Uniform-shear flow over a circular cylinder at low Reynolds numbers

On uniform planar shear flow around a circular cylinder at subcritical Reynolds number

This paper brings together experimental and computational work done in the study of low speed ground effect of rotorcraft. The paper recaps previous work done experimentally to study the unsteadiness in the rotorcraft flowfield using flow visualization and hot wire measurements. These experimental results are compared with computational results obtained using a classical vortex method coupled with an image !system to simulate the ground. The comparisons are adequate; however, the computations use a lifting-line approach leading to some discrepancies in time traces of velocities in the wake. The paper also presents experimental results obtained in measuring fuselage loads in ground effect. I. Introduction The flowfield around a rotorcraft flying close to the ground presents a fluid dynamics problem where large fluctuations are observed under nominallj quasi-steady flight conditions, separated by seemingly-random intervals. In ground effect (IGE) conditions, the wake i)f a helicopter rotor interacts with the ground which causes significant perturbation to the flow near the rotor blades, is well as the rest of the craft. Interactions between the main rotor wake and the ground have been associated with :he formation and passage of a ground vortex in transitional flight. The basic question that arises I rom the reported flight test results, is whether 1. The unsteadiness arises from the craft interacting with different regions of an otherwise quasi-steady flowfield, due to changes in wind direc tion, ground clearance or aircraft speed; 2. Or whether long-period fluc tuations are generated in an otherwise periodic flowfield under fixed flight conditions. Detailed experimental studies of the rotor wake and ground vortex were performed with an isolated model rotor above a static ground plane at low advance ratio, and various ground heights. This study aims to quantify time scaies of unsteadiness by bringing together results from pulsed laser sheet flow visualization, hotwire anemometry, and fuselage force measurement. In pl evious work with this experimental set-up, it was shown that the wake was steady enough in the absence of ground effect, to enable clear quantification of the unsteadiness caused by ground effect. This unsteadiness was quantified using laser sheet imaging of vortex dynamics. It was then shown that large transient velocity fluctuations occurred with long intervals, in the ground-vortex and in the rotor inflow regions. The present paper investigates a decision point in the investigation of unsteady ground effect. It is argued that transients could occur due to two basically different situations, or a combination of these situations

Unsteady Aerodynamics of Rotorcraft in Ground Effect

Vortex-induced vibration mechanism of drilling riser under shear flow

A n experimental study is made of two-dimensional uniform-shear flo w (U=Uc+Gy) past a rotating cylinder of diameter D. A water-tunnel, equipped with a shear generator, was constructed. Laser-Doppler velocity measurements were undertaken to describe the wake characteristics. Data are compiled over the ranges of 600< Re < 1,200, the shear parameter Kl^GD/Uc] up to 0.15, and the value of the cylinder rotation parameter o![ = coZ)/2C/J. -2.0<ci<2.0. The power spectra of velocity measurements at downstream locations were analyzed to examine the vortex shedding patterns. In general, the dominant shedding frequency is shifted to a higher value as \a\ and K increase. When \a\ increases beyond a certain threshold value, the dominant frequency becomes less distinct. If\a\ takes a value larger than around 1.5, the velocity field becomes randomized and diffuse, and the organized Karman vortex street activity weakens. The variations of the Strouhal number with K and a are described. The evolution of mean velocity profiles in the wake field is depicted. Characterizations of the velocity profiles, as K and a. vary, are made based on the measurement data. 1 Introduction Much work has ben reported on the flow characteristics around a circular cylinder which is placed in an oncoming crossflow. The principal issues of this classical flow configu­ration are wake patterns, boundary-layer separation, vortex shedding, and external forces acting on the body, to name a few. In light of the complexities of the problem, the prior studies have been mostly experimental, utilizing a wind tunnel or a water channel. It is to be noted that the majority of past investigations dealt with the cases when the cylinder is placed in a uniform, constant-velocity approaching crossflow. Ob­viously, this poses the most fundamental flow setup and a large body of relevant information has been compiled for this sit­uation (see e.g., Roshko, I954;Friehe, 1980; Williamson, 1989). An important variation of the above basic flow is the case when the oncoming free-stream is uniform-shear flow. Clearly, it is implied that a constant vorticity is embedded in the free-stream, and this gives rise to complicated interactions asso­ciated with the boundary-layer separations. In particular, the subject of vortex shedding has been examined extensively by several researchers (Kiya et al., 1980; Yoshino and Hayashi, 1984; Kwon et al., 1992). These investigations revealed, among others, the changes in the Reynolds number-Strouhal number diagram as well as in the drag coefficient, as the shear in the approach flow increases.These findings lead to an improved understanding of the impact of the free-stream vorticity on the gross characteristics of flow patterns around the body. The study of the behavior of a body in approaching uniform-shear

Experimental study of uniform-shear flow past a rotating cylinder

The Numerical Solution of Flow around a Rotating Circular Cylinder in Uniform Shear Flow

In order to express explicitly the effect of the angle-errors of setting a hot-wire probe in a flow field on the output of the hot-wire anemometer, approximate hot-wire response series equations based on the small angle-error and weak turbulence approximations (called direction-error response equations in this paper) were derived from I-type, slanted-type and X-type hot-wire probes in two-dimensional laminar and turbulent flows from a general hot-wire response equation. The direction-error response equations for laminar flow were confirmed experimentally. The characteristics of the direction-error response equations for turbulent flow are discussed in terms of the order-of-magnitude theory and certain specific turbulent flows. It was found from the direction-error response equations that some of the angle-errors appear in these equations in the form of the sums of the angle-errors of specific directions regardless of laminar or turbulent flow.

Hot-wire direction-error response equations in two-dimensional flow

Fluid-dynamic forces on a rotating circular cylinder in a uniform flow were obtained by numerically solving the vorticity transport equation. the ranges of calculation are from 20 to 100 for the Reynolds number, Re, and from 0 to 2 for the specific rotating speed, |V0|, the ratio of the peripheral speed of the cylinder to the uniform velocity. The results of calculation show that the temporal-mean lift coefficient is nearly independent of Re and is proportional |V0|. On the other hand, the temporal-mean pressure drag coefficient increases proportionately to V02 and that increment is due to induced drag in two-dimensional flow, while the skin-friction drag is independent of V0. The amplitude of the temporally fluctuating lift coefficient is maximum at |V0|e0.5 which is larger when Re is larger. The amplitude and frequency seem to be strongly affected by the width of the formation region.

The numerical solution of flow around a rotating circular cylinder in a uniform flow.

Aerodynamic forces acting on a circular cylinder rotating about its axis in a uniform shear flow were numerically obtained at a relatively low Reynolds number. The range of the Reynolds number is from 20 to 100 while those of the specific circumferential speeds and the velocity gradients of the shear flow are from 0 to -2 and from -0.2 to 0.2, respectively. The following results were obtained : First, the mean lift coefficient C^-l is the sum of the lift due to the rotation of the cylinder (Magnus effect) and that due to the velocity gradient. Second, the mean drag coefficient is the sum of the profile drag on a cylinder standing still in a uniform flow and the Magnus drag due to the induced velocity by vorticity originating at the cylinder in rotation and by that of the shear flow in the wake.

Tatsuo Hayashi

Papers

The Numerical Solution of Flow around a Rotating Circular Cylinder in Uniform Shear Flow

Hot-wire direction-error response equations in two-dimensional flow

The numerical solution of flow around a rotating circular cylinder in a uniform flow.

Aerodynamic forces acting on a rotating circular cylinder in a uniform shear flow. (The case of relatively low-Renolds-number flow).

A method of self-pursued boundary value on a body and the Magnus effect calculated with this method