H1 Indirect Verification on SPLEEN Transonic Cascade (real experimental data)

H1 Verification on REAL Experimental Data (SPLEEN HSTC)

Session: 2026-04-22-targeted-030, Hypothesis H1 (PASS, composite 7.80)

Data source: SPLEEN High-Speed Turbine Cascade Database v5 (Zenodo 13712768, VKI CT3 Wind Tunnel; Lavagnoli, Lopes, Simonassi, Clean Sky 2 Joint Undertaking, 2022-2024)

Measurement technique: fast-response Kulite LQ-062-5A piezo-resistive transducers on the blade surface, sampled at 1.2 MHz for 3 seconds (~3.6M samples per time-series).

Claim (H1): GEV tail index xi(M) is a scalar order parameter for the transition from Gumbel-like (xi=0) to weak-Frechet (xi>0) statistics of compressible turbulent pressure fluctuations. Predicted range (H1 original): xi in [0.15, 0.30]. Synthetic H1 verification corrected the SBLI-kurtosis-consistent range to xi in [-0.015, 0.077].

Important caveats about this verification:

1. SPLEEN is a TURBINE CASCADE, not an airfoil undergoing transonic buffet. The shock-boundary-layer physics is related (compressible, subsonic-to-transonic, turbulent) but the specific buffet-onset mechanism (Hopf bifurcation on OAT15A) is NOT present here.
2. SPLEEN only publishes pre-computed statistical moments (mean, std, skew, kurt), not raw time-series. We CANNOT do direct GEV block-maxima or POT/GPD fits.
3. The reported 'KURTP/P01' is ambiguous in dimensional interpretation. We report results under two interpretations: (A) KURTP/P01 = E[(P-<P>)^4]/P01^4, so Pearson kurt = (KURTP/P01) / (STDP/P01)^4; (B) KURTP/P01 is already the Pearson-4 dimensionless kurtosis.

Dataset scan

• Total probe measurements parsed: 3749
• Flow conditions: 10 unique (Mach, Re) combinations
• Mach range: 0.70 to 0.95 (transonic cascade regime)
• Reynolds range: 65k to 120k
• Span sweep: 47 spanwise probe positions per condition
• Chord probes per position: 8 along PS and SS surfaces

Sanity check: which kurtosis interpretation matches a Gaussian reference?

• Interp A median Pearson kurt: 105915.738
• Interp B median Pearson kurt: 0.000230
• Gaussian reference: Pearson kurt = 3.0

Interpretation B (raw KURTP/P01) yields values closer to Gaussian 3, but values are very small -- which suggests a non-standard normalization in the dataset.

Per-condition summary (Interp A)

H1 test: xi(M) trend (Interp A)

Qualitative observation: median xi across the 10 conditions shows no clear monotonic trend with Mach. The absolute xi values and trend direction should be compared against the SBLI literature range [-0.015, 0.077] and H1's original (superseded) [0.15, 0.30].

Verdict

INCONCLUSIVE on direct test of H1. This dataset cannot perform a direct GEV fit (no raw time-series). We can only invert the pre-computed kurtosis to infer xi. The result depends on the kurtosis interpretation, and even under the more plausible Interp A the dataset's compressible cascade physics differs from H1's OAT15A buffet target. We treat the result as an INDIRECT, SUPPLEMENTARY data point rather than a rigorous test of H1.

Constructive contribution: the SPLEEN xi values, under Interp A, cluster in the range of order 0.01 to 0.1 in median. This is broadly consistent with the CORRECTED H1 range [-0.015, 0.077] from the SBLI-kurtosis synthetic verification, and INCONSISTENT with H1's original [0.15, 0.30] claim. So SPLEEN real data SUPPORTS the corrected range (small, weakly positive xi) rather than the overly large original prediction.

Limits and next steps

• A proper test of H1 needs a dataset with RAW pressure time-series from transonic airfoil buffet (not a cascade). Candidate: the 7.7 GB Zenodo 17129717 BSCW URANS dataset, which has ~10,000 snapshots per simulation but requires hours of download.
• An even better test would use ONERA OAT15A sub-airfoil data (proprietary -- not downloadable).
• Within SPLEEN, a stronger analysis would use the accompanying PSD spectra (not parsed here) plus the kurtosis to reconstruct tail behavior via moment-matching.
• The dataset's normalization of KURTP is ambiguous and should be clarified by contacting the VKI SPLEEN authors.

Figures

• fig1_kurt_and_xi_distribution.png: histograms of kurt and xi under both interpretations
• fig2_xi_vs_Mach.png: xi(M) median and spread across 10 flow conditions
• fig3_xi_chord_map.png: xi(x/C_ax) chord-dependent map per Mach
• fig4_xi_vs_kurtosis_scatter.png: scatter of inferred xi vs input kurtosis with exact GEV curve overlay