Influence of Quantum Turbulence on the Processes of Heat Transfer and Boiling in Superfluid Helium

Kondaurova, L. P.; Efimov, V. B.; Tsoi, A. N.

doi:10.1007/s10909-016-1731-5

Cited by 14 publications

(7 citation statements)

References 24 publications

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“…The better agreement between experimental data on the propagation of intense heat pulses (generating vortices and interacting with these "own" vortices) and the corresponding numerical solution, was obtained when assuming the existence of an initial level of VLD L back , whereas the introduction of the initiating term led to an unsatisfactory correlation with the experimental observations (see e.g. [24]). Thus it may be surmised that this is an argument in favour of the theory of remnant vortices.…”

Section: Solutionsmentioning

confidence: 68%

“…That was the starting point in the construction of the so-called Hydrodynamics of Superfluid Turbulence (HST), which was the unification of the Vinen equation and the classical two-fluid hydrodynamics (see, e.g., [15], [28], [29]). The HST equations have been applied to study a large number of hydrodynamic and thermal problems, including heat transfer and boiling in He II (see, e.g., [30], [31], [32], [33], [34], [35], [24]). The numerical and analytic results were in very good agreement with numerous experimental data.…”

Section: Nonuniform Quantum Turbulence and The Vinen Phenomenological...mentioning

confidence: 99%

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Nonuniform quantum turbulence in superfluids

Nemirovskii

2018

Phys. Rev. B

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The problem of quantum turbulence in a channel with an inhomogeneous counterflow of superfluid turbulent helium is studied. The counterflow velocity V x ns (y) along the channel is supposed to have a parabolic profile in the transverse direction y. Such statement corresponds to the recent numerical simulation by Khomenko et al. [Phys. Rev. B 91, 180504 (2015)]. The authors reported about a sophisticated behavior of the vortex line density (VLD) L(r, t), different from L ∝ V x ns (y) 2 , which follows from the naive, straightforward application of the conventional Vinen theory. It is clear, that Vinen theory should be refined by taking into account transverse effects and the way it ought to be done is the subject of active discussion in the literature. In the work we discuss several possible mechanisms of the transverse flux of VLD L(r, t) which should be incorporated in the standard Vinen equation to describe adequately the inhomogeneous quantum turbulence (QT). It is shown that the most effective among these mechanisms is the one that is related to the phase slippage phenomenon. The use of this flux in the modernized Vinen equation corrects the situation with an unusual distribution of the vortex line density, and satisfactory describes the behavior L(r, t) both in stationary and nonstationary situations. The general problem of the phenomenological Vinen theory in the case of nonuniform and nonstationary quantum turbulence is thoroughly discussed.

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Section: Solutionsmentioning

confidence: 68%

Section: Nonuniform Quantum Turbulence and The Vinen Phenomenological...mentioning

confidence: 99%

Nonuniform quantum turbulence in superfluids

Nemirovskii

2018

Phys. Rev. B

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“…The values of the coefficients α V and β V as recommended by Kondaurova et al are used in Eq. 7, which appear to produce simulation results in good agreement with experimental observations [19]. We then evolve the governing equations using the MacCormack's predictor-corrector scheme, which is accurate to the second or-der in time and space [45].…”

Section: Numerical Modelmentioning

confidence: 99%

Transient heat transfer of superfluid $^4$He in nonhomogeneous geometries -- Part I: Second sound, rarefaction, and thermal layer

Bao,

Guo

2021

Preprint

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Transient heat transfer in superfluid 4 He (He II) is a complex process that involves the interplay of the unique counterflow heattransfer mode, the emission of second-sound waves, and the creation of quantized vortices. Many past researches focused on homogeneous heat transfer of He II in a uniform channel driven by a planar heater. In this paper, we report our systematic study of He II transient heat transfer in nonhomogeneous geometries that are pertinent to emergent applications. By solving the He II two-fluid equation of motion coupled with the Vinen's equation for vortex-density evolution, we examine and compare the characteristics of transient heat transfer from planar, cylindrical, and spherical heaters in He II. Our results show that as the heater turns on, an outgoing second-sound pulse emerges, in which the vortex density grows rapidly. These vortices attenuate the second sound and result in a heated He II layer in front of the heater, i.e., the thermal layer. In the planar case where the vortices are created throughout the space, the second-sound pulse is continuously attenuated, leading to a strong thermal layer that diffusively spreads following the heat pulse. On the contrary, in the cylindrical and the spherical heater cases, vortices are created mainly in a thin thermal layer near the heater surface. As the heat pulse ends, a rarefaction tail develops following the second-sound pulse, in which the temperature drops. This rarefaction tail can promptly suppress the thermal layer and take away all the thermal energy deposited in it. The effects of the heater size, heat flux, pulse duration, and temperature on the thermal-layer dynamics are discussed. We also show how the peak heat flux for the onset of boiling in He II can be studied in our model.

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“…This theory was successful, it explained a lot of experimental results on the nonlinear acoustics of the first and second sounds, the evolution of strong heat pulses, the formation of shock waves etc. It was also successfully applied to the problems of unsteady heat transfer and boiling of He II ( [7], [35], [36]). These examples demonstrate that the way to treat the vortex line density L(r, t) as an additional and equipollent variable seems to be productive and fruitful.…”

Section: Other Ways To Treat the Vortex Line Densitymentioning

confidence: 99%

Coarse-grained Hydrodynamics of turbulent superfluids: HVBK approach and the bundle structure of the vortex tangle

Nemirovskii¹

2019

Preprint

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In the paper I develop a critical analysis of the use of the HVBK method for the study of three-dimensional turbulent flows of superfluids. The conception of the vortex bundles forming the structure of quantum turbulence is controversial and does not justify the use of the HVBK method. In addition, this conception is counterproductive, because it gives incorrect ideas about the structure of the vortex tangle as a set of bundles containing parallel lines. The only type of dynamics of vortex filaments inside these bundles is possible, namely, Kelvin waves running along the filaments. At the same time, as shown in numerous numerical simulations, a vortex tangle consists of a set of entangled vortex loops of different sizes and having a random walk structure. These loops are subject to large deformations (due to highly nonlinear dynamics), they reconnect with each other and with the wall, split and merge, creating a lot of daughter loops. They also bear Kelvin waves on them, but the latter have little impact.I also propose and discuss an alternative variant of study of three-dimensional turbulent flows, in which the vortex line density L(r, t) is not associated with ∇ × vs, but it is an independent equipollent variable described by a separate equation.

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Influence of Quantum Turbulence on the Processes of Heat Transfer and Boiling in Superfluid Helium

Cited by 14 publications

References 24 publications

Nonuniform quantum turbulence in superfluids

Nonuniform quantum turbulence in superfluids

Transient heat transfer of superfluid $^4$He in nonhomogeneous geometries -- Part I: Second sound, rarefaction, and thermal layer

Coarse-grained Hydrodynamics of turbulent superfluids: HVBK approach and the bundle structure of the vortex tangle

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