Owen M. Griffin

A note on bluff body vortex formation

Green & Gerrard (1993) have presented in a recent paper the results of experiments to measure the distribution of vorticity in the near wake of a circular cylinder at low Reynolds numbers (up to Re = 220). They also compared the various definitions of the vortex formation region length which have been proposed by Gerrard (1966), Griffin (1974), and others for both high and low Reynolds numbers. The purpose of this note is to expand the work of Green & Gerrard, and to further their proposition that the end of the vortex formation region at all Reynolds numbers mark both the initial position of the fully shed vortex and the location at which its strength is a maximum. The agreement discussed here between several definitions for the formation region length will allow further understanding to be gained from investigations of the vortex wakes of stationary bluff bodies, and the wakes of oscillating bodies as well.

The vortex street in the wake of a vibrating cylinder

The von Karman vortex streets formed in the wakes of vibrating smooth cylinders and cables were studied using a hot-wire anemometer and flow visualization by fog injection in a wind tunnel. All the experiments took place in the flow regime where the vibration and vortex-shedding frequencies lock together, or synchronize, to control the formation of the wake. Since the flow in the vortex formation region is fundamental to further understanding of the interaction between a vibrating bluff obstacle and its wake, detailed measurements were made of the formation-region flow for Reynolds numbers between 120 and 350. The formationregion length is shown to be a fundamental parameter for the wake, and is dependent on a shedding parameter St * related to the natureally occurring Strouhal number for the von Karman street. The effects of vibration amplitude and frequency on the mean and fluctuating velocity fields in the wake become apparent when the downstream displacement is scaled with the formation length. The von Karman vortex street behind a vibrating cylinder is divided into three predominant flow regimes: the formation, stable and unstable regions. Fundamental differences exist in the vortex streets generated behind stationary and vibrating cylinders, but many classical characteristics, including the manner of vortex breakdown in the unstable region, are shared by the two systems.

Vortex Shedding and Lock-On in a Perturbed Flow

Vortex shedding resonance or lock-on is observed when a bluff body is placed in an incident mean flow with a superimposed periodic component. Direct numerical simulations of this flow at a Reynolds number of 200 are compared here with experiments that have been conducted by several investigators. The bounds of the lock-on or resonance flow regimes for the computations and experiments are in good agreement. The computed and measured vortex street wavelengths also are in good agreement with experiments at Reynolds numbers from 100 to 2000. Comparison of these computations with experiments shows that both natural, or unforced, and forced vortex street wakes are nondispersive in their wave-like behaviour. Recent active control experiments with rotational oscillations of a circular cylinder find this same nondispersive behaviour over a three-fold range of frequencies at Reynolds numbers up to 15,000. The vortex shedding and lock-on resulting from the introduction of a periodic inflow component upon the mean flow exhibit a particularly strong resonance between the imposed perturbations and the vortices.

A universal Strouhal number for the ‘locking-on’ of vortex shedding to the vibrations of bluff cylinders

It is well known that the vortices shed from a circular cylinder lock on in frequency to the vibrations when the cylinder is forced to vibrate or is naturally excited to sufficient amplitudes by flow-induced forces. This paper presents a model for a universal wake Strouhal number, valid in the subcritical range of Reynolds numbers, for both forced and vortex-excited oscillations in the locking-on regime. The Strouhal numbers thus obtained are constant at St * = 0·178 over the range of wake Reynolds numbers Re * = 700-5 × 10 4 . This value is in good agreement with the results obtained by Roshko (1954 a ) and Bearman (1967) for stationary circular cylinders and other bluff bodies in the same range of Reynolds numbers. A correspondence between the amplification of the cylinder base pressure, drag and vortex circulation is demonstrated over a wide range of frequencies and for vibration amplitudes up to a full cylinder diameter (peak to peak). The fraction e of the shed vorticity in the individual vortices is found to be dependent upon the base-pressure parameter K = (1 − C pb ) ½ . Consequently, e is also a function of the amplitude and frequency of the vibrations in the locking-on regime.

On vortex strength and drag in bluff-body wakes

In a recent paper (Griffin & Ramberg 1974) the authors studied the vortex-street wakes behind forced vibrating rigid cylinders. All experimental conditions were within the regime of wake capture or synchronization between the vibration and vortex frequencies. Both mean and fluctuating velocities in the wake together with the length of the vortex formation region were measured as functions of vibration amplitude and frequency at a Reynolds number of 144. The viscous vortex strength, age and spacing at this Reynolds number were then obtained by matching a model for the vortex street with the mean and r.m.s. velocity profiles obtained from hot-wire measurements. These results are employed here to determine the steady drag force on the vibrating cylinder by means of the von Karman drag formulation. The drag coefficients determined in this way are in agreement with the recently published direct force measurements of Tanida, Okajima & Watanabe (1973) and Griffin, Skop & Koopmann (1973) at Reynolds numbers of 80, 500-900 and 4000. From these results a direct relation is drawn between the increased drag on resonantly vibrating structures and changes in the vortex strength, spacing and formation in their wakes.

Kinematic and dynamic evolution of deep water breaking waves

Experiments were performed to exploit the dispersive properties of unsteady surface waves and to induce breaking by using a modified chirp pulse technique to focus the wave energy at a specific location in the Naval Research Laboratory deep water wave channel. The experiments have resulted in a highly resolved archive of breaking events ranging from wave steepening and incipient breaking to spilling and to plunging. The potential energy density, the crest front steepness, the horizontal asymmetry, and other geometric properties of an incipient breaker vary only within a moderate band about their mean values over the extent of these experiments. Thus the properties of an incipient unsteady breaker are well defined. The application of the phase-time or Hilbert transform method to the data set provides new insights into the local properties of the unsteady wave breaking. Recently, spectral and piecewise-linear algorithms for two-dimensional potential flow were developed and used by Schultz et al. [1994] to compare the onset of breaking for several methods of energy input to the unsteady wave system. The computations show that steep plunging waves occur when energy input rates are large. The various energy input methods exhibit similar breaking trends in the limit as the energy input rate becomes small in that incipient spilling breakers form when the potential energy is approximately 52 to 54% of the energy for the most energetic Stokes wave, with the formation of a singularity immediately before the crest.

Potential Energy in Steep and Breaking Waves

Abstract : We find that potential energy rather than wave height is a better experimental and analytic criterion for determining when wave breaking will occur. A simple two-dimensional, periodic algorithm is developed and used to compare breaking onset criteria for energy input from (1) converging sidewalls, (2) a submerged disturbance and (3) wave focusing. Wave-breaking criteria (potential energy or the more classical peak-to-peak wave height) are a function of the rate of energy input. Large plunging waves occur for large energy input rates with a smooth transition to smaller spilling waves for lesser energy input rates. The first two kinds of energy input show similar trends in the limit as the energy input rate becomes small. The third case, wave focusing, is the subject of an ongoing investigation. The effects of wave modulation and reflection are also discussed.

OTEC cold water pipe design for problems caused by vortex-excited oscillations

Abstract Vortex-excited oscillations of marine structures result in reduced fatigue life, large hydrodynamic forces and induced stresses, and sometimes lead to structural damage and to destructive failures. The cold water pipe of an Ocean Thermal Energy Conversion (OTEC) plant is nominally a bluff, flexible cylinder with a large aspect ratio ( L / D = length/diameter), and is likely to be susceptible to resonant vortex-excited oscillations. The objective of this paper is to survey recent results pertaining to the vortex-excited oscillations of structures in general and to consider the application of these findings to the design of the OTEC cold water pipe. Practical design calculations are given as examples throughout the various sections of the report. This paper is limited in scope to the problems of vortex shedding from bluff, flexible structures in steady currents and the resulting vortex-excited oscillations. The effects of flow non-uniformities, surface roughness of the cylinder, and inclination to the incident flow are considered in addition to the case of a smooth cylinder in a uniform stream. Emphasis is placed upon design procedures, hydrodynamic coefficients applicable in practice, and the specification of structural response parameters relevant to the OTEC cold water pipe. There are important problems associated with the shedding of vortices from cylinders in waves and from the combined action of waves and currents, but these complex fluid/structure interactions are not considered in this paper.

Flow similitude and vortex lock‐on in bluff body near wakes

Some years ago a universal Strouhal number for bluff body wakes was introduced, which was based upon the Strouhal frequency fs0 of the vortex shedding, the measured wake width d’ at the end of the vortex formation region, and the mean velocity Ub at the edge of the separated boundary layer on the body. This universal parameter was shown to collapse these characteristic scales of bluff body flows onto a single curve for wake Reynolds numbers between 200 and 107. The results of more recent experiments show the concept of universal wake similitude to be even more general than was previously supposed. In this paper these similarity relationships are applied to the case of vortex lock‐on in oscillatory flow. A full understanding of the macroscopic averaged properties in the wake in this traditional manner is an important precursor to studying, in detail, the microscale wake properties using the most modern experimental measurements and diagnostic techniques and theoretical concepts such as the absolute‐convect...

An integral energy-balance model for the melting of solids on a hot moving surface, with application to the transport processes during extrusion

Abstract This paper describes an energy-balance integral method for analyzing the contact melting of solids on a hot, moving surface. Temperature-dependent viscosity, sensible heat and viscous heat generation terms are included in the melting model, which is suitable in practice for inclusion in any of several proposed formulations for modeling the polymer melting processes in extruders. Two example cases are computed and compared with experimental data for the solid bed profile in an extruder. The first is one in which both viscous heat generation and temperature-dependent viscosity effects are important, while the second example is one in which the large temperature difference across the melt film is predominant and the viscous heat generation is relatively unimportant. Good agreement between the melting model and the experiments is obtained for both cases.