Showing papers on "Vortex shedding published in 1973"

On the stability of vortex rings

Abstract: The stability of vortex rings is investigated both theoretically and experimentally. The theoretical analysis considers the stability of the vortex-filament ring of small but finite core size in an inviscid fluid to small sinusoidal displacements of its centreline. The effect of the vorticity distribution within the finite vortex core on the self-induced motion of each element of the vortex filament is calculated on the basis of the results presented previously by Widnall, Bliss & Zalay (1970). The results of the analysis show that a vortex ring in an ideal fluid is almost always unstable. The number of waves around the perimeter in the unstable mode depends upon the size of the vortex core. For a given vortex core, only one mode is unstable and the smaller the vortex core, the larger the number of waves in the mode. The instability was investigated experimentally with vortex rings generated in air. A laser Doppler velocimeter was used to measure the velocity along the centreline of the ring and thus the circulation. The properties of the vortex core were inferred from the measurements of circulation, ring radius and velocity. The comparisons between theoretical predictions and experimental results show qualitative agreement in the prediction of the number of waves in the unstable mode and quantitative agreement in the prediction of the amplification rate in the early stages of growth.

The effects of wake splitter plates on the flow past a circular cylinder in the range 10 4 < R <5×10 4

Abstract: Experiments were carried out using models having L/D [les ] 2 and the resulting pressure distributions and vortex shedding characteristics are presented. A simple visualization technique which provides explanations of some of the measured results is described. It is concluded that splitter planes reduce the drag markedly by stabilizing the separation points and produce a wake narrower than that for a plain cylinder, raise the base pressure by as much as 50% and affect the Strouhal number to a lesser degree. Careful measurement techniques have enabled these effects to be presented accurately.

An inviscid model of two-dimensional vortex shedding

Abstract: An inviscid model of two-dimensional vortex shedding behind a square-based section is developed. The model uses a discrete-vortex approximation for the free shear layers. The motion of the shear layers is computed from the velocities of the discrete vortices, which in turn are derived through a Schwartz-Christoffel transformation of the section. The flow round the body is impulsively started from rest and initially develops symmetrically. The introduction of a small asymmetric disturbance results in asymmetric interaction of the shear layers amplifying into steady vortex-shedding motion.The model is shown to predict the form of vortex shedding, the Strouhal number and some other flow quantities to a good degree of agreement with experimental results.

Pressure distributions on circular cylinders at critical Reynolds numbers

Abstract: Measurements have been made of the mean and fluctuating pressure distributions on long circular cylinders, having smooth and rough surfaces, at Reynolds numbers of 1·11 × 105 and 2·35 × 105 in both uniform and turbulent streams. The presence of free-stream turbulence a t these Reynolds numbers was found to suppress coherent vortex shedding on the smooth cylinder and give rise to a complex pressure field in which the mean pressure distribution was almost independent of Reynolds number over the small range of Reynolds numbers tested. The pressure distributions on the rough cylinder were found to be completely different in uniform and turbulent streams; the presence of turbulence gave rise to an increase in the level of vortex shedding energy, and produced mean pressure distributions similar to those obtained on smooth cylinders at Reynolds numbers of the order of 107.

Vortex shedding from bluff bodies in a shear flow

Abstract: Experiments are described in which the vortex shedding from a bluff body and the base pressure coefficient have been measured in a shear flow. It is shown that the shedding breaks down into a number of spanwise cells in each of which the frequency is constant. The division between the cells is thought to be marked by a longitudinal vortex in the stream direction and this is supported by evidence from experiments where a longitudinal vortex was generated in an otherwise uniform flow.

Numerical Studies of Two-Dimensional Vortex Motion by a System of Point Vortices

Abstract: The motions of a vortex tube with an elliptic cross section and of a vortex sheet of finite length in an inviscid, incompressible fluid are simulated by a number of discrete vortex filaments, each vortex moving under the action of the velocity field of all the other vortices. By the use of this simulation, rotation of the vortex tube and rolling-up of the vortex sheet are investigated numerically as initial value problems. Comparison with exact solutions shows the validity of this method of approximation. In order to improve the results, an artificial viscosity is introduced to the equations of motion. This diminishes randomization of vortices inherent to the treatment without viscosity and thus leads to regular rolling-up of a vortex sheet.

Vortex generated sound in cavities

Abstract: Cavities in which geometric disturbances are present may produce acoustic waves due to the shedding of vortices from the disturbance in the range 300

A generalized slender-body theory for fish-like forms

Abstract: A consistent slender-body approximation is developed for the flow past a fish- like body with arbitrary combinations of body thickness and low-aspect-ratio fin appendages, but with the fins confined to the plane of symmetry of the body. Attention is focused on the interaction of the fin lifting surfaces with the body thickness, and especially on the dynamics of the vortex sheets shed from the fin trailing edges. This vorticity is convected by the (non-lifting) flow past the stretched-straight body, and departs significantly from the purely longitudinal orientation of conventional lifting-surface theory. Explicit results are given for axisymmetric bodies having fins with abrupt trailing edges, and calculations of the total lift force are presented for bodies with symmetric and asymmetric fin configurations, moving with a constant angle of attack.

A global theory of steady vortex rings in an ideal fluid

Abstract: 5. T H E 5.1. 5.2. 5.3. 5.4. T h e g o v e r n i n g e q u a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . 16 K n o w n s o l u t i o n s : H i l l ' s v o r t e x a n d r i n g s o f s m a l l c r o s s s e c t i o n . . . . . . . . . 18 R e f o r m u l a t i o n of t h e p r o b l e m . . . . . . . . . . . . . . . . . . . . . . . 19 T h e H i l b e r t s p a c e H(D) . . . . . . . . . . . . . . . . . . . . . . . . . 21 F u r t h e r n o t a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Surface dipole strength by cross‐correlation method

Abstract: A new correlation technique enables the determination of local acoustic source strength on the surface of flat plates and simple aerofoil shapes. The method is based on Curle's equation for surface‐generated noise and involves cross‐correlation between local surface pressure and the farfield acoustic pressure. Flat plate airfoils of circular planform were positioned in a “quiet” open jet airflow. The distribution of dipole strength was obtained by moving the point of surface‐pressure measurement around on the surface. Distinctively different distributions were obtained for cases of incident turbulence (airfoil in turbulent mixing layer), separated flow (airfoil at 16° angle of attack in core of jet), and vortex shedding (airfoil at 0° angle of attack in core of the jet). The popular notion that noise comes predominantly from the edges of the plate was not strongly supported. In all cases, however, definite localized source regions were identified. The technique also enabled estimates of the correlation ar...

Numerical Study of Flow past an Inclined Flat Plate by an Inviscid Model

Abstract: Two dimensional vortex shedding behind an inclined flat plate is simulated by point vortex arrays separating from the both edges. The strengths of point vortices are determined from the Kutta condition. The flow round the body is impulsively started from rest with the angle of attack 89{°}, 75{°}, 60{°}, 45{°} or 30{°}. The calculated values of drag coefficients in the case of the angle of attack 89{°} have their marked peak initially and decrease gradually to the values of about one and remain at this stage for some time and then suddenly increase to the values of 4 or 5 and finally oscillate between about 2 and 4. This final stage corresponds to the flow with vortex shedding of Karman's type. Similar results are obtained in other cases.

Bluff body flowmeter utilizing a moveable shutter ball responsive to vortex shedding

Abstract: A bluff body flowmeter is disclosed which includes a bluff body having a base surface facing fluid flow, a pair of converging downstream surfaces, a pair of orifices proximate the downstream surfaces, a cylindrically shaped chamber within the body in communication with the pair of orifices via separate channels, a shuttle ball free to move a relatively short distance within said chamber along the long axis of said bluff body in response to vortex induced pressure changes at the orifices, and means responsive to the movement of the ball for producing electric signals related to volumetric flowrate.

The effect of a bevelled trailing edge on vortex shedding and vibration

Abstract: Experiments using a wind tunnel and a flow visualization technique in a towing tank were conducted to investigate the mechanism of vortex shedding from bevelled trailing edges. These reveal an important difference between the wake structures generated by heaving and steady motion. The suppression of vortex-excited vibration by means of bevelled trailing edges is attributed to the intermittency and rapid decay of the vortex trail resulting from an asymmetric circulation distribution in the vortex formation region.

Low speed calibration formula for vortex shedding from cylinders

Abstract: Calibration formulas are presented for the shedding of vorticies from cylinders at low speeds.

Aerodynamic Forces on a Triangular Cylinder

Abstract: Wind tunnel studies have been conducted on flow around an equilateral triangular cylinder mounted with the point upstream. Instantaneous pressure measurements taken around the cross section have enabled a simple picture to be drawn of the pressure perturbations due to the vortex shedding at the rear. Integration of the pressures produces a mean and fluctuating force and moment coefficients. Mean lift and moment coefficients are found to be zero as anticipated from symmetry. Fluctuating lift and moment coefficients occur at the frequency of shedding of a pair of vortices and vary with Reynolds number. The fluctuating drag coefficient is significantly smaller and occurs at double the frequency. Measurements made of the velocity field in the vortex street showed that the velocity and wave length of the street increased downstream and reached a steady state within 10 days.

The Lift Force Due to von Karman's Vortex Wake

Abstract: Equations are developed which permit the estimation of the oscillating lift forces on bluff cylindrical bodies. The coefficient of lift is seen to be a function of the Strouhal number, the ratio of the lateral to longitudinal vortex spacing of the wake vortices and the ratio of the lateral vortex spacing to the width of the body. Introduction of certain, simplifying assumptions permit the determination of the lift coefficient of any bluff cylindrical body, provided the Strouhal number and the drag coefficient of that body at the Reynolds number of interest are known. The equations also predict an increase in the lift coefficient if the cylinder vibrates with a frequency less than the Strouhal frequency of the stationary cylinder and a decrease in lift coefficient if the cylinder vibrates at a higher frequency.

Computer Model of Vortex Shedding from a Cylinder

Abstract: A mathematical model of unsteady flow around a cylinder gives lift, drag, and velocity fluctuations in reasonable agreement with experimental results. Vorticity is represented by element Rankine vortices, which are superimposed on the potential flow around a cylinder to form the boundary layers and separated shear layers. The solution advances timewise from assumed initial conditions. At each time step, every element vortex is moved through a distance equal to the product of its instantaneous translational velocity and a small time increment, determined after stability tests. Concentrated clouds of vorticity form and are shed from the cylinder, with accompanying fluctuations in lift and drag. The total number of element vortices in the model is minimized by replacing each cloud by a single equivalent vortex. Because feedback from the formation region to the separation points is present in the model, it is potentially well-suited to studies of flow around oscillating cylinders.

Prediction of Normal Force, Pitching Moment, and Yawing Force on Bodies of Revolution at Angles of Attack up to 50 Degrees Using a Concentrated Vortex Flow-Field Model

Abstract: : A method initially proposed by Bryson is extended to include asymmetric shedding. This method employs the impulsive flow analogy, and models each wake vortex using a single-point vortex. Free parameters inherent in the problem formulation are determined empirically. Normal force, pitching moment and yawing force coefficients are predicted for slender bodies with a nose fineness ratio greater than four and at a Mach number less than 0.9. (Modified author abstract)

Vortex Shedding From Slender Cylinders of Various Cross Sections

Abstract: Vortex shedding frequencies were measured for a number of cylinders of various geometrical shapes by placing a hot-wire sensor in the near wake and autocorrelating the turbulence signal. Strouhal numbers are presented for D-section cylinders with the flat face facing both upstream and downstream, isosceles triangular prisms, axially corrugated and helically grooved circular cylinders. For the triangular prisms effect of angle of attack was also studied. Effect of surface roughness on shedding from circular cylinders was observed to be negligible.

Vortex shedding flowmeter

Abstract: A vortex shedding flowmeter in which an obstacle is mounted within a flow conduit to produce periodic vortices whose frequency is a function of the flow rate of the fluid passing through the conduit. The conduit is interposed between an upstream and a downstream pipe section in the line conveying the fluid to be metered. To render the flowmeter insensitive to differences in velocity distribution in the fluid entering the flow conduit, the internal diameter of the conduit is made smaller than that of the upstream pipe section to create a constriction in the flow passage which renders the flow distribution profile more uniform and thereby improves the accuracy and reliability of the meter.

An Analysis of Steady Asymmetric Vortex Shedding from a Missile at High Angles of Attack

Abstract: : Recent developments of highly maneuverable missiles capable of operating at high angles of attack have shown that large unexpected side forces and yawing moments occur due to asymmetric vortex separation from a slender missile body. The objective of the report was to develop a mathematical model which accounted for the viscous effects of the boundary layer fluid that sheds as discrete vortices, and to predict the forces and moments on a missile. An aerodynamic model in the crossflow plane based on von Karman's vortex street theory was developed. The number of vortex filaments which were shed and the positions of the filaments where determined from experimental data as a function of the crossflow Mach number. The Strouhal number was used to relate time in the crossflow plane with time to travel along the missile.

Dynamic Instability of a Cable in Incompressible Flow

Abstract: HE dynamic stability of a cable stretched between two supports is analyzed. The cable is exposed to a uniform, incompressible flow at an angle to the cable axis. Fluid forces are taken to be the quasi-static components of pressure drag and friction drag. Response due to vortex shedding is not considered. A new instability is found which is wavelike in character and has dominant amplitude at the rear support. The instability is due to the presence of bending stiffness in the cable, an effect previously thought negligible and not before considered. The results are important conceptually for studies of cables exposed to flow.

System of vortices in rotating liquid helium

Abstract: The Hamiltonian of a system of N vortex lines moving in an incompressible fluid contained in a circular cylinder is given. The equilibrium state of vortices is constructed through minimization of the energy of the system with the constraints of constancy of number of vortices and their total angular momentum. One and only one assumption is used throughout this work, that pair correlation between vortices is neglected. In equilibrium, the system of vortices rotates uniformly with respect to the central axis of the cylinder. The fluid does not rotate as a solid body, only approaches solid rotation as N→∞. Continuous distribution functions of vortices are found for all N > 1. For N = 1, the distribution is a delta function at the central axis of the cylinder. As N increases the distribution spreads out; in the limit N→∞, it becomes uniform throughout except for a thin layer of order N−1/2 approaching the wall where the density goes to zero rapidly but continuously and remains zero up to the wall. The vortex‐...

Measurements of the Response of Bluff Cylinders to Flow-Induced Vortex Shedding

Abstract: The prediction and measurement of vortex-excited vibrations and associated fluid forces are important in such ocean engineering applications as the determination of the flow-induced lift and drag forces on sea floor pipelines and structural members, tow and mooring cables, and suspended pipelines which must be known in order to implement proper design procedures and to prevent costly failures. This paper discusses a study wherein measurements were made of the response characteristics and flow about circular cylinders that were mounted on springs in a wind tunnel. Free stream Reynolds numbers for two cylindrical models ranged respectively from 350 to 550 and from 550 to 900. The measured vibration frequencies, amplitudes, and phase angles are compared with predictions made with an heuristic wake oscillator model for the vortex-excited vibrations. Steady drag measurements were made and show that the drag coefficient increases by as much as 75 percent at the maximum vibration amplitude from the measured stationary cylinder value. Lift amplification and energy transfer from the flow during resonance are compared over the range of the experiments. Energy determinations made from the measured response and damping data are in good agreement with the results of the theory. The agreement between theory and experiment indicated that further development of the wake oscillator model is warranted.

Analytical Investigation of the Aerodynamic Stability of Helical Vortices Shed from a Hovering Rotor

Abstract: : A small-perturbation stability analysis of a doubly infinite array of interdigitated, right circular helical vortices has been formulated. This array corresponds to the vortices trailed from the tips of the blades of a helicopter rotor or propeller in static thrust or axial flight condition and at great distance from the plane of rotation of the blades. The analysis makes use of the Biot-Savart law of induction and the Vorticity Transport Theorem. The singularities in the Biot-Savart integration for self-induction have been eliminated by substituting approximate functions. Near-singular behavior in other integrals has been minimized by adding and subtracting functions with similar near-singular behavior and which have exact, closed-form integrals.

Crossflow-Induced Vibration of a Circular Cylinder in Water

Abstract: A circular cylinder elastically mounted to have equal flexibility in all lateral directions was exposed to cross (transverse) flow of water. The amplitudes and frequencies of flow-induced vibrations were measured as a function of flow velocity. Resonance-type responses were observed when the vortex-shedding frequency coincided with 50% (Condition A), and 100% (Condition B) of the natural frequency of the cylinder. As expected, Condition B resulted in large-amplitude vibrations in the lift (transverse to flow) direction. However, water excitation at the lower flow velocity of Condition A, which is generally considered unimportant for airflow exposures, resulted in drag (parallel to flow) direction vibrations of moderately large amplitudes. It appears that design applications subject to waterflow under exposure Condition A warrant individual investigation.