Open and closed-loop experiments to identify the separated flow dynamics of a thick turbulent boundary layer

Abstract

Open and closed-loop flow control experiments were performed on the transient attachment and separation mechanisms of a thick turbulent boundary layer (TBL). Without actuation, the TBL is subjected to an adverse pressure gradient and separates downstream of a sharp variation in the wall geometry. Departing from a given geometry and steady operations of vortex generator actuators, the control objective was to attach the flow in the separated region with a minimum of injected fluid using adaptation of the closed-loop control. The large scale of the facility (i.e., δ = 20 cm upstream of separation) induces large time scales and large Reynolds numbers of the flow to be controlled. It is found to consequently induce large time scales of the separation/attachment mechanisms, making the dynamic closed-loop implementation easier. Open-loop tests were first performed to extract the adequate input/output variables for closed-loop implementations. The chosen input variable was the Duty Cycle, DC, which enables sending of a control action at least 10 times faster than the time scales of the attachment/separation process. The chosen output variable was the voltage signal from a hot-film probe located on the flap which characterizes the degree of separation. In open loop, both the large scale (i.e., large time scales) of the present facility (Carlier and Stanislas in J Fluid Mech 535(36):143–188, 2005) and the well-defined excitation (Braud and Dyment in Phys Fluids 24:047102, 2012) help to extract the different time scales involved and to identify the whole system (actuators, baseline flow and sensor). Three Reynolds numbers based on the momentum thickness of the boundary layer near the actuators and upstream of separation were investigated (Re θ = 7,500, 10,500 and 12,600) through variation of the free-stream velocity (U ∞ = 5, 8, 10 m/s). These three systems were found to behave like first-order linear systems, with coefficients that need to be adapted depending on the Reynolds number. From Re θ = 7,500 to Re θ = 12, 600, the time scale and static gain of the linear system needed to be almost doubled. A simple controller (Proportional-Integral) was implemented in closed-loop configuration, improving the reactivity of the system. Robustness was tested by varying the free-stream velocity. Closed-loop control based on a fixed reference was unsuccessful as it failed to account for the effect of the Reynolds number. This was successfully overcome by tracking a given state of the flow using a simple P controller to adapt the reference according to variations of Re. The P controller, acting on the DC variable, compensates the corresponding variations of VR (ratio between the free-stream and the jet exit velocity).