Abstract:
This thesis concerns the numerical investigation of suddenly expanded flows featuring
separation, instabilities and transition, in the context of Implicit Large Eddy Simulation
(ILES). The study of separated flows through suddenly expanded geometries is a classic
yet complex area of research. These types of flows feature instabilities which may
lead to bifurcation. Non-linear bifurcation is of great importance when considering
hydrodynamic stability and the mechanism of laminar to turbulent flow transition.
A detailed numerical investigation of various high-resolution methods and their ability
to correctly predict the flow through a suddenly expanded and contracted geometry
demonstrates that the choice of the particular numerical method employed can lead
to an incorrect solution of the flow. The key di erence between the various highresolution
methods employed is in the calculation of the nonlinear wave-speed dependent
term. It is shown that the nonlinearity of this term provides an asymmetric
dissipation to the flow which triggers symmetry-breaking bifurcation in a fully symmetric
computational set-up. High-resolution simulations of three-dimensional flow
through a plane suddenly expanded channel at low Reynolds numbers show that this
type of flow is characterised by a symmetric separation of the fluid which is nominally
two-dimensional in the spanwise direction. Increasing the Reynolds number reveals
a symmetry-breaking bifurcation of the fluid flow which becomes three-dimensional
as Reynolds number is further increased. Simulations confirm that it is this threedimensional
disturbance which leads to the onset of time-dependent flow characterised
by the periodic shedding of vortices from the upstream recirculation zones.
Preconditioning techniques which aim to alleviate sti ness in the calculation of the
advective fluxes for low Reynolds number flows are shown to be unsuitable for flows
featuring instabilities. The added dissipation to the flow causes the prediction of an
incorrect stable solution or to an improper estimation of the size of the separation
bubbles.
Simulations of a synthetic jet issuing into quiescent air using various slope limiters
manage to capture the flow physics relatively well. Limiters are used to avoid a scheme
from being oscillatory and provide non-linear dissipation in the region of excessively
large gradients. The various limiters di er with regards to the amount of dissipation
they provide to the flow, hence the solution obtained is dependent on the limiter used.