Numerical investigation of unsteady flow and heat transfer in wavy channels

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.