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Navier Stokes computations



This is a pressure distribution on a
business jet from Navier-Stokes code
Click on the thumbnail image above
to view the distibution full sized.


Meanwhile, I've also been working on Navier Stokes computations, the most advanced flow simulation we can do, on a new business jet design from Raytheon Aircraft, to see how well these simulations can predict the ''edge of the envelope'' of transonic flow on jetliners and business jets. My goal is not to compute the performance at the normal cruising conditions, which are about Mach 0.83 and angle of attack of 2 degrees, but rather to compute the flow at Mach 0.86 or so. This higher speed causes a transonic flow problem called buffet. Usually buffet conditions are identified in the wind tunnel, and then during flight tests of the real airplane. In the wind tunnel, we measure the overall lift and drag, but its hard to measure all the distributed lift loads all over the airplane. The structural design people need to know this, so they can be sure that all the individual pieces of the airplane are strong enough. Usually they can't be really sure about the structural strength and the loads until they start flight testing. If something isn't strong enough and they need to re-design it, thats very expensive. So what I want to do is give the structural designers good predictions of these localized structural loads caused by buffet, much sooner in the design process, so there is less need for re-design later.

The challenge is that the buffet flow conditions are very complicated. The formation of turbulence and separated flow has a big effect. The shock waves that form on the wings get so strong that they start to disrupt the smooth flow in the boundary layers where the flow touches the airplane. Eventually, the boundary layer is so disrupted that it lifts off the surface and forms turbulence.

Turbulence and separated flow are two areas of fluid mechanics that still are not very well understood, and the computer simulations don't work very well. Recently, there have been some real improvements in these turbulence models, and my project will put these new methods to the test to see if they can predict the buffet characteristics.

 

Geometry

Once again, the first step is getting the surface shape represented in the computer. For Navier Stokes methods, this surface definition must be much more precise than I usually need for my panel methods. Not only that, but the Navier Stokes methods require that the whole region around the outside the airplane be divided up into a very fine three-dimensional mesh of little cubes. The solution method used for these codes is called a ''finite difference'' method. It approximates the smooth change in flow properties in the real flow by little jumps in the flow properties from one cube to another. If the mesh is very fine, these jumps are very small and approximate the smooth flow changes pretty well. So, the grid generation process to create these little cubes throughout the flow takes a long time.

This project was my first experience at making a fine mesh for a Navier Stokes code. It took me more than a month to go from the basic surface geometry of the whole business jet to the three-dimensional mesh around it. My mesh has over 9,000,000 grid-points.

 

Running the Navier Stokes code

These methods used to take hundreds of hours of computer time on the Cray supercomputer to run. But a new version of the code runs on parallel machines like the IBM SP-2 and the SGI Origin 2000. I got my first results back in about 7 hours of computer time on the Origin 2000. For the first cases, I ran flight conditions pretty close to the cruise conditions, just to compare and make sure everything is working. The next step is to run higher and higher Mach numbers approaching the buffet condition. To start with, I'm using an older turbulence model, then I must incorporate the new turbulence model that is supposed to work much better. We'll see!

 
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