The wakes of spheres in a still environment were studied for sphere Reynolds numbers Re in the range 30-4000. The experiments consisted of towed spheres in ...
AIAA JOURNAL Vol. 31, No. 8, August 1993
Sphere Wakes in Still Surroundings at Intermediate Reynolds Numbers J.-S. Wu* and G. M. Faetht University of Michigan, Ann Arbor, Michigan 48109 The wakes of spheres in a still environment were studied for sphere Reynolds numbers Re in the range 30-4000. The experiments consisted of towed spheres in quiescent baths of glycerin and water mixtures. Measurements included dye traces illuminated by a laser light sheet for visualization and laser velocimetry for streamwise velocities. The recirculation region on the downstream side of the sphere was stable and symmetric for Re < 200, stable and unsymmetric for 200 280. Three wake regions were identified: a fast-decay region that was observed only when vortex shedding was present, followed in succession by turbulent and laminar wake regions. Vortex shedding increased the distance to the onset of the turbulent wake region by an order of magnitude due to the presence of the fast-decay wake region. Mean velocities within the turbulent and laminar wake regions scaled according to classical similarity theories, with transition between these regions at conditions where their estimates of mean streamwise velocities along the axis were the same: this occurred at a local wake Reynolds number ReH -10. Within the turbulent wake region, turbulence intensities along the axis were roughly 85% for Rew > 70; however, as the onset of the laminar wake region was approached, turbulence intensities along the axis were proportional to Rew1/4, which is consistent with scaling proposed earlier for the final decay period of axisymmetric wakes.
numbers (lQ Rew = local wake Reynolds number, tuc/v r = radial distance t = time Us = sphere velocity (C/ 0 )/ = velocity scale for turbulent wake region u = mean streamwise velocity «' = rms streamwise velocity fluctuation x = streamwise distance from center of sphere 0 = initial momentum thickness of wake, Eq. (1) v = kinematic viscosity Subscripts
c cm o tr oo
= centerline value = uncorrected centerline value = virtual origin condition = transition from turbulent to laminar wake = ambient condition
Introduction
T
HE flow associated with spheres has attracted attention due to numerous applications, e.g., dispersed particleladen flows, sprays, and rainstorms, among others. Recent work on the production of turbulence by dispersed phases,1'2 however, has shown the need for more information about the structure of sphere wakes at the intermediate sphere Reynolds
Received Jan. 28, 1992; revision received Nov. 10, 1992; accepted for publication Nov. 16, 1992. Copyright © 1992 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. * Graduate Student Research Assistant, Department of Aerospace Engineering. tProfessor, Department of Aerospace Engineering. Fellow AIAA. 1448
WU AND FAETH:
SPHERE WAKES IN STILL SURROUNDINGS
wakes for intermediate Reynolds numbers, or even whether turbulent wakes are present for such conditions, are unknown in spite of the importance of this Reynolds-number range for dispersed multiphase flows.1'2 The present investigation was undertaken to provide new information about the structure of the flow near spheres at intermediate sphere Reynolds numbers. This included visualization of the flow near the spheres to provide information about the recirculation zone and vortex shedding into the wake, measurements of mean streamwise velocities both near the spheres and in their wakes, and measurements of rms velocity fluctuations along the flow axis, extending to conditions where the wakes were laminar. The experiments involved spheres towed through quiescent water and glycerol mixtures to achieve sphere Reynolds numbers in the range 30-4000. Within both the turbulent and laminar portions of the wakes, velocity measurements were compared with classical similarity correlations and correlations of turbulence properties in wakes,18"27 to help define conditions for the transition between these regimes and the scaling of turbulence properties at intermediate wake Reynolds numbers.
Experimental Methods Apparatus
A sketch of the test apparatus appears in Fig. 1. The experiment involved traversing a sphere through a still liquid bath and observing flow properties at the center of the bath. The liquid bath was filled to a depth of 875 mm within a windowed tank (415 x 535 x 910 mm). The sides and bottom of the tank were covered with insulation (not shown in Fig. 1) to minimize natural convection disturbances, aside from small openings needed for optical access. The viscosity of the bath liquid was varied so that a range of sphere Reynolds numbers could be considered using a sphere of fixed size and a modest range of velocities. . The test sphere was a 10-mm-diam plastic ball (polished polycarb ball, ±50 /mi radius tolerance, sphericity within 50 jum, surface roughness less than 16 jum). The sphere was mounted on a 125-/-tm-diam stainless-steel wire which passed horizontally through its center and was sealed with epoxy. The wire was mounted in tension between two struts that could be traversed down the corners of the tank. Tests with no sphere present showed that disturbances from the wire support system were negligible in comparison to background disturbances. TO
MOTOR
PROGRAMMABLE CONTROLLER TRAVERSING SYSTEM
PLEXIGLASS WALL LDV OUTPUT
Fig. 1 Sketch of the experimental apparatus.
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Additionally, the arrangement was sufficiently rigid so that sphere vibrations during a traverse could not be detected. The traversing system involved a counterbalanced mounting plate, which could move along a linear bearing system, to support the struts. The motion of the plate was controlled by a stepping motor driven linear positioner (Daedal, Model 0082686 single-axis positioner). The positioner was progfammed so that it accelerated to the appropriate sphere velocity (147476 mm/s) in the first 150 mm of travel, just prior to entering the bath. The test velocity was maintained for the next 700 mm (300 mm beyond the measuring station) before decelerating to a stop at the bottom of the tank in the last 150 mm of travel. The arrangement provided test sphere velocities with an accuracy of 1 %, based on the position indicator of the traversing system, with velocity variations within this range for the constant speed portion of the traverse. Instrumentation
Flow Visualization
Light sheet illuminated dye traces were used to observe the recirculation region behind the sphere and the vortex shedding process, similar to past work.6"16 This was done by painting a liquid soluble dye (Higgins drawing ink no. 4085) near the forward stagnation point of the sphere and photographing the dye trace after illumination by a vertical light sheet passing through the axis of the flow. The light sheet was formed by focusing the 488-nm line of an argon-ion laser with a spherical lens to yield a waist diameter of 200 /mi, and then spreading the beam with a cylindrical lens to illuminate a 300-mm section along the axis of motion. The resulting dye pattern was photographed using an SLR camera (3200 ASA black and white film) with exposure times of 1-4 ms to stop the motion of the fluid. Visualizations shown here extend roughly ± 30 mm from the center of the tank. Laser Velocimetry
The laser velocimeter was identical to the fixed channel arrangement used by Parthasarathy and Faeth1 and will be described only briefly. A dual-beam forward-scatter configuration was used which had a measuring volume diameter and length of 0.1 and 1.2mm, respectively. Directional bias and ambiguity were eliminated using a Bragg-cell frequency shifter. The bath liquid was seeded with titanium dioxide particles (2.8 /-mi nominal diameter) to provide data rates in the range 0.5-2 kHz. The velocities were found from the lowpass filtered analog output of a burst-counter signal processor, using a 12-bit analog/digital converter operating at a constant sampling frequency (1-4 kHz), and storing 120 k samples per traverse. The laser velocimeter measuring location was fixed; therefore, the trajectory of the sphere was traversed to observe various points in the flow. The streamwise traverse was carried out by the motion of the sphere itself, with distances known from the position indicator of the linear positioner. Positioning accuracy in the streamwise direction was controlled primarily by uncertainties of locating the center of the sphere at the measuring volume and the time between samples, yielding an uncertainty of 0.4 mm for each velocity determination used during ensemble averaging. Cross-stream traverses were carried out by moving the wire support points with a manual traversing system attached to the struts, yielding a positioning accuracy of 0.2 mm. Measurements were carried out by ensemble averaging results from 20 to 120 traverses at a particular radial position and sphere Reynolds number. The number of traverses was selected to control the experimental uncertainties and was large in regions where effects of vortex shedding were important (due to large traverse-to-traverse variations of flow properties) and when rms velocity fluctuations were sought. Traverses only were initiated after bath disturbances from the previous traverse were sufficiently decayed (specified to be «'/£/,
