Special Section Articles

Offset Turbulent Jets in Low-Aspect Ratio Cavities

[+] Author and Article Information
C. Nath

Environmental Fluid Dynamics Laboratories,
Department of Civil and Environmental
Engineering and Earth Sciences,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: cnath@nd.edu

S. I. Voropayev

Environmental Fluid Dynamics Laboratories,
Department of Civil and Environmental
Engineering and Earth Sciences,
University of Notre Dame,
Notre Dame, IN 46556;
P. P. Shirshov Institute of Oceanology,
Russian Academy of Sciences,
Moscow 117851, Russia

D. Lord

Geotechnology and Engineering Department,
Sandia National Laboratories,
P.O. Box 5800 MS-0706,
Albuquerque, NM 87185

H. J. S. Fernando

Environmental Fluid Dynamics Laboratories,
Department of Civil and Environmental
Engineering and Earth Sciences,
Department of Aerospace
and Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 24, 2013; final manuscript received November 4, 2013; published online April 28, 2014. Assoc. Editor: Ye Zhou.

J. Fluids Eng 136(6), 060911 (Apr 28, 2014) (7 pages) Paper No: FE-13-1449; doi: 10.1115/1.4026023 History: Received July 24, 2013; Revised November 04, 2013

The flow induced by a round turbulent offset jet in a low-aspect ratio cylinder is investigated experimentally, with applications to degassing of U.S. Strategic Petroleum Reserves (SPR). Particle image velocimetry and flow visualization are used for flow diagnostics. The measurements include the jet penetration (mixing) depth l, jet spreading rate, and the mean velocity/vorticity fields for different offset positions Δ. With the introduction of offset, the flow patterns change drastically. For 0 < Δ/D < 0.2 the jet deflects toward the wall while precessing (as in the axisymmetric case), for 0.2 < Δ/D < 0.4 the jet hugs the wall but with an oscillating tail, and for 0.45 < Δ/D the jet appears as a wall jet. In all cases, the jet is destroyed at a certain distance (mixing or penetration depth) from the origin. This mixing depth takes its lowest value for 0 < Δ/D < 0.2, with l ≈ (3.2–3.6)D, becomes maximum at Δ/D = 0.4 with l ≈ 5.2D, and drops to l ≈ 4.5D when the jet is close to the wall. Recommendations are made for suitable Δ/D values for optimal operation of SPR degassing.

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Grahic Jump Location
Fig. 1

(a) Experimental setup: 1: Rectangular tank, 2: glass cylinder (cylinder A; D = 10 cm, L = 110 cm) seeded with Pliolite particles, 3: nozzle (d0 = 0.165 cm), 4: Nd:YAG laser, and 5: jet withdrawal position. The coordinate system used is also shown. (b) Same setup with a shorter cylinder (cylinder B; D = 10 cm, L = 80 cm) fixed to the top cover was employed for streak photography. Tracer particles are shown inside the cylinder, illuminated by the laser sheet. The dashed box indicates the observational area for PIV.

Grahic Jump Location
Fig. 2

Contours of streamlines for different radial offset positions (Δ/D): (a) 0, (b) 0.2, (c) 0.25, (d) 0.4, and (e) 0.49. Experiments conducted at the same Reynolds number of 10,000. The jet location is indicated in the figure. In (c) the arrow points to the oscillatory tail.

Grahic Jump Location
Fig. 3

(a) Pair of velocity vectors shown for offset jet Δ/D = 0.2 in the x-y plane for consecutive (i) first second, (ii) second second, (iii) third second, and (iv) fourth second after the flow reached some quasi-steady state. Reynolds number = 10,000. (b) Pair of velocity vectors for offset jet Δ/D = 0.25 in the xy plane for consecutive (i) first second, (ii) second second, (iii) third second, and (iv) fourth second after the flow reached some quasi-steady state. Reynolds number = 10,000.

Grahic Jump Location
Fig. 4

Mean velocity profiles in the x-y plane for radial offset positions (Δ/D): (a) 0, (b) 0.2, (c) 0.25, (d) 0.4, and (e) 0.49. Vorticity is measured in s−1. Nozzle positions at the top of the cylinder for different radial positions are shown by an arrow.

Grahic Jump Location
Fig. 5

Sequence of particle streak images showing the formation of large-scale (coherent) eddies in the x-y plane for Δ/D = 0.4. Large eddies form clockwise circulation rather than oscillating between cylinder walls. In the rightmost inset, the dotted line indicates laser sheet, whereas the black dot is the nozzle position. Re = 10,000. An exposure of 0.1 s was used.

Grahic Jump Location
Fig. 6

Decay of dimensionless maximum centerline mean velocity Uc*¯ in the x-y plane along the dimensionless distance X = x/D for different radial offset positions of the nozzle. Comparisons between data for axisymmetric confined jet, estimates of model I [12] and that of model II developed in this study are shown. The jet spreading angle β used in model II is experimentally found to be 0.14. This can be compared with unconfined axisymmetric jets, where the spreading angle is ∼0.1 [1]. Note that for the magnification the figure shows that for Δ/D = 0.4, lmax ∼ (5.1–5.3)D.

Grahic Jump Location
Fig. 7

Transverse distribution of mean axial dimensionless velocity U in the x-y plane at different dimensionless distances from the nozzle for different radial offset positions (Δ/D): (a) 0, (b) 0.2, (c) 0.25, (d) 0.4, and (e) 0.49. The symbols representing distances are shown in the bottom of the figure.

Grahic Jump Location
Fig. 8

Variation of mean (normalized) velocity half-width (Y1/2) for different radial offset positions (Δ/D = 0, 0.2, 0.25, 0.4, and 0.49) along the X nozzle distance. Reynolds number = 10,000.

Grahic Jump Location
Fig. 9

Dimensionless mixing length l/D in the flow as a function of different radial offset positions. Mixing lengths are calculated based on different criteria discussed in the text. Three Reynolds numbers have been used: Re = 7000, 10,000, and 15,000.

Grahic Jump Location
Fig. 10

Images from DVC recordings for different radial positions of the nozzle. A cylinder with an open bottom is in a larger beaker filled with water. (a) Initially the free surfaces of the cylinder (1) and beaker (2) coincide, but after the introduction of jet from nozzle exit (3), the water level in the cylinder drops by Δh. In (b), the jet is at the center and in (c) it is near the wall.

Grahic Jump Location
Fig. 11

Variation of the difference in water level height Δh (cm) between the cylinder and beaker as a function of different radial offset positions (where the point shows measurement at Δ/D = 0.01, 0.21, 0.33, and 0.49 and the line represents best fit to measurements). Reynolds number: Re = 20,000.

Grahic Jump Location
Fig. 12

Schematic of jet flow in a cylindrical cavity shown up to jet breakup distance x = Lc. The jet exit velocity and nozzle diameter is u0 and d0, respectively. Here the (uniform) upward velocity is denoted as uu. The dashed line indicates the control volume. Two control volumes are shown, one with the lower end at xc and the other at Lc.




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