Free Surface Profile of a Circular Hydraulic Jump

Impinging jets have excellent heat transfer characteristics and are widely used where a lot of heat has to be moved or removed rapidly.  In the case of a liquid jet directed downward against a horizontal surface, a hydraulic jump forms when the free surface makes a sudden transition from supercritical to subcritical flow.  The jump formed by the radial spread of a circular jet is sometimes called a “circular” hydraulic jump.

This work measured the hydraulic jump surface profile and unsteady fluctuations for several configurations of jet sizes, flow rates and downstream depths.  The downstream depth was controlled by an adjustable height weir shown in the figure as height “w”.

The instantaneous position of the free surface was determined by using a fine wire probe.  A small dc voltage was applied to the water, and the probe completed the circuit between the water and the power supply ground.  The fluctuating surface of the hydraulic jump made it necessary to approximate the jump profile as a statistical representation of a large number of individual measurements.

The figure below shows data for a nozzle diameter of 7.8 mm.  Each symbol represents the dimensionless depth (y/d)  where the probe was in the water 50% of the time.  The vertical error bars on each plotted point represent the 0% and 100% submersion locations.  This  figure provides a representation of the approximate mean location of the free surface, along with the approximate vertical extent of the free surface fluctuations.  As would be expected, the fluctuations are largest near the front edge of the hydraulic jump, and are greater for higher Reynolds number.  The progression from a single jump structure to a double jump structure with increasing downstream depth described by Liu and Lienhard (1993) is clearly visible.

The next figure shows the extent of the vertical fluctuations for several sets of data.  The fluctuations are largest at the front of the hydraulic jump, then drop rapidly and decrease more slowly toward the back of the jump.

 Some measurements were taken in the thin flow layer upstream of the hydraulic jump.  The figure below demonstrates a comparison of some measured layer depths with a correlation of layer depths calculated from velocity measurements in a separate work.  Overall, the comparison shows the same general trends and similar layer depths. 

 

  

References

Stevens, J.W., 1995, “Free Surface Flow Profile and Fluctuations of a Circular Hydraulic Jump Formed by an Impinging Jet,” ASME Journal of Fluids Engineering, Vol. 117, pp. 677-682.

Stevens, J., and Webb, B.W., 1992, “Measurements of the Free Surface Flow Structure Under an Impinging Free Liquid Jet,” ASME Journal of Heat Transfer, Vol. 114, pp. 79-84.

Liu, X., and Lienhard, V.J.H., 1993, “The Hydraulic Jump in Circular Jet Impingement and in Other Thin Liquid Films,” Experiments in Fluids, Vol. 15, pp. 108-116.