A Simplified Maximum-Entropy-Based Drop Size Distribution

The Maximum Entropy Formalism and the Prediction of Liquid Spray Drop-Size Distribution

“…In each situation the peak diameter and distribution width were well estimated. Ahmadi and Sellens [25] furthermore observed that the agreement obtained with this three-parameter distributions (Equation 44) is as good as the one obtained with the four-parameter log-hyperbolic distribution. They concluded that three moments are required as input information to predict a spray drop-diameter distribution, namely, D -10 , D 30 and D 32 and that the advantage of this model compared to empirical distributions such as log-hyperbolic distribution for instance, is that the parameters in the MEF distribution are directly linked to a physical model.…”

“…They also demonstrated that the use of a combined energy constraint, which leads to the solution given by Equation 30, reported a prediction in strong disagreement with the number-based drop-size distribution f n (). Based on Sellens'observations [21], Ahmadi and Sellens [25] emphasized that the constraints on momentum and kinetic energy (Equations 20 and 21) in the spray carry only velocity information, i.e., they have a negligible influence on the number-based drop-size distribution f n (). It is therefore possible to consider drop size and velocity separately.…”

“…They concluded that three moments are required as input information to predict a spray drop-diameter distribution, namely, D -10 , D 30 and D 32 and that the advantage of this model compared to empirical distributions such as log-hyperbolic distribution for instance, is that the parameters in the MEF distribution are directly linked to a physical model. Finally, since Ahmadi and Sellens [25] succeeded in representing experimental data-and in particular those published by Bhatia and Durst [19]-with their maximum entropy distribution as well as with the one due to Li and Tankin [16], they concluded that Bhatia and Durst misapplied the distribution function.…”

Quadratic formula for determining the drop size in pressure-atomized sprays with and without swirl

“…Fluids 28, 063302 (2016) exist in empirical modeling, experimental measurements, and computational simulations of drop size and velocity distributions in various spray configurations (a small set of representative works can be found in Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. More recent work Villermaux and co-workers (e.g., Ref.…”

Trends in Comprehensive Modeling of Spray Formation

“…Noting this, Ahmadi and Sellens [228] argued that a pdf of size distribution may be solely developed using four constraint equations: i.e., normalization condition, conservation of mass and surface energy, and partition constraint condition earlier proposed by Sellens [221]. Van der Geld and Vermeer [229] used the normalization condition along with the conservation of mass and surface energy as constraints in the maximum entropy model and were able to predict a bimodal distribution of droplet size in a spray due to the occurrence of the satellite droplets.…”