Description of sprays using joint hyperbolic distribution in particle size and velocity
Abstract
The joint probability density functions of droplet size and velocity have been represented in sprays by the twodimensional 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, and kinetic energy, applicable under certain restrictions, are obtained. The computations for a water spray issuing from a Danfoss 60deg solid cone oilburner 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.
 Publication:

Combustion and Flame
 Pub Date:
 September 1990
 DOI:
 10.1016/00102180(90)90019N
 Bibcode:
 1990CoFl...81..203B
 Keywords:

 Drop Size;
 Hyperbolic Functions;
 Particle Size Distribution;
 Probability Density Functions;
 Spray Characteristics;
 Velocity Distribution;
 Fuel Sprays;
 Nozzle Flow;
 Spray Nozzles;
 Fluid Mechanics and Heat Transfer