Flow Of Superfluid Helium Research Articles

Effect of temperature and heat input on helium isotope separation driven by an entropy filter

To understand the effect of temperature and heat input on helium isotope separation driven by an entropy filter, the thermomechanical flow of superfluid helium through an entropy filter for obtaining high purity 4He is experimentally investigated. For this method, there are two important indicators: separation flow (flow rate) and separation effect (3He concentration). The separation flow rate is examined at various temperatures ranging from 1.6 K to 1.9 K of feed helium. Different heat inputs (Q) are applied to the entropy filter outlet to drive superfluid 4He flowing through the porous element. The results demonstrate that the flow rate increases as the feed helium temperature decreases and heat input increases. Simultaneously, 3He diffusion is detected as the superfluid helium passes through the entropy filter. The concentration of 3He, filtered at different temperature ranging from 1.6 K to 1.9 K, are analyzed using HELIX SFT Static Vacuum Mass Spectrometer. The findings reveal that the 3He concentration decreases with an increase in the temperature of the feed helium bath. 3He concentration of feed helium is around 3.3×10-8. Specifically, the 3He concentration in the filtered helium at 1.6 K is approximately 3.2×10-10, while at 1.9 K, it reduced to 2.2×10-10. This suggests that 3He diffusion in He II is inversely proportional to the He II temperature from 1.6 K to 1.9 K, resulting in a lower 3He concentration at higher temperatures.

Phenomenology of transition to quantum turbulence in flows of superfluid helium

Transition from laminar to turbulent states of classical viscous fluids is complex and incompletely understood. Transition to quantum turbulence (QT), by which we mean the turbulent motion of quantum fluids such as helium II, whose physical properties depend on quantum physics in some crucial respects, is naturally more complex. This increased complexity arises from superfluidity, quantization of circulation, and, at finite temperatures below the critical, the two-fluid behavior. Transition to QT could involve, as an initial step, the transition of the classical component, or the intrinsic or extrinsic nucleation of quantized vortices in the superfluid component, or a simultaneous occurrence of both scenarios—and the subsequent interconnected evolution. In spite of the multiplicity of scenarios, aspects of transition to QT can be understood at a phenomenological level on the basis of some general principles, and compared meaningfully with transition in classical flows.

Experiments of superfluid helium flow in a channel with a monodisperse backfill

The experimental data on the superfluid helium flow in a U-shaped channel filled with a monodisperse backfill at a certain length is considered in this paper. The entire channel is immersed in a volume of superfluid helium. A flat heater is located in one end of the channel. When the heat load is applied, a vapor plug is formed in the channel. The column of superfluid helium begins to fluctuate in size with a constant amplitude and frequency. On the basis of the video recording of experiments, the dependence of the coordinate of the interfacial surface on time was plotted, and a qualitative analysis of heat and mass transfer processes is performed.

Observation of Second Sound Attenuation Across a Superfluid Suction Vortex

Recently, the authors succeeded in generating a superfluid suction vortex, which is a giant vortex with a hollow core, driven directly by a cryogenic centrifugal pump. The ultimate goal of this study and related work is to determine the distribution of the local density of the quantum vortex lines as a function of the rotational speed and the magnitude of the suction flow. Although the flow of superfluid helium in a rotating bucket, in which the vortex lines are arranged to form a triangular lattice, is known to show rigid body motion, the vortex line distribution of the suction vortex remains an open question. In this study, the attenuation of the second sound across the suction vortex was measured. As a result, it was found that the damping factors of the second sound increased with increasing rotational speed; however, it was found that the apparent vortex line density is not proportional to the rotational speed despite the fact that the total circulation has been previously shown to be proportional to the rotational speed. A possible picture of the quantum vortex lines around the suction vortex is discussed in this paper.

Dynamical similarity and instabilities in high-Stokes-number oscillatory flows of superfluid helium

We present a unified analysis of the drag forces acting on oscillating bodies submerged in superfluid helium such as a vibrating wire resonator, tuning forks, a double-paddle oscillator, and a torsionally oscillating disk. We find that for high-Stokes-number oscillatory flows, the drag force originating from the normal component of superfluid helium exhibits a clearly defined universal scaling. Following classical fluid dynamics, we derive the universal scaling law and define relevant dimensionless parameters such as the Donnelly number. We verify this scaling experimentally using all of our oscillators in superfluid $^{4}\mathrm{He}$ and validate the results by direct comparison with classical fluids. We use this approach to illustrate the transition from laminar to turbulent drag regime in superfluid oscillatory flows and compare the critical velocities associated to the production of quantized vortices in the superfluid component with the critical velocities for the classical instabilities occurring in the normal component. We show that depending on the temperature and geometry of the flow, either type of instability may occur first and we demonstrate their crossover due to the temperature dependence of the viscosity of the normal fluid. Our results have direct bearing on present investigations of superfluids using nanomechanical devices [Bradley et al., Sci. Rep. 7, 4876 (2017)].

Phonon scattering on quantized vortices under quasi-stable laminar flow of superfluid helium

Experimental studies of the coefficient of resistance in a quasi-stable laminar flow of superfluid He II under vibrations of a quartz tuning fork immersed in liquid, at a temperature of 140 mK, were performed. After analyzing various additive contributions to the value of the coefficient of resistance, the contribution from the process of ballistic phonon scattering of quantized vortices of superfluid helium at small vibration amplitudes of the prongs was established; this process changes with the increase in amplitudes of these vibrations and the number of quantized vortices. It was shown that the observed experimental dependencies of the resistance coefficient on the fluid flow rate may be explained by multiple phonon scattering, which was not previously considered a dissipation mechanism. The dependence of the effective cross section of the multiple phonon scattering process upon the vibration rates of the prongs of the tuning forks was plotted.

Течение гелия-II в канале с пористой вставкой при безвихревом сверхтекучем движении

The heat and mass transfer processes associated with flow of superfluid helium (He-II) in a channel filled with porous medium in a certain part of its length are analyzed. The heat flux is directed along the channel axis so that a vapor plug is generated near the heater. The steady-state heat-and-mass transfer processes at the interfaces are calculated using the molecular kinetic theory methods. The motion of He-II in pores is described by equations that take into account the specific features of heat and mass transfer in a quantum fluid. A map of flow modes for normal and superfluid components for a monodisperse porous fill is plotted. The normal component’s laminar and turbulent flow modes for nonvortex superfluid motion are considered. Formulas correlating the porous insert length with the fluid velocity are derived for these modes. It is found that He-II flow toward the heater is possible when the porous insert length exceeds a certain value. The dependences of this reversible length on the porous fill structural features and heat flux density are presented. For the laminar mode of normal motion, the reversible length is determined by the diameter of monodisperse fill particles at a given temperature, whereas in the turbulent mode this length also depends on the heat flux. The influence of liquid temperature is studied. Reversible length calculation examples are given. The results of the performed calculations are analyzed by comparing them with the previously obtained data for He-II flow in a single capillary.

The superfluid helium flow in the channel with porous insert at the presence of longitudinal heat flux

The processes of heat and mass transfer during the flow of helium-II (He-II) in a channel with porous backfilling placed in a particular section of its length are studied. Heat flux is directed along the axis of the channel in such a way that on one side of the backfilling vapor plug is formed. Calculation of steady-state transport processes at vapor-He-II interfaces is carried out using methods of molecular-kinetic theory. The normal fluid flow in the pores in laminar and turbulent regimes is described by equations taking into account features of heat and mass transfer in superfluid helium. The relationships between the length of the porous insert and the velocities of fluids for different flow regimes are formulated. The results of the calculations are analyzed by comparison with previous data for the flow of He-II in the individual capillary.

Pressure driven flow of superfluidHe4through a nanopipe

An experimental study of the flow of superfluid helium through single nanopipes with radii of order 100 nm and lengths of a few millimeters, reveals the existence of two distinct flow regimes above and below a critical pressure drop ${P}_{c}$. For $Pg{P}_{c}$, the flow velocity is more than an order of magnitude higher than the Feynman critical velocity.

Anderson’s considerations on the flow of superfluid helium: Some offshoots

Nearly five decades have elapsed since the seminal 1966 paper of P.W. Anderson on the flow of superfluid helium, $^4$He at that time. Some of his "Considerations" -- the role of the quantum phase as a dynamical variable, the interplay between the motion of quantised vortices and potential superflow, its incidence on dissipation in the superfluid and the appearance of critical velocities, the quest for the hydrodynamic analogues of the Josephson effects in helium -- and the way they have evolved over the past half-century are recounted below. But it is due to key advances on the experimental front that phase slippage could be harnessed in the laboratory, leading to a deeper understanding of superflow, vortex nucleation, the various intrinsic and extrinsic dissipation mechanisms in superfluids, macroscopic quantum effects and the superfluid analogue of both {\it ac} and {\it dc} Josephson effects -- pivotal concepts in superfluid physics -- have been performed. Some of the experiments that have shed light on the more intimate effect of quantum mechanics on the hydrodynamics of the dense heliums are surveyed, including the nucleation of quantised vortices both by Arrhenius processes and by macroscopic quantum tunnelling, the setting up of vortex mills, and superfluid interferometry.

A PISO-like algorithm to simulate superfluid helium flow with the two-fluid model

This paper presents a segregated algorithm to solve numerically the superfluid helium (He II) equations using the two-fluid model. In order to validate the resulting code and illustrate its potential, different simulations have been performed. First, the flow through a capillary filled with He II with a heated area on one side is simulated and results are compared to analytical solutions in both Landau and Gorter–Mellink flow regimes. Then, transient heat transfer of a forced flow of He II is investigated. Finally, some two-dimensional simulations in a porous medium model are carried out.

Longitudinal counterflow in turbulent liquid helium: velocity profile of the normal component

In this paper, the velocity profile of the normal component in the stationary flow of turbulent superfluid helium inside a cylindrical channel is determined, making use of a one-fluid model with internal variables derived from Extended Thermodynamics. In the hypothesis of null barycentric velocity of the fluid (the so-called counterflow situation), it is seen that in the presence of a sufficiently high vortex length density the velocity profile of the normal component becomes very flat in the central region of the channel. Thus, a central flat profile of the normal fluid does not necessarily imply that the flow of the normal component is turbulent.

Dynamical Scaling of the Critical Velocity for the Onset of Turbulence in Oscillatory Superflows

The critical velocity v_c for the onset of turbulence in oscillatory flows of superfluid helium is known to depend on the oscillation frequency omega, namely v_c ~ sqrt(kappa*omega) where kappa is the circulation quantum. Only the numerical prefactor may have some geometry dependence. This universal behaviour was described earlier qualitatively either by employing the superfluid Reynolds number or by extending known dc vortex dynamics to ac flow. In our present work we emphasize that v_c(omega) ~ sqrt(omega) can also be derived rigorously by means of dynamical scaling of equations of vortex dynamics as pointed out by Kotsubo and Swift already two decades ago.

Simulation Study on Application of Nonlinear Model Predictive Control to the Superfluid Helium Cryogenic Circuit

AbstractIn the 27 km circumference Large Hadron Collider, the temperature of more than 1600 main superconducting magnets is stabilized below 2 K by the Superfluid Helium Cryogenic Circuit. The key component of the circuit's Standard Cell is an over 100 m long bayonet heat exchanger with two phase flow of superfluid helium, He II, that is integrated into the magnets submerged in a static bath of He II. The magnets operate under constraints, at variable conditions and their temperature dynamics is highly nonlinear, exhibiting variable dead times of response. We present a simulation study on the application of Nonlinear Model Predictive Control for the temperature stabilization. The controller is based on a simplified, first principles model of the circuit and C/GMRES online optimization algorithm. The good performance with small computational cost of the C/GMRES and real-time feasibility of NMPC are highlighted.

Statistics of Intermittent Switching between Potential Flow and Turbulence around an Oscillating Sphere in Superfluid 4He below 0.5 K

The flow of superfluid helium at very low temperatures around an oscillating microsphere is known to be unstable slightly above the critical velocity. The flow pattern switches intermittently between potential flow and turbulence. From time series recorded at constant temperature and driving force the statistical properties of the switching phenomenon are discussed. Based on our recent understanding of the critical velocity vc of oscillatory superflows, i.e., v_c = sqrt(kappa omega), where kappa is the circulation quantum and omega is the oscillation frequency, the analysis is being refined now. From the exponential distribution of the lifetimes of the turbulent phases quantitative information on the vortex density L can be inferred such as the distribution and the width of the fluctuations of L. The phases of potential flow show a Rayleigh distribution of the excess oscillation amplitude above the amplitude at turbulent flow. The rms value is found to scale as omega^{-3/2}.

Upscaling of superfluid helium flow in porous media

Although the Large Hadron Collider, the particle accelerator at CERN Geneva, did not reach full power, studies have begun for extending its performances. For that matter an increase of the luminosity of the beam by a factor of ten is desired. Achieving such luminosity implies the use of more powerful superconducting magnets experiencing higher heat load. Since the thermal resistance due to the electrical insulations of the superconducting cables is the main thermal resistance for cooling, new types of insulation, based on porous ceramic materials, are developed. In this context, studies of heat transfer in porous media saturated with superfluid helium are of great interest. We present the upscaling of the generalized two-fluid model describing the flow of superfluid helium in the Landau regime using the method of volume averaging. We show that a macro-scale model can be developed for some limiting cases. In particular, we obtain an upscaled version of the superfluid equations in the Landau regime proving the existence of a permeability concept and that allows us to study the relationship between this permeability and the classical intrinsic permeability. This puts the permeability concept previously introduced heuristically by some authors in this context on a much firmer basis. The results are validated against direct numerical simulations of the superfluid helium flow at the pore-scale as well as with comparisons with experimental data.

Porous plug and superfluid helium film flow suppressor for the soft X-ray spectrometer onboard Astro-H

Suppression of superfluid helium flow is critical for the Soft X-ray Spectrometer (SXS) onboard Astro-H, to achieve a life time of the liquid helium over 5 years. The superfluid film flow must be sufficiently small, compared to a nominal helium gas flow rate of the SXS ( 25 μ g / s ) . For this purpose, four devices composed of a porous plug, an orifice, a heat exchanger, and knife edge devices will be employed based on the experience of the X-ray microcalorimeter (XRS for X-Ray Spectrometer) onboard Suzaku. The porous plug is a phase separator of the liquid and gas helium. A potential film flow leaking from the porous plug is suppressed by the orifice. Almost all the remaining film flow evaporates at the heat exchanger. The knife edge devices stop the remaining film flow by using atomically sharp edges. In this paper, we describe the principle and design of these four devices.

Universal Onset of Quantum Turbulence in Oscillating Flows and Crossover to Steady Flows

The critical velocity v_c for the onset of quantum turbulence in oscillatory flows of superfluid helium is universal and scales as v_c \sim \sqrt{\kappa\omega}, where \kappa is the circulation quantum and \omega is the oscillation frequency. This result can be derived from a general argument based on the "superfluid Reynolds number". Only the numerical prefactor may depend somewhat on the geometry of the oscillating object because the flow velocity at the surface of the object may differ from the velocity amplitude of the body. A more detailed analysis derived from the dynamics of the turbulent state gives v_c \approx \sqrt{8\kappa\omega/\beta}, where \beta \sim 1 depends on the mutual friction parameters. This universality is compared with the recently discovered universality of classical oscillatory flows. We also discuss the effect of remanent vorticity on the onset of quantum turbulence. Finally, by employing the "superfluid Reynolds number" again, we argue how v_c changes when the steady case \omega = 0 is approached. In that case v_c scales as \kappa/R, where R is the size of the object.

Vortex dynamics in rotating counterflow and plane Couette and Poiseuille turbulence in superfluid helium

An equation previously proposed to describe the evolution of vortex-line density in rotating counterflow turbulent tangles in superfluid helium [Phys. Rev B 69, 094513 (2004)] is generalized to incorporate nonvanishing barycentric velocity and velocity gradients. Our generalization is compared with an analogous approach proposed by Lipniacki [Eur. J. Mech. B Fluids 25, 435 (2006)], and with experimental results by Swanson et al. [Phys. Rev. Lett. 50, 190 (1983)] in rotating counterflow, and it is used to evaluate the vortex density in plane Couette and Poiseuille flows of superfluid helium.

Stability of Laminar and Turbulent Flow of Superfluid4He at mK Temperatures around an Oscillating Microsphere

The flow of superfluid helium around a vibrating microsphere is investigated at temperatures between 1 K and 25 mK. At small oscillation amplitudes pure potential flow is observed, the linear drag force on the sphere being determined only by ballistic quasiparticle scattering below 0.7 K with phonons contributing exclusively below 0.5 K. At larger oscillation amplitudes a strongly nonlinear drag force gives evidence of stable turbulent flow if at least 0.6 pW are transferred from the sphere to the turbulent superfluid. In an intermediate range of amplitudes (or driving forces) both flow patterns are unstable and intermittent switching between both is observed below 0.5 K. We have recorded time series of this switching phenomenon at constant drives and temperatures lasting up to 36 hours. We have made a statistical analysis of the times series by means of reliability theory. The lifetime of the turbulent phases grows with increasing drive and diverges at a critical value (or at least becomes unmeasurably long). Stability of the laminar phases in the intermediate regime depends on the excess velocity of the sphere above the critical velocity. Metastable laminar phases are observed above the critical velocity having a mean lifetime limited to 25 minutes by natural background radioactivity which occasionally produces local vorticity due to ionization of the liquid. Finally, it is suggested that the breakdown of potential flow belongs to the class of “system failure” experiments which is well known in reliability testing and whose statistical properties are described by extreme-value theory.