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## CFD Analysis

**Introduction**

After some short discussion on my new build page and a concurrent serendipitous post on TRF by David Reese, I wanted to use computational fluid dynamics (CFD) to try and get a better understanding of aerodynamic fin optimization. The first part of the analysis will be looking at the optimal fin location with respect to the end of the rocket measured in body calibers. The experiment will be looking at velocities ranging from subsonic to supersonic and will be ignoring mass and stability optimization, just aerodynamic effects. Subsequent analysis will be looking at different fin shapes, fin fillet radii, nose cone shapes (Von Kármán and x½ power series cone), and a few other configurations.

I’ll be using Cosmos FloWorks as the CFD tool with the following assumptions and configurations:

- Zero angle of attack
- 20 °C and 101.325 kPa, air density of 1.204 kg/m
^{3} - Zero surface roughness
- Laminar and turbulent flow (obviously)
- 4″ airframe 23 calibers long
- Zero fin fillet radius
- Three clipped delta fins with a caliber in span
- Square airfoil fins
- Ogive 5:1 nose cone

Maybe a few others I forgot to list, if you have questions just ask.

I have some experience with FloWorks where I participated in a group project evaluating aerodynamic drag of a (professors’ ) Porshe 914 with different aeropackages. We used CFD and Laser Doppler Velocimetry (LDV) testing in a water tunnel to measure and compare drag data. Additionally, we did full scale yarn tuft testing to validate some of our results..and to just have fun. Our CFD and LDV data matched well and the calculated stock configuration was within a few percent of the manufactures published drag coefficient.

Back to rockets! FloWorks allows you to create a model and and run it at various specified conditions. For this experiment I’m using three similar models all running at three velocities: 300 m/s, 400 m/s, and 680 m/s respectively. The only difference between the models is the fin edge distance from the rear end of the rocket (0, 0.5, and 1 body calibers). I then specify a global goal that solves for the summed forces in the axis of the rocket. After a good 10-11 hours of computations, FloWorks spits out the minimum, maximum and average force in the axis of the rocket. Taking the averaged force we can now easily solve the drag coefficient with the following equation:

where:

*F*is the force of drag_{D}*ρ*is the mass density of the fluid (in this case air)*u*is the velocity of the rocket relative to the fluid*A*is the max cross sectional area

**Baseline Results**

Just to reiterate this analysis was only examining the effects of the placement of 3 clipped delta fins, ignoring stability margins and mass optimization. This is just one piece of the puzzle when trying to get the highest altitude possible. More to follow…

Comments are closed.

#1 by

Phil Babcockon January 5, 2011 - 3:11 pmVery interesting outcome of the testing. It does show some benefits from moving the fins forward, but not all the way to 1 caliber. The decreased stability from moving the fins could be a big downside depending on how many motors one would like to fly with the rocket. Although if going for straight altitude, most have only one motor in mind

#2 by

Clay Dunsworthon February 8, 2011 - 9:57 amDoes floworks allow AOA ? since there will be some aoa canges, seeing how the fin plancement affects changes through foreseeable aoa’s would be worthwile. Very cool!

#3 by

Jameson February 8, 2011 - 6:31 pmI can simulate varying degrees of AOA. This first run was just a baseline run, I hope to complete more simulations in the future.

#4 by

Claude Paquinon February 28, 2011 - 12:31 pmVery good information on the impact of fin position on the overall rocket Cd. I would have one recommendation, however. In your analysis you use no airfoil (square). I would think a performance-oriented vehicle should have airfoiled fins and I suspect it could have an impact on the optimal fin position. Square fins will generate more turbulence than airfoiled ones and it is possible that we would not see the same overall Cd improvement due to fin position for the fins you use in your study, but this time with a nice airfoil. Just some food for thought.

#5 by

Jameson February 28, 2011 - 10:37 pmClaude,

That is something I definitely plan on looking at. This first set of runs is meant to be a baseline to compare all others. If there is enough interest I’ll do a bunch more looking at several other configurations.