Pascal Galon

HLLC-type Riemann solver with approximated two-phase contact for the computation of the Baer–Nunziato two-fluid model

Abstract The computation of compressible two-phase flows with the Baer–Nunziato model is addressed. Only the convective part of the model that exhibits non-conservative products is considered and the source terms of the model that represent the exchange between phases are neglected. Based on the solver proposed by Tokareva & Toro [1] , a new HLLC-type Riemann solver is built. The key idea of this new solver lies in an approximation of the two-phase contact discontinuity of the model. Thus the Riemann invariants of the wave are approximated in the “subsonic” case. A major consequence of this approximation is that the resulting solver can deal with any Equation Of State. It also allows to bypass the resolution of a non-linear equation based on those Riemann invariants. We assess the solver and compare it with others on 1D Riemann problems including grid convergence and efficiency studies. The ability of the proposed solver to deal with complex Equations Of State is also investigated. Finally, the different solvers have been compared on challenging 2D test-cases due to the presence of both material interfaces and shock waves: a shock–bubble interaction and underwater explosions. When compared with others, the present solver appears to be accurate, efficient and robust.

A Mach-Sensitive Implicit-Explicit Scheme Adapted to Compressible Multi-scale Flows

Abstract The method presented below focuses on the numerical approximation of the Euler compressible system. It pursues a two-fold objective: being able to accurately follow slow material waves as well as strong shock waves in the context of low Mach number flows. The resulting implicit–explicit(IMEX) fractional step approach leans on a dynamic splitting designed to react to the time fluctuations of the maximal flow Mach number. When the latter rises suddenly, the IMEX scheme, so far driven by a material-wave Courant number, turn into a time-explicit approximate Riemann solver constrained by an acoustic-wave Courant number. It is also possible to enrich the dynamic splitting in order to capture high pressure jumps even when the flow Mach number is low. One-dimensional low Mach number test cases involving single or multiple waves confirm that the present approach is as accurate and efficient as an IMEX Lagrange-Projection method. Besides, numerical results suggest that the stability of the present method holds for any Mach number if the Courant number related to the convective subsystem arising from the splitting is of order unity.

A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction

Abstract A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler–Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.

A Weighted Splitting Approach for Low-Mach Number Flows

In steady-state regimes, water circulating in the nuclear power plants pipes behaves as a low Mach number flow. However, when steep phenomena occur, strong shock waves are produced. Herein, a fractional step approach allowing to decouple the convective from the acoustic effects is proposed. The originality is that the splitting between these two parts of the physics evolves dynamically in time according to the Mach number. The first one-dimensional explicit and implicit numerical results on a wide panel of Mach numbers show that this approach is as accurate and CPU-consuming as a state of the art Lagrange-Projection-type method.

Some Applications of a Two-Fluid Model

We present in this paper some comparisons of numerical results and experimental data in some two-phase flows involving rather high pressure ratios. A two-fluid two-phase flow model has been used herein, but we also report a few results obtained with some simpler single-fluid two-phase flow models.

LOCA simulation: analysis of rarefaction waves propagating through geometric singularities

The propagation of a transient wave through an orifice is investigated for applications to Loss Of Coolant Accident in nuclear plants. An analytical model is proposed for the response of an orifice plate and implemented in the EUROPLEXUS fast transient dynamics software. It includes an acoustic inertial effect in addition to a quasi-steady dissipation term. The model is experimentally validated on a test rig consisting in a single pipe filled with pressurized water. The test rig is designed to generate a rapid depressurization of the pipe, by means of a bursting disk. The proposed model gives results which compare favourably with experimental data.Copyright