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Technical Briefs

Effects of Jet Obliquity on Hydraulic Jumps Formed by Impinging Circular Liquid Jets on a Moving Horizontal Plate

[+] Author and Article Information
R. P. Kate, P. K. Das

Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721302, India

Suman Chakraborty1

Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721302, Indiasuman@mech.iitkgp.ernet.in

1

Corresponding author.

J. Fluids Eng 131(3), 034502 (Feb 04, 2009) (5 pages) doi:10.1115/1.3059583 History: Received June 05, 2006; Revised October 27, 2008; Published February 04, 2009

The present work attempts to investigate the effects of jet obliquity on the spatial patterns formed as a consequence of hydraulic jumps due to the impingement of circular liquid jets on continuously moving but nonaccelerating horizontal flat plates. Both the normal and the oblique impinging jets are considered, in order to characterize the contrasting features of the associated hydraulic jump mechanisms. Theoretical calculations are executed to obtain the locations of the jump, for different jet and plate velocities and jet inclination angles, using a depth-averaged momentum integral equation for shallow-free surface flows. Comparisons are subsequently made between the theoretical predictions and experimental observations reported in the literature, and a good agreement between these two can be observed. Special cases of a circular hydraulic jump when the target plate is stationary and the impinging jet is vertical, and elliptic hydraulic jumps when the target plate is stationary and the impinging jet is obliquely inclined, are also discussed. It is conjectured that flow due to impinging jets on a horizontal moving plate can be modeled as an equivalent flow due to an inclined impinging jet on stationary horizontal flat plates, with appropriate alterations in the jet velocity and the jet inclination angles.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 1

Qualitative pictures of hydraulic jumps due to impinging circular liquid jets on a stationary smooth horizontal surface: (a) jet impinging normally on the plate and (b) jet inclined at an oblique angle with the plate

Grahic Jump Location
Figure 2

(a) Schematic of an impinging jet on a horizontal moving surface, (b) jet impinging with velocity V and inclination angle ϕ on a plate moving with a velocity U can be considered equivalent to the jet impinging with a velocity Vr and inclination angle α, on a stationary horizontal plate, and (c) deformed impingement zone due to obliquely impinging circular liquid jet on horizontal moving surface

Grahic Jump Location
Figure 3

Hydraulic jump profiles for different jet and plate velocities for normal impinging jets, as compared with the experimental and numerical results reported in Gradeck (10): (a) Vj=0.41 m/s, U=2.04 m/s, (b) Vj=1.0 m/s, U=1.53 m/s, and (c) Vj=1.0 m/s, U=1.02 m/s)

Grahic Jump Location
Figure 4

Hydraulic jump profiles due to circular liquid jet impinging jets on a smooth horizontal moving surface, for (a) a normal impinging jet (Q=3.33×10−5 m3/s, r0=4.4 mm) and (b) an oblique impinging jet (Q=3.33×10−5 m3/s, r0=4.4 mm, ϕ=60 deg)

Grahic Jump Location
Figure 5

Change in aspect ratio (ratio of major axis, a, to the minor axis, b, of the elliptical hydraulic jumps) with change in velocity ratio for different jet inclination angles

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