Progress in the Development of Compressible, Multiphase Flow Modeling Capability for Nuclear Reactor Flow Applications

In nuclear reactor safety and optimization there are key issues that rely on in-depth understanding of basic two-phase flow phenomena with heat and mass transfer. Within the context of multiphase flows, two bubble-dynamic phenomena – boiling (heterogeneous) and flashing or cavitation (homogeneous boiling), with bubble collapse, are technologically very important to nuclear reactor systems. The main difference between boiling and flashing is that bubble growth (and collapse) in boiling is inhibited by limitations on the heat transfer at the interface, whereas bubble growth (and collapse) in flashing is limited primarily by inertial effects in the surrounding liquid. The flashing process tends to be far more explosive (and implosive), and is more violent and damaging (at least in the near term) than the bubble dynamics of boiling. However, other problematic phenomena, such as crud deposition, appear to be intimately connecting with the boiling process. In reality, these two processes share many details

Liquid and liquid-gas flows at all speeds : Reference solutions and numerical schemes

This paper present some reference solutions to be used in order to validate and improve numerical schemes for multiphase flows. We address here exact one-dimensional liquid and liquid-gas compressible flows solutions in nozzles. The exact solution is first derived for the compressible single liquid phase Euler equations and extends the well known ideal gas dynamic nozzle flow solutions.The all Mach number scheme is then derived. A preconditioned Riemann solver is built and embedded into the Godunov explicit scheme. It is shown that this method converges to exact solutions but needs too small time steps to be efficient. An implicit version is then derived, in one dimension first and second in the frame of 3D unstructured meshes

MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock–bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock–bubble, shock–droplet, and shock–water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas–liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock–bubble-vessel-wall and acoustic–bubble-net interactions are used to demonstrate the full capabilities of MFC

MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock–bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock–bubble, shock–droplet, and shock–water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas–liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock–bubble-vessel-wall and acoustic–bubble-net interactions are used to demonstrate the full capabilities of MFC

An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics

Numerical simulation of bubble dynamics and cavitation is challenging; even the seemingly simple problem of a collapsing spherical bubble is difficult to compute accurately with a general, three-dimensional, compressible, multicomponent flow solver. Difficulties arise due to both the physical model and the numerical method chosen for its solution. We consider the 5-equation model of Allaire et al. [1], the 5-equation model of Kapila et al. [2], and the 6-equation model of Saurel et al. [3] as candidate approaches for spherical bubble dynamics, and both MUSCL and WENO interface-capturing methods are implemented and compared. We demonstrate the inadequacy of the traditional 5-equation model of Allaire et al. [1] for spherical bubble collapse problems and explain the corresponding advantages of the augmented model of Kapila et al. [2] for representing this phenomenon. Quantitative comparisons between the augmented 5-equation and 6-equation models for three-dimensional bubble collapse problems demonstrate the versatility of pressure-disequilibrium models. Lastly, the performance of pressure disequilibrium model for representing a three-dimensional spherical bubble collapse for different bubble interior/exterior pressure ratios is evaluated for different numerical methods. Pathologies associated with each factor and their origins are identified and discussed