Abstract:
Unsteady fluid flow and heat transfer are studied numerically in wavy channels by
solving two-dimensional Navier-Stokes and energy equations for both developing
flow and fully developed flow using periodic boundary conditions. The integral
forms of the governing equations are descretized using finite volume method with
collocated variable arrangement in the non-orthogonal bodyfitted grid. Solution
algorithm uses SIMPLE method, TDMA solver and three time level method. Timedependent
simulations are performed for several Reynolds numbers. Developing
flow calculations are presented for a sine shaped wavy channel consisting of 14
waves. It shows that at low Reynolds numbers, the flow is steady throughout the
whole channel. As Reynolds number is progressively increased, the flow remains
steady up to some part, then self-sustained oscillations are induced and the flow
becomes unsteady in the remainder of the channel. As a result of unsteadiness, there
is increased mixing between core and the near-wall fluids, thereby increasing the
heat transfer rate. With the further increase in Reynolds number the flow becomes
unsteady at a much earlier spatial location.
In the flow calculations with periodic boundary conditions, three different wavy
geometries, sine shaped, triangular and arc shaped, are considered. All the channels
are of single wave. Among them, for the same geometric dimensions, flow becomes
unsteady at relatively lower Reynolds number in the arc-shaped channel. For the
sine-shaped channel, individual variations of minimum height, amplitude and
wavelength are studied. Decreasing channel height and increasing amplitude cause
the flow to become more unstable and thereby increase friction factor and heat
transfer, but variation of wavelength has minimal effect. Besides, FFT analyses of
the time signals of u-velocities reveal that fundamental frequencies of the selfsustained
oscillations are independent of Reynolds number but function of geometric
configuration.
