Temperature overshoot due to quantum turbulence during the evolution of moderate heat pulses in He II

Abstract

Transient heat transfer in liquid helium is investigated both experimentally and theoretically in plane and cylindrical geometry in the range of parameters where superfluid turbulence appears to be important. The influence of the main flow parameters – heat flux, pulse duration, and rest time – on the temperature evolution is reported. At high heat inputs the mutual friction force related to the superfluid vortex lines leads to the formation of a temperature overshoot behind the propagating second-sound wave and must be looked upon as a macroscopic effect of microscopic quantum turbulence. The experimental results can be reproduced by a theoretical model when the mutual interaction force is expressed in terms of the vortex line density (VLD), and the Vinen equation, extended to include spatial dependence, is taken into account for its temporal evolution. Fair quantitative agreement between experiment and theory is obtained if the ratio of the temperature overshoot and the shock-wave amplitude is below about 4. At stronger heat inputs the agreement is only qualitative.

Numerical investigation of the influence of period duration on evolution of intense wave of the second sound

“…These pulses, except the first one, propagated in the disturbed liquid with a vortex tangle generated by previous heat pulses and other sources within the experimental volume. A similar effect of the vortex tangle on evolution of powerful heat pulses was also observed in [6].…”

“…At this temperature, the nonlinearity coefficient of the second sound takes a positive value, i.e., the decay is formed at the leading edge of the wave. The radii of cylindrical and spherical heaters are int 0.25 cm, x = which correspond to the radius of cylindrical heater in experiments [6].…”

“…Therefore, at calculations of dynamics of the following pulses we have used the balance equation for vortex filament density (3). It is shown in [8] that experimental data of [6] on dynamics of powerful heat pulses can be described well with the coefficient increased by the factor of 1.5, in the presence of term 3/ 2 L responsible for the growth of vortex filaments. This correction was taken into account in calculations.…”

Study of the transient thermal wave heat transfer in a channel immersed in a bath of superfluid helium

“…Eq. (10) is widely accepted and adopted in the literature [6,[12][13][14], and thus, this formula is adopted to describe the connection between the mutual friction force and the quantized vortices and it is used the numerical calculation.…”

“…The hydrodynamics of He II can be understood by combining LandauÕs two-fluid model and the phenomenological description of the quantized vortices proposed by Vinen [11,[16][17][18]. A group in Max-Planck institute investigated the thermal wave in He II both experimentally and theoretically, and the propagation of the thermal wave in convergent channel was also carried out [14,21]. Nemirovskii and Fiszdon [22] intensively reviewed the development of equations for the description of the hydrodynamic process in He II.…”