Strongly coupled fluid-particle flows in vertical channels. II. Turbulence modeling

In Part I, simulations of strongly coupled fluid-particle flow in a vertical channel were performed with the purpose of understanding, in general, the fundamental physics of wall-bounded multiphase turbulence and, in particular, the roles of the spatially correlated and uncorrelated components of the particle velocity.The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions were presented, and the unclosed terms that are retained in the context of fully developed channel flow were evaluated in an Eulerian–Lagrangian (EL) framework. Here, data from the EL simulations are used to validate a multiphase Reynolds-stress model (RSM) that predicts the wall-normal distribution of the two-phase, one-point turbulence statistics up to second order. It is shown that the anisotropy of the Reynolds stresses both near the wall and far away is a crucial component for predicting the distribution of the RA particle-phase volume fraction. Moreover, the decomposition of the phase-average (PA) particle-phase fluctuating energy into the spatially correlated and uncorrelated components is necessary to account for the boundary conditions at the wall. When these factors are properly accounted for in the RSM, the agreement with the EL turbulence statistics is satisfactory at first order (e.g., PA velocities) but less so at second order (e.g., PA turbulent kinetic energy). Finally, an algebraic stress model for the PA particle-phase pressure tensor and the Reynolds stresses is derived from the RSM using the weak-equilibrium assumption

Bubble Force Balance Formula for Low Reynolds Number Bubbly Flows in Pipes and Channels: Comparison of Wall Force Models

International audienceAbstract In recent work, we investigated analytically low Reynolds number bubbly flows in pipes. We showed that the distribution of bubbles results from a balance between lift, dispersion and wall forces, and exhibited an analytical expression for this void fraction profile. We then performed a comparison of this analytical Bubble Force Balance Formula (BFBF) with an experiment from the literature. Antal’s model was used for the wall force. The objective of the present work is to compare and assess the three main wall force models in the literature: Antal’s, Tomiyama’s and Frank’s models. We begin by deriving two new BFBF, respectively with Tomiyama’s and Frank’s forces. We can see that the choice of the model impacts the velocity with which the analytical void fraction profile goes to zero at the wall. We then compare our three analytical profiles with experimental measurements and DNS simulations of laminar flows from the literature. We restrict ourselves to the near-wall region. The choice of Antal’s wall force model yields the best agreement. The data is also used to estimate the dispersion coefficient at the wall. Interestingly, we obtain the same order of magnitude with the three wall force models

A Second-Order Turbulence Model Based on a Reynolds Stress Approach for Two-Phase Flow-Part I: Adiabatic Cases

In our work in 2008, we evaluated the aptitude of the code Neptune CFD to reproduce the incidence of a structure topped by vanes on a boiling layer, within the framework of the Neptune project. The objective was to reproduce the main effects of the spacer grids. The turbulence of the liquid phase was modeled by a first-order K-ε model. We show in this paper that this model is unable to describe the turbulence of rotating flows, in accordance with the theory. The objective of this paper is to improve the turbulence modeling of the liquid phase by a second turbulence model based on a R ij -ε approach. Results obtained on typical single-phase cases highlight the improvement of the prediction for all computed values. We tested the turbulence model R ij -ε implemented in the code versus typical adiabatic two-phase flow experiments. We check that the simulations with the Reynolds stress transport model (RSTM) give satisfactory results in a simple geometry as compared to a K-ε model: this point is crucial before calculating rod bundle geometries where the K-ε model may fail

Modélisation et simulation des écoulements cavitants par une approche diphasique

Le travail présenté dans cet article porte sur la modélisation et la simulation numérique des phénomènes de cavitation. Les germes de vapeur sont générés en paroi ou sont pré-existants dans l’écoulement. La vapeur créée par nucléation en paroi ou pré-existante dans l’écoulement est convectée et forme des poches de vapeur dans les zones où la pression est sous la pression de saturation.L’écoulement est 3D diphasique compressible turbulent et instationnaire. L’écoulement n’est pas supposé isotherme : on résout les équations d’énergie pour le fluide et sa vapeur. Les propriétés thermodynamiques du fluide réel sont calculées par des tables tabulées en chaque point du domaine et à chaque pas de temps. L’écoulement est simulé par le code NEPTUNE CFD co-développé par EDF R&D et le CEA. La méthode numérique est de type volumes finis collocalisés. L’algorithme utilise une méthode originale de couplage multi-champ de la famille SIMPLE.Les résultats du modèle original de cavitation développé ont donné un bon accord avec les mesures expérimentales sur des grandeurs suffisamment discriminantes comme le taux de vapeur. Le modèle ne dépend par ailleurs d’aucun paramètre ajustable

A Second-Order Turbulence Model Based on a Reynolds Stress Approach for Two-Phase Flow—Part I: Adiabatic Cases

In our work in 2008, we evaluated the aptitude of the code Neptune_CFD to reproduce the incidence of a structure topped by vanes on a boiling layer, within the framework of the Neptune project. The objective was to reproduce the main effects of the spacer grids. The turbulence of the liquid phase was modeled by a first-order K-ε model. We show in this paper that this model is unable to describe the turbulence of rotating flows, in accordance with the theory. The objective of this paper is to improve the turbulence modeling of the liquid phase by a second turbulence model based on a Rij-ε approach. Results obtained on typical single-phase cases highlight the improvement of the prediction for all computed values. We tested the turbulence model Rij-ε implemented in the code versus typical adiabatic two-phase flow experiments. We check that the simulations with the Reynolds stress transport model (RSTM) give satisfactory results in a simple geometry as compared to a K-ε model: this point is crucial before calculating rod bundle geometries where the K-ε model may fail

Numerical Study of the Steady-State Subchannel Test-Case with NEPTUNE_CFD for the OECD/NRC NUPEC PSBT Benchmark

The multifield computational fluid dynamics (CFD) code NEPTUNE_CFD is applied to carry out a numerical study of the steady-state subchannel test-case of the OECD/NRC NUPEC PWR subchannel and bundle tests (PSBTs) international benchmark, focusing on the simulation of a subset of five selected experimental runs of the centered subchannel configuration. First, using a standard choice for the physical models and a constant, predetermined bubble diameter, the calculated void fraction is compared to experimental data. Besides, the mesh sensitivity of the calculated void fraction is investigated by performing simulations of three grid levels, and the propagation of the experimental uncertainties on the input parameters of the simulations is also studied. Last, calculation results with devoted models for the bubble-size distribution are analyzed. Their impact is visible on the subcooled run, giving void fraction closer to experiments than those obtained with a fixed bubble-size. Void-fraction distribution with bubble-size models is also shown to come closer to experiment for another run with a higher equilibrium quality

An analytical relation for the void fraction distribution in a fully developed bubbly flow in a vertical pipe

International audienceThe problem of a steady, axisymmetric, fully developed adiabatic bubbly flow in a vertical pipe is studied analytically with the two-fluid model. The exchange of momentum between the phases is described as the sum of drag, lift, wall and dispersion contributions, with constant coefficients. Under these conditions, we are able to derive an analytical relation between the void fraction, the liquid velocity, and the pressure profiles. This relation is valid independently of the turbulence model in the liquid phase-here, a k-ε model is used-and can serve as a verification case for multiphase flow codes. The analytical void fraction profile vanishes at the wall, as a result of the balance between dispersion and wall forces. This profile is illustrated by calculations performed for upward and downward bubbly flows with the NEPTUNE_CFD code