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Title: A turbulent cylinder wake with cylinder corners modified or a neighbouring cylinder present
Authors: Hu, Juchuan
Keywords: Hong Kong Polytechnic University -- Dissertations
Cylinders -- Fluid dynamics
Fluid dynamics
Issue Date: 2007
Publisher: The Hong Kong Polytechnic University
Abstract: This thesis presents experimental studies of a turbulent cylinder wake in the presence of a neighboring cylinder. The effect of the corners of a square cylinder on the wake is also investigated. The thesis includes four topics. Firstly, flow structures, Strouhal numbers and their downstream evolutions in the wake of two staggered circular cylinders are investigated at Re = 7,000 using hotwire, flow visualization and particle image velocimetry (PIV) techniques. The cylinder center-to-center pitch, P, ranges from 1.2d to 4.0d (d is the cylinder diameter) and the angle (α) between the incident flow and the line through the cylinder centers is between 0° and 90°. Four distinct flow structures are identified at x/d = 10 (x is the downstream distance from the mid point between the cylinders), i.e., two single-street modes (S-I and S-II) and two twin-street modes (T-I and T-II), based on vortex shedding frequencies, flow topology and their downstream evolution. Mode S-I is further divided as two different categories, i.e., S-Ia and S-Ib, in view of their different strength of the vortices. Mode S-Ia occurs when the two cylinders are placed in close proximity (P/d ≤ 1.2). The pair of cylinders behaves like one single body, and shear layers separated from the freestream sides of the cylinders roll up to form one street of alternately arranged vortices. The vortex street is comparable to that behind an isolated cylinder in terms of the strength of vortices. Mode S-Ib occurs at small α (≤ 10°) and a greater P/d (> 1.5). Shear layers separated from the upstream cylinder reattach on or roll up to form vortices before reaching the downstream cylinder, resulting in postponed flow separation from the downstream cylinder. Thus formed single vortex street is characterized by significantly weakened vortices, compared with Mode S-Ia. Mode S-II is identified at P/d = 1.2 ~ 2.5 and α > 20° or 1.5 ≤ P/d ≤ 4.0 and 10° < α ≤ 20°, where both cylinders generate vortices, with vortex shedding from the upstream cylinder at a higher frequency than from the downstream, thus two streets of different width and vortex strength are observed at x/d ≤ 5.0. The two streets interact vigorously, resulting in a single street of the lower-frequency vortices at x/d ≥ 10. The vortices originating from the downstream cylinder are significantly stronger than those in the other row, which are connected to the upstream cylinder. Mode T-I occurs at P/d ≥ 2.5 and α = 20° ~ 88°; the two cylinders produce two streets of different vortex strengths and frequencies, both persisting even beyond x/d = 10. At P/d ≥ 2.5 and α ≥ 88°, Mode T-II is produced, where the two cylinders generated two coupled streets, mostly anti-phased, of the same vortex strength and frequency ( St ≈ 0.21). The connection of the four modes with their distinct initial conditions, i.e., interactions between shear layers around the two cylinders, is discussed. Secondly, heat and momentum transport in the wake of two staggered circular cylinders was studied at x/d =10 and 20 (Re = 7,000). The same P and α ranges as were investigated. In order to characterize heat transport in the flow, both cylinders were slightly heated so that heat generated could be treated as a passive scalar. The velocity and temperature fluctuations were simultaneously measured by traversing a three-wire (one X-wire plus a cold wire) probe across the wake, along with a fixed X-wire, which acted to provide a reference signal. Four typical flow structures, e.g., two single-street modes (S-I and S-II) and two twin-street modes (T-I and T-II), are identified based on the phase-averaged vorticity contours, sectional streamlines, and their entrainment characteristics. Though characterized by a vortex street approximately anti-symmetric about the centreline, two different types of flow structure are identified for Mode S-I, namely, S-Ia and S-Ib. They are distinct in the vorticity strength of vortices, which is no less than 80% of that in the wake of an isolated cylinder for S-Ia but only about 40% or less for S-Ib. The vortex street of Mode S-II is significantly asymmetric about the centreline, vortices near the downstream cylinder being about 50% stronger than those on the other side. Mode T-I consists of two alternately arranged vortex streets; the downstream-cylinder-generated street is significantly stronger than that generated by the upstream cylinder. In contrast, Mode T-II shows two streets approximately anti-symmetrical about the wake centreline. Free-stream fluid is almost equally entrained from either side into the wake in Modes S-Ia and T-II, but largely entrained from the downstream cylinder side in Modes S-II and T-I. The entrainment motion in Mode S-Ib is very weak due to the very weak vortex strength. Vortices decay considerably more rapidly in the twin-street modes, under vigorous interactions between the streets, than in the single-street modes. This rapid decay is particularly evident for the inner vortices near the wake centreline in Modes T-II and T-I. Other than flow structures, heat and momentum transport characteristics are examined in detail. Their possible connection to the initial conditions is also discussed.
Thirdly, the near wake of square cylinders with different corner radii was experimentally studied based on PIV, laser Doppler anemometry (LDA) and hotwire measurements at Re = 2,600. Four bluff bodies, i.e., r/d = 0 (square cylinder), 0.157, 0.236, 0.5 (circular cylinder), where r was corner radius and d was the characteristic dimension of the bluff bodies, were examined. A conditional sampling technique was developed to obtain the phase-averaged PIV data in order to characterize quantitatively the effect of corner radii on the near-wake flow structure. The results show that, as r/d increases from 0 to 0.5, the maximum strength of shed vortices attenuates, the circulation associated with the vortices decreases progressively by 50%, St increases by about 60%, the convection velocity of the vortices increases along with the widening of the wake width by about 25%, the vortex formation length and the wake closure length almost double in size. Meanwhile, both the vortex wavelength, λx, and the lateral spacing, λy, decrease as r/d increases, but the ratio of λy to λx is approximately 0.29, irrespective of r/d, which is close to the theoretical value of 0.281 for a stable Karman vortex street. The decrease in wavelength is probably responsible for the change in the flow structure from the approximately circular-shaped vortex at r/d = 0 to the laterally stretched vortex at r/d = 0.5. The leading edge corner radius is more important than the trailing one in influencing the near wake structure since it determines to a great extent the behaviour of the streamlines, the separation angle and the base pressure. It is further found that the ratio of the mean drag coefficient to the total shed circulation, Cd /T₀, approaches a constant, about 0.25 for different bluff bodies in the subcritical flow regime. The streamwise evolution of vortices and the streamwise fluctuating velocity along the centreline for rounded cylinders are also discussed. Finally, the wake of asymmetric bluff bodies was measured using PIV, LDA, load-cell, hotwire and flow visualization techniques at Re = 2,600 ~ 8,500. Asymmetry is produced by rounding some corners of a square cylinder, and leaving others un-rounded. It is found that, with increasing corner radius, the flow reversal region is expanded and the vortex formation length is prolonged. Accordingly, the vortex shedding frequency climbs and the base pressure rises, resulting in a reduction in the mean drag as well as the fluctuating drag and lift. It is further found that, while the asymmetric cross-section of the cylinder causes the wake centreline to shift towards the sharp corner side of the bluff body, the wake remains globally symmetric about the shifted centreline. The near wake of asymmetric bluff bodies is characterized in detail, including the Reynolds stresses, characteristic velocity and length scale, and is further compared with that of the symmetric ones. Seven publications, including four refereed journal papers and three refereed conference proceedings, have been produced from the present work.
Description: xxvi, 214 p. : ill. ; 30 cm.
PolyU Library Call No.: [THS] LG51 .H577P ME 2007 Hu
Rights: All rights reserved.
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