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NASA C3X Run 145: reduced RANS/CHT benchmark

Rebuild and test analysis

Ansys Fluent 2026 R1 (26.1) + Python benchmark of NASA C3X Run 145, focused on verification, comparison with public experimental data and reproducible analysis. The primary model is a steady two-dimensional compressible Reynolds-averaged Navier-Stokes (RANS) / conjugate heat transfer (CHT) calculation using the shear-stress-transport (SST) k-omega model.

Scope. This is a reduced benchmark focused on numerical verification and comparison with NASA measurements. Internal coolant flow, film cooling and three-dimensional effects are outside the model scope; a complete validation-uncertainty assessment is not included.

At a glance

Item Details
Experiment NASA-CR-168015, Run 145 (code 4512)
Primary CFD model Fluent 26.1, steady 2D compressible RANS/CHT, SST k-omega
Fine grid 44,760 cells; maximum wall y+ = 0.45189
Experimental comparison Pressure ratio, wall temperature and external heat-transfer coefficient (HTC)
Numerical checks Final-window convergence, mass/interface/solid-energy balances, three-grid sensitivity
Sensitivity studies Transition SST inlet conditions; internal-cooling h / Tbulk; internal-HTC ±3% envelope
Reproducibility Python rebuild in CI, released Fluent restart states and headless PyFluent saved-state checks

Fine-grid SST result

Errors are reported using mean absolute error (MAE) and mean absolute percentage error (MAPE).

Metric Pressure side Suction side
Wall-temperature MAE / MAPE 8.887 K / 1.448% 12.999 K / 2.005%
HTC MAPE 7.795% 11.535%
Pressure-ratio MAPE 0.926% 3.980%
Global check Fine SST result
Cells / final iteration 44,760 / 236
Mass-weighted outlet Mach 0.901294
Relative mass imbalance 0.0000509%
Fluid-solid interface mismatch 0.00000558%
Solid heat imbalance 0.001921%
Maximum wall y+ 0.45189

NASA M2 = 0.90 is used to set the operating point. The experimental comparisons use surface pressure, wall temperature and external HTC. The back-pressure adjustment is documented in docs/outlet_pressure_selection.md.

Wall temperature Heat-transfer coefficient
NASA wall-temperature comparison NASA heat-transfer-coefficient comparison
Fine mesh Pressure ratio
Fine-grid mesh NASA pressure-ratio comparison

Fluent outputs

SST residuals, final window SST engineering monitors
SST residuals SST monitors

The retained SST state is iteration 236; the Transition SST state is iteration 556. Raw monitor, residual, wall and global-check exports are under data/fluent_exports/, while the released case/data pairs are listed with their SHA-256 hashes in fluent/restart_manifest.csv.

Numerical checks

  • Convergence and conservation. The fine SST run keeps unchanged second-order settings over its final 20 iterations; engineering-monitor spans remain below 0.02%, with the closure checks reported above.
  • Mesh sensitivity. Coarse, medium and fine SST meshes contain 14,657, 23,781 and 44,760 cells. Medium-to-fine changes in outlet Mach, mean wall temperature and external heat rate are below 0.1%, while local trailing-edge profiles remain more sensitive. The three meshes are therefore reported as a sensitivity study rather than a formal grid convergence index (GCI) assessment.
  • Model sensitivity. Transition SST gives pressure errors similar to SST but substantially larger thermal errors on the fine grid, so it is kept as a sensitivity case rather than the baseline.
  • Internal-cooling uncertainty sensitivity. Applying NASA's reported ±3% internal-HTC magnitude to the existing h sensitivity family gives about ±1.735 K on mean external wall temperature; the SST wall-temperature bias remains positive on both surfaces across that envelope.

Details are in docs/convergence_acceptance.md, docs/meshing_recipe.md, docs/nasa_comparison.md and studies/internal_cooling_sensitivity/NASA_UNCERTAINTY.md.

Model boundary

The calculation resolves the hot-gas passage, solid vane conduction and the fluid-solid CHT interface. Ideal-gas density and the energy equation are retained, with SST k-omega as the primary turbulence model.

The ten internal cooling passages are present geometrically, but coolant flow is not solved. Each passage wall instead uses a passage-specific convection condition based on h and Tbulk. The model also excludes coolant pressure loss and temperature development, film cooling, endwall flow, radiation, structural response and unsteady wake passing.

Full equations, boundary conditions, material values and source references are in docs/model_setup.md.

Sensitivity studies

Controlled perturbation Main observed response
Internal cooling h/h0: 1.00 → 0.90 Tw_mean +6.104 K; external heat rate -5.393%; outlet Mach +0.000804%
Internal h ±3% envelope Tw_mean ±1.735 K; pressure-side bias +6.827 to +10.947 K; suction-side bias +11.416 to +14.582 K
Transition SST mu_t/mu_in: 10 → 1 at Tu_in = 6.5% Near-LE Tu 1.247% → 0.364%; transition-like suction response x/Cx 0.653 → 0.967; external heat rate -19.716%
Transition SST Tu_in: 6.5% → 8.3% at mu_t/mu_in = 10 Near-LE Tu 1.247% → 1.237%; Tw_mean -0.033%; external heat rate -0.122%

See studies/internal_cooling_sensitivity/README.md and studies/transition_sst_sensitivity/README.md.

Reproduce the analysis

Tested in CI with Python 3.13:

python -m venv .venv
source .venv/bin/activate          # Windows: .venv\Scripts\activate
python -m pip install -r requirements.txt -r requirements-preprocess.txt
python scripts/preprocess/build_internal_convection_inputs.py --check
python scripts/run_all.py
python -m pytest -q

run_all.py rebuilds the processed tables, checks and figures from committed Fluent exports; it does not launch Fluent.

The Fluent restart release contains the Fluent 26.1 case/data pairs. SHA-256 values are in fluent/restart_manifest.csv. Headless PyFluent checks reopen the fine SST and Transition SST states and recompute stored scalar reports. Full solver reruns are outside the CI workflow; see docs/reproducibility.md.

Documentation

Source and licence

Primary experimental source: Hylton et al., Analytical and Experimental Evaluation of the Heat Transfer Distribution over the Surfaces of Turbine Vanes, NASA-CR-168015, 1983.

Code is released under the MIT License. Citation metadata are in CITATION.cff. NASA data and Ansys-generated material remain subject to their original terms; see THIRD_PARTY_NOTICES.md.