Eulerian-Eulerian prediction of dilute turbulent gas-particle flow in a backward-facing step

https://doi.org/10.1016/j.ijheatfluidflow.2009.02.012Get rights and content

Abstract

A numerical study of turbulent gas-particle flow in a two-dimensional, vertically oriented backward-facing step is compared with literature data. The dispersed phase is modeled by an Eulerian approach based upon the kinetic theory of granular flow (KTGF) including models for describing the dispersed phase interactions with the continuous phase. The modeling of turbulent motion within the dispersed phase and the correlation between gas and particle velocity fluctuations are discussed. In addition, closure relations for the dispersed phase are extended to incorporate interstitial fluid effects. The continuous phase turbulence is modeled by a k-ϵ model. This work demonstrates that treatment of turbulent characteristics is a key element in predicting the dispersed phase mean motion and turbulence modulation in the continuous phase. The derived models are implemented in a commercial code and simulation results are compared with benchmark experimental data for three particle classes with distinctive particle Stokes number, particle Reynolds number and mass-loading. In general, reasonable predictions are achieved.

Introduction

Knowledge of the hydrodynamics of turbulent gas-particle flows has a great importance for the successful design and determination of optimum operating conditions of numerous industrial applications, e.g., cyclone separators, fluidized beds, dust collectors, and pulverized-coal combustors, to name a few. These systems exhibit complex flow dynamics and interaction of flow components. The particle response in the presence of an interstitial fluid and gas turbulence modulation by particles are two topics that have stimulated research work in recent years (Fessler and Eaton, 1999, Lun, 2000, Zhang and Reese, 2003, Hadinoto and Curtis, 2004).

The presence of particles in turbulent flows may modify the turbulence structure of the continuous gas-phase as a result of momentum transfer from the particles. Elgobashi (1994) identifies a range of particulate phase volume fraction between 10-6 and 10-3 where particles can either augment or attenuate turbulence. Such degree of turbulence modification seems to correlate with both the particle Reynolds number and Stokes number. This is known as two-way coupling regime. Yu et al. (2004) report a numerical investigation of particle-laden turbulent flow over a backward facing step in which the gas-phase flow field is determined by LES and the motion of individual particles is traced throughout the flow domain (Lagrangian approach). However, their numerical investigation neglects the effect of particles on the carrier fluid flow, i.e., one-way-coupling is assumed, particle-particle interactions are not considered and particle-wall collisions are assumed to be perfectly elastic. Their research focuses on the dispersion of particles with different Stokes numbers, rather than turbulence modification by the particles.

The purpose of this paper is to perform a numerical investigation of a particle-laden backward-facing step with a turbulent channel flow inlet (Fig. 1) as it is described by Fessler and Eaton, 1995, Fessler and Eaton, 1999, for three particle sizes with particle Stokes number greater than unity. The modeling of the dispersed phase is accomplished by an Eulerian approach which treats the solids or particulate phase as a continuous medium with properties analogous to those of a fluid. Such technique involves the solution of a second set of Navier–Stokes-like equations in addition to those of the carrier (gas) phase. Furthermore, the significance of gas-particle interaction is reflected in the momentum and kinetic energy coupling terms via mean and fluctuating drag force, respectively.

Turbulence in the dispersed phase is modeled by a transport equation for the turbulent kinetic energy of the particles, or granular temperature. However, this modeling approach, directly derived from KTGF, does not generally consider the effect of gas-phase turbulence on the dispersed phase fluctuating motion (Lun et al., 1984, Gidaspow, 1994). A comprehensive gas-particle turbulence model derived in this paper accounts for such an important flow characteristic. The present work extends the use of KTGF to incorporate the effect of gas-particle interaction on the prediction of mean flow quantities.

Section snippets

Modeling

In an Eulerian model, the dispersed particle phase is treated as a fluid, in the same way as the carrier gas phase, so that a set of Favre-averaged conservation equations for the mass and momentum of both phases, turbulent kinetic energy and dissipation rate can be derived accordingly (Benavides and van Wachem, 2008). As a result, momentum and kinetic energy coupling terms arise in the transport equations due to the mean and fluctuating drag force contributions.

Numerical procedure

The computational domain consists of a two-dimensional channel section which starts 65h upstream from the step and extends up to 34H downstream, as it is illustrated in Fig. 1. A coordinate system is located at the step with the x axis parallel to the channel wall. Gas and particulate phase properties, such as the material density, laminar viscosity and particle diameter are set to constant values, e.g. the gas-phase is air at standard conditions.

The commercial CFD software Fluent 6.3 is used

Results and discussion

Attention is devoted to the comparison of mean quantities of both the gas and dispersed phases, especially the particulate phase mean velocity and turbulence intensity of the gas. The simulated results from the Eulerian two-fluid model are compared against the benchmark experimental data of Fessler and Eaton, 1995, Fessler and Eaton, 1999. For example, Fig. 2 shows the comparison of the detailed gas flow field with benchmark experimental data for single-phase flow (Fessler and Eaton, 1995).

Conclusions

An Eulerian-based computational study of a vertically oriented backward-facing step with turbulent gas-particle flow has been performed. A four-equation model for turbulent gas-particle flow is derived and validated in this work. A balance equation for the turbulent kinetic energy associated with particle velocity fluctuations together with a transport equation for the gas-particle fluctuating velocity correlation are employed to model turbulence in the dispersed phase. A novel particulate

Acknowledgement

This project is funded by STEM (Energimyndigheten). Computer time provided by C3SE is gratefully acknowledged.

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