PhD ThesisFor 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.British Energy (Part of EDF