Date of Award


Document Type


Degree Name

Master of Science (MS)


Aerospace, Physics, and Space Sciences

First Advisor

Mark Archambault

Second Advisor

Gnana Bhaskar Tenali

Third Advisor

Madhur Tiwari

Fourth Advisor

David C. Fleming


Characterizing spray flows has been an issue of interest for years, particularly in regards to fuel injection in engines. Droplet velocity and diameter, among other characteristics, are crucial to understanding spray flows. One approach for determining these quantities in a spray is using a statistical approach that solves for the moments of droplet characteristics as they evolve in space and time. A theoretical probability density function (PDF) can be formulated using various combinations of moments which evolve according to derived moment transport equations (thus evolving the PDF), using the principle of maximum entropy as closure to the system. Building upon previous work completed, this paper performs error analysis on thousands of moment combinations that have been calculated to determine which moments are crucial to reducing the error of a theoretical PDF relative to an experimental PDF. The ultimate goal is to determine which higher-order moments are sufficiently important to be tracked through moment transport equations rather than solving for the evolution of all moments of a given order with such equations. It is determined that most of the third-order moments are equally important, while only βŒ©π‘ˆ4βŒͺ,〈𝐷2𝑉2βŒͺ, and βŒ©π‘ˆ2𝑉2βŒͺ and 〈𝐷4π‘ˆβŒͺ, 〈𝐷4𝑉βŒͺ, and βŒ©π‘‰5βŒͺ are the important fourth and fifth-order moments, respectively.