Derivation of Amplitude Equations by Renormalization Group Method

A proper formulation in the perturbative renormalization group method is presented to deduce amplitude equations. The formulation makes it possible not only avoiding a serious difficulty in the previous reduction to amplitude equations by eliminating all of the secular terms but also consistent derivation of higher-order correction to amplitude equations.Comment: 6 page, revte

Nonlinear Modulation of Travelling Rolls in Magnetoconvection

Modulational dynamics of oscillatory travelling rolls in magnetoconvection is studied near the onset of a Hopf bifurcation. Using weakly nonlinear analysis, we derive an envelope equation of oscillatory travelling rolls in the plane perpendicular to an ambient vertical magnetic field.The envelope equation is the Davey-Stewartson (DS) equation with complex coefficients, from which we obtain criteria for the modulational (Benjamin-Feir) instability of oscillatory travelling rolls.Comment: 8 pages,late

SIMMER-III Analyses of Local Fuel-Coolant Interactions in a Simulated Molten Fuel Pool: Effect of Coolant Quantity

Studies on local fuel-coolant interactions (FCI) in a molten pool are important for the analyses of severe accidents that could occur for sodium-cooled fast reactors (SFRs). To clarify the mechanisms underlying this interaction, in recent years, several experimental tests, with comparatively larger difference in coolant volumes, were conducted at the Japan Atomic Energy Agency by delivering a given quantity of water into a molten pool formed with a low-melting-point alloy. In this study, to further understand this interaction, interaction characteristics including the pressure buildup as well as mechanical energy release and its conversion efficiency are investigated using the SIMMER-III, an advanced fast reactor safety analysis code. It is found that the SIMMER-III code not only reasonably simulates the transient pressure and temperature variations during local FCIs, but also supports the limited tendency of pressurization and resultant mechanical energy release as observed from experiments when the volume of water delivered into the pool increases. The performed analyses also suggest that the most probable reason leading to such limited tendency should be primarily due to an isolation effect of vapor bubbles generated at the water-melt interface

X-Ray Imaging Calibration for Fuel-Coolant Interaction Experimental Facilities

During a severe accident in either sodium-cooled or water-cooled nuclear reactors, jets of molten nuclear fuel may impinge on the coolant resulting in fuel-coolant interactions (FCI). Experimental programs are being conducted to study this phenomenology and to support the development of severe accident models. Due to the optical opacity of the test section walls, sodium coolant, and the apparent optical opacity of water in the presence of intense ebullition, high-speed X-ray imaging is the preferred technique for FCI visualization. The configuration of these X-ray imaging systems, whereby the test section is installed between a fan-beam X-ray source and a scintillator-image intensifier projecting an image in the visual spectrum onto a high-speed camera, entails certain imaging artefacts and uncertainties. The X-ray imaging configuration requires precise calibration to enable detailed quantitative characterization of the FCI. To this end, ‘phantom’ models have been fabricated using polyethylene, either steel or hafnia powder, and empty cavities to represent sodium, molten fuel and sodium vapor phases respectively. A checkerboard configuration of the phantom enables calibration and correction for lens distortion artefacts which magnify features towards the edge of the field of view. Polydisperse steel ball configurations enable precise determination of the lower limit of detection and the estimation of parallax errors which introduce uncertainty in an object’s silhouette dimensions. Calibration experiments at the MELT facility determined lower limits of detection in the order of 4 mm for steel spheres, and 1.7-3.75 mm for vapor films around a molten jet