Date of Award


Document Type


Degree Name

Master of Science (MS)


Aerospace, Physics, and Space Sciences

First Advisor

Mark Archambault

Second Advisor

Jim Jones

Third Advisor

Ju Zhang

Fourth Advisor

Hamid Hefazi


To obtain accurate spray droplet size and velocity distributions, higher-order statistical moments are needed. The Maximum Entropy formalism has been successfully used to predict the motion of spray flow in different models. This work is mainly focused on the use of the fourth-order moment combinations to calculate droplet probability density functions using the Maximum Entropy Formalism. Beginning with the second-order moment combinations, Lagrange multipliers have been calculated subject to given moment constraints, defining the probability density function. All lower moments are included when calculating the possible different higher-order moment combinations. From the results, each moment combination generated a set of unique Lagrange multipliers. An error analysis, defined as the average deviation between the numerical data and experimental data set and the

tendency of numerical errors, decreases with the increasing number of constraints. The important moment combinations are the ones with the least average deviation. A frequency analysis is used to show some of the moments that might significantly affect the probability density functions’ shape. By involving all of the high-frequency moments, a significant quantitive effect of probability density functions and saving the computation cost could become present. Meanwhile, a special comparison shows that all of the lower moments are necessary to be included for calculating the higher-order moment.


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