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TURBULENCE MODEL NUMERICAL ANALYSIS

3D Hemisphere Cylinder Validation Case (NEW)

This is an update of an earlier 3D hemisphere cylinder study. The grids here are new. The purpose here is to provide a test case for a turbulent flow over a smooth body of revolution in 3D. This case is designed primarily for numerical analysis of turbulence model simulations; e.g., convergence properties, effect of order of accuracy, etc.

The geometry is taken from the experimental model studied in AEDC-TR-76-112, 1976, "An Investigation of Separated Flow About a Hemisphere Cylinder at 0- to 19-Deg Incidence in the Mach Number Range of 0.6 to 1.5" authored by Tsieh, T., https://apps.dtic.mil/sti/pdfs/ADA073451.pdf). At the "farfield" boundary, a Riemann invariant BC is employed, with the external boundary assumed to be freestream conditions based on input Mach number.

Boundary conditions are given in the following two figures (one for computing in the full plane and one for half plane). In the experiment, the cylinder diameter was 1 inch and its length was 10 inches. For computing forces, the reference area of this case is taken to be 10 in² (for the full 360 degrees), or 5 in² (for a half-plane computation of 180 degrees). For computing moment coefficient about the y-axis (pitching moment, C_M,y), the moment center is taken at (0,0,0), and the reference chord, C_ref, is taken as 10 inches. If needed, the reference semispan is 0.5 inches. In summary, the following geometry information for computing forces and moment should be used:

• Reference area = 10 in² (for the full 360 degrees), or 5 in² (for a half-plane computation of 180 degrees)
• Reference chord = 10 in
• Reference semispan = 0.5 in
• The x,y,z moment centers are all taken to be 0.0

GRIDS
 

Note, for special purposes (if needed) a second type of grid is supplied with an aft closure geometry and a spherical (or half spherical in the half plane case) farfield. Along this farfield, Riemann boundary condition can be applied uniformly. The body geometry upstream of x=10 is identical to the orginal hemisphere-cylinder geometry. The body is closed downstream of x=10 with a closure taken from reference DTRC/SHD-1298-01 (March 1989), entitled "Geometric Characteristics of DARPA Suboff Models" by Nancy C. Groves, Thomas T. Huang, and Ming S. Chang. Note, even though this closed geometry has the same surface grid and shape as the standard grid between x=0 and x=10, in VERIFICATION exercises its results may be slightly different because of the closed back end and different boundary conditions. Use with caution, or else conduct verification exercises only against other results using the same geometry and BCs.

SPECIAL PURPOSE GRID with aft geometry closure
 

In the first figure below, the experimental surface pressure coefficients from AEDC-TR-76-112 are plotted as functions of x for the turbulent flow at angle of attack of 5 degrees. Results are shown for various positions around the azimuth. In the experiment, phi=0 deg corresponds with the "top" or leeside of the body (which faces away from the wind when the body is at angle of attack), and phi=180 deg corresponds with the "bottom" of the body (facing the wind). Approximate results extracted from a figure in the reference at angle of attack of 0 degrees are shown in the second figure below.

The experimental data are provided here:

• hc_exp_alpha0_mach0p6.dat
• hc_exp_alpha5_mach0p6.dat
• hc_exp_alpha10_mach0p6.dat
• hc_exp_alpha15_mach0p6.dat
• hc_exp_alpha19_mach0p6.dat

What to Expect:

RESULTS	LINK TO EQUATIONS	MRR Level
SA-neg	SA-neg eqns	4

(Other turbulence model results may be added in the future.)
 
 

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Last Updated: 11/10/2021