Session FN: Jet and Wake Instabilities I

Suppressed wake transition and vortex lock-on phenomena in a perturbed flow past a circular cylinder at Re = 220

Direct numerical simulation (DNS) is performed to investigate the change of vortex structure and lock-on phenomena in the wake of a circular cylinder disturbed by sinusoidal perturbation at the Reynolds number of 220 (A-mode instability regime). The sinusoidal perturbation, of which the frequency is near twice the natural shedding frequency, is superimposed on the free stream velocity. The power spectra of the streamwise velocity signal and orthogonal enstrophy are investigated to analyze the change of vortex structure. It is observed that the wake transition behind the circular cylinder can be suppressed due to the sinusoidal perturbation. And this change causes the jump of the Strouhal number from the value corresponding to A-mode instability regime to the value corresponding to retarded wake transition regime (extrapolated from laminar shedding regime) in the Strouhal-Reynolds number relationship. As a result, the vortex shedding frequency is locked on the perturbation frequency depending not on the natural shedding frequency but on the modified shedding frequency.   

Open-loop and closed-loop excitation of the wake behind a circular cylinder

Both open loop and closed loop control were used to modify the flow around a circular cylinder at Re = 20,000. Independent plasma actuators were installed on the sides of the cylinder at +/- 90$^{\circ}$ from the forward stagnation line. The actuators could be excited in-phase or 180$^{\circ}$ out of phase with one another. In the case of open-loop forcing, in-phase excitation at twice the von Karman vortex shedding frequency produced large changes in the wake structure, similar to the experiments done by Williams, Mansy {\&} Amato (JFM, 1992.) Negligible changes in wake structure occurred when the out-of-phase actuation was used, although the lock-on phenomenon was observed, suggesting that the wake structure modification resulting from the interaction between the forcing field and near wake is independent of Reynolds number. Closed-loop excitation using a proportional-derivative controller was done using a hot-film probe positioned at x/D=1.5, y/D = 1.5. The amplitude of the wake oscillation was shown to be sensitive to both the gain and phase of the controller. The amplitude of oscillations at a fixed controller gain are enhanced or suppressed relative to the non-forced level, depending on the controller phase. The vortex shedding frequency is changed when the PD controller is in a region of suppression. The expert assistance of SSgt. Mary S. Church is gratefully acknowledged.   

Global stability analysis of the flow behind an axisymmetric blunt based body

A three-dimensional global mode linear analysis of the flow behind an axisymmetric blunt-based body is numerically investigated. The two-dimensional steady base flow is obtained from time-dependent simulations based on a finite-element spatial discretization and a Lagrange-Galerkin temporal discretization. The generalized eigenvalue problem is solved by use of the Implicitly Restarted Arnoldi method. We show that a helical (m=1) non-oscillating mode, whose eigenmode is mainly located in the recirculating area, becomes unstable at a critical Reynolds number Re=295, and that a helical oscillating mode, whose eigenmode exhibits the spatially periodic downstream structure characteristic of the oscillatory wake instability, becomes unstable at a supercritical Reynolds number Re=409 with a frequency fD/U$_{\infty }$=0.14. As a step to address the relevance of the second bifurcation, we then consider the non-linear saturation amplitude of the non-oscillating mode by solving the amplitude equation associated with the first bifurcation.   

Dynamics and control of hydrofoil wakes

The problem of rotor-stator interaction has been an issue in the turbomachinery field for more than forty years. Manipulation of the stator wakes is one method to minimize the problem. In order to explore this concept, a comprehensive experimental program was carried out in a water tunnel utilizing a series of NACA 0015 hydrofoils. Baseline wake data were collected with a hydraulically smooth foil and compared with various foil modifications including foils covered with riblet tape aligned both span wise and parallel to the main flow, and a foil modified with 3 mm high and 10 mm total length vortex generators (VG), spaced 10 mm apart span wise, that were positioned close to the trailing edge of the foil. Not only was the effect of the modifications on wake spreading investigated but also the effect on wake dynamics such as vortex shedding was studied. PIV has been used for mapping the near wake region extending roughly 1 chord-length (1c) downstream the trailing edge over a range of angle of attack. The results show, as expected, that wake dynamics and wake characteristics such as maximum deficit and width, scale with average drag. It was demonstrated that the use of vortex generators would improve both the dynamics and spreading characteristics of the wake.   

Vortical Structure in the Near Wake of a Bluff Body and its Relationship to Base Pressure

The pressure on the base of a bluff body is known to be directly linked to the dynamic behavior of the vortical structures in the wake of the body. Recently, experimental results have shown that modifying the boundary layer state at the separation can have a large effect on the base pressures observed. To quantify the changes in the wake that correspond to changes in the separating boundary layer, two-dimensional PIV has been used to measure the velocity field in the near wake. Proper Orthogonal Decomposition (POD) is applied to identify changes in the vortical structure shed by the bluff body. The results indicate that, in some cases, the thickening of the separating boundary layer increases the base pressure with a notable change in the vortex structures shed. In other cases, thickening of the boundary layer produced little or no change to the base pressure. Although all cases investigated showed a dominance of the first two spatial POD modes, the cases with thicker separating boundary layers exhibit a much higher fraction of fluctuating energy in the first two modes.   

On the stabilization of bluff-body wakes by low-density base bleed

Base bleed is a simple and well-known means of stabilizing bluff-body wakes at supercritical Reynolds numbers. In the present research we consider a generalization of previous works by studying the effect of the bleed-to-freestream density ratio, $S=\rho_b/\rho_\infty$, on the stability properties of the wake behind an axisymmetric, slender body with a blunt trailing edge. Since a lower density in the slow stream is known to inhibit absolute instability, here we restrict our attention to the case of light bleed fluid, $S<1$. This mechanism is shown to inhibit the wake for values of the bleed coefficient, defined as the bleed-to-freestream velocity ratio $C_b=u_b/u_\infty$, smaller than those obtained in the homogeneous case of $S=1$. Our approach consists of obtaining the basic, axisymmetric flow by integration of the full set of Navier-Stokes and species conservation equations in cylindrical coordinates, and calculating its linear, local, spatio-temporal stability downstream of the body base. The analysis predicts a critical bleed coefficient $C_b^*$, which decreases with the density ratio according to the linear law $C_b^*\simeq 0.01+0.05\,S$ for $0.1\le S\le 1$.   

Initial- value problem for the two-dimensional growing wake

A general three-dimensional initial-value perturbation problem is investigated as to effects in a two-dimensional but growing wake. The linearized perturbation analysis considers both the early transient as well as the asymptotic behavior of the disturbance (Blossey, Criminale \& Fisher, JFM 2006 submitted). The representation of the mean flow is physically accurate, since it has been obtained by considering the lateral entrainment process and associated streamwise evolution of mass flow (increase) and kinetic energy (decrease) (Tordella \& Belan, PoF 2003). This base model is combined with a change of coordinate (moving coordinate trasform) (Criminale \& Drazin, Stud. Appl. Math, 1990). The evolution analysis considers inviscid disturbances that are expanded in terms of small values of the wavenumber. The long time behavior is represented by means of a multiple spatial and temporal scale description of the velocity and vorticity perturbations. The limit for small wavenumbers has been studied. It is seen that an increase of the entrainment in the base flow yields instability and grows algebraically in time. This result is also obtained when considering a more general problem where larger wavenumbers, wavelengths of the order of the thickness of the variable shear region, are allowed. Comparison with a recent spatio-temporal multiscale Orr-Sommerfeld analysis of the 2D wake instability (Tordella, Scarsoglio \& Belan, PoF 2006). is presented. The perturbation dynamics is examined for different base flow configurations.   

3D vortical structures of wake behind a ring with helical disturbances

Wakes behind a circular ring with/without helical disturbances were investigated. Cross-section of the ring was rectangular, and $D/W=5$, where $D$ is outer diameter and $W$ is radial width of the ring. Reynolds number based on $W$ was order of 100. Stereo-PIV was used to measure the three-component of velocity vectors in a plane normal to the free-stream direction. Taylor’s frozen field hypothesis was applied to reconstruct three-dimensional vorticity field. Under the unexcited condition, a series of vortex ring were shed from outer and inner side of the ring. In the case of $Re>200$, streamwise vortices connecting successive vortex rings were observed. Above $Re=300$ a recirculation zone was formed just behind the ring. Under the excited condition, where the ring was slightly tilted and direction of the tilting was rotated in time around the center of the ring, helical vortex structures were observed. In this case, the recirculation zone was not formed and drag applied to the ring was approximately 10\% higher than the unexcited case.   

A physical mechanism for the primary instability of axysymmetric wakes past bluff bodies

The occurrence of the primary instability of the axisymmetric wake past an oblate bubble with a stress-free condition at its surface was studied by means of DNS (Magnaudet \& Mougin, J. Fluid Mech. in press). The results suggest that the base flow becomes unstable when the derivative of the vorticity in the direction perpendicular to the symmetry axis vanishes within a small subregion of the near wake where the iso- vorticity lines have to turn sharply. Existence of this region is specific to axisymmetric flows and results from the combination of the Prandtl-Batchelor constraint within the standing eddy and the condition of weak vorticity on the rear part of the body surface. Examination of the azimuthal vorticity balance indeed suggests that the flow cannot remain stable at high enough Reynolds number when the above condition is fulfilled. The generality of this mechanism is discussed.   

Free fall of a M\"{o}bius band.

A M\"{o}bius band is a 3D surface with the particular feature of having only one side and one edge. A simple geometrical model consists of a circular centerline, and surface elements which are locally tangent to this line and continuously twist around it, completing one half turn going once around the circle. From an aerodynamic perspective, such a M\"{o}bius strip presents a profile that is locally a flat plate with an angle of attack smoothly varying between -90 and 90 degrees, and this regardless of the orientation of the object. Clearly a most peculiar bluff body and irresistible to being studied, in this presentation for its free fall trajectory, body motion and wake dynamics. The governing parameters are the Reynolds number based on the width of the band and the average descent speed, the aspect ratio (perimeter / width) and the mass ratio (band density / fluid density). Free-fall experiments were carried out at low Reynolds numbers in a water tank with M\"{o}bius bands made of different plastic materials, having aspect ratio 14 and mass ratios of around 1.2. The band is found to rapidly adopt a bluff leading edge orientation and to follow a spiral path with an independent frequency of pitching.