Capstone (Math 451H) Spring 2002:
Hele-Shaw flow past obstacles
This project used our newly acquired Hele-Shaw setup to analyze flow around obstacles in highly controlled environment. The performed experiments included flow around a cylinder, flow around a blunt body, and flow around an airfoil under different angles of attack. The figure and the movies below show examples of this flow, where the streamlines of the flow are visualized using ink sources distributed at the entrance to the flow domain (left hand side of the figure).
Movie: Flow past an airfoil
Movie: Flow past a blunt body
The experimental results served as a motivation for studying necessary mathematical tools needed for their understanding. Furthermore, modifying experimental conditions (such as flow rate) allowed for discussion of the applicability of the theoretical results to the performed experiments. The students involved in this project applied the methods from complex analysis (conformal mapping) as well as systematic reduction of Navier-Stokes equations in Hele-Shaw geometry to analyze the results. Both experimental and theoretical results were presented at the seminar attended by faculty and graduate students from Department of Mathematical Sciences.
From final presentation: