Nikesh Yadav, MEiL, ZA, PW, Stability of Flow in a grooved channel

Flow in a channel with grooves parallel to the flow direction has been studied, with the primary goal of establishing channel geometries that enhance achievable mixing at the possibly low drag increase. The geometry considered in this research, is one of a channel fitted with symmetric, sinusoidal grooves parallel to the flow direction of moderate and large amplitudes (up to 80% of the mean opening). The analysis is performed up to the Reynolds numbers resulting in the formation of secondary states. The first part of the analysis is focused on the properties of the two-dimensional, base flow. Mainly the dependence of the drag on the channel’s geometry is characterized. The second part of the analysis discusses the onset of the three-dimensional traveling wave instability. Linear stability is investigated by the Direct Numerical Simulation (DNS) of the Navier-Stokes (NS) equations. Critical conditions for the onset of instabilities at a range of parameters are given. Finally, nonlinear saturation of the unstable modes and the resulting secondary flows are examined. Our results indicate that secondary flows, at saturation, can maintain the drag reducing properties for a limited range of Reynolds numbers.