Research Papers: Flows in Complex Systems

Near-Wake Observations behind Azimuthally Perforated Disks With Varying Hole Layout and Porosity in Smooth Airstreams at High Reynolds Numbers

[+] Author and Article Information
Raf Theunissen

Department of Aerospace Engineering,
University of Bristol,
Bristol BS81TR, UK
e-mail: r.theunissen@bristol.ac.uk

Robert Worboys

Department of Aerospace Engineering,
University of Bristol,
Bristol BS81TR, UK
e-mail: r.worboys@bristol.ac.uk

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 13, 2018; final manuscript received September 25, 2018; published online December 27, 2018. Assoc. Editor: Arindam Banerjee.

J. Fluids Eng 141(5), 051108 (Dec 27, 2018) (16 pages) Paper No: FE-18-1414; doi: 10.1115/1.4041614 History: Received June 13, 2018; Revised September 25, 2018

Porous disks are commonly encountered in experimental studies dealing with flow through objects such as wind turbines, parachutes, and fluidic devices to regulate pressure and/or downstream turbulence. Perforations are typically staggered and only porosity is altered to attain the required disk drag coefficient, despite a documented influence of topology. Few works have reported, however, to which extent the spatial distribution of the circular perforations affect the mean flow pertaining freestanding disks, and for this reason, this work presents a first, more systematic study focused on the effect of azimuthally varying hole topology and porosity on disk drag and near-wake characteristics. An experimental study performed in airflows of negligible freestream turbulence at Reynolds numbers in the order of 105 is reported and related to the existing literature to ensure reliability. Complementary to drag measurements, near-wake surveys have been performed on a variety of perforation layouts using two-component laser Doppler velocimetry and two-component particle image velocimetry. It is shown that minor changes in perforations can cause drastic changes in near-wake flow topology and no perforation layout can be consistently associated with highest drag. Explicit empirical expressions for drag coefficient linked with the simplified topologies considered have been derived.

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Fig. 1

(a) Proposed hole topologies for groups of constant porosity and (b) visual definition of geometric perforated disk parameters

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Fig. 2

(a) Disk and load cell arrangement for force measurements, (b) LDA centerline measurements, (c) disk mount in the test section of the University of Bristols low turbulence wind tunnel, and (d) PIV setup

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Fig. 3

Schematics depicting (a) the orientation of the diagonal, vertical and across PIV measurement planes together with (b) the adopted coordinate systems

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Fig. 4

Analysis of LDA data along the centerline downstream of the solid disk. (a) Spectra in the horizontal u and the vertical v velocity component 1.0 and 2.5 diameters downstream. (b) Evolution in Strouhal number St related to the dominant spectral peaks. (c) Corresponding probability distributions in Strouhal number. The length of the vertical gray lines, which indicate the location of 75% peak height, is used as error heuristic for Strouhal number estimations.

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Fig. 5

Evolution in drag coefficient with (a) Reynolds numbers and (b) reciprocal of porosity for perforated disks of varying β and hole topology. The gray band indicates the error band for the solid disk (CD=1.167).

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Fig. 6

Mean longitudinal velocity fields and streamline pattern obtained with PIV. Left column: vertical plane, middle column: across, and right column: diagonal (cf., Fig. 3). (a)–(c) β = 0.05, topology A. (d)–(f) β = 0.05, topology D. (g)–(i) β = 0.05, topology E.

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Fig. 7

Mean longitudinal velocity fields and streamline pattern obtained with PIV. Left column: vertical plane, middle column: across, and right column: diagonal (cf., Fig. 3). (a)–(c) β = 0.10, topology B. (d)–(f) β = 0.10, topology F. (g)–(i) β = 0.20, topology A.

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Fig. 8

Mean longitudinal velocity fields and streamline pattern obtained with PIV. Left column: vertical plane, middle column: across, and right column: diagonal (cf., Fig. 3). (a)–(c) β = 0.25, topology A. (d)–(f) β = 0.25, topology E. (g) Solid.

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Fig. 9

Mean longitudinal velocity profiles extracted in the vertical ((a),(b)) and across ((c),(d)) PIV planes. Dash-dotted lines in the across planes ((b),(d)) connect the velocity peaks along the downstream locations indicating jets to be curved inward or outward. The horizontal dashed lines in the across planes indicate the geometrical limits of the disks, given by (η/R)=±1−rp2R−2 cos2(πNh−1); (η/D)=±0.472 (A), ±0.475 (B), ±0.483 (D), ±0.455 (E), ±0.448 (F). Pores in the vertical plane are located at r/D=±rp/D and η/D=±(1/2)S/D across.

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Fig. 10

Identified perforated disk near-wake flow regimes based on sequential longitudinal velocity along disk centerlines. Symbolic flow evolution (flow direction; +: forward, -: reverse. Velocity gradient; >: decelerating, =: constant, <: accelerating); (a) −<,−>,+<; (b) +>,−<,−>,+<; (c) −=,−>,+<; (d) −>,+<; and (e) +>,+>, (−<,−>, if β = 0.10, A), +<. (f) Evolution in merging/rear-stagnation point with porosity (cf., Table 3). Error bars relate to the measured standard deviation in velocity (±u′2¯) and translate to errors at 95% CL when multiplied by a factor 1.96/8000.

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Fig. 11

Variation in pore exit velocity with disk porosity for the various perforation topologies. Data were captured at X/D=0.3. Error bars are derived from horizontal turbulence intensity levels. Symbols have been slightly offset in the horizontal direction for clarity.

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Fig. 12

Evolution in Strouhal number St based on (a) the longitudinal (u;Stu) and (b) the transversal (v;Stv) velocity component measured along the centerline of disks of varying porosity and hole topology. Symbols have been offset in the horizontal direction for clarity. Marker sizes are proportional to the probability of indicated Strouhal number relative to the probability of the dominating peak (Fig. 4). Colors correspond to different porosities as is the case in preceding figures. Gray bands are associated with the natural frequency of the test rig.

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Fig. 14

Free-body diagram of the load cell (a) during calibration and (b) during instantaneous drag measurements

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Fig. 13

Variation in drag coefficient with (a) proposed parameter ξf incorporating pore Reynolds number Rep based on data presented in Fig. 11, number of holes Nh, average hole spacing Sa, and porosity β and (b) proposed parameter ξg implicating solely geometric quantities



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