Conservative numerical schemes for unsteady one-dimensional two phase flow.

摘要

The thesis is devoted to the modelization of non steady two phase mixtures of liquid and vapour. It has been motivated by the great amount of industrial applications in which we find these phenomena. Transient two phase flow is a very important issue in nuclear, chemical and industrial applications. In the case of the nuclear industry due to the importance of preventing loss of coolant accidents (LOCA) and guaranteeing a good performance of the coolant system in power plants.;We justify the present development by means of the introduction of the most important codes developed during the last two decades and their associated mesh techniques. It is basically focused on the extension of some conservative and explicit schemes to obtain approximate solutions of the system of equations in one dimensional one pressure two phase flow. They have been centred and upwind schemes to solve multiphase flow problems, most of them based on the exact or approximate solution of Riemann problems using Godunov's like methods such as Approximate Riemann solvers or Flux Splitting methods. We have studied mainly TVD schemes, Adapted TVD schemes (ATVD) and the AUSM family of schemes.;Firstly we introduce the 1D two phase flow system of equations with which we will work.;We consider the systems of equations more used depending on the model. Thus we introduce the homogeneous model, the isentropic model and the separated model will be treated in some detail.;The evaluation of the eigenstructure of the homogeneous and the separated two phase flow is studied. Different methods to determine the eigenvalues are presented. A general method to determine the eigenvectors is studied as well.;We extend different conservative schemes to two phase flow whose good behaviour in single phase has been well proved.;They are basically TVD schemes, the Adapted TVD schemes developed by Gascon and Corberan and the AUSM family of schemes, firstly introduced by Steffen and Liou.;Most of the extensions developed in this thesis are based on including the non conservative terms of the equations of momentum and energy in the source term. The behaviour of each development has been analysed by means of the following benchmarks: (1) Faucet test; (2) shock tube; (3) sedimentation; (4) Oscilating manometer; (5) Boiling tube (only for the homogeneous model).