Three-dimensional control is considered in the flow past a backward-facing step (BFS). The BFS flow at Reynolds number $Re=500$ (defined with the step height and the maximum inlet velocity) is two-dimensional and linearly stable but increasingly receptive to disturbances, with a potential for amplification as the recirculation length increases. We compute optimal spanwise-periodic control (steady wall blowing/suction or wall deformation) for decreasing the recirculation length, based on a second-order sensitivity analysis. Results show that wall-normal velocity control is always more efficient than wall-tangential control. The most efficient spanwise wavelength for the optimal control depends on the location: $β=0.6$ on the upper wall and $β=1$ on the upstream part of the lower wall. The linear amplification of the optimal control resembles the maximum linear gain, which confirms the link between recirculation length and amplification potential in this flow. Sensitivity predictions for blowing/suction amplitudes up to $O(10^{-3})$ and wall deformation amplitudes up to $O(10^{-2})$ are in good agreement with three-dimensional direct numerical simulations.
For larger wall deformation amplitudes, the flow becomes unsteady. This study illustrates how the concept of second-order sensitivity and the associated optimization method allow for a systematic exploration of the best candidates for spanwise-periodic control.
The flow downstream a backward-facing step is controlled using a pulsed jet placed upstream of the step edge. Experimental velocity fields are computed and used to the recirculation area quantify. The effects of jet amplitude, frequency and duty cycle on this recirculation area are investigated for two Reynolds numbers (Re=2070 and Re=2900). The results of this experimental study demonstrate that upstream actuation can be as efficient as actuation at the step edge when exciting the shear layer at its natural frequency. Moreover it is shown that it is possible to minimize both jet amplitude and…
We investigate flow instability created by an oblique shock wave impinging on a Mach 5.92 laminar boundary layer at a transitional Reynolds number. The adverse pressure gradient of the oblique shock causes the boundary layer to separate from the wall, resulting in the formation of a recirculation bubble. For sufficiently large oblique shock angles, the recirculation bubble is unstable to three-dimensional perturbations and the flow bifurcates from its original laminar state. We utilize Direct Numerical Simulation (DNS) and Global Stability Analysis (GSA) to show that this first occurs at a cri…
Many experimental and numerical studies report a large reduction of the recirculation bubble in Backward-Facing Step flows or airfoils in stall situation when excited at the natural shedding frequency $f_0$. Through a simple experiment using Dielectric Barrier Discharge actuator, we find a different result. For a given Reynolds number, the frequency of the perturbation is varied for a fixed duty-cycle dc = 27%. Through phase-averaging of Particle Image Velocimetry measurements, we show that the actuation creates a forced vortex which interacts with the natural shedding with a different phase v…
The paper presents a numerical investigation of the leading-edge vortices generated by rotating triangular wings at Reynolds number $Re=250$. A series of three-dimensional numerical simulations have been carried out using a Fourier pseudo-spectral method with volume penalization. The transition from stable attachment of the leading-edge vortex to periodic vortex shedding is explored, as a function of the wing aspect ratio and the angle of attack. It is found that, in a stable configuration, the spanwise flow in the recirculation bubble past the wing is due to the centrifugal force, incompressi…
Fluid and solute transfer in X-junctions between straight channels is shown to depend critically on the junction angle in the Stokes flow regime. Experimentally, water and a water-dye solution are injected at equal flow rates in two facing channels of the junction: Planar Laser Induced fluorescence (PLIF) measurements show that the largest part of each injected fluid "bounces back" preferentially into the outlet channel at the lowest angle to the injection; this is opposite to the inertial case and requires a high curvature of the corresponding streamlines. The proportion of this fluid in the …
This study seeks to characterise the breakdown of the steady 2D solution in the flow around a 180-degree sharp bend to infinitesimal 3D disturbances using a linear stability analysis. The stability analysis predicts that 3D transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $Re<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqβ\leq5$. This range of $Re$ and $β$ captures both steady-state 2D flow solutions as well as the inception of unsteady 2D flow. For $0.…
The separated flow downstream a backward-facing step is controlled using visual information for feedback. This is done when looking at the flow from two vantage points. Flow velocity fields are computed in real-time and used to yield inputs to a control loop. This approach to flow control is shown to be able to control the detached flow in the same way as has been done before by using the area of the recirculation region downstream the step as input for a gradient descent optimization scheme. Visual feedback using real-time computations of 2D velocity fields also allows for novel inputs to the…
In this study, a simple model based closed-loop algorithm is used to control the separated flow downstream a backward-facing step. It has been shown in previous studies that the recirculation bubble can be minimized when exciting the shear layer at its natural Kelvin-Helmholtz instability frequency. In this experiment, the natural shedding frequency is identified through real-time analysis of 2D velocity fields. Actuation (pulsed jet) is then locked on this frequency. If flow characteristics stray too far from a set point, shedding frequency is updated and actuation changed. The present work d…
Rich recirculation patterns have been recently discovered in the electrically conducting flow subject to a local external magnetic termed "the magnetic obstacle" [Phys. Rev. Lett. 98 (2007), 144504]. This paper continues the study of magnetic obstacles and sheds new light on the core of the magnetic obstacle that develops between magnetic poles when the intensity of the external field is very large. A series of both 3D and 2D numerical simulations have been carried out, through which it is shown that the core of the magnetic obstacle is streamlined both by the upstream flow and by the induced …
Flow topology and unsteady cavitation dynamics in the wake of a backward facing step was investigated using high speed videography and time-resolved X-Ray densitometry, along with static and dynamic pressure measurements. The measurements are used to inform the understanding of underlying mechanisms of observed flow dynamics as they are related to shock wave induced instabilities. The differences in cavity topology and behaviour at different cavitation numbers are examined to highlight flow features such as the pair of cavitating spanwise vortices in the shear layer and propagating bubbly shoc…
The effect of the Strouhal number on periodic forcing of the flow over a backward-facing step (height, $H$) is investigated experimentally. Forcing is applied by a synthetic jet at the edge of the step at Strouhal numbers ranging from $0.21<St_H<1.98$ ($St_H = f H/U_\infty$) at a Reynolds number of $Re_H = HU_\infty/ν= 41000$. In the literature, the effect of Strouhal number on the reattachment length is often divided into low- and high frequency actuation, referring to different frequency modes in the unforced flow. In the present paper, variations with Strouhal number are explained based on …
Rotor blades of wind turbines in the atmospheric boundary layer regularly experience the aerodynamic phenomenon of dynamic stall consisting of a temporary overshoot of lift and detrimental fatigue loads. Particularly the formation of dynamic stall under three-dimensional inflow conditions raises open questions. Aerodynamic behavior of a DU 91-W2-250 wind profile undergoing light dynamic stall is thus analyzed in a wind tunnel. Effects of a gust with streamwise and spanwise periodic variation are investigated by comparing total and local lift generation with flow formation above the airfoil. Th…
With the aim of providing a first step in the quest for a reduction of the aerodynamic drag on the rear-end of a car, we study the phenomena of separation and reattachment of an incompressible flow focusing on a specific aerodynamic geometry, namely a backward-slanted step at 25 degrees of inclination. The ensuing recirculation bubble provides the basis for an analytical and numerical investigation of streamwise-streak generation, lift-up effect, and turbulent-wake and Kelvin-Helmholtz instabilities. A linear stability analysis is performed, and an optimal control problem with a steady volumic…
A novel, model free, approach to experimental closed-loop flow control is implemented on a separated flow. Feedback control laws are generated using genetic programming where they are optimized using replication, mutation and cross-over of best performing laws to produce a new generation of candidate control laws. This optimization process is applied automatically to a backward-facing step flow at Re=1350, controlled by a slotted jet, yielding an effective control law. Convergence criterion are suggested. The law is able to produce effective action even with major changes in the flow state, de…
Direct numerical simulation (DNS) of flow in a turbulent channel with a random rough wall is performed at $Re_τ=400$ and $600$. The roughness geometry corresponds to the experiments of Flack and Schultz (personal communication). The rough surface is used on the bottom wall of the channel. DNS of a smooth channel flow and a rod-roughened channel flow are also performed at $Re_τ=400$ for validation and comparison. The skin friction coefficient of the random-rough channel shows good agreement with the experimental results of Flack and Schultz. Due to the roughness, the slip velocity on the rough …
Turbulent shear flows have triggered fundamental research in nonlinear dynamics, like transition scenarios, pattern formation and dynamical modeling. In particular, the control of nonlinear dynamics is subject of research since decades. In this publication, actuated turbulent shear flows serve as test-bed for a nonlinear feedback control strategy which can optimize an arbitrary cost function in an automatic self-learning manner. This is facilitated by genetic programming providing an analytically treatable control law. Unlike control based on PID laws or neural networks, no structure of the co…
