Showing papers on "Starting vortex published in 2003"

The influence of wing-wake interactions on the production of aerodynamic forces in flapping flight

Abstract: We used two-dimensional digital particle image velocimetry (DPIV) to visualize flow patterns around the flapping wing of a dynamically scaled robot for a series of reciprocating strokes starting from rest. The base of the wing was equipped with strain gauges so that the pattern of fluid motion could be directly compared with the time history of force production. The results show that the development and shedding of vortices throughout each stroke are highly stereotyped and influence force generation in subsequent strokes. When a wing starts from rest, it generates a transient force as the leading edge vortex (LEV) grows. This early peak, previously attributed to added-mass acceleration, is not amenable to quasi-steady models but corresponds well to calculations based on the time derivative of the first moment of vorticity within a sectional slice of fluid. Forces decay to a stable level as the LEV reaches a constant size and remains attached throughout most of the stroke. The LEV grows as the wing supinates prior to stroke reversal, accompanied by an increase in total force. At stroke reversal, both the LEV and a rotational starting vortex (RSV) are shed into the wake, forming a counter-rotating pair that directs a jet of fluid towards the underside of the wing at the start of the next stroke. We isolated the aerodynamic influence of the wake by subtracting forces and flow fields generated in the first stroke, when the wake is just developing, from those produced during the fourth stroke, when the pattern of both the forces and wake dynamics has reached a limit cycle. This technique identified two effects of the wake on force production by the wing: an early augmentation followed by a small attenuation. The later decrease in force is consistent with the influence of a decreased aerodynamic angle of attack on translational forces caused by downwash within the wake and is well explained by a quasi-steady model. The early effect of the wake is not well approximated by a quasi-steady model, even when the magnitude and orientation of the instantaneous velocity field are taken into account. Thus, the wake capture force represents a truly unsteady phenomenon dependent on temporal changes in the distribution and magnitude of vorticity during stroke reversal.

The significance of vortex ring formation to the impulse and thrust of a starting jet

Abstract: The recent work of Gharib, Rambod, and Shariff [J. Fluid Mech. 360, 121 (1998)] studied vortex rings formed by starting jets generated using a piston-cylinder mechanism. Their results showed that vortex rings generated from starting jets stop forming and pinch off from the generating jet for sufficiently large values of the piston stroke to diameter ratio (L/D), suggesting a maximization principle may exist for propulsion utilizing starting jets. The importance of vortex ring formation and pinch off to propulsion, however, rests on the relative contribution of the leading vortex ring and the trailing jet (which appears after pinch off) to the impulse supplied to the flow. To resolve the relative importance of the vortex ring and trailing jet for propulsion, a piston-cylinder mechanism attached to a force balance is used to investigate the impulse and thrust generated by starting jets for L/D ratios in the range 2–8. Two different velocity programs are used, providing two different L/D values beyond which pinch off is observed, in order to determine the effect of vortex ring pinch off. Measurements of the impulse associated with vortex ring formation show it to be much larger than that expected from the jet velocity alone and proportionally larger than that associated with a trailing jet for L/D large enough to observe pinch off. The latter result leads to a local maximum in the average thrust during a pulse near L/D values associated with vortex rings whose circulation has been maximized. These results are shown to be related to the nozzle exit over-pressure generated during vortex ring formation. The over-pressure is in turn shown to be associated with the acceleration of ambient fluid by vortex ring formation in the form of added and entrained mass.

Probabilistic Two-Phase Wake Vortex Decay and Transport Model

Abstract: A new parametric wake vortex transport and decay model is proposed that predicts probabilistic wake vortex behavior as a function of aircraft and environmental parameters in real time. The probabilistic two-phase wake vortex decay model (P2P) accounts for the effects of wind, turbulence, stable stratie cation, and ground proximity. The model equations are derived from the analytical solution of the spatiotemporal circulation evolution of the decaying potential vortex and are adapted to wake vortex behavior as observed in large-eddy simulations. Vortex decay progresses in two phases, a diffusion phase followed by rapid decay. Vortex descent is a nonlinear function of vortex strength. Probabilistic components account for deviations from deterministic vortex behavior inherently caused by the stochastic nature of turbulence, vortex instabilities, and deformations, as well as uncertainties and e uctuations that arise from environmental and aircraft parameters. The output of P2P consists of cone dence intervals for vortex position and strength. To assign a dee ned degree of probability to the predictions reliably, the model design allows for the continuous adjustment of decay parameters and uncertainty allowances, based on a growing amount of data. The application of a deterministic version of P2P to the Memphis wake vortex database yields favorable agreement with measurements.

The physical mechanism for vortex merging

Abstract: In this paper, we study the interaction of two co-rotating trailing vortices. It is well-known that vortices of like-sign ultimately merge to form a single vortex, and there has been much work on measuring and predicting the initial conditions for the onset of merger, especially concerning the critical vortex core radius. However, the physical mechanism causing this merger has received little attention. In this work, we directly measure the structure of the antisymmetric vorticity field that causes the co-rotating vortices to be pushed towards each other during merger. We discover that the form of the antisymmetric vorticity comprises two counter-rotating vortex pairs, whose induced velocity field readily pushes the two centroids together. The merging velocity computed from the antisymmetric vorticity field agrees closely with the merging velocity measured directly from the total (original) flow field.The co-rotating vortex pair evolves through four distinct phases. The initial stage comprises a diffusive growth, which can be either viscous or turbulent. In either case, the number of turns that they rotate around one another until the vortices start to merge increases with Reynolds number (Re). If one observes the streamlines in a rotating reference frame (moving with the vortices), then one finds an inner and outer recirculating region of the flow bounded by a separatrix streamline. When the vortices grow large enough in the first stage, diffusion across the separatrix places vorticity into the outer recirculating region of the flow, and this leads to the generation of the antisymmetric vorticity, causing convective merger. This second (convective) stage corresponds to the motion of the vortex centroids towards each other, and is a process which is almost independent of viscosity. During the late part of this stage, the antisymmetric vorticity is diminished by a symmetrization process, and the final merging into one vorticity structure is achieved by a second diffusive stage. The fourth and ultimate phase is one where the merged vortex core grows by diffusion.

Flexible Flapping Airfoil Propulsion at Zero Freestream Velocity

Abstract: Thrust generation for an airfoil plunging at zero freestream velocity, the case relevant to hovering birds and insects, has been studied. The objective was to investigate the effect of airfoil stiffness. Particle image velocimetry and force measurements were taken for three airfoils of relative bending stiffnesses 1:8:512 in a water tank. The deformation of the flexible airfoils produces an angle of attack that varies periodically with a phase angle with respect to the plunging motion. Amplitude and phase of this combined plunging/pitching motion play a major role in the flowfield and thrust generation. Vortex pairs or alternating vortex streets were observed depending on the amplitude and phase lag of the trailing edge. The strength of the vortices, their lateral spacing, and the time-averaged velocity of the induced jet were found to depend on the airfoil flexibility, plunge frequency, and amplitude. Direct force measurements confirmed that at high plunge frequencies the thrust coefficient of the airfoil with intermediate stiffness was greatest, although the least stiff airfoil can generate larger thrust at low frequencies. It is suggested that there is an optimum airfoil stiffness for a given plunge frequency and amplitude. The thrust/input-power ratio was found to be greater for the flexible airfoils than for the rigid airfoil.

A model for combustion instability involving vortex shedding

Abstract: Vigorous burning of vortices, formed behind flame stabilizers, can drive significant pressure oscillations inside premixed-type combustors. The goal of this work is to derive a reduced-order model for interaction among vortex shedding, chamber acoustics, and combustion process. A dump combustor is considered a general system configuration. Formation of vortices at the sudden expansion in a chamber is affected by the oscillatory flow. A new quasi-steady model is proposed for determining the moment of vortex separation. Vortex burning is assumed to be localized in space and time. A "kicked" oscillator model is utilized for deriving the appropriate dynamical system. The moment of burning and the corresponding vortex location are dependent on the chamber geometry, velocity field, and characteristic chemical and hydrodynamic times. If Rayleigh's criterion is satisfied, acoustic waves can develop in the chamber. Model and experimental results are compared for a chosen configuration. A study of model performance for a realistic system is carried out by variation of parameters where the mean flow velocity and the number of modes are treated as variables.

Experimental study of the instability of unequal-strength counter-rotating vortex pairs

Abstract: A rapidly growing instability is observed to develop between unequal-strength counter- rotating vortex pairs. The vortex pairs are generated in a towing tank in the wakes of wings with outboard triangular flaps. The vortices from the wing tip and the inboard tip of the flap form the counter-rotating vortex pair on each side of the wing. The flow fields are studied using flow visualization and particle image velocimetry. Both chord- based and circulation-based Reynolds numbers are of O(105). The circulation strength ratios of the flap- to tip-vortex pairs range from −0.4 to −0.7. The initial sinuous stage of the instability of the weaker flap vortex has a wavelength of order one wing span and becomes observable in about 15 wing spans downstream of the wing. The nearly straight vortex filaments first form loops around the stronger wing-tip vortices. The loops soon detach and form rings and move in the wake under self-induction. These vortex rings can move to the other side of the wake. The subsequent development of the instability makes the nearly quasi-steady and two-dimensional wakes unsteady and three-dimensional over a distance of 50 to 100 wing spans. A rectangular wing is also used to generate the classical wake vortex pair with the circulation ratio of −1.0, which serves as a reference flow. This counter-rotating vortex pair, under similar experimental conditions, takes over 200 spans to develop visible deformations. Velocity, vorticity and enstrophy measurements in a fixed plane, in conjuction with the flow observations, are used to quantify the behaviour of the vortex pairs. The vortices in a pair initially orbit around their vorticity centroid, which takes the pair out of the path of the wing. Once the three-dimensional interactions develop, two-dimensional kinetic energy and enstrophy drop, and enstrophy dispersion radius increases sharply. This rapid transformation of the wake into a highly three-dimensional one offers a possible way of alleviating the hazard posed by the vortex wake of transport aircraft.

Slotted aircraft wing

Abstract: An aircraft wing includes a leading airfoil element (36) and a trailing airfoil element (38). At least one slot (12) is defined by the wing during at least one transonic condition of the wing. The slot (12) may either extend spanwise along only a portion of the wingspan, or it may extend spanwise along the entire wingspan. In either case, the slot (12) allows a portion of the air flowing along the lower surface (18) of the leading airfoil element (36) to split and flow over the upper surface (20) of the trailing airfoil element (38) so as to achieve a performance improvement in the transonic condition.

Off-Surface Aerodynamic Measurements of a Wing in Ground Effect

Abstract: The off-surface aerodynamic characteristics of a wing in ground effect are investigated using a number of methods including laser Doppler anemometry and particle image velocimetry. The study focuses on two aspects of the flow: turbulent wake and edge vortex. These features are closely associated with the behavior of the aerodynamic force in ground effect. The size of the wake increases in proximity to the ground. A downward shift of the path of the wake is also observed. Discrete vortex shedding is seen to occur behind the wing. As the wing height is reduced, separation occurred on the suction surface of the wing, and the spanwise vortex shedding is found to couple with a flapping motion of the wake in the transverse direction. An edge vortex is also observed off the edge of the end plate of the wing, which contributes to force enhancement and helps to define the force behavior in the force enhancement region. The rate of change in the downforce vs height curve is linked to the strength of the edge vortex. The vortex breakdown signals a slowdown in the force enhancement. When the maximum downforce height is reached, the edge vortex breaks down completely.

A formal theory for vortex rossby waves and vortex evolution

Abstract: A formal theory is presented for the balanced evolution of a small-amplitude, small-scale wave field in the presence of an axisymmetric vortex initially in gradient-wind balance and the accompanying changes induced in the vortex by the azimuthally averaged wave fluxes. The theory is a multi-parameter, asymptotic perturbation expansion for the conservative, rotating, f-plane, shallow-water equations. It extends previous work on Rossby-wave dynamics in vortices and more generally provides a new perspective on wave/mean-flow interaction in finite Rossby-number regimes. Some illustrative solutions are presented for a perturbed vortex undergoing axisymmetrization.

The Bidirectional Vortex. Part 1: An Exact Inviscid Solution

Abstract: In this paper, we derive an exact solution that describes the bulk fluid motion of a bidirectional coaxial vortex appropriate of a liquid propellant combustion chamber. The study is prompted by the need to characterize the flow inside a laboratory-scale thrust chamber. This chamber has the advantage of confining mixing and combustion to an inner vortex tube that remains separated from the chamber walls by an outer stream of swirling, low temperature oxidizer. Our mathematical model is based on steady, rotational, axisymmetric, incompressible, and inviscid flow conditions. In contrast to other studies of columnar vortices (where the axial dependence is ignored), our model accounts for the chamber’s finite body length. In fact, it incorporates the proper inlet and head-end flow conditions associated with a bipolar swirl-driven combustor. Based on the exact solution, several important flow attributes are illuminated. Among them is the location of the nontranslating vortex layer known as the mantle. This cylindrical layer separates the outer and inner vortex tubes (i.e., the updraft and the downdraft) and is confirmed using computational fluid dynamics and flow visualization.

Correlation Between Vortex Strength and Axial Velocity in a Trailing Vortex

Abstract: The vortices that trail from the wingtips of a large aircraft provide a significant hazard to an aircraft that follows in its wake. The objective is to contribute to the understanding of these vortices by identifying the conditions where an axial velocity in excess of the freestream value will be generated in the core of a trailing vortex. The axial velocity near the core of a trailing vortex was measured using a triple-sensor hot-wire probe and compared with measured values of vortex circulation strength. The vortex was generated in a wind tunnel using a NACA 0015 wing model with a semispan aspect ratio of 0.80. A linear relationship between the axial velocity and a nondimensional circulation parameter is indicated. For small values of the circulation parameter, the axial velocity shows a velocity deficit

Short-wavelength stability analysis of thin vortex rings

Abstract: The linear stability of thin vortex rings are studied by short-wavelength stability analysis. The modified Hill–Schrodinger equation for vortex rings, which incorporates curvature effect, is derived. It is used to evaluate growth rates analytically. The growth rates are also evaluated by numerical calculation and they agree well with analytical values for small e which is the ratio of core radius to ring radius. Two types of vortex rings are considered: Kelvin’s vortex ring and a Gaussian vortex ring. For Kelvin’s vortex ring the maximum first-order growth rate is found to be 165256e. For the Gaussian vortex ring the first-order growth rate is large in the skirts of the vortex core. The first-order instability is significant for both vortex rings.

A new family of uniform vortices related to vortex configurations before merging

Abstract: Stimulated by experimental observations of vortex merging, we compute a new family of uniform-vorticity steady solutions of the Euler equations in two dimensions. In experiments with two co-rotating vortices, one finds that, prior to the convective merging phase, and the formation of vortex filaments, the initial pair diffuses into a single structure (with two vorticity peaks) in the form of a symmetric ‘dumb-bell’. In the present computations, our exploration of the existence of vortex solutions has been guided by the streamline patterns of the co-rotating reference frame, and by the simple concept that the vortex boundary must be one of these streamlines. By varying the parameters which define the vortex patches, we find a family of vorticity structures which pass from the limiting case of point vortices, through the case of two equal co-rotating uniform vortices (as previously computed by Saffman & Szeto 1980; Overman & Zabusky 1982; Dritschel 1985), to the regime where the vortices touch in the form of a dumb-bell. Further exploration of this family of solutions leads to an elliptic vortex, which joins precisely to the local transcritical bifurcation from elliptic vortices with ) found by Wu, Overman & Zabusky (1984).

Dynamics and mixing in jet/vortex interactions

Abstract: This study describes large eddy simulations of the interaction between an exhaust jet and a trailing vortex, in the near-field of an aircraft wake. Two cases are analyzed: in the first one, typical of cruise flight, the jet and the vortex axes are sufficiently well separated to study first the jet dynamics before considering its interaction with the vortex. Dynamics and mixing are controlled both by the jet diffusion and its entrainment around the vortex core. In the second case the jet partially blows in the vortex core, making the flow similar to a Batchelor vortex. The strong perturbations injected into the core cause an instability of the system which is continuously fed by the jet elements wrapping around the core. This leads to a strong decay of angular momentum and diffusion of the core. Global mixing properties, such as plume area and global mixedness evolutions, are analyzed and two applications to environmental problems are finally discussed.

Effects of Pulsing on a Vortex Generator Jet

Abstract: The evolution of a pulsed vortex generator jet embedded in a turbulent boundary layer was examined experimentally. The jet, which was pitched 45 deg and skewed 90 deg, had a velocity three times greater than the freestream. The velocity e eld in planes normal to the freestream was measured by the particle-image-velocimetry method at four stations downstream of the jet exit. The pulsed jet created a starting vortex ring followed by a pair of counter-rotating streamwise vortices, one of them being markedly stronger. Phase-averaged data indicate that the maximum circulation and peak vorticity of the stronger vortex are approximately 30% greater than the average values for a steady jet with the same velocity. However, circulation averaged over the entire pulse was less than that fora steady jet at the samelocation. Thecoreof theprimary streamwisevortex penetratesapproximately 50% farther into the boundary layer than a steady jet with the same velocity. The larger penetration takes place during the initial portion of the pulse and is caused by the jet starting vortex ring.

Experimental study of the flow in a compact heat exchanger channel with embossed-type vortex generators

Abstract: The isothermal flow in a model channel of plate-fin heat exchanger with periodically arranged embossed-like vortex generators is investigated. Velocity measurements are performed by LDA in the transitional regime (Reynolds number from 1000 up to 5000). Strong longitudinal vortices are observed downstream of each generator. The vortex roll-up process is highlighted by the evolution of the velocity vector field in the cross section of the flow. The modifications of the vortex characteristics after successively encountered generators are investigated. This work shows most of the flow features which are known to produce heat transfer enhancement, and shows that these smooth shaped vortex generators are very promising for enhanced heat exchangers.

Vortex nucleation in Bose-Einstein condensates in time-dependent traps

Abstract: Vortex nucleation in a Bose-Einstein condensate subject to a stirring potential is studied numerically using the zero-temperature, two-dimensional Gross-Pitaevskii equation. In the case of a rotating, slightly anisotropic harmonic potential, the numerical results reproduce experimental findings, thereby showing that finite temperatures are not necessary for vortex excitation below the quadrupole frequency. In the case of a condensate subject to stirring by a narrow rotating potential, the process of vortex excitation is described by a classical model that treats the multitude of vortices created by the stirrer as a continuously distributed vorticity at the center of the cloud, but retains a potential flow pattern at large distances from the center.

Space–time development of the onset of a shallow-water vortex

Abstract: An impulsively started jet in shallow water gives rise to vortices having a characteristic diameter larger than the water depth. A technique of high-image-density particle image velocimetry allows characterization of the space–time development of the instantaneous flow patterns along planes representing the quasi-two-dimensional and three-dimensional vortex structure. The quasi-two-dimensional patterns exhibit different categories of vortex development and interaction, depending upon the depth of the shallow water layer. Despite these distinctions, the variations of normalized vortex position, diameter, and circulation, as well as peak vorticity within the vortex, are very similar for sufficiently small water depth.These quasi-two-dimensional patterns are, in turn, related to specific forms of three-dimensional flow structure, which is highly ordered. A prevalent feature is a vortex orthogonal to, and just ahead of, the primary, quasi-two-dimensional vortex. Its streamline topology, on a plane parallel to the axis of the quasi-two-dimensional vortex, exhibits a separation bubble with a well-defined separatix at the bottom (bed) surface. Moreover, its vorticity can exceed that of the quasi-two-dimensional pattern by a factor of two. This feature is consistent for all values of water depth. When the depth becomes sufficiently large, however, the three-dimensional vortex pattern involves an array of vorticity concentrations, which extends across the entire depth of the water.On a plane very close to the bottom surface (bed), global instantaneous distributions of velocity and vorticity exhibit large gradients; they are associated with small-scale vorticity concentrations characteristic of rapid transition. The corresponding streamline topology of the averaged flow close to the bed, however, exhibits a stable focus and is a direct indicator of the topology well above the bed.

Vortex Motion Law for the Schrödinger--Ginzburg--Landau Equations

Abstract: In the Ginzburg--Landau model for superconductivity a large Ginzburg--Landau parameter $\kappa$ corresponds to the formation of tight, stable vortices. These vortices are located where an applied magnetic field pierces the superconducting bulk, and each vortex induces a quantized supercurrent about the vortex. The energy of large-$\kappa$ solutions blows up near each vortex, which brings about difficulties in analysis. Rigorous asymptotic static theory has previously established the existence of a finite number of the vortices, and these vortices are located precisely at the critical points of a renormalized energy. We consider the motion of such vortices in a dynamic model for superconductivity that couples a U(1) gauge-invariant Schrodinger-type Ginzburg--Landau equation to a Maxwell-type equation under the limit of large Ginzburg--Landau parameter $\kappa$. It is shown that under an almost-energy-minimizing condition each vortex moves in the direction of the net supercurrent located at the vortex posit...

Non-spherical bubble behavior in vortex flow fields

Abstract: The boundary element method (BEM) is applied to solve the unsteady behavior of a bubble placed in a vortex flow field. The steady vortex field is given in terms of the viscous core radius and the circulation, both of which may vary along the vortex axis. For this study, 2DynaFS©, an axisymmetric potential flow code which has been verified successfully for diverse type of fluid dynamic problems, is extended. The modifications to accommodate the ambient vortex flow field and to model the extreme deformations of the bubble are presented. Through the numerical simulations, the time history of the bubble geometry and the corresponding pressure signal at a fixed field point are obtained. A special effort is made to continue the numerical simulation after the bubble splits into two or more sub-bubbles. Indeed, it is found that an elongated bubble sometimes splits into smaller bubbles, which then collapse with the emission of strong pressure signals. The behavior of the axial jets after the split is also studied in more detail.

Vortex shedding in subcritical conditions

Abstract: An expressly developed apparatus has been applied to the study of the phenomenon of vortex shedding at Reynolds numbers inferior to the critical value. During previous research it was discovered that vortex shedding could be triggered under subcritical conditions by imparting low-amplitude transversal vibrations at specific frequencies to a cylinder positioned in the flow.

Measurements Within Vortex Cores in a Turbulent Jet

Abstract: High-pass filtering of instantaneous two-dimensional PIV data is employed to educe vortices occurring in the axial plane of a self-similar turbulent axisymmetric jet. An automated method is used to identify the vortices and to measure circulation, tangential velocity, vorticity, and centrifugal force within their cores (defined here as the region within the largest losed streamline). Results include radial variation of these quantities within vortex cores, and the energy of vortices. We find that the vorticity is maximum at the vortex center and decreases monotonically with the radial coordinate. Results indicate that the center of a larger vortex spins faster than a smaller vortex (in an ensemble averaged sense); however, the trend reverses to give the expected result at the core edge. Vorticity results for different vortex radii collapse upon normalisation. The average energy of vortices is seen to increase as the square of the vortex radius. In addition, three possible regimes of vortex number versus vortex size are suggested by our data

Birth of three-dimensionality in a pulsed jet through a circular orifice

Abstract: The pulsed flow about a circular non-centred orifice inside a cylindrical duct is analysed to obtain insight into the basic three-dimensional vortex dynamics that may be expected behind natural cardiac valves. The problem is approached by a highresolution numerical simulation. Results show how a small finite eccentricity generates af ully three-dimensional vortex wake that evolves quite differently from that found under an axisymmetric approximation. The flow field is analysed in terms of velocity and vorticity fields. The vortex wake structure is that of an initially quasi-axisymmetric vortex ring that progressively deforms into a three-dimensional structure, and whose vortex lines tend to reconnect with the boundary-layer-induced vorticity. The vortex structure explains secondary circulation and the presence of a diastolic backflow jet localized behind the longer orifice edge, in agreement with previous experimental observations. Possible relevance of the results to flows of cardiovascular interest is discussed.