Induced air velocity within droplet driven sprays

Abstract

A study of the fundamental mechanics of the droplet and gas motion in liquid sprays is presented in this paper. Only vertical sprays without any externally applied gas flow are considered. First a detailed account of the origin of induced air motion within spray jets is given, and this lays the basis for a new one-dimensional model for predicting the induced axial air velocity. Two main flow zones (zone I and zone II) are identified, where the droplet velocity is much greater and of the same order as the induced air velocity respectively. Within zone I there is a near-sub-zone I, close to the nozzle where the droplet velocities deviate little from their initial values, and it is found that the air velocity decreases or increases to a maximum value, depending on whether its initial value is greater or less than a critical value, which itself is a function of the drag coefficient, the initial spray radius and the droplet velocity. In this zone the average induced air velocity decays more slowly, as z$^{-\frac{1}{2}}$ (z being the downstream distance) than the rate of decay, as z$^{-1}$, in regular unforced jets. Further downstream in the adjacent forced jet sub-zone, the drag of the faster moving droplets forces an air jet to develop with a rate of growth that is determined by the turbulence if the angle of the spray droplets is small or by the angle of the spray if the angle is large. In this second sub-zone, which typically extends to the stopping distance of the droplets, the flow is largely independent of the flow in the near sub-zone. The 1D model was applied to a rose-head axisymmetric spray and a flat-fan agricultural spray. The calculations agree closely with experimental observations. To calculate the radial variation of the air velocity a 2D axisymmetric model was developed where the air velocity was obtained in the form of a similarity solution. The predictions were in good agreement with the measurements of Binark & Ranz (1958). Finally it is shown that the 1D and the 2D models are consistent with each other.