A numerical and experimental study of buoyancy-driven flow in the
annulus between
two horizontal coaxial cylinders at Rayleigh numbers approaching and exceeding
the
critical values is presented. The stability of the flow is investigated
using linear theory
and the energy method. Theoretical predictions of the critical Rayleigh
number for
onset of secondary flows are obtained for a wide range of radius ratio
R and are verified
by comparison with results of previous experimental studies. A subcritical
Rayleigh
number which provides a necessary condition for global flow stability is
also
determined. The three-dimensional transient equations of fluid flow and
heat transfer
are solved to study the manifestation of instabilities within annuli having
impermeable
endwalls, which are encountered in various applications. For the first
time, a thorough
examination of the development of spiral vortex secondary flow within a
moderate gap
annulus and its interaction with the primary flow is performed for air.
Simulations are
conducted to investigate factors influencing the size and number of post-transitional
vortex cells. The evolution of stable three-dimensional flow and temperature
fields with
increasing Rayleigh number in a large gap annulus is also studied. The
distinct flow
structures which coexist in the large gap annulus at high Rayleigh numbers
preceding
transition to oscillatory flow, including transverse vortices at the end
walls which have
not been previously identified, are established numerically and experimentally.
The
solutions for the large-gap annulus are compared to those for the moderate-gap
case
to clarify fundamental differences in behaviour. Heat transfer results
in the form of
local Nusselt number distributions are presented for both the moderate-
and large-gap
cases. Results from a series of experiments performed with air to obtain
data for
validation of the numerical scheme and further information on the flow
stability are
presented. Additionally, the change from a crescent-shaped flow pattern
to a
unicellular pattern with centre of rotation at the top of the annulus is
investigated
numerically and experimentally for a Prandtl number of 100. Excellent agreement
between the numerical and experimental results is shown for both Prandtl
numbers
studied. The present work provides, for the first time, quantitative three-dimensional
descriptions of spiral convection within a moderate-gap annulus containing
air, flow
structures preceding oscillation in a large-gap annulus for air, and unicellular
flow
development in a large-gap annulus for large Prandtl number fluids.