A Revised Model for Impinging Sheet based on the Velocity Measurement

As two liquid jets impinge on each other, a liquid sheet surrounded by a rim is formed around the impinging point. In the existing sheet models, the velocity of the sheet is assumed to be a constant along the radial direction centered to the impinging point. With this assumption, the sheet thickness and rim diameter are estimated by evaluating the conservations of mass, momentum, and energy. To verify such an assumption, in the present work, the velocity of an impinging sheet formed by two ethanol jets is measured via particle tracking velocimetry (PTV) by adding tracer particles into the fluid. With the aid of an imaging acquiring system and the post-processing algorithm, the locations of those particles in different frames are identified and the fluid velocity is measured. When PTV images are recorded, the shadow of the particles is enlarged by the liquid wrapped around them. This lens effect enables a magnified measurement of much smaller particles. The experimental results show a velocity distribution that changes both along the angular and radial directions on the impinging sheet. To explain the observed velocity change, the air friction must be taken into consideration and the theoretical analysis is given. The air boundary layer over the sheet is solved by introducing the stream function and similarity approach. Additionally, with the air velocity distribution attached to the sheet, a revised sheet model is developed to describe the impinging sheet. The model coefficients are determined using the experimental data. The comparisons between the model prediction and the experimental results of the sheet velocity show a relative error lower than five percent.