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TURBULENCE MODEL NUMERICAL ANALYSIS

3D Hemisphere Cylinder Validation (NEW)

SA-neg Model Results

Results are shown for the 3D Hemisphere Cylinder Validation (NEW), for the SA-neg variant of the SA model. Note that SA-neg is passive to the original (SA) model in well-resolved flowfields, and hence is expected to yield essentially identical results as SA for the cases here. For all results, the farfield value of the Spalart turbulence variable is $\tilde \nu_{farfield} = 3 \nu_{\infty}$ . In all codes the Prandtl number Pr is taken to be constant at 0.72, and turbulent Prandtl number Pr_t is taken to be constant at 0.9. The dynamic viscosity is computed using Sutherland's Law (See White, F. M., "Viscous Fluid Flow," McGraw Hill, New York, 1974, p. 28). In Sutherland's Law, the local value of dynamic viscosity is determined by plugging the local value of temperature (T) into the following formula:

$\mu = \mu_0 \left( \frac{T}{T_0} \right)^{3/2} \left( \frac{T_0 + S}{T+S} \right)$

where $\mu_0 = 1.716 \times 10^{-5} kg/(ms)$ , $T_0 = 491.6 R$ , and $S = 198.6 R$ . The same formula can be found online (with temperature constants given in degrees K and some small conversion differences). Note that in terms of the reference quantities for this particular case, Sutherland's Law can equivalently be written:

$\left( \frac{\mu}{\mu_{ref}} \right) = \left( \frac{T}{T_{ref}} \right)^{3/2} \left( \frac{T_{ref} + S}{T+S} \right)$

where $\mu_{ref}$ is the reference dynamic viscosity that corresponds to the freestream in this case, and freestream $T_{ref}$ is 540R. This latter form may be more convenient for nondimensional codes. (Specific details regarding an implementation of Sutherland's Law in nondimensional codes can be found in handwritten notes describing Sutherland's Law in CFL3D and FUN3D.)

The results on this page have been reported in AIAA Paper 2018-1102, https://doi.org/10.2514/6.2018-1102. Also, many of the other papers from two special sessions at AIAA SciTech 2018 dealt with this case: see AIAA Papers 2018-1101 through 1104, and AIAA Papers 2018-1566 through 1570.

Grid Convergence Behavior of Forces, Moment, and Maximum Eddy Viscosity

Plots are shown to illustrate grid convergence for the lift, drag, moment coefficient, and nondimensional maximum eddy viscosity for the hemisphere-cylinder at several different angles of attack. The contributions to the drag coefficient due to the viscosity and pressure are also presented separately. For forces and moment, results from 4 different codes (on different versions of the grids) appear to be approaching nearly the same results as the grid is refined (i.e., as h approaches zero). CFL3D is a structured-grid code, while all others are unstructured-grid codes. For eddy viscosity, it is not as clear that all results are approaching the same answer in all cases; finer grids are likely required. Recall that all codes were run using SA-neg.

Alpha=0:
SA-neg - lift coefficient vs h for alpha=0 SA-neg - drag coefficient vs h for alpha=0
SA-neg - pressure drag coefficient vs h for alpha=0 SA-neg - viscous drag coefficient vs h for alpha=0
SA-neg - moment coefficient vs h for alpha=0 SA-neg - max eddy viscosity vs h for alpha=0

Alpha=5:
SA-neg - lift coefficient vs h for alpha=5 SA-neg - drag coefficient vs h for alpha=5
SA-neg - pressure drag coefficient vs h for alpha=5 SA-neg - viscous drag coefficient vs h for alpha=5
SA-neg - moment coefficient vs h for alpha=5 SA-neg - max eddy viscosity vs h for alpha=5

Alpha=10:
SA-neg - lift coefficient vs h for alpha=10 SA-neg - drag coefficient vs h for alpha=10
SA-neg - pressure drag coefficient vs h for alpha=10 SA-neg - viscous drag coefficient vs h for alpha=10
SA-neg - moment coefficient vs h for alpha=10 SA-neg - max eddy viscosity vs h for alpha=10

Alpha=15:
SA-neg - lift coefficient vs h for alpha=15 SA-neg - drag coefficient vs h for alpha=15
SA-neg - pressure drag coefficient vs h for alpha=15 SA-neg - viscous drag coefficient vs h for alpha=15
SA-neg - moment coefficient vs h for alpha=15 SA-neg - max eddy viscosity vs h for alpha=15

Alpha=19:
SA-neg - lift coefficient vs h for alpha=19 SA-neg - drag coefficient vs h for alpha=19
SA-neg - pressure drag coefficient vs h for alpha=19 SA-neg - viscous drag coefficient vs h for alpha=19
SA-neg - moment coefficient vs h for alpha=19 SA-neg - max eddy viscosity vs h for alpha=19

Results that generated the above plots can be found in the following data file: HC_combined_forces_pitchmom_maxmut.dat.

Comparisons of Cp, Cfx, Cftangent, and Offbody Quantities at Alpha=19 on Finest (L1) Grids

Plots are shown to illustrate behavior of various quantities, for alpha=19 deg only. Comparisons between codes on the finest (L1) grid are made as follows. Surface Cp and Cfx are shown along the symmetry plane (y=0).

SA-neg - Cp vs x for alpha=19 at y=0 SA-neg - Cfx vs x for alpha=19 at y=0

Surface Cp, Cfx, and Cftangent are shown along z=0 (the tangential direction is defined on the hemisphere-cylinder surface as a unit vector tangential to the surface, normal to the x-direction, and pointing up.)

SA-neg - Cp vs x for alpha=19 at z=0 SA-neg - Cfx vs x for alpha=19 at z=0
SA-neg - Cftangent vs x for alpha=19 at z=0

Surface Cp, Cfx, and Cftangent are shown versus azimuthal angle (phi) in the cross-flow plane corresponding to x=5. The azimuthal angles phi=0 deg and phi=180 deg correspond to the leeside and windside, respectively in the symmetry plane (y=0). The azimuthal angle phi=90 deg corresponds to the horizontal plane z=0.

SA-neg - Cp vs phi for alpha=19 at x=5 SA-neg - Cfx vs phi for alpha=19 at x=5
SA-neg - Cftangent vs phi for alpha=19 at x=5

Offbody plots of p, u, v, and w are shown off the upper surface along a vertical line corresponding to x=5, y=0.21.

SA-neg - upper surface offbody nondimensional p for alpha=19 along x=5 and y=0.21

Grid Convergence Behavior of of Cp, Cfx, Cftangent, and Offbody Quantities at Alpha=19

Plots are shown to illustrate grid convergence behavior of various quantities for each code, for alpha=19 deg only. First, surface Cp is plotted near the leeside minimum Cp location (along y=0).

SA-neg - Cp vs x for alpha=19 at y=0 using USM3D on 4 grids near leeside min

Surface Cp is plotted near the leeside outflow (along y=0).

SA-neg - Cp vs x for alpha=19 at y=0 using USM3D on 4 grids near outflow

Surface Cfx is plotted on the leeside near x=6 (along y=0).

SA-neg - Cfx vs x for alpha=19 at y=0 using USM3D on 4 grids near x=6

Surface Cfx is plotted along x=5.

SA-neg - Cfx vs phi for alpha=19 at x=5 using USM3D on 4 grids

Surface Cp is plotted near the minimum Cp location along x=5.

SA-neg - Cp vs phi for alpha=19 at x=5 using USM3D on 4 grids near min

Surface Cfx is plotted near the minimum Cp location along x=5.

SA-neg - Cfx vs phi for alpha=19 at x=5 using USM3D on 4 grids near min Cp

Offbody plots of p, u, v, and w are shown off the upper surface along a vertical line along x=5, y=0.21.

SA-neg - upper surface offbody nondimensional p for alpha=19 along x=5 and y=0.21 using USM3D on 4 grids

Results that generated the above plots can be found in data files in the following tarred gzipped directory: HC_data_alpha19.tar.gz.

Effect of 2nd Order Turbulence Advection at Alpha=19

The effects of 2nd order accuracy for the convection in the SA model are shown below for FUN3D solutions at alpha=19 deg. The major difference is seen in the skin friction near x=6. The effects on surface pressure (shown) and integrated lift and drag (not shown) are less significant.
SA-neg - Cp vs x for alpha=19 at y=0 using FUN3D comparing 1st vs. 2nd order turb advection SA-neg - Cfx vs x for alpha=19 at y=0 using FUN3D comparing 1st vs. 2nd order turb advection

Results that generated the above plots can be found in the following data files: HC_A19_Z0_FUN3D_2ndSA.dat, HC_A19_Y0_FUN3D_2ndSA.dat, HC_A19_X5_FUN3D_2ndSA.dat. The forces, moment, and max mu_t are give in the file: HC_combined_forces_pitchmom_maxmut_aoa19_fun3d_2ndSA.dat.

Sample input files are available for FUN3D and CFL3D: fun3d.nml_HC_L2MIX, cfl3d_HCsampleinput_L3.inp.

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Recent significant updates:
04/17/2019 - added sample input files for FUN3D and CFL3D
06/19/2018 - added FUN3D results using 2nd order turbulence advection at alpha=19 deg

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Last Updated: 11/10/2021