Mathematical models for turbulent round jets based on “ideal” and “lossy” conservation of mass and energy

Abstract

[EN] We propose mathematical models for turbulent round atomized liquid jets 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 fluid with the phases in local dynamic equilibrium, or so-called locally homogeneous flow (LHF). The models differ in their particular balance of explanatory capability and precision. To derive them we impose partial conservation of the initial mass and energy fluxes, introducing loss factors again as disposable parameters. Depending on each model, the equations admit explicit or implicit analytical solutions or a numerical solution in the discretized model case. The described variables are the the two-phase fluid’s composite density and velocity, both as functions of the distance from the nozzle, from which the dynamic pressure is calculated.