The joint probability density functions of droplet size and velocity have been represented in sprays by the two-dimensional hyperbolic distribution. A brief description of the hyperbolic distribution is provided, and a procedure to compute its eight parameters outlined. Analytical expressions for certain statistical quantities, such as mean diameters, momentum, kinetic energy etc., applicable under certain restrictions, are obtained. The computations for a water spray issuing from a Danfoss 60° solid cone oil-burner nozzle demonstrate not only that the hyperbolic distribution provides an excellent approximation for the joint size and velocity distributions for the measurements taken along the entire length of the spray axis, but also that such representation presents a clear insight into the physics of the motion and the related size formation. The computations reveal a developing region, with areas dominated by breakup or coalescence of droplets, followed by a developed state with little change in droplet size but continuously decreasing velocity. It is concluded that this novel approach is well suited to the description of sprays. Suggestions are made for further research in this direction. © 1990.
Bhatia, J. C., & Durst, F. (1990). Description of sprays using joint hyperbolic distribution in particle size and velocity. Combustion and Flame, 81(3–4), 203–218. https://doi.org/10.1016/0010-2180(90)90019-N