Session L17: Flow Control: Coherent Structures

Stability and Resolvent Analysis of plane Couette flow in the distinguished limit Re → ∞, α → 0 with Re · α = O(1) without and with wall-transpiration

For turbulent plane Couette flow at large Reynolds numbers, large streamwise- elongated very persistent channel-wide coherent structures are observed with weak streamwise variation. For a deeper understanding of this phenomenon we investigated this flow at high Reynolds numbers Re → ∞ and small streamwise wavenumbers α → 0 in the distinguished limit Reα = Re · α = O(1) using the temporal linear stability theory as well as the resolvent analysis approach. In this distinguished limit, Reα plays a significant role in the behaviour of the first singular value σ1 over both Re and α and thus the energy of the system. Furthermore, Reα has a significant influence on both the eigenfunctions obtained from the linear stability theory and the response modes obtained from the resolvent analysis. We find that the appearance of the structures in this asymptotic limit is mainly influenced by Reα and not by Re or α alone. The conducted analysis is expanded on the plane Couette flow with constant wall-transpiration V0 and wall velocity Uw, where the first singular value σ1 is the largest for a certain invariant depending on V0 and Uw within the limit of Reα =O(1).   

Structured Input-Output Analysis of Oblique Laminar-Turbulent Flow Patterns in Transitional Plane Couette-Poiseuille Flow

In this work, we apply structured input-output analysis to study laminar-turbulent patterns in transitional plane Couette-Poiseuille flow. The results demonstrate that this approach predicts the high structured gain of perturbations with wavelengths corresponding to the oblique turbulent bands observed in experiments. The inclination angles of these structures and their Reynolds number dependence are also consistent with previously observed trends. Reynolds number scalings of the maximally amplified structures for an intermediate laminar profile that is equally balanced between plane Couette and Poiseuille flow show an exponent that is at the midpoint of previously computed values for these two flows. However, the dependence of these scaling exponents on the shape of the laminar profile as the relative contribution moves from predominately plane Couette to Poiseuille flow is not monotonic and our analysis indicates the emergence of different optimal perturbation structures over the parameter regime. Finally we perform spectral analysis on the frequency response operator to obtain its principal singular vectors, which provide insights regarding the wall-normal structures of velocity fluctuation modes with the largest structured gain.   

Energy reduction of streamwise streaks in high-speed boundary layer flows via optimally controlled wall deformations.

Previous work has shown that streamwise oriented vortices and accompanying streaks, originating from streamwise disturbances or surface imperfection, contribute to the transition to turbulence in boundary layer flows over curved surfaces and induce a significant increase in noise in supersonic and hypersonic wind tunnels, which can cause interference with the measurements in the test section. In this study, we develop a Lagrange multiplier-based wall deformation optimal control technique to suppress the growth rate of the streamwise vortex system in high-speed boundary layer flows. We formulate the method by first deriving the nonlinear compressible boundary region equations (NCBRE) from the full-compressible Navier-Stokes equations in a high Reynolds number asymptotic framework. We then utilize Lagrange multipliers to transform the constrained optimization problem into an unconstrained form. The transformation process results in another set of equations in the form of the adjoint compressible boundary region equations (ACBRE) and corresponding optimality conditions. In the present formalism, the wall displacement in the wall-normal direction and the wall shear stress designate the control variable and the cost functional, respectively. We report and discuss the results of the wall-deformation technique for a range of high-supersonic and hypersonic flows.

    

Turbulent flow control through superhydrophobic surfaces

Turbulent shear flows are abundant in geo and astrophysical systems and in engineering-technology applications. They are often riddled with large-scale secondary flows that drastically modify the characteristics of the primary stream, preventing or enhancing mixing and mass and heat transfer. We study the possibility of modifying these secondary flows by using superhydrophobic surface treatments which reduce the local shear. We focus on the canonical problem of Taylor-Couette flow, the flow between two coaxial and independently-rotating cylinders, which has robust pinned secondary structures called Taylor rolls that persist even at significant levels of turbulence. We show that a spanwise superhydrophobic treatment can destructively interfere with Taylor rolls by inducing additional secondary flows through surface heterogeneity, as long as the structure size can be fixed. We compare experiments and Direct Numerical Simulations and quantify the effects of heterogeneity caused by superhydrophobic surface on Taylor rolls at Re_s=O(10⁴) . We rationalize the minimum treatment hydrophobicity required for this flow control, and show that it can be effective beyond the Reynolds numbers here studied.   

Coherent Structures in the Wake of an Actively-Controlled Cylinder

The wake behind a cylinder with circumferential, moving-wall actuators was modified by means of a reinforcement-learning, active-control scheme designed to reduce the net drag force. Experimental measurements of the cylinder system were carried out in a high speed water tunnel facility using particle image velocimetry in the actuation and wake regions in order to identify specific coherent structures associated with the drag modification. The spatial and temporal behavior of these coherent structures was studied using correlation analysis, with an emphasis on the unsteady scale interactions between large- and small-scale motions in the wake, and the inner/outer interactions between the wake and the near-wall region of the cylinder. Phase-locked measurements were used to synchronize the actuation inputs, time-resolved forced measurements, and resulting coherent motions in order to characterize the non-linear dynamics of the system and to identify the most salient coherent motions associated with the drag modification.   

Control of Vortical Structures over a Tailless Chined Forebody-Delta Wing configuration

Modern fighter aircraft designed for low observability commonly combine delta wings with chine forebodies. However, both produce strong leading-edge vortices which may interact in ways that can cause non-linear moments and loss of control. Furthermore, it is expected that future fighter aircraft will be tailless to further reduce their radar cross-section, adding to the loss of longitudinal stability and control. The present research explores experimentally the effectiveness of finite-span synthetic jets on the aerodynamic forces and moments acting on a Tailless Chined Forebody-Delta Wing configuration. The finite span synthetic jets are located on the model's forebody and act on the vortices produced by the chine shape, with the intention of influencing the downstream interaction of these vortices with the vortices produced at the wing's leading edge, to in turn then delay the onset of vortex breakdown over the wing itself. The mean and unsteady forces and moments are analyzed and compared for a baseline case (no flow control) and several different configurations of finite-span synthetic jets. In addition, SPIV results are used to explain the effects of the jets on the aerodynamic loads.   

Evolution of a Synthetic Jet with Triangular Orifice Geometry at Varying Skew Angles in a Laminar Boundary Layer

Synthetic jets have been widely investigated as an actuator for active flow control. The present experimental study investigates the interaction of a finite aspect ratio synthetic jet actuator having a triangular orifice geometry with a laminar boundary layer over a flat plate, and the effect of the skew angle of the orifice on this interaction. The skew angles studied are 0°, 45°, 90°, 135°, and 180°, with 0° corresponding to the jet orifice oriented parallel to the flow with the tip of the triangle pointing downstream. The study was conducted using Stereoscopic Particle Image Velocimetry (SPIV). Results show that the near field is highly unsteady at all orientations. Moreover, the triangular orifice produces a pair of counter-rotating vortices with the far-field characteristics varying significantly with skew angle. While at a skew angle of 0° a pair of symmetric vortices are present, only a single dominant vortex is present at 45° skew. The vortices produced are also found to be stronger and extend farther downstream when the orientation is such that the base of the triangle is upstream of the tip. The variation in the number and strength of the vortices with skew could prove a synthetic jet with a triangular orifice to be a versatile actuator.

    

Effects of Active Control on Near-Field Pressure Fluctuations in Supersonic Rectangular Twin Jets

Supersonic rectangular twin jets (RTJ) are of interest for current and future generations of tactical aircraft. However, the adverse effects of coupling have previously been documented to increase the near-field pressure fluctuations (NFPF) that can damage the nearby aft components of aircraft. In-phase coupling (IPC) is reported to be more damaging than out-of-phase coupling (OOPC). The focus of this work is to explore and control the coupling effects on RTJ NF pressure fluctuations by using localized arc filament plasma actuators (LAFPAs). The aspect ratio of the RTJ is 2, the design Mach number is 1.5, and the IPC or OOPC is shown to be along the minor axis. The results have confirmed that the pressure fluctuations in the inter-nozzle region, near the nozzles, were significantly higher for IPC than OOPC. The LAFPAs have shown great control authority by leveraging natural flow instabilities in the flow and the results have shown significant reduction in the near-nozzle pressure fluctuations switching from IPC to OOPC. The control authority and reduction in the near nozzle pressure fluctuations have been demonstrated over the entire flow regimes of overexpanded to design to underexpanded explored in this research. More detailed work is underway to further analyze the data.   

Control of the Aerodynamic Loads on an Axisymmetric Cylindrical Body at High Incidence using Forebody Bleed Actuation

Fluidically-controlled variations of the aerodynamic loads on a slender cylinder wire-mounted at high angles of incidence (up to 60o) are investigated in wind tunnel experiments. The loads are effected using azimuthally-segmented aerodynamic bleed actuation through an ogive forebody with variable porosity. The actuation selectively alters the formation of the forebody counter rotating vortex pair to either promote or suppress its asymmetry, and thereby the evolution of the hierarchy of streamwise-successive vortices that form within the separating flow along that side of the cylinder's near wake. The present investigations show that that azimuthally-controlled bleed actuation can selectively strengthen or override the direction and magnitude of side forces that are randomly effected by natural asymmetries of the forebody vortices. Furthermore, changes in axial distributions of streamwise vorticity concentrations along the cylinder the near wake effected by asymmetric bleed patterns can lead to significant imbalance of the aerodynamic side force (and yawing moment) over a range of incidence angles that are comparable to the cylinder's normal and axial loads.   

Aerodynamically Adaptive Control of a Flexible 3-D Wing using Distributed Bleed Actuation

The aerodynamic loads effected by controlled interactions between a flexible cantilevered 3-D wing model and the embedding cross flow are explored in wind tunnel investigations to effect tunable structural and aeroelastic characteristics.  The aerodynamic loads are regulated using distributed air bleed driven by flow induced pressure difference between the wing’s pressure and suction sides through clusters of surface ports and the bleed flow rate is dynamically regulated using activated louvers on the suction side.  The effectiveness of the induced loads is demonstrated by forcing time-periodic cross-stream bending vibrations of the wing using bleed actuation near its tip, while inboard bleed actuation is used independently to mitigate the forced vibrations using a limited-state feedback proportional controller of the wingtip motion that achieves a 70% reduction in the RMS of tip motion.  High speed stereo PIV measurement in the spanwise cross-stream (y-z) plane in the wing’s near wake are used to measure the unsteady changes in spanwise distributions of streamwise vorticity concentrations and reveal the effect of bleed actuation on the spanwise load distribution through unsteady changes in sectional circulation.  These measurements demonstrate how the actuation leads to forcing and control of the wing’s time-dependent bending motion.  The effect of the bleed actuation on the apparent structural properties of the wing are assessed and demonstrate significant changes in damping in the presence of vibration control.