More Fun with CFD

In the early 1950s, the National Advisory Committee for Aeronautics (NACA) performed a series of wind tunnel and flight tests on a research model called the RM-10. The purpose was to study the effects of supersonic flight. A series of reports were written, discussing the coefficient of lift and the coefficient of drag of speeds from Mach 0.85 up to Mach 6.9 (references 1 through 3). Comparisons with finned models to body-alone were made, developing some of the basic understanding of supersonic drag we have today. The reports are available on-line from the NACA Technical Report Server. Searching around on this site will yield many treasures for aerodynamics enthusiasts!

The dimensions of the model are based on the length, so that standardized models could be built for different wind tunnels and flight models. The basic dimensions are contained in NACA report TN 2944 [Ref 1].

I modeled the 73.25" flight test vehicle with a CAD solid modeling system, and used Computational Fluid Dynamics (CFD) software to analyze the flow patterns around the rocket at various speeds and to compare the drag coefficient to the values reported by NACA.

NACA used CW Doppler radar to measure velocity and total drag of the free flight models. Acceleration and pressure data was telemetered to ground receiving stations to obtain a second total drag calculation, and to measure base drag.

The Mach number range was approximately 0.85 to 2.5 and the Reynolds number range was from 12 x 106 to 140 x 106. Data presented for the free flight models were obtained during the decelerating portion of the flight trajectory after rocket-motor burnout.[Ref 1]

The following chart compares the total drag coefficient (Cdt) measured by NACA to the values computed by the CFD software. The NACA values up to Mach 2.4 were taken from Figure 9b of Ref 1. Cdt at M6.9 is from Figure 5 of Ref 3 for zero angle of attack

The CFD results for Cd varied from the measured results. In some cases the calculated Cd was higher than measured, in other cases it was lower. This could be due to differences in the Reynolds number(s), Re. The NACA report notes that there were discrepancies in the flight data and the wind tunnel results and even between the two sizes of flight models (73.25 inch long, and 146.5 inch).

In the computer simulations, the air temperature was manipulated to adjust the density and viscosity to obtain a Reynolds number that matched that reported in the NACA reports. The atmospheric models used are found on the NASA educational website [Ref 6].

The following figures show the pressure and density distributions around the model at various velocities. The shear stress plots show the drag acting on the rocket body. It is fascinating to see the shock waves form over the model,and see them change as the velocity increases.

The RM-10 would make a neat scale model. The flight versions were produced from spun magnesium alloy skins, and cast magnesium alloy tail cones. All models had a polished finish. One version was 146.5 inches long, and the other was 73.25 inches long. All models carried a sustainer motor internally, while the shorter model utilized various booster rocket motors to obtain high Mach numbers.[Ref 1]

The body could be produced from styrofoam using the Team Vatsaas method for making bodies . The CAD drawing of the 73.25" sustainer exists it 3 formats: DXF (zipped), TIF, and EPS (zipped). The drawings are scaled to fit a "D" size sheet of paper (24" x 36").

Note a free viewer for encapsulated postscript files can be obtained from the Ghostscript site.

If you don't have Autocad, you can download a free viewer that will let you view the files and print them out. It is available at the Autodesk web page--be sure to use the "Volo View" freebie to view ".dxf" files!

References

[1] "The Zero-Lift Drag Of A Slender Body Of Revolution (NACA RM-10 Research Model) As Determined From Tests In Several Wind Tunnels And In Flight At Supersonic Speeds" Evans, Albert J.; NACA; NACA TN2944; 1953.
[2] "Investigation Of The Aerodynamic Characteristics Of The NACA RM-10 Missile (With Fins) At A Mach Number Of 1.62 In The Langley 9-Inch Supersonic Tunnel" Coletti, Donald E; NACA; NACA RM-L52J23a; 1952.
[3] "An Investigation Of The Characteristics Of The NACA RM-10 (With And Without Fins) In The Langley 11-Inch Hypersonic Tunnel At A Mach Number Of 6.9" Macauley, William D Feller, William V; NACA; NACA RM-L54I03; 1954.
[4] "Equations, Tables, And Charts For Compressible Flow" Ames Research Staff; NACA; NACA Report 1135; 1953.
[5] "Aerodynamics for Engineers" Bertin, John J., Smith, Michael L.; Prentice Hall; 3rd Edition; 1998.
[6] "NASA Glenn Learning Technologies Home Page" Earth Atmosphere Model - English Units