Droplet size and velocity distribution function in sprays based on maximum entropy principle

A droplet size and velocity distribution function was theoretically derived based on the maximum entropy principle and the momentum conservation law.The numerical calculations for the function on the droplet size and velocity distribution of pure diesel and L30(mixed liquefied petroleum gas(LPG)/diesel fuel in a mass ratio of 30 per cent LPG) were done, and a comparison analysis of the spray characteristics between diesel and L30 was conducted.The result shows that because of the influence of flash boiling injection, the peaks of the droplet size distribution curve of L30 are evidently higher than those of diesel, the curve and its peaks move toward smaller droplet diameters region, which indicates that the droplets produced by injecting L30 are smaller than those of diesel; the peaks of the velocity distribution curves of L30 are higher than those of diesel, and locate a lower velocity region, which shows that the droplet number of lower speed is more than that of higher speed for the L30.The size-velocity(D-u) contour maps of diesel and L30 obtained by the droplet size and velocity distribution curves shows that smaller drops occupy a wide velocity space, and lower speed droplets have a wide size space.The size and velocity distribution of L30 converges faster than that of diesel, which indicates that the smaller size and lower velocity drops of L30 are more than those of diesel, and the spray quality of L30 is better than that of diesel.