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Research Papers: Fundamental Issues and Canonical Flows

# Structure and Dynamics of Bounded Vortex Flows With Different Nozzle Heights

[+] Author and Article Information
A. M. Green

School of Engineering,
University of Vermont,
Burlington, VT 05405

J. S. Marshall

School of Engineering,
University of Vermont,
Burlington, VT 05405
e-mail: jmarsha1@uvm.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 12, 2014; final manuscript received April 21, 2015; published online June 8, 2015. Assoc. Editor: Alfredo Soldati.

J. Fluids Eng 137(10), 101202 (Oct 01, 2015) (14 pages) Paper No: FE-14-1311; doi: 10.1115/1.4030485 History: Received June 12, 2014; Revised April 21, 2015; Online June 08, 2015

## Abstract

A bounded vortex flow is generated by a nozzle with a central suction outlet surrounded by inlet jets with a 15 deg inclination in the azimuthal direction. The jets impinge on a flat surface called the impingement surface. The circulation introduced by azimuthal tilting of the inlet jets is concentrated at the flow centerline by the suction outlet to form a wall-normal vortex, with axis nominally orthogonal to the impingement surface. An experimental study was conducted in water to examine the structure and dynamics of bounded vortex flows with balanced inlet and outlet flow rates for different values of the separation distance h between the nozzle face and the impingement surface. The experiments used a combination of laser-induced fluorescence (LIF) to visualize the vortex and jet flow structure and particle-image velocimetry (PIV) for quantitative velocity measurements along a planar slice of the flow. Different liquid flow rates were examined for each separation distance. The results show that a stationary wall-normal vortex is formed at small separation distances, such as when the ratio of h to the inlet jet radial position R is set to $h/R=0.67$. When the separation distance is increased such that $h/R=1.3$, the intake vortex first becomes asymmetric, drifting to the one side of the flow, and then bifurcates into a vortex pair that rotates in a V-state around the flow centroid. At large separation distances (e.g., $h/R=6.7$), the intake vortex adopts a spiral structure that is surrounded by the inlet jets, with upward-flowing exterior fluid at the center of the spiral vortex structure. The arms of this spiral are advected downward with time by the inlet jet flow until they reach the impingement surface. Knowledge of this flow structure at different separation distances is necessary in order to design systems that utilize this flow field for enhancement of particle removal rate or heat/mass transfer from a surface.

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## Figures

Fig. 1

Schematic diagrams of the experimental system. (a) Water flow network, showing: (1) sump pump, (2) water reservoir, (3) constant-head tank, (4) overflow tank, (5) globe valve, (6) Omega FLR 1009 flow meter, (7) dye reservoir (red), (8) turbulent mixer, (9) nozzle with jets oriented 15 deg in the azimuthal direction, (10) test tank with impingement surface on the bottom, and (11) waste water. (b) Close-up of test section, showing: (A) laser, (B) cylindrical lens, (C) vertical laser sheet, (D) impingement surface, (E) nozzle, (F) jet intake port, and (G) suction outlet port. The figure also shows the coordinate system used in the paper and the separation distance h between the nozzle face and the impingement surface. (c) Close-up drawing of the nozzle face, showing the eight jet inlets (white) in a ring surrounding the suction outlet (gray). (d) Photograph of the nozzle and impingement surface in a side view, showing the distance z upward from the impingement surface and the distance Δz downward from the nozzle face.

Fig. 2

Dimensionless velocity magnitude contour plot obtained by PIV in a horizontal slice at the midplane between the nozzle face and the impingement surface with Re = 555 and dimensionless separation distance of ξ = 0.67. The planar streamlines are initialized at points (x, y) = (0.5,0), (0,0.5), (−0.5,0), and (0,−0.5), with one streamline on each side of the image.

Fig. 3

Velocity magnitude contour plots obtained by PIV in a vertical slice with Re = 555 and separation distances of: (a) ξ = 0.67, (b) ξ = 1.33, and (c) ξ = 6.7

Fig. 4

Azimuthally averaged azimuthal, radial, and axial velocity components as a function of radius, evaluated on a horizontal plane immediately below the nozzle. Cases are shown for separation distances of: (a) ξ = 0.67, (b) ξ = 1.33, and (c) ξ = 6.7, with curves given for Re = 155 (A), 378 (B), and 555 (C).

Fig. 15

LIF figure in the vertical plane for a case with Re = 155 and ξ = 6.7 showing the downward propagation of the waves on the central spiral vortex. Images are separated by a dimensionless time interval Δt = 0.0058.

Fig. 12

Time series of LIF figures in the horizontal plane for a case with Re = 155 and nozzle separation distance ξ = 1.33. The imaging plane is located Δz = 0.25 below the nozzle surface. The images show a pair of wall-bounded vortices (marked using white dashed lines) rotating clockwise about the center of the flow, with a dimensionless time interval Δt = 0.0058 between images.

Fig. 11

Horizontal cross sections of the bounded vortex flow with Reynolds number Re = 155 for a case with dimensionless separation distance ξ = 1.33 between the nozzle and the impingement surface. The horizontal slices are shown at distances of: (a) Δz = 0.25, (b) 0.50, (c) 0.75, and (d) 1.0 below the nozzle surface. The jet flows induced by each of the eight jet inlets are numbered and are shown to exhibit a clockwise change in position with distance from the nozzle.

Fig. 10

Contour plots showing the shear stress magnitude and shear stress lines for cases with Re = 555 and (a) ξ = 0.67 and (b) ξ = 1.33. The separatrix is indicated by a dark line in both plots. Inside the separatrix shear stress lines spiral inward, whereas outside the separatrix shear stress lines spiral outward.

Fig. 9

Azimuthally averaged dimensionless shear stress on the impingement surface in the azimuthal and radial directions for cases with separation distances of: (a) ξ = 0.67 and (b) ξ = 1.33 and Reynolds numbers Re = 155 (A), 378 (B), and 555 (C)

Fig. 8

Swirl number S plotted as a function of distance Δz to the nozzle face for the case with ξ = 6.7 and Re = 555. An exponential fit of the form S = S0 exp(-βΔz), with β = 0.977 and S0 = exp(-12.306), is shown as a dashed line.

Fig. 7

Plots of the radial flow rate (top) as a function of radius r and of the axial flow rate (bottom) as a function of distance Δz below the nozzle, for cases with separation distances of: (a) ξ = 0.67, (b) ξ = 1.33, and (c) ξ = 6.7 and Reynolds numbers Re = 155 (A), 378 (B), and 555 (C)

Fig. 6

Plot showing the azimuthally averaged dimensionless velocity profiles in the: (a) azimuthal and (b) axial directions, for a case with Re = 555 and ξ = 6.7. The profiles are presented in two groups, for horizontal cross sections above the waist of the hourglass profile (UPPER) and for cross sections below the waist of the hourglass (LOWER). The lines correspond to distances below the nozzle face in the UPPER plot of Δz = 0.13 (A), 0.67 (B), 2.18 (C), and in the LOWER plot of Δz = 2.18 (C), 3.87 (D), 4.93 (E), and 6.0 (F). Additional curves were necessary to show variation of the azimuthal velocity, which are drawn using dashed lines and indicated with lowercase letters, at heights Δz = 1.2 (a), 1.73 (b), 2.8 (c), and 3.33 (d).

Fig. 5

Plot showing time-averaged velocity magnitude field and a few representative planar streamlines obtained from PIV data for a case with Re = 555 and ξ = 6.7, taken in horizontal planes at distances of: (a) Δz = 0.25, (b) 1.3, (c) 2.7, and (d) 4.0 below the nozzle. Each figure is obtained by averaging over 100 images. The planar streamline in each image is initialized at (x,y) = (-0.5,0).

Fig. 16

LIF figure in the horizontal plane for a case with Re = 155 and ξ = 6.7 showing the oscillation of the spiral vortex over one period. The imaging plane is located Δz = 4.0 below the nozzle face. The slice through the spiraling vortices is marked using a dashed line, and the up-flow regions correspond to the dark region marked by a solid white line. Images are separated by a dimensionless time interval Δt = 0.0058.

Fig. 14

Plots showing computational results for region covered by vortex patches (red) for a touching vortex V-state and associated streamlines with: (a) no sink and (b) a sink of dimensionless strength m = 1.3×105 located at the origin

Fig. 13

Velocity planar streamlines illustrating motion induced by the wall-bounded vortex, obtained from an instantaneous PIV image in a horizontal plane with Re = 200 and nozzle separation distance ξ = 1.33. The imaging plane is located Δz = 0.50 below the nozzle surface. The vortex has an oval form that rotates with time about its centroid with an inward suction flow.

Fig. 17

Schematic diagram illustrating the formation of inward and outward regions of radial drift, separated by a separatrix curve, for the bounded vortex flow near the impingement surface

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