Dispersion and deposition of heavy particles in turbulent flows

Abstract

For nearly 40 years, engineers, researchers and scientists from the nuclear industry across the World have been trying to understand the behaviors of deposition, bounce and re-suspension of heavy, radioactive particles suspended as a dilute secondary phase in the cooling circuits of primary reactor systems. The aim is to understand the mechanism of transport and deposition of such particles through large, complex geometry systems, so that the risk of dispersal of radioactive particles may be assessed, and confirmed to be acceptably small both in closed containers and in the atmosphere in the case of an accident scenario. The first part of the present work addresses the challenge of robustly and efficiently predicting the behaviors of rigid and spherical particles (referred to as heavy particles) within turbulent boundary layers, the underlying physics of which is the controlling factor on particle deposition in smooth pipes and ducts. In the second component of work we study the deposition and bounce of heavy particles suspended in turbulent flows across heat exchanger tube banks, using Large Eddy Simulation (LES). It was originally proposed to extend the boundary layer work to this application, but it was quickly identified that the deposition mechanisms here are governed by the high core flow turbulence, rather than boundary layer phenomena, so that LES provides the only realistic modelling approach. In both cases the dispersed heavy particles are expressed in a Lagrangian framework solved in an independently developed large-scale parallel code; whilst the fluid phase is described in an Eulerian framework, either based on correlations from published Direct Numerical Simulation (DNS) for the boundary layer models, or from Computational Fluid Dynamics (CFD) simulations for both the boundary layer and tube-bank models, making use of the unstructured-grid based Navier-Stokes solver ANSYS FLUENT. Underpinning this work we implement a complete stochastic Lagrangian particle tracking module, based on a robust and efficient particle localization algorithm which can determine and update the cell containing each particle as the particles move through an unstructured finite volume grid overlying the flow domain. The module can handle correctly the interactions of particles with complex boundaries, and uses a novel numerical scheme for interpolating the carrier-phase velocity field seen by the particles from cell-centred values obtained from CFD computation. It implements a Gear three-level implicit scheme to compute the particle velocity, which is more robust, accurate and efficient than the conventional explicit and implicit schemes. The module has been fully parallelized using MPI (Message Passing Interface) settings on a Linux cluster consisting of 20 single CPU node, and further been successfully integrated with both the steady and unsteady ANSYS FLUENT solvers, complete replacing the built-in Lagrangian particle tracking model provided by ANSYS FLUENT. The algorithm and numerical schemes have been validated against analytical solutions of particle transport in a two-dimensional straining shear flow and other cases. For turbulent boundary layer flows, a simpler but more promising stochastic quadrant model, inspired by the discrete random walk model of Kallio and Reeks and the quadrant analysis of Wu and Willmarth, is developed in order to account for the effects of near wall large-scale coherent structures, e.g. sweeps and ejections, on particle transport. The input parameters for the stochastic quadrant model are educed from the corresponding statistics obtained from a Large Eddy Simulation (LES) of a fully developed channel flow. The model is applied to the prediction of deposition of heavy particles in a turbulent boundary layer; both using a Kallio and Reeks correlation based model of the flow, and also a Reynolds-Averaged Navier-Stokes (RANS) flow solution of using ANSYS FLUENT, the latter flow model having the potential to be extended to complex duct geometries. These solutions are compared to those of by solving an alternative Langevin equation of Dehbi, or continuous random walk model, which satisfies the fully mixed condition and describes the fluid velocity fluctuations seen by heavy particles. Prior to the current work no systematic investigation of the potential errors in particle deposition in turbulent boundary layers due to the modified hydrodynamic forces experienced by particles when very close to the wall has been carried out, possibly because of the complexity of the correlations involved. The effect is explored with the present stochastic quadrant model, using recently published composite correlations of Zeng and Balachandar for the particle drag coefficient CD and lift coefficient CL for near wall particles. This work provides an important first confirmation that for practical cases hydrodynamic effects can reasonably be neglected for particle deposition in turbulent boundary layers. The boundary layer methods developed in the first part of this thesis are applicable to the prediction of heavy particle deposition in fairly complex duct geometries, but are shown to be inappropriate for flow over tube-banks, where the boundary layers are no longer the rate limiting feature. Consequently the parallel Lagrangian stochastic particle tracking model is extended to study the particle impaction efficiency on tube banks in a turbulent flow in the framework of Large Eddy Simulation (LES). The flow field, obtained from Large Eddy Simulation with the dynamic Smagorinsky sub-grid scale model within ANSYS FLUENT, is fully validated against existing experimental data. As far as the dispersed particle phase is concerned, the energy losses when particles impact on and generally, but not always, rebound from cylinders within the tube-bank is taken into account using an empirical critical-impact velocity model. The efficiency of particle impaction is measured for particles of three Stokes number, and the results are compared with existing experimental data.