Numerical Solution of Two-Phase Flows

The work presented in this thesis has been partly carried out at the von Karman Institute for Fluid Dynamics in Brussels.
The need to improve existing thermofluid codes, for the simulation of flows inside the cooling circuits of nuclear power, has pressed the scientific community to intensify the research in recent years.
In this context, the ASTAR project (Advanced 3D Two-Phase Flow Simulation Tool for Application to Reactor Safety) was started in 2001.
This project, funded by the European Commission, is supported by several European research institutes, including the von Karman Institute (VKI).

In particular, at the VKI have been recently proposed:

1) A new formulation for the Conservation of residue distribution patterns (CRD), for which the conservative properties do not depend any more by the Roe linearization.
2) A consistently upwind discretization of source terms, which keeps the properties of Linearity preservation (LP), and then the second order of accuracy at the steady state, even for non-homogeneous problems.

The main objective of this thesis is to investigate the application of new schemes (CRD) to inhomogeneous complex systems as those represented by the biphasic model with two-fluids proposed by Stadtke, for which the hyperbolic-ness is guaranteed by the particular modeling of non-viscous interaction of the interface between the two phases on the amount of motion.
As a first step has been developed a one-dimensional solver for the Euler equations, which was then applied to test selected.
It has been verified that the above scheme does not satisfy the entropic condition and an appropriate entropy-fix has been developed, since the traditional remedy of Harten is not applicable to this scheme.
The implementation of the boundary conditions and source terms is validated on typical non-homogeneous problems.
The biphasic model was then implemented in a planned two-phase solver based on the same numerical tools used for the Euler solver. However, this extension is not direct, and some difficulties occurred, especially related to the presence of stiff source terms, and some singularity occurring in the structure of the eigenvalues of the equation system of government under certain flow regimes.
Finally, the biphasic solver has been successfully tested using various stationary and nonstationary test cases, defined as part of the ASTAR.