Standard Physics

A turbine blade with 25.5% less loss than a classic benchmark.

The LS89 is a standard test blade that researchers use to compare designs. Archimedes reshaped it to waste less energy without turning the flow any less, and finished ahead of a published optimized design. These are 2D simulations of a slice of the blade, not a full engine.

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Recorded geometry
Exact recorded 2D section and pitch with arbitrary display-span extrusion; not a 3D vane. Source f38f5076936fe4a8. Drag to inspect.
25.5%less energy lost than the benchmark blade, in 2D simulation
2.2 pointsahead of a published optimized design for the same blade
1,333designs tried on 18 cloud machines in 30 hours
The ask

Waste less energy as gas flows through a row of turbine blades.

Without turning the flow any less, or changing how much gas gets through.

What it found

Wider spacing helps, until a shock wave forms.

Spacing the blades further apart cuts friction, but loads each blade harder until a shock wave appears and undoes the gain.

What it did

Spaced the blades out and reshaped them to keep the shock weak.

It widened the spacing from 57.5 to 78 mm, re-angled the blades, and added a subtle contour on one surface.

Fine print

It caught a flaw in the published comparison.

The published design it compared against turned the flow slightly less than the rules allow, so Archimedes fixed that before comparing. Its own blade leads at most, but not all, off-design conditions.

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For engineers

The full record, unedited.

Interactive comparisonexplore the measured results
Measured comparison

A constraint-compliant loss comparison

Every point is the reduction in mass-averaged entropy loss against the LS89 baseline under the same solver and turning constraint. The plate compares the exact recorded baseline and generation 502 sections.

RECORDED GEOMETRY COMPARISONFIXED PROJECTION · COMMON SCALEA · BASELINE / VKI LS89SOURCE ID 1ffd82dfb4aa53d4B · RESULT / Generation 502SOURCE ID f38f5076936fe4a8PITCH 57.5 mm01837x [mm]-64-2710y [mm]37.0 mmPITCH 78.0 mm01837x [mm]-64-2710y [mm]37.0 mm
Recorded 2D midspan section. section coordinates · mm. Geometry is reconstructed from the recorded campaign artifacts.Geometry only. No inferred streamlines, pressure field, or unrecorded physical detail is shown.A source: evolve/ls89/robustness_designs/baseline.py · 1ffd82dfb4aa53d4 · Exact recorded 2D section with arbitrary display-span extrusion; not a 3D vane.
B source: evolve/ls89/robustness_designs/open16_g502.py · f38f5076936fe4a8 · Exact recorded 2D section and pitch with arbitrary display-span extrusion; not a 3D vane.
Entropy loss reductionhigher is better →

Numerical basis: 2D midspan compressible RANS (HiSA HLLC, Spalart-Allmaras, y+ < 1) · 4-level grid study to 0.66M cells

Constraint-compliant loss comparison

Mass-averaged entropy loss against the VKI LS89 baseline at exit isentropic Mach 0.90. Turning must remain at least the baseline value.

GeometryLoss reductionPitchTurningEvidence level
VKI LS890%57.5 mmReference floorCalibrated baseline
Restaggered Chatel23.52%Published familyMade compliantRefined comparison
Excluded family21.2%Independent familyConstraint retained1.5x mesh
Generation 50225.50%78.0 mm+0.021 deg margin0.6M-cell mesh

Grid and off-design record

The formal convergence statement uses the recorded mesh triplet. The off-design map is incomplete where a point did not finish.

StudyRecorded resultQualification
Mesh series1x, 1.5x, and 2.25x plus the 0.6M-cell solve2D midspan RANS only
Fine result25.50% on 0.6M cellsNot an engine-efficiency number
Off-designEight completed winner pointsThe -2.5 deg incidence point did not complete
Adverse pointsTrails the compliant Chatel referenceM2is 1.02 and -5 deg incidence

Applicability

This is a 2D midspan cascade result at one design point plus a partial off-design map. It does not establish 3D endwall, cooling, structural, or whole-engine performance.

References and source records

  • Arts, Lambert de Rouvroit, and Rutherford (1990), VKI Technical Note 174.
  • Chatel et al. (2018), digitized and re-solved on this evaluator.
  • Sanchez Torreguitart, Verstraete, and Mueller (2018).
  • Celik et al. (2008), procedure used for the grid-convergence statement.
The exact briefas given to the agents

Minimize mass-averaged entropy generation J across the VKI LS89 transonic turbine nozzle guide vane cascade at exit isentropic Mach 0.90 (inlet 159.6 kPa, 420 K, Spalart-Allmaras, y+ < 1). Exit flow angle must be >= baseline (74.81 deg) with mass flow per unit pitch matched within +/- 0.7%. Both airfoil surfaces, pitch, stagger, throat, and LE radius are free; axial chord and TE are fixed.

Archimedes
30 h across 2 campaigns (1,333 CFD solves)
Compute record
18 cloud machines · 4 grid levels to 0.66M cells
Decision loghow the agents reasoned, step by step
Reasoning trace

What changed, and why

The search did not simply smooth a blade. It widened the cascade, recovered turning through stagger and throat control, then shaped the suction-side pressure recovery so the shock penalty stayed smaller than the boundary-layer gain.

Digitizing & Re-Solving Published Optima

Catching a 0.06 deg turning violation in the published benchmark leader

Observed
Digitizing the Chatel et al. (2018) and Torreguitart et al. (2018) optima (0.06 mm registration accuracy) and solving them on our VKI MUR47-validated HiSA evaluator showed Chatel's published blade misses the exit turning floor by 0.046-0.06 deg.
Inferred
To establish a constraint-compliant comparison, Archimedes created a restaggered Chatel reference (-23.52% on the 1.5x mesh) and reported both the published and compliant forms.
Changed and measured
Wrote 40 physically distinct concept blade programs; before evolution even began, Archimedes' aft-loaded high-pitch concept reached -23.45% on the search mesh, already surpassing the restaggered Chatel bar (-22.7%).
Engineering findingheadline numbers and the mechanism

A stronger benchmark result with its constraints intact

The value is not only the 25.5% loss reduction. It is a reproducible demonstration that program-level geometry search can challenge a published adjoint result while retaining the stage quantities a turbine designer must protect.

-25.5%entropy loss vs the LS89 blade on the 0.6M-cell mesh (25.99 +/- 0.61% Richardson-extrapolated), turning and mass flow matched2D midspan RANS CFD · 4-level grid study
+2.20 ptslead over the compliant Chatel et al. reference (+2.20 +/- 0.35 pts extrapolated)Same solver · 4-level grid study
-21.2%loss of a second, geometrically distinct blade family discovered when all Chatel-like shapes were mathematically forbidden1.5x refined mesh · nearly 2x Torreguitart 2018

Why the mechanism works

Archimedes coordinated three coupled geometric moves: it opened pitch from 57.5 to 78.0 mm, restaggered to 60.35 deg with throat/pitch = 0.269 to hold exit turning at a +0.021 deg margin, and added a localized CST suction-side contour that controls the loaded vane's M = 1.138 peak and approximately 0.105 Mach recovery jump.

What the baseline got wrong

Over 98% of the entropy loss in the LS89 transonic cascade comes from wetted boundary layers and the trailing-edge wake. Widening blade pitch cuts wetted surface area per unit mass flow, but higher per-blade loading drives the rear suction side supersonic - triggering a normal shock wave that destroys the efficiency gain and under-turns the exit flow.

Full technical recordappendices, families and limits
Campaign record and limitations

Appendix

The detailed brief, decision record, search families, solver basis, and verification checks are exposed below without tabs or collapsed panels.

Appendix A: Frozen brief and campaign scale

Minimize mass-averaged entropy generation J across the VKI LS89 transonic turbine nozzle guide vane cascade at exit isentropic Mach 0.90 (inlet 159.6 kPa, 420 K, Spalart-Allmaras, y+ < 1). Exit flow angle must be >= baseline (74.81 deg) with mass flow per unit pitch matched within +/- 0.7%. Both airfoil surfaces, pitch, stagger, throat, and LE radius are free; axial chord and TE are fixed.

Search duration
30 h (14.3 h + 15.7 h)
Evaluations
1,333
Compute fleet
18 cloud machines
Solver basis
2D midspan compressible RANS (HiSA HLLC, Spalart-Allmaras, y+ < 1) · 4-level grid study to 0.66M cells

Appendix B: Full decision log

01

Step 1 · Literature Audit · Digitizing & Re-Solving Published Optima

Catching a 0.06 deg turning violation in the published benchmark leader

Observation
Digitizing the Chatel et al. (2018) and Torreguitart et al. (2018) optima (0.06 mm registration accuracy) and solving them on our VKI MUR47-validated HiSA evaluator showed Chatel's published blade misses the exit turning floor by 0.046-0.06 deg.
Reasoning
To establish a constraint-compliant comparison, Archimedes created a restaggered Chatel reference (-23.52% on the 1.5x mesh) and reported both the published and compliant forms.
Action and result
Wrote 40 physically distinct concept blade programs; before evolution even began, Archimedes' aft-loaded high-pitch concept reached -23.45% on the search mesh, already surpassing the restaggered Chatel bar (-22.7%).
02

Step 2 · Open & Excluded Campaigns · 1,333 Compressible RANS Evaluations

Co-evolving 78 mm pitch with a 57%-chord shock-control contour

Observation
Opening pitch above 75 mm cuts boundary-layer wetted area by 16%, but pushes peak suction Mach above 1.18 with a strong trailing shock.
Reasoning
Adding a localized class-shape-function inflection near 57% chord controls the supersonic expansion and recovery while holding exit turning within 0.007-0.021 deg of the floor.
Action and result
Reached -25.14% on the 1.5x mesh and -25.50% on the 2.25x (0.6M-cell) mesh (25.99 +/- 0.61% extrapolated), plus a second completely distinct family at -21.2% when all Chatel-like shapes were banned.

Appendix C: Search families

2 profile families + 40 concepts. These are distinct programs or engineering configurations, not cosmetic renders.

  • High-pitch shock-contoured B-spline / CST family (Open winner Gen 502, -25.5% at 2.25x mesh)
  • Excluded-Chatel curvature-integrated drooped-LE family (Explore winner Gen 449, -21.2%)
  • Aft-loaded high-pitch concept seeds (-23.45% before evolution began)
  • Restaggered Chatel 2018 (-23.52%) & Torreguitart 2018 (-10.96%) replications

Appendix D: Numerical basis and verification

2D midspan compressible RANS (HiSA HLLC, Spalart-Allmaras, y+ < 1) · 4-level grid study to 0.66M cells

  • Frozen HiSA evaluator validated against VKI MUR47 experimental blade-surface Mach measurements (mean error 0.020 in isentropic Mach).
  • Four-level grid study up to 656,656 winner cells: finest-grid reduction 25.5016%, Richardson-extrapolated reduction 25.9873% +/- 0.6072%.
  • Nine-point off-design map: the winner leads the compliant Chatel reference across Mach 0.84-0.95 and at +2.5/+5 deg incidence, but not at the two trailing conditions (Mach 1.02 and -5 deg incidence).

Appendix E: Reported outcomes and limits

-25.5%
entropy loss vs the LS89 blade on the 0.6M-cell mesh (25.99 +/- 0.61% Richardson-extrapolated), turning and mass flow matched Basis: 2D midspan RANS CFD · 4-level grid study.
+2.20 pts
lead over the compliant Chatel et al. reference (+2.20 +/- 0.35 pts extrapolated) Basis: Same solver · 4-level grid study.
-21.2%
loss of a second, geometrically distinct blade family discovered when all Chatel-like shapes were mathematically forbidden Basis: 1.5x refined mesh · nearly 2x Torreguitart 2018.

Explicit limitations

  • The evidence is 2D midspan cascade RANS, not a 3D vane, endwall, cooling, structural, or engine-efficiency result.
  • The winner trails the compliant Chatel reference at M2is 1.02 and at -5° incidence.
  • Chatel et al. is a hybrid evolutionary and adjoint reference, not an adjoint-only comparator.

Recorded Archimedes run: 30 h across 2 campaigns (1,333 CFD solves). Compute record: 18 cloud machines · 4 grid levels to 0.66M cells.