Data assimilation for control of a plane mixing layer

The design of active model-based flow controllers requires the knowledge of a dynamical model of the flow. However, real-time and robust estimation of the flow state remains a challenging task when only limited spatial and temporal discrete measurements are available. In this study, the objective is to draw upon the methodologies implemented in meteorology to develop dynamic observers for flow control applications. Well established data assimilation (DA) method using Kalman filter is considered. These approaches are extended to both estimate model states and parameters. Simple non-linear dynamical models are first considered to establish quantitative comparisons between the different algorithms. An experimental demonstration for the particular case of a plane mixing layer is then proposed.

Turbulent wake behind side-by-side flat plates: computational study of interference effects

The complex wake behind two side-by-side flat plates placed normal to the inflow direction has been explored in a direct numerical simulation study. Two gaps, $g=0.5d$ and $1.0d$ , were considered, both at a Reynolds number of 1000 based on the plate width $d$ and the inflow velocity. For gap ratio $g/d=0.5$ , the biased gap flow resulted in an asymmetric flow configuration consisting of a narrow wake with strong vortex shedding and a wide wake with no periodic near-wake shedding. Shear-layer transition vortices were observed in the wide wake, with characteristic frequency 0.6. For $g/d=1.0$ , two simulations were performed, started from a symmetric and an asymmetric initial flow field. A symmetric configuration of Kármán vortices resulted from the first simulation. Surprisingly, however, two different three-dimensional instability features were observed simultaneously along the span of the upper and lower plates. The spanwise wavelengths of these secondary streamwise vortices, formed in the braid regions of the primary Kármán vortices, were approximately $1d$ and $2d$ , respectively. The wake bursts into turbulence some $5d$ – $10d$ downstream. The second simulation resulted in an asymmetric wake configuration similar to the asymmetric wake found for the narrow gap $0.5d$ , with the appearance of shear-layer instabilities in the wide wake. The analogy between a plane mixing layer and the separated shear layer in the wide wake was examined. The shear-layer frequencies obtained were in close agreement with the frequency of the most amplified wave based on linear stability analysis of a plane mixing layer.