19  2D Transonic Airfoil — RAE2822 RANS Validation

Comparison of shock location and surface pressure distribution against the AGARD Case 6 experiment

19.1 Run Provenance and Artifacts

Item Value
Wake CFD baseline version 0.22.2
Solver DBNS
Compute device CPU
Parallel execution 1 MPI rank
Arithmetic precision FP64
Run date 2026-08-18
Note

Results depend on the solver build that produced them. Read every figure in this report together with the version and date above — re-running the same input on a later build may give different numbers.

19.1.1 Downloadable Files

Not available: standalone input decks and solver result files have not yet been published for download.

19.2 Validation Objective

For a transonic airfoil, small changes in conditions can substantially alter the shock location and lift. This case compares the surface pressure distribution of the widely used RAE2822 airfoil with experiment to establish the range over which Wake CFD reproduces two-dimensional transonic turbulent flow with a shock.

For users, this result supports review of airfoil pressure distributions, shock locations, and lift levels during early design. In particular, the default Roe scheme reproduces both the suction-side shock and lift level observed in experiment.

19.3 Reference Solution and Data

Item Setting
Reference AGARD AR-138 RAE2822 Case 6 pressure distribution and lift (C_L=0.743)

19.4 Simulation Conditions

Item Setting
Geometry RAE2822 2D airfoil
Analysis Steady, compressible RANS
Freestream Mach 0.729
Angle of attack 2.31°
Reynolds number Re_c=6.5×10^6
Reference temperature 288.15 K

This setup uses the free-air-corrected condition for AGARD Case 6. The Case 9 pressure data in the same data set use a different angle of attack and lift level, and therefore are not compared directly with the Case 6 result. Checking the case number for both conditions and experimental data is essential when reproducing this case.

19.5 Mesh

Item Setting
Mesh 2D C-mesh, 192 points on the airfoil surface

The baseline mesh is a 2D C-mesh with 192 points on the airfoil surface, comprising 13,937 nodes and 22,842 elements. The airfoil surface and near field where the shock forms are refined, with progressively coarser spacing toward the farfield.

Full domain of the RAE2822 Case 6 baseline C-mesh

Leading-edge region of the RAE2822 Case 6 baseline C-mesh

19.6 Boundary and Initial Conditions

N/A: Detailed boundary and initial conditions are not documented for this case.

19.7 Numerical Methods

Item Setting
Turbulence model Spalart–Allmaras (SA)
Convective schemes Roe, HLLC, JST, AUSM+up, AUSM+up2, SLAU, SLAU2, and AUSM (compared below)

Time integration and convergence settings: Not reported.

19.8 Results

19.8.1 Key Results

The baseline Roe configuration converged in 4,697 iterations and predicted C_L=0.7455, a 0.3% difference from the Case 6 experimental value of 0.743. The suction-side shock was also captured near the experimental location, x/c≈0.55.

The Mach contour shows the flow accelerating over the suction side to form a local supersonic region, followed by sharp compression near x/c≈0.55. The pressure-coefficient contour likewise shows a distinct pressure recovery at the same location, consistent with the shock location identified in the surface pressure comparison.

RAE2822 Case 6 — Roe-scheme Mach contour

RAE2822 Case 6 — Roe-scheme pressure-coefficient contour

RAE2822 Case 6 — comparison of Wake CFD Roe results with AGARD experiment and NASA WIND 5.0 SA results

RAE2822 Case 6 — surface pressure-coefficient distribution from the Roe scheme, compared with experiment and NASA WIND

The pressure-distribution shape on both sides of the shock and the pressure recovery agree well overall with the experimental points. Because interpolation near the sharp leading-edge pressure variation can make RMS error appear large, this case considers shock location, pressure-distribution shape, and lift coefficient together.

19.8.2 Comparisons for Scheme Selection

Only the convective scheme was varied while keeping the mesh and turbulence model fixed. The pressure distribution is reproduced similarly by several schemes, but reaching the target convergence is as important as accuracy in practice.

Scheme Lift coefficient Iterations Convergence status Assessment
Roe 0.7455 4,697 Converged Default choice
HLLC 0.7471 4,693 Converged Roe alternative
JST 0.7266 5,205 Converged Usable
AUSM+up 0.7564 4,663 Converged Usable
AUSM+up2 0.7383 4,712 Converged Usable
SLAU / SLAU2 0.7404 / 0.7385 20,000 Residual stagnation* Further tuning required
AUSM 0.7589 20,000 Leading-edge oscillation Not recommended

* The pressure distribution and force coefficients stabilized, but the specified residual-reduction criterion was not reached.

RAE2822 Case 6 — surface pressure-coefficient distribution with HLLC

RAE2822 Case 6 — surface pressure-coefficient distribution with JST

RAE2822 Case 6 — surface pressure-coefficient distribution with AUSM+up

RAE2822 Case 6 — surface pressure-coefficient distribution with AUSM+up2

RAE2822 Case 6 — surface pressure-coefficient distribution with SLAU

RAE2822 Case 6 — surface pressure-coefficient distribution with SLAU2

RAE2822 Case 6 — surface pressure-coefficient distribution with AUSM

19.9 Conclusions and Applicable Scope

  • Roe is recommended as the default scheme for this condition. It gives the closest lift to experiment and reaches the specified convergence criterion robustly.
  • If an alternative is required, consider HLLC, JST, AUSM+up, or AUSM+up2. All reproduced the shock and pressure distribution stably in this case.
  • Plain AUSM produced leading-edge pressure oscillations. SLAU/SLAU2 did not reach the target residual without additional CFL or linear-solver tuning.
  • This result validates one airfoil, one Reynolds number, and a two-dimensional steady RANS condition. It does not guarantee the same accuracy for a real three-dimensional wing, transition or separation, unsteady buffet, other turbulence models, or other mesh quality.

19.10 References