Dissipative Collisions of Impinging Liquid Jets Having Uniform Velocity Profiles

TL;DR

This paper investigates energy dissipation in impinging liquid jets with uniform velocity profiles by revising mass and momentum balances to include non-ideal collisions, developing empirical correlations for the coefficient of restitution and stagnation point location.

Contribution

It introduces a revised theoretical framework for impinging jets accounting for energy loss and provides empirical correlations for the coefficient of restitution based on impingement angle.

Findings

Coefficient of restitution decreases with larger impingement angles.

Stagnation point location correlates with energy dissipation levels.

Theoretical model predicts thickness distribution considering dissipative effects.

Abstract

The dissipation of energy in the impingement zone from the collision of impinging, free, equal jets of liquids was investigated by comparison with studies on the energy dissipation from the collision of impinging, free, equal sheets of liquids. Loss of energy was studied in terms of the coefficient of restitution (COR) of the collision. With few exceptions, previous analytical studies have assumed that there is no loss of energy resulting from the collision of the jets (COR = 1), and for jets with uniform velocity profiles, the sheet velocity (velocity after the collision) is equal to the jet velocity (velocity before the collision). In this study, mass and momentum balances of impinging jets with uniform velocity profiles are revised to include the impact of non-equal velocities (COR < 1). After development of the applicable theory, the COR for impinging jets is calculated from available data in the literature on jet and sheet velocities as well as the location of the stagnation point in the impingement zone. Simple empirical correlations were developed for 1) the COR of impinging jets as a function of impingement angle and 2) the relationship of the location of the stagnation point to the COR. A theoretical equation was also derived for the impact of dissipative collisions on the thickness distribution in the liquid sheet.