The Liquid Sheet Shape and Thickness Predictions in Two Impinging Jets Based on Minimum Energy Principle

TL;DR

This paper applies the minimum energy principle to select the most physically accurate liquid sheet thickness in impinging jet atomizers, resolving non-uniqueness issues among existing theoretical solutions.

Contribution

It introduces a new criterion based on minimum stored energy to determine the most physical solution for liquid sheet shape and thickness in impinging jets.

Findings

Hasson and Peck's solution is most physically accurate.

The minimum energy principle effectively distinguishes physical solutions.

Theoretical predictions align well with experimental shadowgraph results.

Abstract

In an impingement atomizer, a thin sheet of liquid generates by impinging two identical jets. The thickness is one of the most crucial parameters in quantifying the spray characteristics for which several non-unique solutions have been acquired theoretically, so far. Among all, three theoretical solutions presented by Hasson and Peck, Ranz, and Miller are the most reliable expressions in terms of precision. Apparently, all these distinctive solutions cannot be physical simultaneously. However, a theoretical satisfactory explanation for having various non-unique solutions has not been presented. Moreover, a meaningful criterion to recognize the most physical solution is highly desirable. To address this gap, it is hypothesized that an additional constraint should be considered in couple with the continuity and momentum equations to have a unique prediction for the liquid sheet thickness. By employing the minimum energy principle, the minimum stored energy in the liquid sheet is considered the crucial constraint to achieving a unique solution and rejecting non-physical ones. Since the inviscid flow assumption is reasonably valid for the liquid sheet, the minimum energy principle satisfies when the minimum lateral surface predicts. To quantify the lateral surface area the sheet shape is presented in terms of the sheet thickness and numerically calculated by the fourth-order Runge-Kutta method for the three mentioned expressions. Using the liquid shape, the lateral surface areas are calculated and compared in three different impingement angles of 58, 89, and 117 degrees. In addition, the liquid shapes are visually compared with the experimental results obtained by the Shadowgraph technique. In sum, it is proved that Hasson and Peck presented the most physical solution for the liquid sheet thickness.