Periodic flow features in a planar sudden expansion with pulsatile inflow velocity

Abstract

Flow through sudden expansion finds its application in several engineering and biological processes. Though the stability of flow through steady sudden expansion has garnered much attention, little to none is given to the pulsatile flow through sudden expansion. Hence, in the present work we study the influence of inflow pulsatility on flow characteristics in a sudden expansion. The inflow velocity is a sinusoidal waveform that is modulated to encompass a wide range of amplitudes, ${{a}}$ , and reduced velocities, ${{U_{r}}}$ . We report four different modes, namely, synchronized growth of the recirculation region (at high ${{U_{r}}}$ ), necking and diffusion of the recirculation region (at moderately high ${{U_{r}}}$ ), splitting and convection of the recirculation region (at moderate ${{U_{r}}}$ ) and inverse growth of the recirculation region (at low ${{U_{r}}}$ ). In each mode, the symmetry-breaking critical Reynolds number is obtained through numerical experiments and compared with those of Floquet stability analysis. We found that diffusion and the convection mode of the recirculation region increases the stability of the flow while the inverse growth mode of the recirculation region decreases the same. The effect of the expansion ratio, ${{ER}}$ , is also explored, and we found that as ${{ER}}$ increases, the absolute stability of flow decreases, but relative stability between the modes remains similar. Finally, we explain the dynamics of the modes by using terms involving the vorticity transport equation.