Tennis: Computational Fluid Dynamics (CFD)

Computational Fluid Dynamics of Tennis Balls

Computers are used extensively throughout aeronautics to aid in the design and analysis of aircraft, watercraft, and even sports equipment. Scientists have developed mathematical models which emulate the physics of fluids. These mathematical fluid models are programmed into software applications which can be used on the computer. An engineer can take an object, like an airplane or ball, and use the fluid model to analyse how this object would perform in "flight". It's kind of like having a virtual wind tunnel. There is a special name for this type field of work. It's called "Computational Fluid Dynamics" or "CFD" for short. In this section we will show you the steps we take in doing a CFD simulation, by performing a simulation of the tennis ball.

Gathering the Correct Information

Before we can start we must first gather information about the tennis ball. Information like the tennis ball's size, the speed of the tennis ball, and the rate at which the tennis ball spins. We also need to note any distinguishing features of the tennis ball, such as the shape of its seam and its fuzz. The tennis ball is roughly a 2.5 inch sphere. It has a continuous hourglass shaped seam, and a felt-like fuzz. The fuzz of the tennis-ball is a very porous and non-uniform surface. This makes the fuzz surface very difficult to simulate with a CFD model. For this reason we chose to leave out the fuzz, and model the tennis ball as if it had a smooth surface. The seam of the tennis-ball, however, can be modelled easily. We left this feature of the tennis ball in our simulation. The average professional tennis player serves the ball at 120mph, and the spin of the ball during a serve can reach around 1000rpm.

Determining What Cases to Run

Once we have taken down all the information about the tennis ball we need to decide what cases to set up so we learn what we want to from our CFD model. One thing that is often done in aeronautics, and science in general, is comparing and contrasting. Scientists compare and contrast in their experiments in order to see how much little changes effect their results. Here we set up four different cases, so that we can compare and contrast between them. The first case is a smooth ball with no seam and no spin. The second case is a smooth ball with no seam spinning at 1000rpm. The third case is a ball with a seam but no spin. The fourth case is a ball with both a seam and spin. By comparing these four cases, we hope to see how much spin and the seam of the tennis ball effect its flight.

Creating a Computer Model of the Flying Body: Grid Generation:

In order to simulate fluid flow on the computer, the space around the object we are observing must be divided up into small pieces or sections; much like how street maps are divided up into squares. A divided portion of space is called a "grid" or "mesh", and individual sections are called "grid cells". The following pictures show the grids for a tennis ball with seams and a tennis ball without seams.

Tennis Ball with Seam	Tennis Ball without Seam

Once the grids are done and we know what cases we want to study, we can run our CFD simulation! CFD simulations can take a long time to run. Depending on the problem, running simulations can take an from and hour to a few weeks! The tennis ball simulations we ran took about a half a day. The links below will take you to the results.

Results:

• Tennis Ball with No Seam, No Spin
• Tennis Ball with No Seam, Spin
• Tennis Ball with Seam, No Spin
• Tennis Ball with Seam, Spin

Most of the results you'll see are in the form of colorful graphs. The two types of graphs that are shown are contour graphs and vector graphs. These graphs are used to show the pressure and the velocity of the flow. Pressure plots help to show what the forces are acting on the ball, and velocity plots show how the flow is moving around the ball.

You'll notice that the results for the tennis balls are displayed under two headings "Laminar" and "Turbulent". Laminar and turbulent are terms which refer to the boundary layer of the fluid flow, which in simple terms is flow very close to the surface of a solid body. Laminar flow is boundary layer flow that is "orderly". Turbulent flow is boundary layer flow which is "random" and "chaotic". Laminar and turbulent flow are modeled differently on the computer, so sometimes we have to guess which type of flow will be predominant in our simulation and use the appropriate model. The tennis ball is special because at the speed it travels, it lies around the border of being both predominantly laminar and predominately turbulent. Consequently, for some of the simulations we performed we used both a laminar and a turbulent model.

If you've ever gone hiking in the outdoors, or browsed through an atlas you've might have seen a contour map. Contour maps are covered with several sets of curved lines accompanied by numbers. The curved lines are called "contour lines", and they represent levels of constant elevation. The numbers marked on or next to the contours mark the number of feet above sea-level that the contour line is at. If you were to walk along a contour line, you would neither go uphill or downhill; you're elevation would remain the same.

Contour maps are not only used to display elevation. Watch a weather forecast on television. Sometimes the weather person will show a colored map with temperatures over a large region. Regions colored red are where the temperature is hot. Regions which are yellow or green are where the temperature is moderate. Regions colored blue are where temperatures are cold. This colored weather map is also a kind of contoured map. Here the contours represent temperature instead of elevation.

Contour maps are used a lot in CFD for displaying results. Take a look at the following samples of CFD results we calculated for a tennis ball.

Pressure Contours	Velocity Contours

The picture on the left shows contours of pressure. The picture on the right shows contours of velocity. Just as the colored regions on the temperature weather map represented values of temperature, the color of the contour lines in the above pictures represent values pressure or velocity. Red stands for high pressures or high velocities. Blue stands for low pressures or low velocities.

Vectors show both magnitude (how big or strong something is) and direction. They are usually represented by an arrow. Vectors are kind of like the wind vales you might see on a barn. The wind vale will point in the direction which the wind is blowing. However wind vales do not tell you how strong the wind is blowing. Vectors do. The length of a vector depends upon how strong the flow is. Long vectors mean the flow is strong and fast. Short vectors mean the flow is weak and slow. Vectors are often used to show how fluid flows around an object, like in the picture below.

Velocity Vectors

Take a close look at the vectors in the picture. Notice how in front of the ball are directed smoothly along the surface of the ball. Behind the ball the vectors start to "leave" the surface and become jumbled. Sometimes the vectors make "swirling" patterns. When the flow around a body no longer follows the body's surface, it is called separation, because the flow "separates" from the surface. In all the tennis ball results we show, there is separation. When you look at the results, notice where and how the flow separates from the ball. Almost all our tennis ball results will show different separation. Differences in where and how flow separates from an object, effect the object's "flight".