Mass entrainment rate of an ideal momentum turbulent round jet

TL;DR

This paper introduces a simple two-phase-fluid model for turbulent round jets that predicts the mass entrainment rate based on the cone angle, validated by experimental data.

Contribution

The paper presents an analytical two-phase model for turbulent jets that links the entrainment rate to the cone angle, providing a theoretical basis and experimental validation.

Findings

The model predicts a constant entrainment rate coefficient based on cone angle.

Experimental data for air jets agree with the model's predictions.

Analytical solutions describe density and velocity profiles as functions of distance.

Abstract

We propose a two-phase-fluid model for a full-cone turbulent round jet that describes its dynamics in a simple but comprehensive manner with only the apex angle of the cone being a disposable parameter. The basic assumptions are that (i) the jet is statistically stationary and that (ii) it can be approximated by a mixture of two fluids with their phases in dynamic equilibrium. To derive the model, we impose conservation of the initial volume and total momentum fluxes. Our model equations admit analytical solutions for the composite density and velocity of the two-phase fluid, both as functions of the distance from the nozzle, from which the dynamic pressure and the mass entrainment rate are calculated. Assuming a far-field approximation, we theoretically derive a constant entrainment rate coefficient solely in terms of the cone angle. Moreover, we carry out experiments for a single-phase turbulent air jet and show that the predictions of our model compare well with this and other experimental data of atomizing liquid jets.