Investigations of a Two-Phase Fluid Model

We study an interface-capturing two-phase fluid model in which the interfacial tension is modelled as a volumetric stress. Since these stresses are obtainable from a Van der Waals-Cahn-Hilliard free energy, the model is, to a certain degree, thermodynamically realistic. Thermal fluctuations are not considered presently for reasons of simplicity. The utility of the model lies in its momentum-conservative representation of surface tension and the simplicity of its numerical implementation resulting from the volumetric modelling of the interfacial dynamics. After validation of the model in two spatial dimensions, two prototypical applications---instability of an initially high-Reynolds-number liquid jet in the gaseous phase and spinodal decomposition in a liquid-gas system--- are presented.Comment: Self unpacking uuencoded and compressed postscript file (423928 bytes). Includes 6 figure

An Euler Solver Based on Locally Adaptive Discrete Velocities

A new discrete-velocity model is presented to solve the three-dimensional Euler equations. The velocities in the model are of an adaptive nature---both the origin of the discrete-velocity space and the magnitudes of the discrete-velocities are dependent on the local flow--- and are used in a finite volume context. The numerical implementation of the model follows the near-equilibrium flow method of Nadiga and Pullin [1] and results in a scheme which is second order in space (in the smooth regions and between first and second order at discontinuities) and second order in time. (The three-dimensional code is included.) For one choice of the scaling between the magnitude of the discrete-velocities and the local internal energy of the flow, the method reduces to a flux-splitting scheme based on characteristics. As a preliminary exercise, the result of the Sod shock-tube simulation is compared to the exact solution.Comment: 17 pages including 2 figures and CMFortran code listing. All in one postscript file (adv.ps) compressed and uuencoded (adv.uu). Name mail file `adv.uu'. Edit so that `#!/bin/csh -f' is the first line of adv.uu On a unix machine say `csh adv.uu'. On a non-unix machine: uudecode adv.uu; uncompress adv.tar.Z; tar -xvf adv.ta

Lattice Boltzmann Model for Axisymmetric Multiphase Flows

In this paper, a lattice Boltzmann (LB) model is presented for axisymmetric multiphase flows. Source terms are added to a two-dimensional standard lattice Boltzmann equation (LBE) for multiphase flows such that the emergent dynamics can be transformed into the axisymmetric cylindrical coordinate system. The source terms are temporally and spatially dependent and represent the axisymmetric contribution of the order parameter of fluid phases and inertial, viscous and surface tension forces. A model which is effectively explicit and second order is obtained. This is achieved by taking into account the discrete lattice effects in the Chapman-Enskog multiscale analysis, so that the macroscopic axisymmetric mass and momentum equations for multiphase flows are recovered self-consistently. The model is extended to incorporate reduced compressibility effects. Axisymmetric equilibrium drop formation and oscillations, breakup and formation of satellite droplets from viscous liquid cylindrical jets through Rayleigh capillary instability and drop collisions are presented. Comparisons of the computed results with available data show satisfactory agreement.Comment: 17 pages, 11 figures, to be published in Physical Review

Comparison and Uncertainty Quantification of Two-Fluid Models forBubbly Flows with NEPTUNE_CFD and STAR-CCM+

International audienceThe nuclear industry is interested in better understanding the behavior of turbulent boiling flowsand in using modern computational tools for the design and analysis of advanced fuels and reactorsand for simulation and study of mitigation strategies in accident scenarios. Such interests serve asdrivers for the advancement of the 3-dimensional multiphase Computational Fluid Dynamicsapproach. A pair of parallel efforts have been underway in Europe and in the United States, theNEPTUNE and CASL programs respectively, that aim at delivering advanced simulation tools thatwill enable improved safety and economy of operations of the reactor fleet. Results from acollaboration between these two efforts, aimed at advancing the understanding of multiphaseclosures for pressurized water reactor (PWR) application, are presented. Particular attention is paidto the assessment and analysis of the different physical models implemented in NEPTUNE_CFDand STAR-CCM+ codes used in the NEPTUNE and the CASL programs respectively, forapplication to turbulent two-phase bubbly flows. The experiments conducted by Liu and Bankoff(Liu, 1989; Liu and Bankoff 1993a and b) are selected for benchmarking, and predictions from thetwo codes are presented for a broad range of flow conditions and with void fractions varyingbetween 0 and 50percent. Comparison of the CFD simulations and experimental measurements revealsthat a similar level of accuracy is achieved in the two codes. The differences in both sets of closuremodels are analyzed, and their capability to capture the main features of the flow over a wide rangeof experimental conditions are discussed. This analysis paves the way for future improvements ofexisting two-fluid models. The benchmarks are further leveraged for a systematic study of thepropagation of model uncertainties. This provides insights into mechanisms that lead to complexinteractions between individual closures (of the different phenomena) in the multiphase CFDapproach. As such, it is seen that the multi-CFD-code approach and the principled uncertaintyquantification approach are both of great value in assessing the limitations and the level of maturityof multiphase hydrodynamic closures

Enhanced inverse-cascade of energy in the averaged Euler equations

For a particular choice of the smoothing kernel, it is shown that the system of partial differential equations governing the vortex-blob method corresponds to the averaged Euler equations. These latter equations have recently been derived by averaging the Euler equations over Lagrangian fluctuations of length scale α, and the same system is also encountered in the description of inviscid and incompressible flow of second-grade polymeric (non-Newtonian) fluids. While previous studies of this system have noted the suppression of nonlinear interaction between modes smaller than α, we show that the modification of the nonlinear advection term also acts to enhance the inverse-cascade of energy in two-dimensional turbulence and thereby affects scales of motion larger than α as well. This latter effect is reminiscent of the drag-reduction that occurs in a turbulent flow when a dilute polymer is added. 1 The two-dimensional incompressible, Euler equations are ∂tω + ∇ · (uω) = 0, ∇ · u = 0, ω(t = 0) = ω0, (1