terms of temperature are analogous to those of black holes: this may be of interest for establishing further connections between topological defects in superfluids and cosmology.
Coupled normal fluid and superfluid profiles of turbulent helium II in channels
2015
We perform fully coupled two--dimensional numerical simulations of plane channel helium II counterflows with vortex--line density typical of experiments. The main features of our approach are the inclusion of the back reaction of the superfluid vortices on the normal fluid and the presence of solid boundaries. Despite the reduced dimensionality, our model is realistic enough to reproduce vortex density distributions across the channel recently calculated in three--dimensions. We focus on the coarse--grained superfluid and normal fluid velocity profiles, recovering the normal fluid profile recently observed employing a technique based on laser--induced fluorescence of metastable helium molec…