Offset Turbulent Jets in Low-Aspect Ratio Cavities

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.

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.

(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.

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.

(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.

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, l_max ∼ (5.1–5.3)D.

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.

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.

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.

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

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.

Variation of mean (normalized) velocity half-width (Y_1/2) 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.