Mathematical Modeling and Associated Numerical Simulation of Fusion/Solidification Front Evolution in the Context of Severe Accident of Nuclear Power Engineering

Considering transient processes where liquid/solid phase change occurs, this paper focuses on the associated modeling and numerical treatment in the frame of “Computational Fluid Dynamics” simulations. While being of importance in many industrial applications involving solidification and melting of mixed materials, including power and manufacturing engineering, the first application of this work pertains to the analysis of severe accidents in a nuclear reactor. Indeed, in this context, the molten core materials (a.k.a. corium) can form a high-temperature multiphase liquid pool at the boundary of which fusion and solidification phenomena are of prime importance. In this context, even if materials at play are treated as pure components, it is mandatory to distinguish two different phase change temperatures with a solid fusion temperature and a liquid solidification temperature. Accordingly, in the frame of a sharp interface representation, the paper introduces non-classical heterogeneous conditions at the liquid/solid boundary in such a way that both moving interface (through Stefan conditions associated with fusion or solidification) and static interface (imposing heat flux continuity) are supported at the same time on different spatial locations along this boundary. Within a monolithic resolution of Navier–Stokes and heat conduction equations, this interface is explicitly tracked with combined Front-Tracking and VOF methods. In order to ensure zero velocity in the solid phase, an Immersed Boundary Method and a direct forcing penalization are also introduced. The main relevant features of this combination of numerical methods are discussed along with their implementation in the TrioCFD code taking advantage of the pre-existing code capabilities. Numerical simulations including both verification tests and a case of interest for our industrial application are reported and demonstrate the applicability of the proposed triptych model+methods+code to treat such problems. The numerical tools and the simulation code developed in this work could be used not only in the several accident context but also to simulate melting, solidification and fusion processes occurring in aerodynamics, hypersonic reentry vehicles and laser applications to cite but a few.

Transient Marangoni convection induced by an isothermal sidewall of a rectangular liquid pool

Transient Marangoni convection induced by an isothermal sidewall of a rectangular pool under a zero-gravity condition is studied using scaling analysis. Scaling analysis shows that there exist a number of flow regimes in each evolution scenario, depending on the Marangoni number, the Prandtl number and the aspect ratio. In a typical evolution scenario, a horizontal surface flow and a vertical flow adjacent to the sidewall may appear. Additionally, a number of scaling laws of the velocity and thickness of transient Marangoni convection are obtained. Further, numerical simulation is performed for validation of the selected scaling laws. There exits good agreement between the numerical results and the scaling predictions.

Numerical Simulation of Leakage and Diffusion Process of LNG Storage Tanks

To investigate the evolution process of LNG (Liquefied Natural Gas) liquid pool and gas cloud diffusion, the Realizable k-ε model and Eluerian model were used to numerically simulate the liquid phase leakage and diffusion process of LNG storage tanks. The experimental results showed that some LNG flashed and vaporized rapidly to form a combustible cloud during the continuous leakage. The diffusion of the explosive cloud was divided into heavy gas accumulation, entrainment heat transfer, and light gas drift. The vapor cloud gradually separated into two parts from the whole “fan leaf shape”. One part was a heavy gas cloud; the other part was a light gas cloud that spread with the wind in the downwind direction. The change of leakage aperture had a greater impact on the whole spill and dispersion process of the storage tank. The increasing leakage aperture would lead to 10.3 times increase in liquid pool area, 78.5% increase in downwind dispersion of methane concentration at 0.5 LFL, 22.6% increase in crosswind dispersion of methane concentration at 0.5 LFL, and 249% increase in flammable vapor cloud volume. Within the variation range of the leakage aperture, the trend of the gas cloud diffusion remained consistent, but the time for the liquid pool to keep stable and the gas cloud to enter the next diffusion stage was delayed. The low-pressure cavity area within 200 m of the leeward surface of the storage tank would accumulate heavy gas for a long time, forming a local high concentration area, which should be an area of focus for alert prediction.

Experimental Study on Droplet Impact Phenomena on Burning Liquid Pool Surfaces

In this study, the phenomena of water droplet impact on burning methanol and n-heptane pool surfaces were experimentally investigated under various size and velocity conditions of impact droplet. In the n-heptane pool, the temperature increased to the deeper location of the pool and the droplet impact velocity was slower, as compared with those in the methanol pool. These results were caused by the higher heat release rate of the n-heptane pool. However, the impact droplet sizes on the burning methanol and n-heptane pool surfaces appeared to be similar. By visualizing the droplet impact phenomena, the impact pattern maps of burning methanol and n-heptane pool surfaces were constructed and compared with the previous impact pattern maps of their unburned pool surfaces. In the burning and unburned methanol and unburned n-heptane pools, patterns of single jet and splash with secondary jet were observed. On the contrary, in the burning n-heptane pool, patterns of single jet and canopy were observed.