Wladimir Bergez

Note: Void effects on eddy current distortion in two-phase liquid metal

A model based on the first order perturbation expansion of magnetic flux in a two-phase liquid metal flow has been developed for low magnetic Reynolds number Rem. This model takes into account the distortion of the induced eddy currents due to the presence of void in the conducting medium. Specific experiments with an eddy current flow meter have been realized for two periodic void distributions. The results have shown, in agreement with the model, that the effects of velocity and void on the emf modulation are decoupled. The magnitude of the void fraction and the void spatial frequency can be determined from the spectral density of the demodulated emf.

Towards Quantitative Void Fraction Measurement With an Eddy Current Flowmeter for Fourth Generation Sodium Cooled Fast Reactors: A Simplified Model

We propose an experimental methodology for the purpose of quantitative void fraction measurements in fourth generation Sodium cooled fast reactors with a standard Eddy Current Flow Meter (ECFM) sensor. The methodology consists of using the technique of ellipse fit and correlate the fluctuations in the angle of inclination of this ellipse with the void fraction. This methodology is applied in this paper to an ideal configuration of periodic grooves on solid aluminium cylinder with various volumic fractions. The effects of physical parameters such as coil excitation frequency, coil current and motion have been studied. The first results show that ECFM is sensitive to void fractions between 0.3% and 6.9%. It further demonstrates that the response to void fraction is insensitive to the mean velocity of the two-phase medium.

Influence of skin depth on convective heat transfer in induction heating

We investigate convection driven by induction heating of a horizontal fluid layer with direct numerical simulations (DNS). This problem is of particular interest in the context of nuclear severe accident mastering. In a real severe accident, the molten core is subjected to homogeneous internal sources resulting from nuclear disintegrations. This situation is mimicked in the laboratory using induction heating as the internal source. In induction heating however, heat sources are localized in the skin layer. Consequently, this concentration of heat may modify the flow and wall heat transfer, compared to the case of homogeneous internal sources. DNS are carried out for three typical skin depths and three total deposited powers. Skin depth variations show surprising results regarding flow structures and heat transfer. It is found that the heat sources heterogeneity has a weak effect on flow structures. Consequently, models of heat transfer in the case of homogeneous sources remain valid even with strong localized heating near the bottom.

Experimental study of bubble detection in liquid metal

Bubble detection in liquid metal is an important issue for various technological applications. For instance, in the framework of Sodium Fast Reactors conception, the presence of gas in the sodium flow of the primary and secondary loops is a problematic of crucial importance for surety and reliability. Here, the two main measurement methods of gas in sodium are Ultrasonic testing and Eddy-current testing; we investigate the second method in our study. In a first approach, we have performed experiments with liquid metal – galinstan – containing insulating spherical beads of millimeter order. The liquid metal is probed with an Eddy-current Flowmeter (ECFM) in order to detect the beads, and characterize their diameter and position. Results show that the signal measured by the ECFM is correlated to the effect of these parameters. Finally, an analytical model is proposed and compared to the experimental results.

Destabilization of a liquid metal by nonuniform Joule heating

We study the effect of an impressing AC magnetic field at the bottom of a liquid metal layer of thickness h. In this situation the fluid is set in motion by the buoyancy forces caused by internal heat sources. The heat sources, caused by the Joule effect induced by the AC field, present an exponentially decaying profile, with characteristic length δ. As the magnetic field is horizontal, the Lorentz force has no influence on the dynamics of the system since it contributes only to the magnetic pressure. We propose an analysis of both the transient and fully developed regimes using linear stability analysis (LSA) and direct numerical simulations (DNSs). The transient period is governed by the temporal evolution of the temperature field as well as the development of the convective instability, which can be concomitant and therefore requires adopting a transient LSA algorithm to track these two effects. The DNSs have been performed for various distributions of the heat sources and various total heat input. This corresponds to independently varying δ/h in the range 0.04≤δ/h≤0.45 and a Rayleigh number 1.1×10^{4}≤Ra≤1.2×10^{5}. We observe the relaxation of the temperature up to the steady conductive profile before the transition to the nonlinear regime when Ra is small, whereas for larger Ra, nonlinear effects appear during the relaxation of the temperature profile. The unsteadiness of the temperature field significantly alters the development of the instability because of a much smaller growth rate. Surprisingly, we observe that δ/h has only a limited influence on averaged quantities as well as on the patterns for both the linear and nonlinear regimes. This comes with the fact that the profiles present an apparent reflectional symmetry, despite the asymmetry of the governing equations.

Magnetoconvection transient dynamics by numerical simulation

Abstract.We investigate the transient and stationary buoyant motion of the Rayleigh-Bénard instability when the fluid layer is subjected to a vertical, steady magnetic field. For Rayleigh number, Ra, in the range 103-106, and Hartmann number, Ha, between 0 and 100, we performed three-dimensional direct numerical simulations. To predict the growth rate and the wavelength of the initial regime observed with the numerical simulations, we developed the linear stability analysis beyond marginal stability for this problem. We analyzed the pattern of the flow from linear to nonlinear regime. We observe the evolution of steady state patterns depending on

Magnetic flux distortion in two-phase liquid metal flow: Model experiment

Ra/Ha^{2}

Thermo-magnetic behaviour of AFM–MFM cantilevers

Ra/Ha2 and Ha. In addition, in the nonlinear regime, the averaged kinetic energy is found to depend on Ra and to be independent of Ha in the studied range.Graphical abstract

Influence of gravity on pool boiling on a flat plate: Results of parabolic flights and ground experiments

In this paper, we present the model experiments in order to study the magnetic flux distortion of a two-phase liquid metal flow excited by an AC magnetic field in a range of pulsation where Faraday induction and Lorentz force effects are significant. These experiments realized with solid aluminum rods allow to characterize the effects of flow velocity (0 ≲ U≤1 ms−1), void fraction (0≤α≤6.9 %), pulsation of the AC magnetic field (1.5×103≤ω≤12.5×103 rad s−1), and of two different void geometries. The results are analyzed on the basis of a first order expansion of magnetic flux in U and α. Despite the strong coupling between Faraday induction and Lorentz force effects, the results show that the contributions of U and α on a magnetic flux distortion can be well separated at both low magnetic Reynolds number and α values. These results are independent of void geometry.

Pool Boiling with Non-condensable Gas in Microgravity: Results of a Sounding Rocket Experiment

Atomic force microscopy (AFM) experiments were performed to study the behaviour of AFM cantilevers under an external magnetic field B and temperature field produced by a coil with an iron core. Four cantilever types were studied. Forces were measured for different B values and at various coil-to-cantilever separation distances. The results were analysed on the basis of a phenomenological model. This model contains the contribution of two terms, one monopole-monopole interaction at short distance, and one apparent paramagnetic interaction in del B-2 at large distance, which represents the temperature effects. We observe a good agreement between the model and the experimental data.