Team #75 Interim Report

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    Team Number: 74

    School Name: Santa Fe High School

    Area of Science: Fluid Dynamics

    Project Title: Computer Study of Navier-Stokes equation solutions across a Delauney triangular mesh

Final Report


The objective is to study the flow characteristics of air, such as non-laminar flow, through the solution of the Navier-Stokes 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
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 non-overlapping 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 Urbana-Champaign 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 Navier-Stokes 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, non-laminar flow, vortex flow, and other fluid flow behaviors characteristic of current aerodynamic theory.

Team Members

Sponsoring Teachers

Project Advisor(s)