Splitter plate effect on the global dynamics of two-phase mixing layer flow

We combine two-dimensional volume-of-fluid direct numerical simulation (2D-VOF) and dynamic mode decomposition analysis (DMD) to investigate the splitter plate thickness effect on the global dynamics of a planar two-phase mixing layer. The flow configuration consists of two parallel fluid streams with different densities ρ1<ρ2 and velocities U1>U2, which meet downstream of a separator (splitter) plate. The interaction between the fast U1 and slow U2 fluid layers determines a Kelvin–Helmholtz (KH) instability at the interface, which is found to be crucially affected by the parameter e/δ1, being e the splitter plate thickness and δ1 the vorticity thickness of the fast phase (placed above the slow phase). For e/δ1<1, the KH instability results in a wavy dynamics of the interface, whose temporal oscillations are characterized by the reduced frequency StML=fδ1/U1≈0.018. In such conditions, the DMD analysis identifies the dominant global mode of the flow as a spatio-temporal interfacial travelling wave moving with the celebrated Dimotakis velocity, UD=ρ1U1+ρ2U2/ρ1+ρ2, and oscillating at the same frequency StML. On the other hand, for e/δ1>1, the reduced frequency of the interface oscillations undergoes a sudden transition (shift) to the lower value StMLW≈0.012. The leading spatio-temporal coherent structure identified by the DMD analysis correspondingly shifts to the same frequency. By inspection of the velocity field, it is found that, as e/δ1 increases, the wake region located right downstream of the splitter plate undergoes a transition from steady conditions to periodic oscillations at the reduced frequency StW≈0.024. Therefore, it is argued that the observed frequency shift in the mixing layer global dynamics is determined by the interaction between the characteristic frequencies of the wake StW and the mixing layer StML, resulting in the third-order intermodulation frequency StMLW=2StML−StW, which is known to arise for wave signals propagating in nonlinear systems potentially. We corroborate this argument by applying a simple actuation at the splitter plate edge, which inhibits the wake oscillations and restores the frequency StML even in the e/δ1>1 regime, thereby suppressing the frequency shift.