Why Airfoils and Computational Science?

Introduction
Airfoils generally end up being wings on aircraft. Usually these aircraft end up carrying people. Flying airplanes with wings that don't provide enough lift or are unstable can be fatal! This is where computational science comes in. To just look at the shape of an airfoil is not enough. Scientists and engineers must understand how the airfoil is going to perform.

There are two ways to do this:
1. Build the wing and convince someone to fly it!
2. Build a computer simulation to predict how the wing will perform.

Before the age of computers, scientists and engineers built model wings and tested them in wind tunnels. But, no one really knew how the wing would perform until it was actually flown. Early pioneers of flight had many disasters in search of the better wing, some fatal. Not only is this costly in terms of human live, but costly in terms of actual dollars.

Building protype aircraft can cost in the billions of dollars. Scientists and engineers don't like to watch their entire budget and years of work crash and burn. With computational science and computers, model aircraft can be built tested and flown in a laboratory. This process still takes many hours of work and many dollars, but is still much cheaper than building a full scale working model.

As time went on, aviation merged with aerospace and the "Space Race" began in the 1950's. Pilots volunteered to fly rocket planes in the hope of becoming the first human being in space, these pilots had the "Right Stuff". This merger lead to large amounts of research and produced radical designs for the times! These radical designs where the beginning of the modern jet airplanes.

Building the model using computational science
Computational science incorporates several steps to solving a problem:
1.having a precise mathematical statement,
2.being intractable by traditional methods,
3.having a significant scope,
4.requiring an in-depth knowledge of science, engineering or the arts.

A Precise Mathematicl Statement.
In order to understand aerodynamics we must be concerned with pressure, temperature density,velocity, gas properties and forces on bodies.
Where does pressure come from? Air is made of molecules and as they strike a surface they bounce off. The momentum of the molecule is then transferred to the surface. In general, pressure on a surface increases as more molecules hit it and transfer their momentum to the surface. Pressure is often the most considered force when studying aerodynamics.

True fluid motion is difficult to analyze, there are just to many variables. To simplify matters many of these complications are ingnored and the fluid is considered to be a steady flow. A steady flow means that all the particles of the fluid have the same velocity as they pass a given point. The path of the flow is represented by a streamline.
Streamlines imply that:
1.every particle along the streamline passes over the same point along a surface
2.particles move along the same path as the particles before
3.streamlines never cross
4.the closer together the streamlines, the faster the velocity.

This simplified model works well with lower velocities, but as the velocity increases, flows tend to become turbulent. turb.