Team #75 Interim Report
Team Number: 74 School Name: Santa Fe High School Area of Science: Fluid Dynamics Project Title: Computer Study of NavierStokes equation solutions across a Delauney triangular mesh 



Problem:
The objective is to study the flow characteristics of air, such as
nonlaminar flow, through the solution of the NavierStokes momentum and
energy equations. We want to look at the way air behaves and be able to
make predictions without using equations specifically created from
experimental data. For example, we want to study the turbulent or vortex
flow created at the trailing edge of an airfoil by using theoretical flow
equations instead of specific vortex equations.
Computational Plan:
We will use a 2D mesh generation program to create a mesh
surrounding a cross section of an arbitrary airfoil. The mesh will
consist of either a structured rectangular mesh or an unstructured
triangular or polygonal mesh. The program(s) we will create will analyze
fluid flow equations in each mesh cell; it will take introductory
parameters such as pressure, density, and velocity, solve for the final
solutions, and pass those values onto the next mesh cell. We will
decrease the average cell size near the boundary of the airfoil and
increase the size near the edge of the boundary box. This will increase
the accuracy of the data near the airfoil and save computing power. By
using the data from each cell, we will determine where various airfoils
can remain in laminar flow, and solve for velocity and pressure
distributions.
Progress to Date:
We obtained a mesh program from
wwwdinma.univ.trieste.it/~nirftc/research/easymesh
It is written by Bojan Niceno and creates Delauney triangle and Voronoi
polygon meshes inside a geometric figure of designated size and shape.
The mesh forms itself around another figure inside the outer boundary. At
the moment we are using only the Delauney triangles which are defined at
follows:
A Delauney network consists of nonoverlapping triangles where no
points in the network are enclosed by the circumscribed circles of any
triangle.
We have access to the University of Illinois at UrbanaChampaign
Airfoil Data Site where over 1100 airfoils are listed in x,y coordinate
format. EasyMesh takes input files in an x,y format similar to the
airfoil data files. We are currently writing a program that converts the
airfoil data files into the EasyMesh format. The EasyMesh input files
describe the shape of the outside boundary, at this moment a simple box,
and the shape of the inner boundary, the airfoil. The files also
prescribe the fineness and coarseness of the mesh at the outer and inner
boundaries.
The EasyMesh program creates a number of different output files
that define the points, or nodes, of the mesh, the corresponding segments
that connect the triangles, and the elements that neighbor each other. We
are currently working on creating a program that reads in one of the
EasyMesh output files and saves the information into a large array. The
program will then take this information and solve for the areas of the
triangles and their corresponding centroids.
At this moment we are working on breaking down and solving
NavierStokes equations which we will use to determine the velocity,
pressure, and force distributions.
Results we expect:
We expect to see velocity and pressure distributions across the
airfoil that match experimental or other theoretical data. We also expect
to see turbulence, nonlaminar flow, vortex flow, and other fluid flow
behaviors characteristic of current aerodynamic theory.
Team Members
Sponsoring Teachers
Project Advisor(s)