Passive Control of the Vortex Wake Past a Flat Plate at Incidence

A passive control, based on wall suction acting at the leading edge, is proposed to stabilize the vortex shedding from a flat plate at incidence. The correct suction amount is determined by a potential flow model where the large-scale vortical structures formed near the plate edges are represented by point vortices of variable intensity, and the wall suction by an adequately placed sink. We concentrate on the case of a plate that is broadside to the flow and show that the stabilization of the vortex wake can be obtained by simple passive backside suction. In such a case geometric shaping and passive suction have similar effects on the vortex Hamiltonian. The model predictions compare well with the results obtained by blob-vortex simulations, thus confirming the stabilization of the unsteady wake past the plate. Received 5 April 2002 and accepted 6 August 2002 Published online 3 December 2002 Communicated by M.Y. Hussaini     

Nonlinear interaction of a large vortex with a boundary layer

The nonlinear problem of boundary layer instability under the influence of a plane vortex is investigated for high Reynolds numbers. The vortex occupies the entire thickness of the boundary layer and has a longitudinal dimension of the order of the Tollmien-Schlichting wavelength. The initial vortex is rapidly swept away by the flow, inducing a Stokes layer near the surface of the plate. Expanding, this layer reaches the dimensions of the viscous sublayer of free interaction theory, where wave packet generation takes place. In the case in question a feature of the nonlinear stage of development of the disturbances is the formation of a concentrated vortex, which arises in the Stokes layer and grows rapidly, whereas the wave packet propagated ahead of it remains linear. From the calculations there emerges a tendency for the new vortex to be formed above the wail, whereas the maximum vorticity of the vortex generated in the Stokes layer corresponds to the wall itself.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 70–77, January–February, 1993.The authors are grateful to V. V. Kozlov for his interest in their work.     

Reynolds number effects on leading edge vortex development on a waving wing

The waving wing experiment is a fully three-dimensional simplification of the flapping wing motion observed in nature. The spanwise velocity gradient and wing starting and stopping acceleration that exist on an insect-like flapping wing are generated by rotational motion of a finite span wing. The flow development around a waving wing at Reynolds number between 10,000 and 60,000 has been studied using flow visualization and high-speed PIV to capture the unsteady velocity field. Lift and drag forces have been measured over a range of angles of attack, and the lift curve shape was similar in all cases. A transient high-lift peak approximately 1.5 times the quasi-steady value occurred in the first chord length of travel, caused by the formation of a strong attached leading edge vortex. This vortex appears to develop and shed more quickly at lower Reynolds numbers. The circulation of the leading edge vortex has been measured and agrees well with force data.     

Acoustic waves emitted by a vortex ring passing near a wedge-like plate

Acoustic waves emitted by a vortex ring moving near a thin wedge-like plate of finite width have been studied. The experiments are performed for three configurations: the plate (A) is held edgeways to the direction of the vortex motion, (B) is held sideways to the direction, and (C) is held edgeways at an angle of 45° against the vortex motion. The observed sound wave is of dipole radiation type, and the magnitude of the pressure is large in the direction of the normal to the plate plane and small in parallel. The observed pressure is proportional to the third power of the vortex speed. The instantaneous force exerted on the plate by the vortex motion has also been examined. The force vector is mainly normal to the plate plane. The observed profiles agree within a reasonable degree of accuracy with the theoretical ones calculated for the vortex ring interacting with the flat plate of thickness zero.     

Vortex dynamics of a sphere wake in proximity to a wall

Toward getting the vortex dynamics characteristics and wake structure of a sphere in proximity to a wall, the effect of a proximal flat plate on the wake of a stationary sphere is investigated via direct numerical simulation. The vortex shedding process and the significant variation of the wake structure are described in detail. The drag coefficient reduces and the wake structure of the sphere becomes complex due to the combined effect of the wake flow and the wall. A jet flow forms between the sphere and the flat plate, which suppresses the vortex separation on the bottom of the sphere. The asymmetric distributions of the coherent structures and the recirculation region behind the sphere are discussed. Besides vortex shedding patterns, the time-averaged velocity distribution, vortex dynamics, distribution regularities of turbulent kinetic energy and enstrophy are investigated.     

Effect of a Thin Longitudinal Inviscid Vortex on a Two-Dimensional Pre-Separation Boundary Layer

For large Reynolds numbers, an asymptotic solution of the Navier-Stokes equations describing the effect of a thin longitudinal vortex with a constant circulation on the development of an incompressible steady two-dimensional laminar boundary layer on a flat plate is obtained. It is established that, in a narrow wall region extending along the vortex filament, the viscous flow is described by the 3-D boundary layer equations. A solution of these equations for small values of the vortex circulation is studied. It is found that the solution of the two-dimensional pre-separation boundary layer equations collapses. This is attributable to the singular behavior of the 3-D disturbances near the zero-longitudinal-friction points.     

VORTEX BREAKDOWN FROM A PITCHING DELTA WING INCIDENT UPON A PLATE: FLOW STRUCTURE AS THE ORIGIN OF BUFFET LOADING

A delta wing is subjected to both static and dynamic variations of angle-of-attack; the vortices from the wing impinge upon a stationary plate. A technique of high-image-density particle image velocimetry is employed to compare the patterns of vortex development with and without the impingement plate. For the limiting case of static variations of angle-of-attack, the presence of the plate exerts a large influence on the onset of vortex breakdown. In contrast, dynamic (unsteady) variation of angle-of-attack yields changes of breakdown location that are generally similar for cases with and without the impingement plate. The detailed structure of the vortex breakdown-plate interaction is represented by patterns of instantaneous velocity and vorticity, which serve as the origin of buffet-induced loading of the surface of the plate.     

Study on multiple ring-like vortex formation and small vortex generation in late flow transition on a flat plate

A high-order direct numerical simulation (DNS) of flow transition over a flat plate at a free stream Mach number 0.5 has been carried out. During the simulation, we cannot find, according to the classical theory of boundary layer transition, the “hairpin vortex breakdown to smaller structures” in the last stage of flow transition on a flat plate. However, we did discover the so-called spikes as a result of a multibridge or multiring formation. This indicated a large and stable vortex structure which can travel for a long distance. We believe that this is a result of ring heads that are located in an inviscid region. These heads of the “turbulence spot” never seem to break down and persist as a stable structure. In addition, we discovered that the U-shaped vortex is a part of an existing coherent structure instead of a newly generated one. The U-shaped vortex also provides an additional channel to transfer vorticity to the ring from the wall. During travel, the leading primary ring in the front of the spot is sloped and skewed, causing disappearance of the second sweep. As a consequence, no energy is brought down to the lower boundary layer near the vortex ring head of the spot. Thus, the small length scale structures become damped and the existing U-shaped vortex structure becomes distinguishable. So, the question is where do the turbulent small length scale vortices come from? We will address this with a new theory which states that all of small length scales (turbulence) are generated by high-shear (HS) layers rather than being produced by “vortex breakdown.” The new DNS shows that the HS layers are produced by strong positive spikes surrounded by low-speed fluids and by the interaction between the secondary and higher-level vortices and the wall surface especially near the ring neck. This multiple ring-like vortex generation also follows the first Helmholtz vortex conservation law. Furthermore, the Λ-shaped vortex is formed and rolling up, and the Λ-vortex is stretched and narrowed, and a new bridge is generated after the neck. The bridge will further become a second ring and so on. Besides the original vortex legs, there are also U-shaped vortex tubes. Finally, the multiple ring vortex structure is formed. From this process, no evidence is found to support that two consequent multiring circles are mixed to generate small vortices. The connection of downdraft/updraft motions is also studied.     

The flexibility effect of a plate according to various angles of attack in a free-stream

This paper presents a computational fluid–structure interaction analysis for a flexible plate in a free-stream to investigate the effects of flexibility and angle of attack on force generation. A Lattice Boltzmann Method with an immersed boundary technique using a direct forcing scheme model of the fluid is coupled to a finite element model with rectangular bending elements. We investigated the effects of various angles of attack of a flexible plate fixed at one of the end edges in a free-stream at a Reynolds number of 5000, which represents the wing flapping condition of insects and small birds in nature. The lift of the flexible plate is maintained at the large angle of attack, whereas the rigid plate shows the largest lift at angles of attack around 30–40° and then drastic reductions in the lift at the large angle of attack. If we consider the efficiency as the lift divided by the drag, the flexible plate shows better efficiency at angles of attack greater than 30° compared to the rigid plate. The better performance of the flexible plate at large angles of attack comes from the deformation of the plate, which produces an interaction between the trailing edge vortex and the short edge vortex. The horseshoe-shaped vortex produced by a large vortex interaction at the trailing edge side has an important role in increasing the lift, and the small projection area due to the deformation reduces the drag. Furthermore, we investigate the role of flexibility on the lift and the drag force of the rectangular plate in a free-stream as the Reynolds number increases. Whenever a large vortex interaction at the trailing edge side is shown, the efficiency of the rectangular plate is improved. Especially, the flexible plate shows better efficiency as the Reynolds number increases regardless of the angle of attack.     

Evolution of an initially columnar vortex terminating normal to a no-slip wall

The early evolution of an initially columnar vortex normal to a solid wall was examined. The vortex was generated by a pair of flaps in a water tank. Detrimental effects from the wall during the vortex generation were avoided by producing the vortex normal to a free surface and subsequently bringing a horizontal plate into contact with the surface. Digital particle image velocimetry (DPIV) measurements of the velocity and vorticity, together with laser induced fluorescence (LIF) visualizations, in a meridional plane revealed a toroidal structure with the appearance of an axisymmetric vortex breakdown bubble. Agreement was found between the measurements and numerical simulations of the axisymmetric Navier–Stokes equations. The results show that the flow in the effusive corner region is dominated by a Bödewadt-type spatially oscillatory boundary layer within the core region and a potential-like vortex boundary layer at large radii. The toroidal structure results from the interaction between these two boundary layers, leading to the roll up of a dominant shear layer within the Bödewadt structure, and does not develop from the columnar vortex itself.     

Wind-Up of a Spanwise Vortex in Deepening Transition and Stall

A fundamental flow problem of unsteady wind-up of a spanwise vortex is studied in this theoretical work on deepening dynamic stall and transition in a boundary layer, internal layer or related unsteady motion. It examines the nonlinear evolution of the spanwise vortex produced when the local wall pressure develops a maximum or minimum, subsequent to the finite-time break-up of an interacting layer and the impact of normal pressure gradients. The evolution is controlled by an inner–outer interaction between the effects of the normal pressure gradient and the momentum jumps across and outside the vortex, which is situated near the strong inflexion point induced in the mean flow. Although the work concentrates on a particular internal-flow context, many of the flow properties found are generic and in particular apply for a more general case including external flows. Analysis and associated computations point to two main distinct trends in the vortex response, depending to a large extent on a parameter gauging the relative strengths of the above effects. The response is either an explosive one, provoking enhanced wind-up, growth and pressure in the vortex, or it is implosive, causing the vortex to shrink and virtually empty itself through unwinding, leaving little local pressure variation. A further discussion includes the after-effects of this vortex response and some of the connections with experiments and direct computations on deepening stall and transition. Received 22 February 1999 and accepted 28 March 2000     

Aeroelastic analysis of large horizontal wind turbine baldes

A nonlinear aeroelastic analysis method for large horizontal wind turbines is described. A vortex wake method and a nonlinear finite element method (FEM) are coupled in the approach. The vortex wake method is used to predict wind turbine aerodynamic loads of a wind turbine, and a three-dimensional (3D) shell model is built for the rotor. Average aerodynamic forces along the azimuth are applied to the structural model, and the nonlinear static aeroelastic behaviors are computed. The wind rotor modes are obtained at the static aeroelastic status by linearizing the coupled equations. The static aeroelastic performance and dynamic aeroelastic responses are calculated for the NH1500 wind turbine. The results show that structural geometrical nonlinearities significantly reduce displacements and vibration amplitudes of the wind turbine blades. Therefore, structural geometrical nonlinearities cannot be neglected both in the static aeroelastic analysis and dynamic aeroelastic analysis.     

Vortex formation and saturation for low-aspect-ratio rotating flat-plate fins

We investigate experimentally the unsteady, three-dimensional vortex formation of low-aspect-ratio, trapezoidal flat-plate fins undergoing rotation from rest at a 90° angle of attack and Reynolds numbers of O(10³). The objectives are to characterize the unsteady three-dimensional vortex structure, examine vortex saturation, and understand the effects of the root-to-tip flow for different velocity programs. The experiments are conducted in a water tank facility, and the diagnostic tools are dye flow visualization and digital particle image velocimetry. The dye visualizations show that the low-aspect-ratio plate produces symmetric ring-like vortices comprised mainly of tip-edge vorticity. They also indicate the presence of the root-to-tip velocity. For large rotational amplitudes, the primary ring-like vortex sheds and a secondary ring-like vortex is generated while the plate is still in motion, indicating saturation of the leading vortex. The time-varying vortex circulation in the flow symmetry plane provides quantitative evidence of vortex saturation. The phenomenon of saturation is observed for several plate velocity programs. The temporal development of the vortex circulation is often complex, which prevents an objective determination of an exact saturation time. This is the result of an interaction between the developing vortex and the root-to-tip flow, which breaks apart the vortex. However, it is possible to define a range of time during which the vortex reaches saturation. A formation-parameter definition is investigated and is found to reasonably predict the state corresponding to the pinch-off of the initial tip vortex across the velocity programs tested. This event is the lower bound on the saturation time range.     

Intermittency in a cantilever plate in a randomly fluctuating fluid flow

Fluid–elastic systems nearing dynamic instabilities are known to be sensitive to fluctuations in fluid flow. A cantilever plate in axial flow with random temporal fluctuations, is examined numerically for its dynamical behaviour. The numerical model comprises of a nonlinear structural model for the flexible plate, coupled with unsteady lumped vortex model for the fluid forces. As the mean flow velocity is increased, the system transitions to limit cycle oscillations from a state of rest, through a regime of intermittent oscillations. The conditions for onset and disappearance of intermittency are discussed and are interpreted using stochastic bifurcation theories. While the onset of intermittency is found to be unaffected by the time scales of the flow fluctuations, they are observed to affect the length of the intermittency regime. The effect of plate flexibility on intermittency is also discussed.     

Point vortex model of the unsteady separated flow past a semi-infinite plate with transverse motion

Two-dimensional unsteady separated flow past a semi-infinite plate with transverse motion is considered. The rolling-up of the separated shear-layer is modelled by a point vortex whose time-dependent circulation is predicted by an unsteady Kutta condition. A power-law starting flow is assumed along with a power law for the transverse motion. The effects of the motion of the plate on the starting vortex circulation and trajectory are presented. A suitable vortex shedding mechanism is introduced and a class of flows involving several vortices is presented. Finally, some possibilities for actively controlling the production of circulation by moving the plate are discussed.     

Vortex structure simulation for supersonic mixing layers using nonlinear PSE method

The method of nonlinear parabolized stability equations (PSE) is applied in the simulation of vortex structures in compressible mixing layer. The spatially-evolving unstable waves, which dominate the vortex structure, are investigated through spatial marching method. The instantaneous flow field is obtained by adding the harmonic waves to basic flow. The results show that T-S waves do not keep growing exponentially as the linear evolution, the energy transfer to high order harmonic modes, and that finally all harmonic modes get saturated due to nonlinear interaction. The mean flow distortion induced by the nonlinear interaction between the harmonic modes and their conjugate harmonic ones, makes great change of the average flow and increases the thickness of mixing layer. PSE methods can well capture the two- and three-dimensional large scale nonlinear vortex structures in mixing layers such as vortex roll-up, vortex pairing, and Λ vortex.     

The effect of a single vortex generator jet on the characteristics of a turbulent boundary layer

A flat plate experiment was performed in a water tunnel to determine the effects of a vortex generator jet on the characteristics of a turbulent boundary layer at various wall normal locations. The results show that the characteristic distributions of the turbulent fluctuation quantities are nearly unaffected by the induced vortex structures neither in the steady nor in the dynamic blowing case. The shear layer interaction between the turbulent main flow and the jet flow produces less turbulent fluctuations than it is expected from a turbulent free jet flow. Thus, the mixing process of this flow control strategy is based only on a large-scale momentum transport superimposed by the turbulent fluctuation quantities. This allows a separation of scales for physical interpretation and numerical simulations.     

Controlling supersonic boundary layer stability by means of distributed mass transfer through a porous wall

The interaction between disturbances in a compressible boundary layer in the presence of distributed mass transfer (injection or suction) through a permeable porous wall is considered in the linear and nonlinear approximations (weakly nonlinear stability theory). The regimes of moderate and high supersonic velocities (Mach numbers M = 2 and 5.35) are studied. The boundary conditions for the disturbances on a permeable wall are derived with account for the gas compressibility in pores and the presence of a suction chamber. Maximum pore dimensions, at which the surface properties have no effect on the disturbance characteristics, which are stabilized upon suction and destabilized upon injection, are determined. When the surface properties are taken into account, intense growth of the first-mode vortex disturbances occurs, which can completely undo the stabilizing effect of the suction. Injection leads to the vortex and acoustic mode destabilization on the linear range and the enhancement of the nonlinear processes on the transitional range.     

Experimental identification of hardening and softening nonlinearity in circular laminated plates

This work investigates nonlinear characteristics of a circular laminated plate. A nonparametric identification method based on the Hilbert transform is applied to identify the nonlinear system. The results demonstrate that the force–displacement curve has a soft nonlinear characteristic under small displacements and a hard nonlinear characteristic under large displacements. The force–velocity curve also has a soft nonlinear characteristic. A circular isotropic plate is treated to test the method. The force-state method is adopted to confirm the identification results. The effects of the plate diameter are examined. A combination of a cubic polynomial and a hyperbolic tangent function is proposed to fit the experiment data. The fitting results are verified by time domain simulations under random excitations. The work illustrates some novel nonlinear characteristics in transverse vibration of a circular laminated plate via a nonlinear system identification process.     

An experimental and numerical study of heave added mass and damping of horizontally submerged and perforated rectangular plates

Forced harmonic heave motions of horizontally submerged and perforated rectangular plates are studied experimentally and numerically at both a deep and shallow submergence. The steady-state vertical forces are expressed in terms of added mass and damping coefficients. The numerical results are partly obtained by combining potential flow with linear free-surface conditions and a nonlinear viscous pressure loss condition at the mean oscillatory plate position. A domain decomposition technique is applied with a boundary element method in the inner domain and an analytical representation of the velocity potential in the outer domain. A drag term accounts for the vortex shedding at the outer plate edges. The numerically predicted Keulegan–Carpenter number dependent heave added mass and damping coefficients agree reasonably with experimental values, in particular for the deeper submergence.