Frédéric Couderc

Benchmarks and numerical methods for the simulation of boiling flows

Comparisons of different numerical methods suited to the simulations of phase changes are presented in the framework of interface capturing computations on structured fixed computational grids. Due to analytical solutions, we define some reference test-cases that every numerical technique devoted to phase change should succeed. Realistic physical properties imply some drastic interface jump conditions on the normal velocity or on the thermal flux. The efficiencies of Ghost Fluid and Delta Function Methods are compared to compute the normal velocity jump condition. Next, we demonstrate that high order extrapolation methods on the thermal field allow performing accurate and robust simulations for a thermally controlled bubble growth. Finally, some simulations of the growth of a rising bubble are presented, both for a spherical bubble and a deformed bubble.

An explicit asymptotic preserving low Froude scheme for the multilayer shallow water model with density stratification

We present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy is based on a regularized model where the transport velocity in the advective fluxes is shifted proportionally to the pressure potential gradient. Using a similar strategy for the potential forces, we show the stability of the method in the sense of a discrete dissipation of the mechanical energy, in general multilayer and non-linear frames. These results are obtained at first-order in space and time and extended using a simple second-order MUSCL extension. With the objective of minimizing the diffusive losses in realistic contexts, sufficient conditions are exhibited on the regularizing terms to ensure the schemes linear stability at first and second-order in time and space. The other main result stands in the consistency with respect to the asymptotics reached at small and large time scales in low Froude regimes, which governs large-scale oceanic circulation. Additionally, robustness and well-balanced results for motionless steady states are also ensured. These stability properties tend to provide a very robust and efficient approach, easy to implement and particularly well suited for large-scale simulations. Some numerical experiments are proposed to highlight the scheme efficiency: an experiment of fast gravitational modes, a smooth surface wave propagation, an initial propagating surface water elevation jump considering a non trivial topography, and a last experiment of slow Rossby modes simulating the displacement of a baroclinic vortex subject to the Coriolis force.

On 2D Liquid Sheet Atomization

Liquid sheet atomization by coflowing air flows appears in a broade range of industrial process, but still remains not well understood. This paper is devoted to the numerical investigation of the air-assisted disintegration of a planar liquid sheet by two parallel air streams flowing on both sides. To do that, a DNS solver for two-phase incompressible viscous flows with interface capturing feature for non miscible fluids has been developped and validated [1]. The interface is captured by a Level-Set method, which has become very popular during the last ten years. However, unlike classical approaches, stress tensor jump conditions across the interface are explicitly taken into account without introducing any smoothing. Although the physical phenomenon is tridimensional, experimental studies show that the initial stage of the liquid sheet oscillations is mainly two-dimensional which justifies the two dimensional simulations done in this paper. We present a first two-dimensional spatial simulation which shows the gas flow dynamics in interaction with the liquid sheet oscillations. By separation of the air boundary layer behind the liquid sheet at its maximum amplitude location, vortical structures are created and evolve in time with the frequency of the liquid sheet global oscillation. We investigate the effects of the main flow parameters such as outer air velocity, air boundary layer thickness on the main characteristics of the flow and the global oscillation frequency. The first result from our study concerning the frequency oscillation shows a linear variation of the frequency with air velocity. This is in complete agreement with experimental results of [2], whereas inviscid linear stability theory predicts a quadratic evolution. Evidence from those results shows that two-dimensional spatial simulations can provided relevant information on the early stage of liquid sheet atomization.Copyright

Sharp Interface Capturing Methods Based on Level-Set Method for Incompressible Flow With Surface Tension

In this paper, we present the development of a code for two-phase incompressible flow simulation with interface. Interface between non miscible fluid is captured by a level-set method. However, unlike classical approachs, jump conditions throught the interface are explicitely taken into account without any smoothing. Different tests cases are then simulated and show drastic improvement compared to existing methods like VOF or others.Copyright