Dynamical model of a turbulent round jet through conservation of mass flux and power

Abstract

We propose a family of two-phase-fluid models for a full-cone turbulent round jet that describe its dynamics in a simple but comprehensive manner with the apex angle of the cone being the main 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 (so-called Locally Homogeneous Flow). To derive the model, we impose either full or partial conservation of the initial mass and total power fluxes, introducing mass and power loss factors as disposable parameters. Our model equations admit implicit analytical and numerical 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. Moreover, we show that the predictions of our models compare well with experimental data for single-phase turbulent air jets and atomizing liquid jets.