Contribution to the verification and the validation of an unsteady two-phase flow model

This thesis contributes to the verification and the validation of the Baer-Nunziato (BN) model, to model water hammer phenomena in industrial piping systems. It consists of two parts, the first is to model water hammer flows with the BN model in Eulerian representation and the second is to extend this model to the ALE (Arbitrary Lagrangian Eulerian) formalism so as to take into account fluid-structure interaction (FSI). To model water hammer flows, closure laws of the BN model concerning the interfacial/source terms and the equations of state (EOS) were first studied. Then the whole system was simulated with a fractional step method including two steps, one for the resolution of the convective part, the other for the source terms. For the convective part, the Rusanov scheme was first checked, and some stability problems have been observed. Thus a more stable fractional step scheme has been proposed and verified. Regarding the source terms, four non-instantaneous relaxation schemes which represent the return to equilibrium of pressure, the transfers of momentum, heat and mass were successively applied. These schemes have been extended to 'generalized Stiffened Gas' EOS in order to represent phase-change. After regaining some typical phenomena associated with water hammer flows, the BN model was validated with the Simpson experiment, a classical water hammer test case, and the Canon experience, a rapid decompression of fluid in a high pressure duct. Moreover, the model was compared with two homogeneous models on these two experiments. Finally, an ALE version of the BN model was implemented, and verified on a case of wave propagation in a 'single' phase flow and a two-phase flow in a flexible pipe. The variation of wave propagation speed due to the coupling between the fluid and the structure has been well retrieved. The validation was performed on an experiment which examines the response of a pipe filled with water, subjected to a violent pressure peak (140 bar). The simulations are in good agreement with the experimental data. (author)