B. Chabaud

Turbulent Rayleigh–Bénard convection in gaseous and liquid He

In this article we deal with the turbulent regimes of Rayleigh–Benard convection, namely the 2/7 regime and beyond. An experiment with He at low temperature allows us to explore a large Rayleigh number (Ra) range up to 2×1014, under Boussinesq conditions, while the Prandtl number (Pr) is equal to and larger than 0.7. Calorimetric measurements evidence a departure from the 2/7 regime above Ra=1011 toward a new regime where the heat transfer is enhanced. Local measurements with two nearby thermometers allows us to relate this change to a laminar–turbulent transition of the velocity boundary layer induced by the large-scale flow near the walls of the cell. The features of the observed new regime match those of the ultimate regime predicted by R. Kraichnan [Phys. Fluids 5, 1374 (1962)] at moderate Pr; in particular, our experimental data show that the thermal boundary layer lies inside the viscous sublayer of the turbulent boundary layer.

Universality of small scale turbulence.

The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from 8500 to 10(6) (max(R(lambda) approximately 1200). The traditional analysis of the statistics of velocity increments by means of structure functions or probability density functions is replaced by a new method which is based on the theory of Markov processes. It gives access to a more complete characterization by means of joint probabilities of finding velocity increments at several scales. Based on this more comprehensive method, our results are very far from a possible universal state, even for R(lambda) above 1000.

Energy cascade and the four-fifths law in superfluid turbulence

The 4/5-law of turbulence, which characterizes the energy cascade from large to small-sized eddies at high Reynolds numbers in classical fluids, is verified experimentally in a superfluid 4He wind tunnel, operated down to 1.56 K and up to R_lambda ~ 1640. The result is corroborated by high-resolution simulations of Landau-Tiszas two-fluid model down to 1.15 K, corresponding to a residual normal fluid concentration below 3 % but with a lower Reynolds number of order R_lambda ~ 100. Although the Karman-Howarth equation (including a viscous term) is not valid \emph{a priori} in a superfluid, it is found that it provides an empirical description of the deviation from the ideal 4/5-law at small scales and allows us to identify an effective viscosity for the superfluid, whose value matches the kinematic viscosity of the normal fluid regardless of its concentration.

Hot wire anemometer operating at cryogenic temperatures

A micronic‐size hot wire anemometer operating at cryogenic temperatures (4 K) has been developed; using superconducting and resistive thin films, its electrical resistance is very sensitive to the velocity of a gaseous 4He subsonic jet. The fabrication procedure is described and the measured characteristics are compared with a simple thermal equilibrium model.

Heat Transfer in Turbulent Rayleigh–Bénard Convection Below the Ultimate Regime

A Rayleigh–Bénard cell has been designed to explore the Prandtl (Pr) dependence of turbulent convection in the cross-over range 0.7<Pr<21 and for the full range of soft and hard turbulences, up to Rayleigh number Ra≃1011. The set-up benefits from the favourable characteristics of cryogenic helium-4 in fluid mechanics, in situ fluid property measurements, and special care on thermometry and calorimetric instrumentation. The cell is cylindrical with diameter/height=0.5. The effective heat transfer Nu(Ra, Pr) has been measured with unprecedented accuracy for cryogenic turbulent convection experiments in this range of Rayleigh numbers. Spin-off of this study include improved fits of helium thermodynamics and viscosity properties. Three main results were found. First the Nu(Ra) dependence exhibits a bimodality of the flow with 4–7% difference in Nu for given Ra and Pr. Second, a systematic study of the side-wall influence reveals a measurable effect on the heat transfer. Third, the Nu(Pr) dependence is very small or null: the absolute value of the average logarithmic slope (d ln Nu/d ln Pr)Ra is smaller than 0.03 in our range of Pr, which allows to discriminate between experiments with contradictory results [Ashkenazi et al., Phys. Rev. Lett.83, 3641 (1999)] [Ahlers et al., Phys. Rev. Lett.86, 3320 (2001)].

Conditional statistics of velocity fluctuations in turbulence

Abstract Using experimental data recorded in a low temperature helium jet, we have studied the statistics of velocity increments: vr(x) = v(x+r) − v(x) conditioned on a “rate of energy transfer” anzatz, er: P(vr|er). For a fixed value of er, the histograms of vr are found Gaussian at all scale, i.e. there is no intermittency at fixed er. Intermittency is caused by the fluctuations of the latter quantity. If P(vr|er) is Gaussian, it is characterized uniquely by its variance σ2 = 〈vr2|er〉 − 〈vr|er〉2 and mean v0 = 〈vr|er〉. We show that σ is related to er by a power law, valid at any scale, and that v0 is close to logarithmic in er in the inertial range. With these two relationship, the statistics of vr at fixed er are completely determined by er. Therefore, the relevant quantity to describe intermittency is the transfer rate of energy, acting as a driving process for the velocity fluctuations.

High rayleigh number convection with gaseous helium at low temperature

This article presents an experimental set-up to study the turbulent regime of free thermal convection in a Rayleigh-Bénard cell. Helium gas around 4 K is confined in a cell of aspect ratio 0.5. With a thermocouple technique we can measure temperature differences across the cell as low as 0.2 mK, which allows to test the adiabatic gradient effect. Covering a large range of Rayleigh numbers (103 to 5 × 1012), Nusselt numbers from 1 to 103 are obtained. The results are compared with previous works. They show a departure from the 2/7 power law above Ra = 3 × 1010.

Ultimate regime of convection : Robustness to poor thermal reservoirs

A transition to Kraichnan ultimate regime of convection has been reported in very high Rayleigh numbers experiments, but not in all of them. These apparently contradictory results can be explained by a recent phenomenological model that accounts for the nonideality of the plate thermal properties [Chilla et al., Phys. Fluids 16, 2452 (2004)]. In this paper, we present a direct test of this model, using a low conductivity plate. We found an unaltered transition, not compatible with the model’s predictions.

Superconducting instrumentation for high Reynolds turbulence experiments with low temperature gaseous helium

Turbulence is of common experience and of high interest for industrial applications, despite its physical grounds is still not understood. Cryogenic gaseous helium gives access to extremely high Reynolds numbers (Re). We describe an instrumentation hosted in CERN, which provides a 6 kW @ 4.5 K helium refrigerator directly connected to the experiment. The flow is a round jet; the flow rates range from 20 g/s up to 260 g/s at 4.8 K and about 1.2 bar, giving access to the highest controlled Re flow ever developed. The experimental challenge lies in the range of scales which have to be investigated: from the smallest viscous scale η, typically 1 μm at Re=107 to the largest L∼10 cm. The corresponding frequencies: f=v/η can be as large as 1 MHz. The development of an original micrometric superconducting anemometer using a hot spot and its characteristics will be discussed together with its operation and the perspectives associated with superconducting anemometry.

Micronic-size cryogenic thermometer for turbulence measurements

Micronic-size thermometers (1.5×1.5×0.5 μm3) designed for local measurements in turbulent gaseous helium in the range of 4–80 K, have been developed and tested. Their very short time response (⩽1 μs) and micronic spatial resolution allow to perform measurements down to the Kolmogorov dissipative length scale, for high Reynolds or Rayleigh numbers flows. These thermometers, designed to be nonperturbative in the flow, are based on Au–Ge thin films deposited by sputtering process on drawn glass fibers. Their relative sensitivities σ=|(T/R)(dR/dT)| are ranging from 0.15 to 0.9, and are nearly constant on the whole temperature range.