Potential Flow over an Airfoil

What does flow over an airfoil have to do with cardiology?  Quite a lot actually.  Cardiologists employ the simplified Bernoulli equation to obtain information about pressure differences across obstructions.  The same approximation is applied to understanding how a moving airfoil develops lift.  This section, however, entails much more.  It allows exploration of nonlinear fluid dynamics using a simplified model that allows rapid computation of velocity and pressure.

This section makes extensive use of an active figure that you can download and use to explore flow dynamics.  The active figure was used to create the images shown on the associated pages.

Click HERE to download the Joukowski Active Figure executable file to your C drive.  This is a software file.  While there is no intention for this to be a malicious computer program, the outcome of running this software is not guaranteed.  Many malicious individuals have abused the privilege of the Internet to damage your computer and to steal your personal property.  I am not one of those individuals.  You will have to give your permission to download the file and use it at your own risk.  The software is subject to change without notification.

Click HERE for a webpage that describes the Joukowski Active Figure and what the various controls do.  Playing with the figure yourself is probably more fun than reading about how to use the Figure or about the following:

Vector and Scalar Fields -- Some tools of the trade
Ideal Fluid -- An approximation useful in understanding cardiovascular applications
Mathematical Models -- General Comments about mathematical determination of complicated outcomes
Velocity and Pressure Distribution for Flow over a Cylinder
Model Limitations -- Boundary layer separation and turbulence
Streamlines and Stream Tubes
Continuity/Conservation of Mass
Circulation and Lift


The image depicts pressure distribution over a Joukowski airfoil.  Flow is from left to right across the model.   Pressure is represented both by color and contour lines where warmer colors represent higher pressure and contour lines represent isobars, i.e. lines of constant pressure.


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