Flow bifurcations, Eulerian chaos and flow mixing in open block tandem channels

Heat transfer enhancement in open channels with geometrical inhomogeneities may occur when the flow evolves from a laminar to a turbulent regime through a transition scenario by increasing a critical flow parameter as the Reynolds number. In converging-diverging wavy channels for example, flow regimes of Lagrangian chaos -that enhances the flow mixing- and Eulerian chaos are the responsible for the enhancement of heat transfer from a hot surface to a mean flow. Chips attached to a motherboard generate a high amount of heat that needs to be removed. The chip performance depends on the chip temperature, which must remain in a low (reasonable) value. One way of removing heat is through a forced flow that extracts the heat from the chip surface. The heat transport rate depends strongly on the flow characteristics, which vary with the Reynolds number. A set of chips can be seen as a block tandem channel, where each block generates heat that needs to be extracted through the chip surface by a flow that circulates between the block and upper surfaces. This paper reports flow characteristics numerical investigations in a block tandem channel. The flow characteristics are obtained from direct numerical simulations of the Navier-Stokes and continuity equations using spectral element methods for laminar and transitional Reynolds numbers flow regimes. Extended and reduced 2D computational models are used to determine the appropriated computational domain for the simulations, which are meshed to capture and describe flow characteristics, such as velocity gradients, vortex dynamics, and flow mixing that develops for transitional flows. The flow characteristics, obtained in terms of vortex dynamics, Fourier spectra, and pseudo-phase spaces, show a transition scenario characterized by a first Hopf bifurcation as the flow evolves from a laminar to a periodic flow, and a second Hopf bifurcation as the flow evolves to quasi-periodic flow for higher Reynolds numbers. The first flow bifurcation occurs to a critical Reynolds number that is significantly lower than the critical value for a plane Poiseuille flow. The quasi-periodic flow adds a new frequency ω2 to the existing ω1 frequency of the periodic flow. Friction factor and pumping power values are much higher than those of the plane Poiseuille flow due to the geometrical inhomogeneities of the block channel. The flow bifurcations scenario is very similar to the Ruelle-Takens-Newhouse transition scenario to chaos obtained in converging-diverging wavy channels. Calculations of Eulerian Lyapunov exponents are performed to determine if Eulerian chaos develops. Refs. 3 (author)