Simulations of liquid metal flows over plasma-facing component edges and application to beryllium melt events in JET

Abstract

Navier-Stokes simulations of liquid beryllium flows over the straight edge of plasma-facing components are carried out in conditions emulating upper dump plate melting observed experimentally in JET. The results demonstrate the existence of three main hydrodynamic regimes featuring various degrees of downstream flow attachment to the underlying solid surface. Transitions between these regimes are characterized by critical values of the Weber number, which quantifies the relative strength of fluid inertia and surface tension, thereby providing a general stability criterion that can be applied to any instance of transient melt events in fusion devices. The predictive capabilities of the model are tested by comparing numerical output with JET data regarding the morphology of the frozen melt layers and the location of beryllium droplets splashed onto nearby vacuum vessel surfaces as a result of disruption current quench plasmas interacting with the solid beryllium tiles protecting the upper main chamber regions. Simulations accounting for the coupling between fluid flow and heat transfer confirm the key role played by re-solidification as a stabilizing process, as previously found through macroscopic melt dynamics calculations performed with the MEMOS-U code. The favourable agreement found between the simulations and the general characteristics of the JET beryllium upper dump plate melt splashing give confidence that the same approach can be applied to estimate the possibility of such mechanisms occurring during disruptions on ITER.

Dust and powder in fusion plasmas: recent developments in theory, modeling, and experiments

“…In transient melting experiments, the melt layer thickness and melt life time, typically 100 μ m to several 100's μ m and no more than several ten's of ms , are smaller than those anticipated for ITER transient melting, where predictive modelling reports melt layers in excess of 1 mm for the duration of few 100's of ms (Coburn et al 2020(Coburn et al , 2022. From a practical perspective, the unstable modes of interest for melt splashing are those whose wavelength is smaller than the melt pool depth and whose growth time is smaller than the duration of the melt-inducing energetic transient or than the time required for the melt to cross the edge (Bazylev et al 2008;Vignitchouk et al 2022b). Droplet sizes are of the order of the most unstable wave length (Lefebvre 1989; Maroteaux et al 2002;Brailovsky et al 1995;Bazylev et al 2008;, thus the extended thin molten layers created by energetic events with large plasma wetted areas are susceptible to splash into large, fraction of melt thickness, droplets.…”

“…Depending on the scenario and location of the collection/observation site, the measured size and overall mass might not necessary correspond to those of the original droplets. For example, the time scale for the development of a large enough oscillation amplitude to induce material ejection from the edge of the molten JET UDP (Vignitchouk et al 2022b) is comparable to duration of a typical VDE (responsible for the melting) (Jepu et al 2019;, so that droplets are ejected essentially into a vacuum and do not lose mass due to interaction with the plasma prior to impacting on the wall. Yet, in the case that droplets encounter dense and/or hot plasma during their trajectory towards the wall, the final solid population might not be a faithful representation of the original droplet distribution.…”

“…cross-sectional areas), translation of splat sizes to ejected droplet volumes requires knowledge of the maximum droplet spread (Pasandideh-Fard et al 1998;Liu 1999). In the case of the JET Be splashes on the vacuum vessel wall, two opposite limits yield the sizes of several 10's of μ m and several 100's of μ m (Jepu et al 2019;Vignitchouk et al 2022b).…”

Analytical expressions for thermophysical properties of solid and liquid beryllium relevant for fusion applications

“…In JET, the most melting prone Be areas have been identified to be the upper dump plates, where heating to elevated temperatures is caused mainly by unmitigated plasma disruptions [111]. However, the thickness of these BeO nearsurface layers has been measured to be of the order of microns [110], which is much thinner than the typical Be melt layer thickness of several hundreds of microns [17,111] and also thinner than the estimated Be ejected droplet size of the order of hundred microns [111,112]. The above indicate that there is no real benefit in attempting to consider the presence of BeO in heating, macroscopic melt motion and dust generation studies in JET, especially given the fact that the temperature dependence of most BeO thermophysical properties has not been investigated yet.…”

“…The thermophysical properties of interest are the latent heats of phase transitions (fusion, hcp-to-bcc polymorphic transition, vaporization), the specific isobaric heat capacity, the electrical resistivity, the thermal conductivity, the mass density, the vapor pressure, the work function, the total hemispherical emissivity and the absolute thermoelectric power (for the solid and the liquid phases) as well as the surface tension and the dynamic viscosity (only for the liquid phase). The primary objective is to identify and to critically evaluate reliable experimental datasets in order to propose accurate empirical expressions for the temperature dependence of these thermophysical quantities that will standardize their description in the multiple thermal analysis [11,12], vapor shielding [13,14,15], macroscopic melt motion [16,17,18], arcing [19,20,21], dust generation [22,23] and dust transport codes [24,25,26,27,28,29] that are being developed by the fusion community. In the case when no reliable experimental datasets are available, the objective is to propose analytical extrapolations that do not violate general statistical mechanics principles and are consistent with well-established semi-empirical rules.…”