Wake Motion Research Articles

Turbulence Effect on Frequency Characteristics of Unsteady Motions in Wake of Wing

The ine uences of the freestream turbulence intensity on the frequency characteristics of the instability wave and vortex shedding in the wake of a NACA 0012 wing model are studied experimentally. The functional relationships among the Strouhal, Roshko, and Reynolds numbers in the viscous-effect-dominated and the inertialeffect-dominated regimesareobtained. Thefreestream turbulence hasapparenteffect on theStrouhal and Roshko numbers in the regimes of instability wave and laminar and subcritical vortex-shedding modes that are obtained at low Reynolds numbers. However, at large Reynolds numbers in the supercritical vortex-shedding mode, particularly at large angles of attack, the effect of freestream turbulence intensity on the frequency selection is not signie cant. For the instability wave, the Roshko number decreases with the increase of freestream turbulence and then approaches constant values when the freestream turbulence intensity is larger than a critical value between 0.45 and 0.5%. However, the Strouhal number of the vortex shedding of laminar and subcritical modes increases signie cantly with an increase of turbulence intensity and then decreases when the freestream turbulence intensity is larger than a critical value between 0.45 and 0.5%. The change of the characteristic surface e ow modes may contribute to the dominant mechanism of the existence of critical freestream turbulence intensity. Nomenclature C = chord length of wing, 6 cm d = length of wing-section projection on cross-stream plane f = frequency of instabilities in wake region, Hz ` = distance in X direction measured from mesh screen M = mesh size of turbulence generation screen Rec = Reynolds number based on chord length of wing, uwC/m Red = Reynolds number based on cross-stream projection of wing section, uwd/m Rod = Roshko number of vortex shedding, f d 2 /m Srd = Strouhal number of vortex shedding, f d/uw T = freestream turbulence intensity u = x component of local instantaneous velocity uw = average freestream velocity X = streamwise coordinate, originated from leading edge of wing model on root-plane Y = spanwise coordinate, originated from leading edge of wing model on root-plane Z = crosse ow coordinate, originated from leading edge of wing model on root-plane a = root angle of attack m = kinetic viscosity of air stream q = density of air stream U = power spectrum of e uctuating velocities

2042 フォトクロミック染料による気泡後流中の乱流混合の研究

Turbulent mass mixing caused by a rising bubble in a still fluid in a circular pipe is investigated by visualization and noninvasive concentration measurement using a photochromic dye. Visualized dye patterns indicate that the dye was mixed by vortex motions in the turbulent wake and this phenomenon is different from that of low Reynolds numbers where the dye was drawn straightly along the laminar wake of the bubble. The concentration distribution deduced from the dye image using Lambert-Beer's law shows rather isotropic mixing in longitudinal direction. Turbulent diffusion coefficients calculated by the temporal changes in the concentration distribution are compared to those of a solid sphere.

Immediate and Near Wake Flow Patterns Behind Slotted Disks

The effect of spacing ratio on the near-wake regions immediately behind porous disks that consisted of multiple annular elements is investigated experimentally. Annular jets through individual slots merge into groups of highmomentum regions that displace a global recirculating region downstream. Multiple wake patterns result from the same overall conditions. Once the pattern forms, it remains nearly unchanged unless the e ow is disturbed. Compared to the e ow behind a solid disk, three-dimensional large-scale motions are suppressed downstream and the wake motions are more axisymmetric. The patterns of jet mergings are also axisymmetric and persistent. The mean and time-dependent large- and small-scale velocity e uctuations are characteristic of individual spacing ratios and e ow patterns, and they are analyzed and compared with e ow visualizations. The process of how the wake settles into a certain e ow pattern also is addressed.

Immediate and near wake flow patterns behind slotted disks

The effect of spacing ratio on the near-wake regions immediately behind porous disks that consisted of multiple annular elements is investigated experimentally. Annular jets through individual slots merge into groups of high-momentum regions that displace a global recirculating region downstream. Multiple wake patterns result from the same overall conditions. Once the pattern forms, it remains nearly unchanged unless the flow is disturbed. Compared to the flow behind a solid disk, three-dimensional large-scale motions are suppressed downstream and the wake motions are more axisymmetric. The patterns of jet mergings are also axisymmetric and persistent. The mean and time-dependent large- and small-scale velocity fluctuations are characteristic of individual spacing ratios and flow patterns, and they are analyzed and compared with flow visualizations. The process of how the wake settles into a certain flow pattern also is addressed

Numerical Simulations of Commercial Aircraft Wakes Subjected to Airport Surface Weather Conditions

Using tower e yby data for validation, we have developed a two-dimensional numerical simulation of the ine uence of surface weather conditions on wake vortex motion and decay for representative commercial aircraft. Our simulations support the conjecture that the ratio of eddy viscosity to kinematic viscosity, appropriate for modeling aircraft wakes, scales linearly with circulation, which yields a nominally constant equivalent Reynolds number for all commercial aircraft sizes. We have tested the constant eddy viscosity approximation for three different aircraft types and six surface weather states, showing the utility of the approach in predicting wake vortex motion and decay. Subsequently, we have shown how data from one aircraft e ight test can be used to infer the decay behavior of another, and we have examined the ine uence of the six surface weather states on the vortex decay behavior predicted for a large commercial aircraft. Based upon these simulations, we have determined that the two-dimensional, constant eddy viscosity approach can be useful in assessing the ine uence of surface weather conditions on wake vortex decay.

Novel approach to aerodynamic analysis using analytical/numerical matching

Novel approach to aerodynamic analysis using analytical/numerical matching

The vortex shedding of a streamwise-oscillating sphere translating through a linearly stratified fluid

The flow past a horizontally translating, streamwise oscillating sphere through a linearly stratified fluid is investigated in a series of laboratory experiments. The pertinent governing parameters are shown to be the internal Froude number Fi, the Reynolds number Re, the Keulegan–Carpenter number KC, and the normalized forcing frequency Sf. A KC against Sf regime diagram for flows at Fi=0.07 and Re=190 is developed; for these parameters the flow is approximately two dimensional in the horizontal zone, −1/2≲z/D≲1/2, where z is the vertical coordinate and D is the sphere diameter. Numerous flow regimes are delineated, and it is shown that the regime boundaries approximate the lines of constant u1/u0=2π(KC)(Sf), where u1 is the amplitude of the sphere oscillation and u0 is the magnitude of the mean background flow. Vortex shedding occurs for the entire range of experiments at these Fi, Re values. Lock-on of the shedding frequency to the sphere oscillation frequency occurs for u1/u0≳0.1. Flows at large Fi are shown to exhibit three-dimensional motions in the near wake, and, owing to stratification, exhibit vertical collapse at a certain distance downstream. The far wake develops into a horizontal vortex street pattern for all flows when stratification is present. At large Fi, Re combinations, turbulent patches are found in the wake. The inverse normalized streamwise distance between shed vortices (an effective Strouhal number) is shown to scale as Sf, independent of KC. Measurements of the horizontal separation angles and times for the collapse of the vertical structure are also presented.

12 主流方向の軸まわりに回転する球の後流の可視化

The wake configuration of a rotating sphere with smooth surface in axial flow was visualized by means of smoke wire method in a low-speed vertical wind-tunnel at Reynolds number of 2600. The test was conducted using the sphere with rotational speed ratio of 0, 1.19, 3.57, and a shedding vortex and a three dimensional wake motion behind the sphere was observed.

Prediction of solid concentration profiles in three-phase reactors by a wake shedding model

A structural model for predicting axial solid concentration profile in three-phase reactors is presented. The model takes account of the entrainment of solid particles due to bubble wake motion in the axial solid mixing. The prediction of axial solid concentration profiles from the model shows good agreement with data obtained in a wide range of experimental conditions.

Self-Excited Oscillation of Transonic Flow Around an Airfoil in Two-Dimensional Channels

A self-excited oscillation of transonic flow in a simplified cascade model was investigated experimentally, theoretically and numerically. The measurements of the shock wave and wake motions, and the unsteady static pressure field predict a closed-loop mechanism, in which the pressure disturbance that is generated by the oscillation of boundary layer separation propagates upstream in the main flow and forces the shock wave to oscillate, and then the shock oscillation disturbs the boundary layer separation again. A one-dimensional analysis confirms that the self-excited oscillation occurs in the proposed mechanism. Finally, a numerical simulation of the Navier–Stokes equations reveals the unsteady flow structure of the reversed flow region around the trailing edge, which induces the large flow separation to bring about the antiphase oscillation.

Numerical model of unsteady subsonic aeroelastic behavior

A method for predicting unsteady, subsonic aeroelastic responses was developed. The technique accounts for aerodynamic nonlinearities associated with angles of attack, vortex-dominated flow, static deformations, and unsteady behavior. The fluid and the wing together are treated as a single dynamical system, and the equations of motion for the structure and flow field are integrated simultaneously and interactively in the time domain. The method employs an iterative scheme based on a predictor-corrector technique. The aerodynamic loads are computed by the general unsteady vortex-lattice method and are determined simultaneously with the motion of the wing. Because the unsteady vortex-lattice method predicts the wake as part of the solution, the history of the motion is taken into account; hysteresis is predicted. Two models are used to demonstrate the technique: a rigid wing on an elastic support experiencing plunge and pitch about the elastic axis, and an elastic wing rigidly supported at the root chord experiencing spanwise bending and twisting. The method can be readily extended to account for structural nonlinearities and/or substitute aerodynamic load models. The time domain solution coupled with the unsteady vortex-lattice method provides the capability of graphically depicting wing and wake motion.

Calculation of unsteady flows in turbomachinery using the linearizedEuler equations

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

On the formation and shedding of vortices from side-wall mounted obstacles in rotating systems

The flow of a homogenous, incompressible, rotating (vertically upward) fluid past cylinders of triangular and semi-circular cross-section mounted on either the left or right wall (facing downstream) of a channel is investigated experimentally. The pertinent system parameters are the Rossby and Ekman (or Reynolds) numbers and the obstacle width to fluid depth ratio. The experiments indicate that the shedding of tip eddies from the triangular obstacle leads to a rather complex wake motion which is critically dependent on the system parameters. For certain parameter combinations the tip eddies advect downstream as single entities while in other regions of parameter space two or more eddies merge and advect downstream as large-scale eddy structures. The Strouhal numbers for both the shedding of the tip eddies as well as of the large-scale structures are measured as functions of the system parameters. Measurements of the dimensionless size of the large-scale starting eddies are made as functions of a dimensionless time and other system parameters. It is shown that eddies formed in the lee of obstacles mounted on the right (anticyclonic) tend to shed more quickly, other parameters being fixed, than those on the left (cyclonic). Measurements of the dimensionless vorticity of the cores of the large-scale structures at a fixed dimensionless time indicate that, within the accuracy of the experiments and for the range of parameters considered, this quantity is independent of the Rossby and Reynolds numbers and the side to which the obstacle is mounted. Finally some of the experimental flow patterns are shown to be similar to a recent observation of a southeastward ocean current past the western tip of Grand Bahama Island.

An approximate model of vortex decay in the atmosphere

An approximate analysis of atmospheric effects on wake vortex motion and decay is presented. The effects of density stratification, turbulence, and Reynolds number are combined in a single model so that the relative importance of different parameters can be determined. Predicted wake motion is shown to be in good agreement with limited data from both ground facility and flight test measurements taken under low turbulence conditions. Wake decay was found to depend strongly on both density stratification and turbulence. For typical levels of turbulence, wake decay was found to result from the 'Crow instability' except under strongly stratified conditions.

Vortex Shedding from Oscillating Bluff Bodies

When placed ih a fluid stream, some bodies generate separated flow over a substantial proportion of their surface and hence can be classified as bluff. On sharp-edged bluff bodies, separation is fixed at the salient edges, whereas on bluff bodies with continuous surface curvature the location of separation depends both on the shape of the body and the state of the boundary layer. At low Reynolds numbers, when separation first occurs, the flow around a bluff body remains stable, but as the Reynolds number is increased a critical value is reached beyond which instabilities develop. These instabilities can lead to organized unsteady wake motion, dis­ organized motion, or a combination of both. Regular vortex shedding, the subject of this article, is a dominant feature of two-dimensional bluff-body wakes and is present irrespective of whether the separating boundary layers are laminar or turbulent. It has been the subject of research for more than a century, and many hundreds of papers have been written. In recent years vortex shedding has been the topic of Euromech meetings reported on by Mair & Maull (1971) and Bearman & Graham (1980), and a comprehensive review has been undertaken by Berger & Wille (1972). Vortex shedding and general wake turbulence induce fluctuating pres­ sures on the surface of the generating bluff body, and if the body is flexible this can cause oscillations. Oscillations excited by vortex shedding are usually in a direction normal to that of the free stream, and amplitudes as large as 1.5 to 2 body diameters may be recorded. In addition to the generating body, any other bodies in its wake may be forced into oscillation. Broad-band force fluctuations, induced by turbulence produced in the flow around a bluff body, rarely lead to oscillations as severe as those caused by vortex shedding. Some form of aerodynamic instability, such that move-

Vortex Shedding from Oscillating Bluff Bodies

When placed ih a fluid stream, some bodies generate separated flow over a substantial proportion of their surface and hence can be classified as bluff. On sharp-edged bluff bodies, separation is fixed at the salient edges, whereas on bluff bodies with continuous surface curvature the location of separation depends both on the shape of the body and the state of the boundary layer. At low Reynolds numbers, when separation first occurs, the flow around a bluff body remains stable, but as the Reynolds number is increased a critical value is reached beyond which instabilities develop. These instabilities can lead to organized unsteady wake motion, dis­ organized motion, or a combination of both. Regular vortex shedding, the subject of this article, is a dominant feature of two-dimensional bluff-body wakes and is present irrespective of whether the separating boundary layers are laminar or turbulent. It has been the subject of research for more than a century, and many hundreds of papers have been written. In recent years vortex shedding has been the topic of Euromech meetings reported on by Mair & Maull (1971) and Bearman & Graham (1980), and a comprehensive review has been undertaken by Berger & Wille (1972). Vortex shedding and general wake turbulence induce fluctuating pres­ sures on the surface of the generating bluff body, and if the body is flexible this can cause oscillations. Oscillations excited by vortex shedding are usually in a direction normal to that of the free stream, and amplitudes as large as 1.5 to 2 body diameters may be recorded. In addition to the generating body, any other bodies in its wake may be forced into oscillation. Broad-band force fluctuations, induced by turbulence produced in the flow around a bluff body, rarely lead to oscillations as severe as those caused by vortex shedding. Some form of aerodynamic instability, such that move-

Vorticity Transport Integral Concept for Determining Wave Forces on Submerged Bodies

The vorticity transport integral (VTI) concept affords an anaIytica1 procedure that is well suited to determining the wave lnrces on bodies and structural dements in a marine environment. The concept can be applied to any unsteady flow; however, it is especially suited lo the treatment of flows assucimted with ocean waves in which an object experiences complete flow reversal with wake motion confined to the vicinity of the body. As ad integral approach it allows forces to be determined accurately with either an approximate description ar an exact soluliun uf the flow. Because the integrals have significadt values only near the body, the approach avoids the problems inherent with the evaluation of integrals over large volumes of fluid. The resulting expresslonu are used in a qualitative appraise1 of the varlous contributions to the tots1 force on a body in an unsteady flowfleld.

The motion of a trailing vortex-wake in a stratified medium

An analytical study of a trailing vortex-wake in a uniform and a stratified environment is presented. A turbulent entrainment velocity is postulated based on the assumption of similarity of the wake surface and consistent with several averaged conservation equations. In a homogeneous density environment, the descending wake is brought to rest due to its buoyancy in the initial phase of wake motion. It is then accelerated upwards. The lifetimes of the wakes are found to be in excellent agreement with previous experimental results. In the absence of mutual interaction of vortices in the wake, the final ascending phase is a decelerating phase. The effect of weak linear stratification is to damp the movement of the vortex wake. The wake oscillates with decreasing amplitude and wavelengths with increasing magnitudes of linear stratification.

Flow Separation on a Vibrating Circular Cylinder

The location of the boundary-layer separation point on a circular cylinder has been investigated experimentally for a stationary cylinder and for a cylinder which is performing vortex-excited oscillations. The results for the stationary cylinder are in close agreement with published data. For the vibrating cylinder, the range of angular displacement of the separation point was found to depend upon the vibration amplitude and frequency, and the peak displacement occurred at a different frequency from that which gave the peak cylinder amplitude. As the frequency of the wake motion increases beyond that which gives that maximum range in the location of the separation point, the range of the motion of the separation point decreases. For given cylinder and wake frequencies, the higher the cylinder amplitude, the greater the motion of the wake. The phase shift of the actual wake was found to be close to 180 deg behind that of an ideal wake which aligns itself behind the relative velocity vector of the flow. The phase shift was found to be independent of cyclinder amplitude.