Tennis: Computational Fluid Dynamics (CFD)

Tennis: Computational Fluid Dynamics (CFD)

The team developed these computer simulations of a tennis ball. For background on these computer simulations click here.

Results:

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.

What is a Contour?:

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.

What is a Vector?:

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".

Another thing to note when looking at the vector plot are the vectors' length. As we get closer to the tennis ball, notice how the vectors become shorter and shorter. This means that the flow near the tennis ball slows down. If you were able to take a close-up view of the flow at the tennis ball surface, you'd see that the vectors length would shrink to nothing. At the surface flow stops, because the surface "grabs" on to the fluid or air that touches it.

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