Type
Text
Type
Dissertation
Advisor
Glimm, James | Li, Xiaolin | Jiao, Xiangmin | Ladeinde, Foluso.
Date
2012-05-01
Keywords
eigen frequency, front tracking, parachute inflation, spring model | Applied mathematics
Department
Department of Applied Mathematics and Statistics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71519
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
We use the front tracking method on a spring system to model the dynamic evolution of parachute canopies. The canopy surface of a parachute is represented by a triangulated surface mesh with preset equilibrium length on each side of the simplices. The stretching and wrinkling of the canopy and its supporting string chords (risers) are modeled by the spring system. The spring constants of the canopy and the risers are chosen based on the analysis of Young's modulus for fabric surface and string chord. The mass-spring system is a nonlinear ODE system. Added by the numerical and computational analysis, we show that the spring system has an upper bound of the eigen frequency. We analyzed the system by considering three spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for eigen-frequency. Based on this analysis, we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal motion. We used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system. And also high order method helps to control amplification of system. Damping is added to dissipate the excessive spring internal energy. The current model does not have radial reinforcement cables and has not taken into account the canopy porosity. This mechanical structure is coupled with the incompressible Navier-Stokes solver through the "Impulse method" which computes the velocity of the point mass by superposition of momentum. We analyzed the numerical stability of the spring system and used this computational module to simulate the flow pattern around a static parachute canopy and the dynamic evolution during the parachute inflation process. The numerical solutions have been compared with the available experimental data and there are good agreements in the terminal descent velocity and breathing frequency of the parachute. | 105 pages
Recommended Citation
Kim, Joung-Dong, "Modeling of Parachute Dynamics with Front Tracking Method" (2012). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 725.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/725