# Analysis of Two-Dimensional Fluid-Structure Interactions of a Plunging Flat Plate using Unsteady Discrete Vortex Method with MATLAB

## Abstract

Fundamental intuition of aerodynamics begins with understanding steady flow, a time- independent flow state. A fluid region undergoing steady flow consists of constant properties such as pressure and velocity at different positions in the flow field. This time-independent principle is crucial for beginning a foundation of understanding aerodynamics; however, analyzing this state of flow was beyond the limit at my university's Fundamentals of Aerodynamics course. There was minimal education on time-dependent unsteady flow, which created a vacuum on my understanding of how flow can be analyzed with time. The purpose of writing this thesis is to create a framework for aspiring learners of aerodynamics to better comprehend unsteady flow, including myself. The basis for developing an understanding of unsteady flow is accomplished by analyzing the aerodynamics of a simple two-dimensional zero-thickness flat plate, using a numerical method called Discrete Vortex Method under steady and unsteady conditions. Constructing a numerical method for steady and unsteady flow requires a software to compute enormous quantities of linear equations, therefore a combination of numerous arguments, functions, and loops were developed on MATLAB written in the C/C++ languages. Results from the numerical methods will be compared with the experimental and theoretical results from Katz & Plotkin (2001). The Steady Discrete Vortex Method was a basis for calculating the circulation of the flat plate at varying angles of attack and freestream velocities. The Unsteady Discrete Vortex Method derived much of the self-induced calculations in the body-fixed coordinate system. At the same time, a time-stepping method was developed to calculate the coordinates as the flat plate and shed vortices translated from the origin of an additional frame of reference called the inertial coordinate system. A wake vortex is shed from the trailing-edge of the flat plate at each time step iv to model vorticity shed from a body in motion. The flat plate undergoes sudden acceleration and plunging maneuvers to demonstrate further effects of unsteady aerodynamic conditions. The results from the flat plate undergoing sudden acceleration with a Reynolds number of 68,435.8 was an increasing proportionality between the lift and circulation of the steady and unsteady case until reaching a constant trend as time increases, demonstrating the nature of low-speed flow reaching a steady state after a given period. The results from the flat plate undergoing plunging with a Reynolds number of 106,759.8 demonstrate a sinusoidal trend in the normal force experienced as the flat plate traverses in its sinusoidal plunging translation like that observed in the theoretical results. This thesis intends to expand on the understanding of unsteady aerodynamics by developing a numerical method that can alter its dependent factors to visualize the effects of changing specific parameters on pressure and force acting on the two-dimensional body.

2023

## Semester

Spring

Bhattacharya, Samik

## Degree

Bachelor Science in Aerospace Engineering (B.S.A.E.)

## College

College of Engineering and Computer Science

## Department

Mechanical and Aerospace Engineering

## Degree Program

Aerospace Engineering

English

Campus Access

5 years

5-15-2028

COinS