Unified Lagrangian Formulation for Fluid and Solid Mechanics, Fluid-Structure Interaction and Coupled Thermal Problems using the PFEM

Alessandro Franci

Prof. Eugenio Oñate Ibañez de Navarra Dr. Josep Maria Carbonell i Puigbó

Structural Analysis (CIMNE)

The objective of this thesis is the derivation and implementation of a unied Finite Element formulation for the solution of fluid and solid mechanics, Fluid-Structure Interaction (FSI) and coupled thermal problems. The unied procedure is based on a stabilized velocity-pressure Lagrangian formulation. Each time step increment is solved using a two-step Gauss-Seidel scheme: First the linear momentum equations are solved for the velocity increments, next the continuity equation is solved for the pressure in the updated conguration. The Particle Finite Element Method (PFEM) is used for the fluid domains, while the Finite Element Method (FEM) is employed for the solid ones. As a consequence, the domain is remeshed only in the parts occupied by the fluid. Linear shape functions are used for both the velocity and the pressure elds. In order to deal with the incompressibility of the materials, the formulation has been stabilized using an updated version of the Finite Calculus (FIC) method. The procedure has been derived for quasi-incompressible Newtonian fluids. In this work, the FIC stabilization procedure has been extended also to the analysis of quasi-incompressible hypoelastic solids. Specific attention has been given to the study of free surface flow problems. In particular, the mass preservation feature of the PFEM-FIC stabilized procedure has been deeply studied with the help of several numerical examples. Furthermore, the conditioning of the problem has been analyzed in detail describing the efect of the bulk modulus on the numerical scheme. A strategy based on the use of a pseudo bulk modulus for improving the conditioning of the linear system is also presented. The unied formulation has been validated by comparing its numerical results to experimental tests and other numerical solutions for fluid and solid mechanics, and FSI problems. The convergence of the scheme has been also analyzed for most of the problems presented. The unied formulation has been coupled with the heat tranfer problem using a staggered scheme. A simple algorithm for simulating phase change problems is also described. The numerical solution of several FSI problems involving the temperature is given. The thermal coupled scheme has been used successfully for the solution of an industrial problem. The objective of study was to analyze the damage of a nuclear power plant pressure vessel induced by a high viscous fluid at high temperature, the corium. The numerical study of this industrial problem has been included in the thesis.

The PFEM is a very useful tool for describing highly deformed bodies as the metals involved in hot forming processes. In fact, with the PFEM the mesh nodes coincide with the material points and this is extremely useful for following the evolution of the deformed shape of the metals. The accurate description of the deforming topology and the fine FE mesh guaranteed by the powerful remeshing procedure of the PFEM, allow the correct computation of the thermo-plastic deformations undergone by the metal pieces. The thesis includes many practical applications (not only for forming processes), from the collapse of a water column against a deformable membrane to the filling of an elastic container with viscous fluids and the melting of a piece of ice in a tank filled with hot water. The last chapter of the thesis has been completed devoted to an industrial application solved with the proposed computational method. The numerical results showed in this chapter makes part of the project carried out with the Japanese company Nippon Steel and Sumimoto Metal Corporation (NSSMC) in the three-month period June-September of 2014. The object of the project was to simulate two hypothetical scenarios during a nuclear core melt situations, one of the most severe accident in a nuclear power plant. During a nuclear meltdown, a lava-like material, called corium, is formed by a blend of melted fuel and reactor components. The effects of the corium on the surrounding are devastating and it is extremely important to prevent its leakage from the nuclear reactor in order to avoid radioactive contamination of the environment. In the thesis two models have been analyzed. In the first one, a volume of corium falls over a steel plate inducing its melting and collapse. In the second model the corium is placed over the pressure vessel and around a control rod and the collapse of the rod produced by the accumulation of thermo-plastic deformations is reproduced. This The numerical results have been highly rated by the contractor, who decided to propose to the authors a prolongation of the project and the realization of two new studies of nuclear severe accident. The second project started this year in May and finished in September. Dr. Franci himself presented the numerical results on occasion of his visit to the NSSMC plant in Kimitsu, Japan. Also the second project has been highly evaluated by the company and further collaboration works have been discussed. The success of these projects showed the applicability to real industrial problems of the numerical strategy proposed in the thesis of Dr. Franci.

Unified Finite Element Formulation; Fluid Mechanics; Solid Mechanics; Fluid-Structure Interaction (FSI); Coupled Thermal Problems; Stabilized Velocity-Pressure Lagrangian Formulation; Two-step Gauss-Seidel Scheme; Linear Momentum Equations; Velocity Increments; Continuity Equation; Pressure; Updated Configuration; Particle Finite Element Method (PFEM); Fluid Domains; Finite Element Method (FEM); Solid Domains; Remeshing; Linear Shape Functions; Velocity Fields; Pressure Fields; Incompressibility; Finite Increment Calculus (FIC) Method; Quasi-Incompressible Newtonian Fluids; FIC Stabilization Procedure; Quasi-Incompressible Hypoelastic Solids; Free Surface Flow Problems; Mass Preservation Feature; PFEM-FIC Stabilized Procedure; Numerical Examples; Conditioning of the Problem; Bulk Modulus; Numerical Scheme; Pseudo Bulk Modulus; Linear System; Numerical Results; Experimental Tests; Other Numerical Solutions; Convergence; Heat Transfer Problem; Staggered Scheme; Phase Change Problems; Temperature; Thermal Coupled Scheme; Industrial Problem; Nuclear Power Plant Pressure Vessel; Damage Analysis; High Viscous Fluid; High Temperature; Corium