Coherent structures produced by the interaction between synthetic jets and a laminar boundary layer and their surface shear stress patterns

In this paper, the results from 3D numerical simulations of circular synthetic jets issued into a zero-pressure-gradient laminar boundary layer developing along a flat plate are reported. The simulations are undertaken using FLUENT at a wide range of actuator operating conditions. The formation and development of the coherent structures produced as a result of the interaction between the synthetic jets and the boundary layer were examined using the Q-criterion. Non-dimensional parameter space maps were established to illustrate the variations in the appearance of these resultant structures and their shear stress footprints upon the changes in the operating conditions of synthetic jets. Finally, the parameter boundary separating the two distinct types of vortical structures and surface shear stress patterns is identified. It is found that the location of this boundary correlates closely with the jet-to-freestream velocity ratio of VR = 0.4 when the Strouhal number (Str) is less than 1, whereas for Str > 1 the boundary deviates from this trend, approaching the line of dimensionless stroke length of L = 1.6. In order to investigate the potential impact of the synthetic jets on the boundary layer, the increase in the space- and time-averaged skin friction coefficient relative to the baseline case without the synthetic jets is calculated. It appears that in order to maximise the impact on the near-wall flow while keeping the energy expenditure down, it is wise to maximise the accumulated effect of hairpin vortices by keeping the spacing between consecutive hairpin vortices similar to the local boundary layer thickness upstream of the separated flow instead of producing stronger individual structures.     

Control of mixing by boundary feedback in 2D channel flow

We address the problem of enhancing mixing by means of boundary feedback control in 2D channel flow. This is done by first designing feedback control strategies for the stabilization of the parabolic equilibrium flow, then applying this feedback with the sign of the input reversed. The result is enhanced instability of the parabolic equilibrium flow, which leads rapidly to highly complex flow patterns. Simulations of the deformation of dye blobs positioned in the flow indicate (qualitatively) that effective mixing is obtained for small control effort as compared with the nominal (uncontrolled) flow. A mixedness measure P_ε is constructed to quantify the mixing observed, and is shown to be significantly enhanced by the application of the destabilizing control feedback.     

Chattering in sliding mode control systems with boundary layer approximation of discontinuous control

It has been a widely accepted notion that approximation of discontinuous control by certain continuous function in a boundary layer results in chattering elimination in sliding mode control systems. It is shown through three different types of analysis that in the presence of parasitic dynamics, this approach to chattering elimination would work only if the slope of the continuous nonlinear function within the boundary layer is low enough, which may result in the deterioration of performance of the system. A few examples are provided. An approach to robust stability of linear systems from the consideration of the saturating control is proposed.