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INTERACTION OF VORTEX SYSTEMS AT A FLOW OF BODIES

A.S. Guzeev, A.I. Korotkin, S.Yu. Solovyev

Krylov State Research Centre

196158, St. Petersburg, Russia

The paper presents the experimental results regarding some aerohydrodynamic phenomena

arising in incompressible liquid flows around bodies. The described phenomena were observed in

the experiments carried out at the Krylov State Research Centre, and, in the authors’ opinion, could

be of interest for the researchers dealing with aerohydrodynamic model experiments.

Effect of artificial model surface roughness on the “hydrodynamic asymmetry” force. The

essence of the phenomenon can be explained by the example of flow around an elongated body of

rotation at incidence α, which is measured between the body axis and the velocity vector of incident

flow (see the schematic drawing showing the angle α, forces and moments). In this case it appears

that besides the resistance and lifting forces lying in the centerline plane of body of revolution, the

body is subjected to a lateral force perpendicular to the centerline plane. This force is equal to zero

at α = 0 and grows with α. When α = 40-50°, the lateral force reaches its maximum, which is ap-

proximately equal to the lifting force maximum at the same incidence. If α is increased up to 90°,

the lateral force is decreased by 20-30% of its maximum value. In case of cross flow with respect to

the body’s major axis the flow separated from the surface of body of rotation has a “cellular” pat-

tern (Fig. 1). The longitudinal vortices (of Gortler’s vortices type) come off the body surface into

Fig. 1. Paint visualization of flow separation area on the ellipsoid of rotation with aspect ratio equal to 9 at α=90° from the

beginning of paint spread (a) to the steady pattern (b) and the scheme of longitudinal vortices behind the ellipsoid (c)

А.S. Guzeev, А.I. Korotkin, S.Yu. Soloviev, 2015

c

b

a

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the flow. The pressure distribution in the area of flow separation from the body surface is stable and

periodical at Re = 4·105 to 10

6 (calculated for the body’s cross dimension). The longitudinal vorti-

ces break the transverse Karman’s vortex street. The axes of longitudinal vortices shed from the up-

per and lower sides of the body of rotation (the major semi-axis is assumed to be horizontal) are

shifted with respect to each other. Shifting of “cells” causes a shift of relatively increased pressure

areas on the upper side of the body of rotation. Therefore, pressure areas on the lower and upper

surfaces of the rotation body are not compensated. The vertical force and the corresponding mo-

ment are generated.

For illustration of the above explanation let us briefly describe two wind-tunnel experiments

on ellipses of rotation with aspect ratio λ = 3 and maximum diameter d = 300 mm.

The first experiment (Fig. 2). An ellipsoid was suspended on a long rope in the center of

wind-tunnel test section so that its major axis was vertical. The lower part of the ellipsoid was fixed

with a guy rope located in the centerline plane of the wind tunnel test section to keep the ellipsoid

from drifting with flow. At flow velocities < 28 m/s corresponding to sub-critical flow conditions,

the ellipsoid did not move in the flow. When the velocity was raised to 30 m/s, the ellipsoid moved

laterally as far as the guy ropes allowed. Attempts to return the ellipsoid in the initial position were

useless, because the lateral pushing force on the ellipsoid was rather strong.

The second experiment (Fig. 3). The same ellipsoid was fixed as an airscrew on transversal

axis in the wind- tunnel test section. The bearing provided its free rotation about the axis. The ellip-

soid was completely balanced with respect to the rotation axis. When the wind tunnel velocity was

increased up to 10 m/s, the ellipsoid began to rotate with the speed of about 1 rps. This speed of ro-

tation increased slightly (up to 1.5 rps) when the wind tunnel velocity was raised to 28 m/s. After

the wind tunnel velocity was raised to 30 m/s, the ellipsoid stopped and then began to rotate in the

opposite direction. Within 2 to 3 seconds it reached such rotating speed, that it was impossible to

see it with unaided eye. It is evident that the rapid increase of torque is related to the transition to

supercritical flow conditions. The experiments proved that application of artificial roughness on the

original polished surface of model provides significant reduction of the forces and moment related

to the “hydrodynamic asymmetry”.

Effect of longitudinal vortices on Karman’s system of vortices generated behind a stream-

lined foil at low incidence angle. The very fact that Karman’s vortices are generated behind

a streamlined foil at low incidence (Fig. 4) indicates that the vortex street is caused by instability of

Fig. 2. Schematic setup: suspension of ellipsoid of rotation

in the wind tunnel

Fig. 3. Wind-tunnel setup of free-rotating ellipsoid tests

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Fig. 4. Vortex wake behind the airfoil at incidences α = 0°, 2°, 4°, 6°. Re=104

Fig. 5. Vortex wake behind the circular cylinder

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vortex layer in wake flow. The patterns of vortices generation behind a circular cylinder [1, 2]

(Fig. 5) and a foil (Fig. 4) [3– 5] are rather similar. While in case of circular cylinder the pattern of

vortex formation depends only on Reynolds number, the flow around foil is, in addition, strongly

influenced by incidence (see Fig. 4). Periodic vortices in wake of the foil may give rise to variable

aerohydrodynamic forces on the foil even in case of separation-free flow around it. If a longitudinal

vortex generator is placed in the aft of the foil, the street of Karman’s vortices will disappear

(Fig. 6) or considerably weaken, which may significantly reduce the variable aerohydrodynamic

forces.

Fig. 6. Absence of Karman’s vortices in wake of the foil with vortex generators, incidence α = 5°

a

b

Fig. 7. Wake of the bridge superstructure model. а) Karman’s vortices behind the bridge model; b) the absence of Karman’s vortices in the wake of bridge model fitted with

longitudinal vortex generators.

a

5

Study on interaction of longitudinal vortex generator with Karman’s vortex street formed

behind the model of Volgograd bridge superstructure in case of cross flow (Fig. 7,a). The flow

around the Volgograd bridge raised concern because of its heavy vibrations observed on May 10,

2010 with full-scale amplitudes reaching up to 1 meter (Fig. 8). The specialists on bridges’ aerody-

namics [6] explained this phenomenon as a coincidence of natural frequency of bridge vibration

with the frequency of Karman’s vortex separation. The Krylov State Research Centre developed the

technology for manufacturing special structures to be placed on the bridge superstructure to gener-

ate a system of longitudinal vortices eliminating the Karman’s vortex street (Fig. 7,b).

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Fig. 8. Vibrations of Volgograd bridge.