Wake Of Bluff Body Research Articles

Polymeric flexible plate in the wake of a bluff body for energy harvesting

Piezoelectric polymeric flexible plates can be placed in the wake of bluff bodies to harvest the fluid flow energy. The undulating motion of such plates generated by the vorticity in the wake has been described by previous researchers; the influence of different aspect ratios of the plate on the strain energy has also been investigated. Less information is given on the fluid-structure interaction mechanism and on the mode shapes contribution to strain energy. Moreover, the optimum thickness and aspect ratios of the plates are still to be determined. As a reason, different polyethylene thin plates were clamped to a square cylinder and placed in a water tunnel. We used a high speed camera to capture the plate deflection and the flow pattern. From the deflection, we proceeded to modal decomposition into cantilever beam mode shapes and to strain energy calculation. The flow pattern for several characteristic plate deflection shapes were computed using the software PIVlab. Two way fluid-structure interaction modelling was carried out using ANSYS. We observed that the plate deflection evolves from splitter plate oscillation type into travelling wave type where strain energy is maximized. Strain energy is proportional to the thickness until an optimum thickness after which any further increase renders the plate too stiff to undergo significant bending. The particle image velocimetry analysis and the fluid structure-interaction modelling showed that there is no deflection when the flow is symmetrical or when there is no perpendicular flow impinging on the plate. Deflection occurs when the flow impinges in a different fashion on the two sides of the plate. The motion of the plate drastically influences the wake flow by increasing the drag and generating vorticity.

Characteristics of flow configurations around side-by-side twin wind blades

The effects of gap ratio (g∗) and angle of attack (α) on side-by-side twin wind blades were investigated in an open-channel wind tunnel. Characteristic wake-flow patterns and aerodynamic performance were analyzed using smoke-streak flow visualization, hot-wire velocimetry, and six-force balancer. Seven smoke-streak flow patterns were defined – attached surface flow, wake instability wave, vortical wake, gap flow, bluff-body wake, anti-phase vortex shedding, and in-phase vortex shedding. For g∗≈0, the flow characteristics were similar to those of a single wind blade. As g∗ increased, these two wind blades induced the vortical wake, gap flow, and anti-phase vortex shedding modes. With further increase in g∗, the wake-flow patterns were similar to those behind a single wind blade. The hot-wire velocimeter detected that the maximum velocity fluctuation occurred at g∗=0.083. This velocity fluctuation decreased toward that of free stream as g∗ increased. The vortex-shedding frequency decreased as α increased. For a single wind blade, the maximum lift occurred at α=10° and the drag increased with α. The pitching momentum increased with α when α<45°. The lift, drag, and pitching momentum on the lower wind blade decreased significantly due to the existence of upper wind blade. The effect of upper wind blade on the lower one deceased as g∗ increased.

Extremum seeking to control the amplitude and frequency of a pulsed jet for bluff body drag reduction

Feedback control of fluid flows presents a challenging problem due to nonlinear dynamics and unknown optimal operating conditions. Extremum seeking control presents a suitable method for many flow control situations but involves its own challenges. In this paper, we provide a brief analysis of the extremum seeking method, with attention to modifications that we find to be advantageous. In particular, we present an adaptation for optimisation of the frequency of a harmonic input signal, a common scenario for open-loop flow control systems. We then present results from the experimental implementation of our modified method to the open-loop control system of Oxlade et al. (J Fluid Mech 770:305–318, 2015), an axisymmetric bluff-body wake, forced by a pulsed jet. We find that the system is able to achieve optimal operating conditions in both the amplitude and frequency of the harmonic input signal, and is able to largely reject the disturbances arising from measurements of a highly turbulent flow. We finally show the ability of the extremum seeking system to adapt to changing conditions.

Stochastic modelling and feedback control of bistability in a turbulent bluff body wake

A specific feature of three-dimensional bluff body wakes, flow bistability, is a subject of particular recent interest. This feature consists of a random flipping of the wake between two asymmetric configurations and is believed to contribute to the pressure drag of many bluff bodies. In this study we apply the modelling approach recently suggested for axisymmetric bodies by Rigaset al.(J. Fluid Mech., vol. 778, 2015, R2) to the reflectional symmetry-breaking modes of a rectilinear bluff body wake. We demonstrate the validity of the model and its Reynolds number independence through time-resolved base pressure measurements of the natural wake. Further, oscillating flaps are used to investigate the dynamics and time scales of the instability associated with the flipping process, demonstrating that they are largely independent of Reynolds number. The modelling approach is then used to design a feedback controller that uses the flaps to suppress the symmetry-breaking modes. The controller is successful, leading to a suppression of the bistability of the wake, with concomitant reductions in both lateral and streamwise forces. Importantly, the controller is found to be efficient, the actuator requiring only 24 % of the aerodynamic power saving. The controller therefore provides a key demonstration of efficient feedback control used to reduce the drag of a high-Reynolds-number three-dimensional bluff body. Furthermore, the results suggest that suppression of large-scale structures is a fundamentally efficient approach for bluff body drag reduction.

Wake of tandem cylinders near a wall

This article reports an experimental investigation on the near wake of two identical circular cylinders in crossflow arranged in tandem configuration in the streamwise direction and with the additional interference of the ground. The Reynolds number based on the cylinders diameter is 4.9×103. The present study analyses the effect of longitudinal pitch-to-diameter ratios spanning the well known flow regimes of tandem cylinders in absence of ground effect, i.e. single bluff body, shear layer reattachment and vortex co-shedding of twin cylinders. Particle Image Velocimetry measurements are performed to extract first and second order statistics of the wake. The wake features have been analyzed and compared with the bluff-body wake models present in literature. Additionally, the flow fields are decomposed in Proper Orthogonal modes to characterize the main coherent structures. The time coefficients of the modes are analyzed to extract phase relations between vortical features.Far enough from the wall the cylinders wake is symmetric, with Von Kármán vortices shed symmetrically in the wake with respect to cylinders centerline. The measured average wake characteristics and vortical structures are consistent with the data reported in the literature for tandem cylinders without ground effect. For a wall-to-cylinder gap equal to 1 diameter, the ground strongly influences the flow field, introducing asymmetry in the typical Von Kármán wake. The ground boundary layer is thickened past the downstream cylinder and a wall-jet appears, enclosed between the wall boundary layer and the cylinders wake. Eventually these flow structures are not distinguishable when the cylinders wake and the wall boundary layer are grown enough to merge. From POD analysis, vorticity blobs appear on the wall, paired with vortex shedding.If the wall gap is decreased to 0.3 diameters, an extended low speed region appears close downstream of the cylinders. A POD mode similar to a vortex shedding is still present; however it cannot be associated to an alternate Von Kármán street. The shed structures show a shorter wavelength than the Von Kármán shedding in far-from-the ground cases and are accompanied by a flapping jet-like structure ejected from the wall gap between the cylinder and the wall. The jet strongly changes the features of the wake on the side opposite to that of the wall, thus suggesting a possible coexistence between jet oscillations and shedding.

Numerical study of two-dimensional flow around two side-by-side circular cylinders at low Reynolds numbers

Incompressible flows at low Reynolds numbers over two identical side-by-side circular cylinders have been investigated numerically using unstructured finite volume method. The gap between the cylinders (g) and Reynolds number (Re) considered in the study lies respectively in the range of 0.2 ≤ g/D ≤ 4.0 (D being the diameter of the cylinder) and 20 ≤ Re ≤ 160. Low Reynolds number steady flows are given considerable importance. Two types of wakes are observed in the steady flow regime; the first type is characterized by attached vortices as in the case of an isolated cylinder and the other type is identified by detached standing vortices in the downstream. Reynolds number at which flow turns unsteady is quantified for each gap width. Five different types of wake patterns are observed in the unsteady flow regime: single bluff body wake, deflected wake, flip-flopping wake, in-phase synchronized, and anti-phase synchronized wakes. Present simulations of the evolution of single bluff-body wake demonstrate presence of vortices in the gap side too. The very long time simulations show that below a limiting Re depending on the gap, there is a transition of fully developed initial anti-phase flow to the in-phase flow at a later time. The limiting Reynolds number for this phase bifurcation phenomenon is evaluated in the (Re, g/D) space. A properly calibrated reduced order model based stability analysis is carried out to investigate the phase transition.

Transition of a Steady to a Periodically Unsteady Flow for Various Jet Widths of a Combined Wall Jet and Offset Jet

In the present paper, a dual jet consisting of a wall jet and an offset jet has been numerically simulated using two-dimensional unsteady Reynolds-Averaged Navier–Stokes (RANS) equations to examine the effects of jet width (w) variation on the near flow field region. The Reynolds number based on the separation distance between the two jets (d) has been considered to be Re = 10,000. According to the computational results, three distinct flow regimes have been identified as a function of w/d. For w/d ≤ 0.5, the flow field remains to be always steady with two counter-rotating stable vortices in between the two jets. On the contrary, within the range of 0.6 ≤ w/d &lt; 1.6, the flow field reveals a periodic vortex shedding phenomenon similar to what would be observed in the wake of a two-dimensional bluff body. In this flow regime, the Strouhal number of vortex shedding frequency decreases monotonically with the progressive increase in the jet width. For w/d ≥ 1.6, the periodic vortex shedding is still evident, but the Strouhal number becomes insensitive to the variation of jet width.

Experimental investigations on flow induced vibration of an externally excited flexible plate

Flow-induced vibration of a harmonically actuated flexible plate in the wake of an upstream bluff body is experimentally investigated. The experiments are performed in an open-ended wind tunnel. A flexible plate trailing a bluff body is under fluid induced excitation due to the flowing fluid. The additional external excitation to the trailing plate is applied using an electro-magnetic exciter. The frequency and amplitude of the external harmonic excitation are selected as variable parameters in the experiments and their effect on the plate vibration and is investigated. To know the nature of acoustic pressure wave generated from the vibrating system, near-field acoustic pressure is also measured. A laser vibrometer, a pressure microphone and a high-speed camera are employed to measure the plate vibration, pressure signal, and instantaneous images of the plate motion respectively. The results obtained indicate that the dynamics of the plate is influenced by both the flow-induced excitation and external harmonic excitation. When frequency of the two excitations is close enough, a large vibration level and a high tonal sound pressure are observed. At higher amplitude of external excitation, the frequency component corresponding to the flow-induced excitation is found to reduce significantly in the frequency spectrum of the vibration signal. It is observed that, for certain range of excitation frequency, the plate vibration first reduces, reaches a minimum value and then increases with increase in the level of external excitation. A fair qualitative agreement of the experimental results with numerical simulation result of the past study has been noted. In addition to the experiments, the role of phase difference between the flow-induced excitation generated from the front obstacle and externally applied harmonic excitation is investigated through numerical simulations. The result obtained reveals that the final steady state vibration of the coupled system is independent of the initial phase difference between the two excitations.

A universal three-dimensional instability of the wakes of two-dimensional bluff bodies

Linear stability analysis of a wide range of two-dimensional and axisymmetric bluff-body wakes shows that the first three-dimensional mode to became unstable is always mode E. From the studies presented in this paper, it is speculated to be the universal primary 3D instability, irrespective of the flow configuration. However, since it is a transition from a steady two-dimensional flow, whether this mode can be observed in practice does depend on the nature of the flow set-up. For example, the mode E transition of a circular cylinder wake occurs at a Reynolds number of $\mathit{Re}\simeq 96$, which is considerably higher than the steady to unsteady Hopf bifurcation at $\mathit{Re}\simeq 46$ leading to Bénard–von-Kármán shedding. On the other hand, if the absolute instability responsible for the latter transition is suppressed, by rotating the cylinder or moving it towards a wall, then mode E may become the first transition of the steady flow. A well-known example is flow over a backward-facing step, where this instability is the first global instability to be manifested on the otherwise two-dimensional steady flow. Many other examples are considered in this paper. Exploring this further, a structural stability analysis (Pralits et al.J. Fluid Mech., vol. 730, 2013, pp. 5–18) was conducted for the subset of flows past a rotating cylinder as the rotation rate was varied. For the non-rotating or slowly rotating case, this indicated that the growth rate of the instability mode was sensitive to forcing between the recirculation lobes, while for the rapidly rotating case, it confirmed sensitivity near the cylinder and towards the hyperbolic point. For the non-rotating case, the perturbation, adjoint and structural stability fields, together with the wavelength selection, show some similarities with those of a Crow instability of a counter-rotating vortex pair, at least within the recirculation zones. On the other hand, at much higher rotation rates, Pralits et al. (J. Fluid Mech., vol. 730, 2013, pp. 5–18) have suggested that hyperbolic instability may play a role. However, both instabilities lie on the same continuous solution branch in Reynolds number/rotation-rate parameter space. The results suggest that this particular flow transition at least, and probably others, may have a number of different physical mechanisms supporting their development.

Local stability analysis and eigenvalue sensitivity of reacting bluff-body wakes

This paper presents an experimental and theoretical investigation of high-Reynolds-number low-density reacting wakes near a hydrodynamic Hopf bifurcation. This configuration is applicable to the wake flows that are commonly used to stabilize flames in high-velocity flows. First, an experimental study is conducted to measure the limit-cycle oscillation of this reacting bluff-body wake. The experiment is repeated while independently varying the bluff-body lip velocity and the density ratio across the flame. In all cases, the wake exhibits a sinuous oscillation. Linear stability analysis is performed on the measured time-averaged velocity and density fields. In the first stage of this analysis, a local spatiotemporal stability analysis is performed on the measured time-averaged velocity and density fields. The stability analysis results are compared to the experimental measurement and demonstrate that the local stability analysis correctly captures the influence of the lip-velocity and density-ratio parameters on the sinuous mode. In the second stage of the analysis, the linear direct and adjoint global modes are estimated by combining the local results. The sensitivity of the eigenvalue to changes in intrinsic feedback mechanisms is found by combining the direct and adjoint global modes. This is referred to as the eigenvalue sensitivity throughout the paper for reasons of brevity. The predicted global mode frequency is consistently within 10 % of the measured value, and the linear global mode shape closely resembles the measured nonlinear oscillations. The adjoint global mode reveals that the oscillation is strongly sensitive to open-loop forcing in the shear layers. The eigenvalue sensitivity identifies a wavemaker in the recirculation zone of the wake. A parametric study shows that these regions change little when the density ratio and lip velocity change. In the third stage of the analysis, the stability analysis is repeated for the varicose hydrodynamic mode. Although not physically observed in this unforced flow, the varicose mode can lock into longitudinal acoustic waves and cause thermoacoustic oscillations to occur. The paper shows that the local stability analysis successfully predicts the global hydrodynamic stability characteristics of this flow and shows that experimental data can be post-processed with this method in order to identify the wavemaker regions and the regions that are most sensitive to external forcing, for example from acoustic waves.

Effect of gap flow on the shallow wake of a sharp-edged bluff body – mean velocity fields

ABSTRACTThis experimental study was carried out to investigate the turbulent shallow wake generated by a vertical sharp-edged flat plate suspended in a shallow channel flow with a gap near the bed. The objective of this study is to understand the effect of the gap flow on the wake by studying two different gap heights between the channel bed and the bottom edge of the bluff body. These two cases will be compared to the no-gap case which is considered as a reference case. The maximum flow velocity was 0.45 m/s and the Reynolds number based on the water depth was 45,000. Extensive measurements of the flow field in the vertical mid-plane and in the horizontal near-bed, mid-depth, and near-surface planes were made using particle image velocimetry. This paper is part of an extensive study to characterise the gap-flow effects and is primarily concerned with the mean velocity fields, while a companion paper discusses the turbulence characteristics. The size of the wake identified in the horizontal planes is found to vary in the three planes, where the gap flow enhances the entrainment in the near-wake region in the near-bed velocity field. The results also revealed that, if the gap flow is weak, it is engulfed by the recirculation zone formed just behind the bluff body whose axis is perpendicular to the vertical mid-plane. On the other hand, if the gap flow is relatively strong, it penetrates in the downstream direction and only a portion of it is diverted upward to feed the recirculation zone.

A stratified wake of a hydrofoil accelerating from rest

Wakes of towed and self-propelled bodies in stratified fluids are significantly different from non-stratified wakes. Long time effects of stratification on the development of the wakes of bluff bodies moving at constant speed are well known. In this experimental study we demonstrate how buoyancy affects the initial growth of vortices developing in the wake of a hydrofoil accelerating from rest. Particle image velocimetry measurements were applied to characterize the wake evolution behind a NACA 0015 hydrofoil accelerating in water and for low Reynolds number and relatively strong stable stratified fluid (Re=5000, Fr∼O(1)). The analysis of velocity and vorticity fields, following vortex identification and an estimate of the circulation, reveal that the vortices in the stratified fluid case are stretched along the streamwise direction in the near wake. The momentum thickness profiles show lower momentum thickness values for the stratified late wake compared to the non-stratified wake, implying that the drag on an accelerating hydrofoil in a stratified medium is reduced at the acceleration stage. The findings may improve our ability to predict drag due to maneuvering of micro-air/water-vehicles in stratified conditions.

Characteristics of Flow Structures in the Wake of a Bed-Mounted Bluff Body in Shallow Open Channels

The characteristics of the flow structures observed in the wake of a bluff body mounted vertically on the bed and normal to the flow in a shallow open channel are investigated using detached eddy simulation (DES). The flow structures in the shallow wake are identified using the λ2-criterion. A distinctive feature in the time-averaged flow field, referred to as the owl face of the first kind, is observed. The position of this spiraling structure is stable at locations close to the bed, while its rotation sense switches from stable inward to unstable outward spiraling as it moves toward the free surface, where the bed friction becomes insignificant and the flow develops into a traditional two-dimensional (2D) wake. A three-dimensional (3D) structure resulting from a horizontally oriented secondary roll-up process is observed immediately downstream of the base of the bluff body in the center of the near-wake region. In addition to the horseshoe vortex, a new structure that wraps around the bluff body in the toe region is identified, referred to as a collar vortex. The presence of the coherent structures in the near-bed region is highlighted and their influence on the wake region is discussed.

Temperature Ratio Effects on Bluff-Body Wake Dynamics Using Large Eddy Simulation and Proper Orthogonal Decomposition

In this article, we describe the use of proper orthogonal decomposition (POD) to investigate how the dominant wake structures of a bluff-body-stabilized turbulent premixed flame are affected by the heat released by the flame itself. The investigation uses a validated large eddy simulation (LES) to simulate the dynamics of the bluff-body's wake (Blanchard et al., 2014, “Simulating Bluff-Body Flameholders: On the Use of Proper Orthogonal Decomposition for Wake Dynamics Validation,” ASME J. Eng. Gas Turbines Power, 136(12), p. 122603; Blanchard et al., 2014, “Simulating Bluff-Body Flameholders: On the Use of Proper Orthogonal Decomposition for Combustion Dynamics Validation,” ASME J. Eng. Gas Turbines Power, 136(12), p. 121504). The numerical simulations allow the effect of heat release, shown as the ratio of the burned to unburned temperatures, to be varied independently from the Damköhler number. Five simulations are reported with varying fractions of the heat release ranging from 0% to 100% of the value of the baseline experiment. The results indicate similar trends reported qualitatively by others, but by using POD to isolate the dominant heat release modes of each simulation, the decomposed data can clearly show how the previously reported flow structures transition from asymmetric shedding in the case of zero heat-release to a much weaker, but fully symmetric shedding mode in the case of full heat release with a much more elongated and stable wake.

Flow field in the wake of a bluff body driven through a steady recirculating flow

The wake produced by a bluff body driven through a steady recirculating flow is studied experimentally in a water facility using particle image velocimetry. The bluff body has a rectangular cross section of height, $$H$$ , and width, $$D$$ , such that the aspect ratio, AR = H/D, is equal to 3. The motion of the bluff body is uniform and rectilinear, and corresponds to a Reynolds number based on width, Re D = 9,600. The recirculating flow is confined within a hemicylindrical enclosure and is generated by planar jets emanating from slots of width, $$h$$ , such that $$Re_h=500$$ . Under these conditions, experiments are performed in a closed-loop facility that enables complete optical access to the near-wake. Velocity fields are obtained up to a distance of $$13D$$ downstream of the moving body. Data include a selection of phase-averaged velocity fields representative of the wake for a baseline case (no recirculation) and an interaction case (with recirculation). Results indicate that the transient downwash flow typically observed in wakes behind finite bodies of small aspect ratio is significantly perturbed by the recirculating flow. The wake is displaced from the ground plane and exhibits a shorter recirculation zone downstream of the body. In summary, it was found that the interaction between a bluff body wake and a recirculating flow pattern alters profoundly the dynamics of the wake, which has implications on scalar transport in the wake.

Stabilisation of the Absolute Instability of a Flow Past a Cylinder via Spanwise Forcing at Re = 180

Vortex shedding in the wake of bluff bodies is often an undesired phenomenon which generates unsteady loads, vibrations and fluctuations of the aerodynamic forces. Consequently, the attenuation or suppression of the self-sustained oscillations associated to the vortex shedding is a fundamental problem in a wide range of engineering applications. Three-dimensional control techniques to control the vortex shedding are characterised by a variation of the control input along the spanwise direction and offer a promising methodology due to their versatility and high potential efficiency 1. In the present paper, the control of vortex dynamics of the wake of a flow past a cylinder at Reynolds number Re = 180 is performed by means of spanwise distributed forcing 1 2; starting from a fully developed shedding, a sufficiently high spanwise forcing is introduced on the surface of the cylinder, close to the separation regions, to stabilise the near-wake in a time-independent state, similarly to the effect of a sinusoidal stagnation surface 3,4. The effects of the forcing on the drag reduction and the dynamics of the vorticity have been investigated using a spanwise gaussian forcing, which generates a significant redistribution of the spanwise vorticity into streamwise and vertical components was ob- served, leading to a minor susceptibility of the three-dimensional shear layers to roll-up into the vortex street 4? . An insight into the main physical mechanisms underlying the suppression is provided by the hydrodynamic stability theory. Three different regimes were found for different forcing amplitude and the computation of the leading modes helps to shed light on some mechanisms responsible for the suppression of the Von-Karman shedding.

Structure and dynamics of the wake of a reacting jet injected into a swirling, vitiated crossflow in a staged combustion system

Secondary injection of the fuel, also referred to as staged combustion, is being studied by gas turbine manufacturers as a means of increasing the power output of the gas turbine systems with minimal contribution to NO x emission. A reacting jet issuing into a swirling, vitiated crossflow operating at gas turbine relevant conditions was investigated as a means of secondary injection. In this study, the flow field of the reacting jet was investigated using high repetition rate (HRR) (5 kHz), two-component particle imaging velocimetry and OH-PLIF. In applications similar to the one currently studied in this work, viz. secondary injection of fuel in a gas turbine combustor, rapid mixing and chemical reaction in the near field of jet injection are desirable. Based on our analysis, it is hypothesized that the shear layer and wake field vortices play a significant role in stabilizing a steady reaction front within the near wake region of the jet. Premixed jets composed of natural gas and air were injected through an extended nozzle into the vitiated flow downstream of a low-swirl burner that produced the vitiated, swirled flow. The jet-to-crossflow momentum flux ratio was varied to study the corresponding effect on the flow field. The time-averaged flow field shows a steady wake vortex very similar to that seen in the wake of a cylindrical bluff body which helps to stabilize the reaction zone within the wake of the jet. The HRR data acquisition also provided temporally resolved information on the transient structure of the wake flow associated with the reacting jet in crossflow.

Low-order modeling of wind farm aerodynamics using leaky Rankine bodies

We develop and characterize a low-order model of the mean flow through an array of vertical-axis wind turbines (VAWTs), consisting of a uniform flow and pairs of potential sources and sinks to represent each VAWT. The source and sink in each pair are of unequal strength, thereby forming a “leaky Rankine body” (LRB). In contrast to a classical Rankine body, which forms closed streamlines around a bluff body in potential flow, the LRB streamlines have a qualitatively similar appearance to a separated bluff body wake; hence, the LRB concept is used presently to model the VAWT wake. The relative strengths of the source and sink are determined from first principles analysis of an actuator disk model of the VAWTs. The LRB model is compared with field measurements of various VAWT array configurations measured over a 3-yr campaign. It is found that the LRB model correctly predicts the ranking of array performances to within statistical certainty. Furthermore, by using the LRB model to predict the flow around two-turbine and three-turbine arrays, we show that there are two competing fluid dynamic mechanisms that contribute to the overall array performance: turbine blockage, which locally accelerates the flow; and turbine wake formation, which locally decelerates the flow as energy is extracted. A key advantage of the LRB model is that optimal turbine array configurations can be found with significantly less computational expense than higher fidelity numerical simulations of the flow and much more rapidly than in experiments.

Effects of weak noise on oscillating flows: Linking quality factor, Floquet modes, and Koopman spectrum

Many fluid flows, such as bluff body wakes, exhibit stable self-sustained oscillations for a wide range of parameters. Here we study the effect of weak noise on such flows. In the presence of noise, a flow with self-sustained oscillations is characterized not only by its period, but also by the quality factor. This measure gives an estimation of the number of oscillations over which periodicity is maintained. Using a recent theory [P. Gaspard, J. Stat. Phys. 106, 57 (2002)], we report on two observations. First, for weak noise the quality factor can be approximated using a linear Floquet analysis of the deterministic system; its size is inversely proportional to the inner-product between first direct and adjoint Floquet vectors. Second, the quality factor can readily be observed from the spectrum of evolution operators. This has consequences for Koopman/Dynamic mode decomposition analyses, which extract coherent structures associated with different frequencies from numerical or experimental flows. In particular, the presence of noise induces a damping on the eigenvalues, which increases quadratically with the frequency and linearly with the noise amplitude.

Experimental Closed-Loop Flow Control of a von Kármán Ogive at High Incidence

The asymmetric vortex regime of a von Kármán ogive with a fineness ratio of 3.5 is experimentally studied at a Reynolds number of 156,000. The wake of an axisymmetric bluff body is an ideal candidate for active feedback flow control because minute fluidic disturbances and geometry perturbations near the tip of the ogive get amplified through the flow’s convective instability. The resulting disturbance interacts with the quasi-steady vortex location and produces a deterministic port or starboard asymmetric vortex state (i.e., side force). Accurate control or manipulation of this asymmetric vortex state holds the potential for increased maneuverability and stability characteristics of slender flight vehicles. For implementation of an active feedback flow-control system, plasma actuators at the tip of the ogive are used as the flow effector, and surface-mounted pressure sensors are used to estimate the vortex configuration in real time. A linear time invariant model developed from open-loop experimental tests and a proportional-integral control law are used to close the loop in the experimental setting. Closed-loop experimentation shows the ability to arbitrarily track a side force set point while also suppressing low-frequency fluctuations. Thus, the adopted model-based feedback flow-control approach is validated experimentally for a complex, three-dimensional flow.