Geometry
The turbine blade section is a UTRC/Pratt & Whitney design of JT9D vintage. The airfoil mean-camber-line inlet and exit angles are 44 and 26 degrees, respectively. The 2d calculations used a pitch to axial chord ratio of 0.955.
The calculation grid was designed to cover the entire range of Reynolds numbers considered. The near-wall grid spacing was about 0.00005 times the axial chord. At the highest Reynolds number (709,000), the maximum y+ value at the near-wall points was 4. This occurred on the leading edge and again on the pressure surface near the trailing edge.
Near the walls, the grid spacing was increased using a spacing factor of 1.5 (e.g. points at 0, 1, 2.5, 4.75, ...).
Overall the grid had 132 points going from 0.8 axial chords upstream of the blade row to 0.6 axial chords downstream. There were 60 points and a repeating boundary condition in the blade-to-blade direction. Two points in the spanwise direction make the grid compatible with the 3D code. This grid is used for the mean velocity components and the 7 turbulence model properties. Static pressure is calculated over the half grid spacing, i.e. on a 263 by 119 grid, to accommodate the use of variable, flow dependent control volumes.
Baseline Calculation
The baseline calculation is case C and corresponds to the low Reynolds number high turbulence measurements of Van Treuren et al. (VSKBBR2002). For this case Van Treuren et al. give ReNASA=24,000, an inlet flow angle of 46 degrees, a turbulence intensity (u/U) of 9%, and a turbulence macroscale of .04m compared to the axial chord, c=.171m.
Inlet turbulence properties. We assumed the inlet turbulence was isotropic, so that the turbulence anisotropy, bij=0. A turbulence intensity of 9% gives a turbulence velocity scale, q=sqrt(k), of q/Uo=0.11. The turbulence dissipation rate was estimated from the macroscale using Eq. 17.4.5 in Functional Reynolds Stress Modeling,
dissipation rate, e = 0.59 (uu)3/2/macroscale,
which gave a dimensionless turbulence length scale of q3/(ec)=0.73. For case C the corresponding inlet turbulence Reynolds number is Rt=724.Additional Calculations
For the additional calculations at different Reynolds numbers, the laminar viscosity was changed to change Re. This also changed the turbulence Reynolds number.
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