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.

The stability of internal gravity waves in a bounded atmospheric shear layer in the presence of moisture

The stability characteristics of internal gravity waves, generated by an isothermal bounded tangent velocity profile in the presence of a saturated finite layer, are studied. The moist layer with constant thickness the structure of the ness is introduced at different levels in respect to the point of inflection and the variations of moisture content and distance from the origin are examined. The characteristics of the unstable waves are obtained by solving numerically the linearized versions or the full equations of motion, in the inviscid and Boussinesq limit, through the technique of Lalas and Elnaudi (1976). It is shown that the presence of the moist layer can significantly affect the stability characteristics of the waves. Increases in the moisture and distance of the layer from the Inflection point are found to amplify or decay the wave response, because the saturated layer behaves as a solid boundary to the flow. The presence of such effective layer is shown to stabilize short wavelengths and destabilize. Finally, an application of the model's results to the real atmosphere is discussed.

A Novel Improved Coupled Dynamic Solid Boundary Treatment for 2D Fluid Sloshing Simulation

In order to achieve stable and accurate sloshing simulations with complex geometries using Smoothed Particle Hydrodynamic (SPH) method, a novel improved coupled dynamic solid boundary treatment (SBT) is proposed in this study. Comparing with the previous SBT algorithms, the new SBT algorithm not only can reduce numerical dissipation, but also can greatly improve the ability to prevent fluid particles penetration and to expand the application to model unidirectional deformable boundary. Besides the new SBT algorithm, a number of modified algorithms for correcting density field and position shifting are applied to the new SPH scheme for improving numerical stability and minimizing numerical dissipation in sloshing simulations. Numerical results for three sloshing cases in tanks with different geometries are investigated in this study. In the analysis of the wave elevation and the pressure on the tank, the SPH simulation with the new SBT algorithm shows a good agreement with the experiment and the simulations using the commercial code STAR-CCM+. Especially, the sloshing case in the tank with deformable bottom demonstrates the robustness of the new boundary method.

An Immersed Boundary–Lattice Boltzmann Approach to Study Deformation and Fluid–Structure Interaction of Hollow Sealing Strip

A combined immersed boundary–lattice Boltzmann approach is used to simulate the dynamics of the fluid–structure interaction of a hollow sealing strip under the action of pressure difference. Firstly, the multiple relaxation times LBM model, hyper-elastic material model and immersed boundary method were deduced. According to the strain characteristics of hyper-elastic materials and the specific situation of friction between the elastic boundary and solid boundary, the internal force and the external force on the immersed boundary were discussed and deduced, respectively. Then, a 2D calculation model of the actual hollow sealing strip system was established, during which technical problems such as the equivalent wall thickness of the sealing strip and the correction of the stiffness of the contact corner were solved. The reliability of the model was verified by comparing results of FEM simulation of quasi-static deformation. Following this, the simulation results of three typical cases of sealing strips were presented. The results show that when the sealing strip fails, there will be a strong coupling phenomenon between the flow field and the sealing strip, resulting in the oscillation of the flow field and the sealing strip at the same frequency.

An experimental and simulation study of the flow pattern characteristics of water jet impingements in boreholes

Hydraulic slotting has become one of the most common technologies adopted to increase permeability in low permeability in coal field seams. There are many factors affecting the rock breaking effects of water jets, among which the impact force cannot be ignored. To study the influencing effects of contact surface shapes on jet flow patterns and impact force, this study carried out experiments involving water jet impingement planes and boreholes under different pressure conditions. The investigations included numerical simulations under solid boundary based on gas–liquid coupling models and indoor experiments under high-speed camera observations. The results indicated that when the water jets impinged on different contact surfaces, obvious reflection flow occurred, and the axial velocity had changed through three stages during the development process. Moreover, the shapes of the contact surfaces, along with the outlet pressure, were found to have impacts on the angles and velocities of the reflected flow. The relevant empirical formulas were summarized according to this study's simulation results. In addition, the flow patterns and shapes of the contact surfaces were observed to have influencing effects on the impact force. An impact force model was established in this study based on the empirical formula, and the model was verified using both the simulation and experimental results. It was confirmed that the proposed model could provide important references for the optimization of the technical parameters water jet systems, which could provide theoretical support for the further intelligent and efficient transformation of coal mine drilling water jet technology.

Effects of Physical Coordinate Clustering on Boundary Vorticity Approximations in von Mises Coordinates

Forward finite difference expressions of first-order accuracy for boundary vorticity on a solid boundary are evaluated in this work when the physical coordinates are clustered and mapped using von Mises coordinates. Results show that schemes using in-field grid points do not improve solutions obtained. Results also show that the finer the grid used in the physical domain, and the more clustered it is, improves the boundary vorticity values in the computational domain. The “best” expressions forward finite difference expressions are identified when two, three, four and five grid points are used.

Extraction of New Applicable Dimensionless Relations in the Wedge Impact Problem Using WCSPH Method

Impact problem associated with water entry of a wedge has important applications in various aspects of naval architecture and ocean engineering. In the present study, the 2DOF (2 Degrees of Freedom) wedge impact problem into the water with various wedge deadrise angles and impact velocities is investigated using Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method. Artificial viscosity and density correction are used to create stability and also to prevent the penetration of fluid particles into the solid boundary. Solving the impact problem is very time-consuming, therefore extracting new mathematical relations can be very useful to calculate some important and applicable parameters in a certain range of wedge angles and impact velocities. In the present research, some new dimensionless applicable relations using the Buckingham π theorem are extracted to investigate important parameters such as acceleration and slamming force in general cases of a wedge impact problem. Then, these mathematical relations are validated by the results obtained from the simulations.

Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems

This study examines the invariance properties of the thermodynamic entropy production in its global (integral), local (differential), bilinear, and macroscopic formulations, including dimensional scaling, invariance to fixed displacements, rotations or reflections of the coordinates, time antisymmetry, Galilean invariance, and Lie point symmetry. The Lie invariance is shown to be the most general, encompassing the other invariances. In a shear-flow system involving fluid flow relative to a solid boundary at steady state, the Galilean invariance property is then shown to preference a unique pair of inertial frames of reference—here termed an entropic pair—respectively moving with the solid or the mean fluid flow. This challenges the Newtonian viewpoint that all inertial frames of reference are equivalent. Furthermore, the existence of a shear flow subsystem with an entropic pair different to that of the surrounding system, or a subsystem with one or more changing entropic pair(s), requires a source of negentropy—a power source scaled by an absolute temperature—to drive the subsystem. Through the analysis of different shear flow subsystems, we present a series of governing principles to describe their entropic pairing properties and sources of negentropy. These are unaffected by Galilean transformations, and so can be understood to “lie above” the Galilean inertial framework of Newtonian mechanics. The analyses provide a new perspective into the field of entropic mechanics, the study of the relative motions of objects with friction.

Exact Solutions of Boundary Layer Equations in Polymer Solutions

The paper presents new exact solutions of equations derived earlier. Three of them describe unsteady motions of a polymer solution near the stagnation point. A class of partially invariant solutions with a wide functional arbitrariness is found. An invariant solution of the stationary problem in which the solid boundary is a logarithmic curve is constructed.

Toroidal free oscillations of a viscous liquid spherical shell with mixed boundary conditions

The problem of toroidal eigenmodes of free oscillations of a viscous fluid spherical shell is solved under mixed boundary conditions. These conditions are a combination of free surface conditions and solid boundary conditions. Such an artificial combination is used sometimes in the numerical simulation of geodynamo problem. The scheme for calculating the eigenmodes is described. It is shown that the use of mixed conditions leads to the disappearance of the first eigenmode with the smallest eigenvalue. A possible reason for this is the physical incorrectness of the mixed boundary conditions.