Revised Modeling of the Thickness and Velocity Distribution of the Impinging Sheet Formed by Two Jets

The modeling of liquid sheets formed by two impinging jets dates back to the 1960s, with early studies primarily focusing on predicting the sheet thickness. These classical models typically assumed a constant velocity within the sheet and applied conservation of mass and momentum to derive the thickness distribution. However, recent experimental studies have revealed that the velocity within the sheet is not uniform, suggesting that energy losses—particularly due to air friction—should be considered to accurately describe the velocity decay as the fluid travels away from the impingement point.

This research presents a revised model of the impinging liquid sheet by incorporating the effect of air friction acting on the sheet surface. By simultaneously solving the conservation equations for the sheet flow and the boundary layer equations for the surrounding air, the velocity distribution within the sheet is derived. Consequently, the sheet thickness distribution is obtained through mass conservation. Additionally, the modeling of the rim structure is addressed by balancing the inertial and surface tension forces at the sheet edge. As a byproduct, the velocity profile of the air boundary layer over the sheet surface is also obtained, though it is not the focus of this study.

The revised model demonstrates improved agreement with experimental observations and identifies key parameters influencing sheet dynamics. This work contributes to a more accurate understanding of impinging sheet behavior and offers valuable insights for enhancing atomization performance in engineering applications.