#### Recommended Citation

January 1, 2014.

#### Abstract

This project explores the stability analysis of a given flow field. Specifically, where the peak disturbance occurs in a flow as this is the disturbance that is most likely to occur. In rocket combustion, it is important to understand where the maximum disturbance occurs so that the mixing of fuel can be stabilized. The instabilities are the results of frequencies in the area surrounding the flow field. The linear stability governing equations are employed to better understand the disturbance. The governing equations for continuity and momentum in the *x* and *y* directions are used to form an equation for the second derivative of the transverse complex velocity disturbance amplitude (the transverse perturbation) in terms of *y*. This research uses the shooting method and Euler’s method of numerical integration to find a frequency (ω) that affects the flow field of a given velocity profile. The shooting method involves making an educated guess for ω, numerically integrating the second derivative of the transverse perturbation across the flow field to find the transverse perturbation, and comparing the final value with the expected asymptotic solution. Euler’s method of numerical integration and the computing language Python are used to find a method to predict the frequencies (ω) that cause disturbances for a given velocity profile.

#### Disciplines

Aerodynamics and Fluid Mechanics | Engineering Physics | Numerical Analysis and Computation | Ordinary Differential Equations and Applied Dynamics | Other Applied Mathematics | Other Mathematics | Propulsion and Power

#### Mentor

David Forliti

#### Lab site

Air Force Research Laboratory (AFRL)

#### Funding Acknowledgement

This material is based upon work supported by the S.D. Bechtel, Jr. Foundation and by the National Science Foundation under Grant No. 0952013. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the S.D. Bechtel, Jr. Foundation or the National Science Foundation. This project has also been made possible with support of the National Marine Sanctuary Foundation. The STAR program is administered by the Cal Poly Center for Excellence in Science and Mathematics Education (CESaME) on behalf of the California State University (CSU).

#### Included in

Aerodynamics and Fluid Mechanics Commons, Engineering Physics Commons, Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons, Other Applied Mathematics Commons, Other Mathematics Commons, Propulsion and Power Commons

**URL:** https://digitalcommons.calpoly.edu/star/256