| --- |
| configs: |
| - config_name: default |
| data_files: |
| - split: VT_shape |
| path: VT/all_shapes_meta.parquet |
| license: cc-by-sa-4.0 |
| tags: |
| - AI4CFD |
| - RANS |
| - Airfoils |
| --- |
| |
| **SuperFoil** is a collection of supercritical airfoil datasets. It contains **1420** distinct airfoils, with around **20k** of their flow field under multiple operating conditions, designed |
| for different purposes. The key feature of SuperFoil is that an Output Space Sampling (OSS) strategy is used, which makes the airfoils in the dataset have |
| **great diversity in both geometric and flow features**. |
|
|
|  |
|
|
| # Overview |
|
|
| SuperFoil uses the Class Shape Transformation methods to describe airfoils. It contains two groups of shapes, where the `FT` set has lower variation in shapes, and |
| `VT` set has a much larger variation. The `VT` shape set has 1420 shapes (which means 1420 groups of CST coefficients), and we use these shapes to generate several flow field |
| datasets by simulating the flow around these airfoils under multiple operating conditions. Specifically, for each dataset, a *varying operating condition* is selected. Its |
| value is perturbed around the airfoil's *reference operating condition* for each airfoil. |
|
|
| A summary of these datasets is provided below: |
|
|
|
|
| |Folder | Dataset | Varying Var. | \\((t/c)_{\max}\\) | \\(Ma_{\infty}\\) | \\(C_L\\) | \\(AoA\\)(deg.) | \\(N_{\mathrm{Airfoils}}\\) | \\(N_{\mathrm{flowfileds}}\\) | Comment | |
| | ------- | --------------- | --------- | ---------------------- | -------------------------- | -------------------- | ------------ | ---- | ----- | --------------------------| |
| |`FT` |A-1 | \\(C_L\\) | 0.095 | 0.76 | `ls(0.6, 1.0, 0.04)` | / | 1498 | 16478 | FIX MAX. THICKNESS |
| |`VT/BUF` |A-3-1 (n3; 5) | \\(AoA\\) | `ls(0.09, 0.13, 0.01)` | `ls(0.71, 0.76, 0.01)` | / | `[-3.0-5.0]` | 1217 | 25607 | for buffet onset prediction | |
| |`VT/DD` |A-3-2 (ma-n4; 7) | \\(Ma\\) | `ls(0.09, 0.13, 0.01)` | `[0.65-0.80]` | `ls(0.6, 0.9, 0.01)` | / | 1266 | 17386 | for drag divergence prediction | |
| |`VT/GU` |A-3-3 (n5-1; 10) | \\(C_L\\) | `U[0.085-0.135]` | `U[0.705-0.765]` | `[0.0-1.0]` | / | 1341 | 16031 | | |
| |
| The dataset was established by Runze Li and Yunjia Yang @ AeroLab, Tsinghua University. Please cite the corresponding paper for the datasets: |
| |
| > `FT`: Yang, Yunjia, Runze Li, Yufei Zhang, and Haixin Chen*. 2022. “Flowfield Prediction of Airfoil Off-Design Conditions Based on a Modified Variational Autoencoder.” AIAA Journal 60 (10): 5805–20. https://doi.org/10.2514/1.J061972. |
| > |
| > `VT/BUF`: Yang, Yunjia, Runze Li, Yufei Zhang, and Haixin Chen*. 2024. “Fast Buffet-Onset Prediction and Optimization Method Based on Pretrained Flowfield Prediction Model.” AIAA Journal 62 (8): 2979–95. https://doi.org/10.2514/1.J063634. |
| > |
| > `VT/DD`: Yang, Yunjia, Runze Li, Yufei Zhang, and Haixin Chen*. 2026. "Uncertainty-aware data-based method for fast and reliable shape optimization." Structural and Multidisciplinary Optimization 69 (4): 95. https://link.springer.com/10.1007/s00158-026-04259-0 |
| > |
| > `VT/GU`: Yang, Yunjia, Runze Li, Yufei Zhang, Lu Lu, and Haixin Chen*. 2025. "Rapid aerodynamic prediction of swept wings via physics-embedded transfer learning." AIAA Journal 63 (6): 2545-59. |
| |
| |
| # Sampling of the shape coefficients |
| |
| ## Basics of CST |
| |
| The upper and lower surfaces are represented independently using CST functions. The surface is described with |
| |
| $$ |
| y_\text{u,b}(x) = C(x) \cdot \sum_{i=0}^{9} u_i \cdot \Phi_i(x),\quad y_\text{l,b}(x) = C(x) \cdot \sum_{i=0}^{9} l_i \cdot \Phi_i(x), |
| $$ |
| where \\(C(x) = x^{0.5}(1-x)^{1.0}\\) is the class function, and where \\(\phi_i(x)=\binom{n}{i}x^i(1-x)^{n-i}\\) denotes the \\(i\\)-th Bernstein basis polynomial of |
| degree \\(n\\). |
|
|
| ## Output Space Sampling (OSS) |
|
|
| > Please refer to this paper for the detailed methodology. Runze, LI, Yufei Zhang, and Haixin Chen*. 2022. "Pressure distribution feature-oriented sampling for statistical |
| > analysis of supercritical airfoil aerodynamics". Chinese Journal of Aeronautics, 35 (4): 14. |
| |
| The OSS method aims to obtain geometric parameters with more abundant and diverse flow features (here, the pressure distribution features are mainly considered, e.g., the |
| position and the intensity of the shock wave. The sampling process can be simply recognized as a series of optimizations, where the objectives are the diversity of flow |
| features under several reference operation conditions. It follows the steps below: |
| |
| 1. Decide the *reference operating conditions*. Here we use \\(Ma_{\infty}\\) and \\(C_L\\). The values for `VT` can be found in `VT\all_shapes_meta.parquet` under `Ref_minf` and `Ref_cl`. |
| 2. Get an initial population. Here, we use the linear combination of several common supercritical airfoils (OAT15A, RAE2822, RS16SC1, VA2, etc.). |
| 3. Conduct optimization under the reference operating conditions. The objectives are the diversity of shock wave position and strength, and constraints are leading-edge radius is larger than 0.007 and the cruise point drag coefficient does not exceed 0.1 |
| |
| # Simulation |
| |
| ## Meshing |
| |
| - Structured C-type grid solved with the elliptic equation to ensure grid orthogonality |
| - Grid size is 381×81 in the circumferential direction (i-direction) and wall-normal direction (j-direction). |
| - The grid contains 300 cells on the airfoil surface. The far-field location is 80 chords away from the airfoil. The height of the first mesh layer is 2.7e-6 chord. |
| |
| ## CFD |
| |
| - Computed using the Reynolds Average Navier–Stokes (RANS) solver `CFL3D`. |
| - finite volume method |
| - MUSCL scheme, ROE scheme |
| - Gauss-Seidel algorithm |
| - Turbulence model: shear stress transport (SST) model |
| |
| # Data format |
| |
| ## shape parameters (`all_shapes_meta.parquet`) |
| |
| > Please refer to this paper for a detailed description. Runze, LI, Yufei Zhang, and Haixin Chen*. 2023. "Knowledge discovery with computational fluid dynamics: Supercritical |
| > airfoil database and drag divergence prediction". Physics of Fluids, 35 (1): 016113. |
|
|
| | Var | Description | |
| | ---------- | -------------------------------------------------------------------------------------------- | |
| | Running_ID | Running sample ID for the sample. This is the unique ID for the shape among the `VT` dataset | |
| | Ref_Minf | Reference Mach number | |
| | tmax | Maximum relative thickness | |
| | Ref_CL | Reference lift coefficient |
| | Cd | Drag coefficient under reference condition |
| | X-1 | shock wave position on chord |
| | Mw-1 | Wall Mach number at the beginning of the shock wave |
| | Mw-A | The highest wall Mach number behind the shock wave |
| | Mw-L | The highest wall Mach number on the upper surface (suction peak) |
| | Mw-Q | |
| | Mw-M | The highest wall Mach number on the lower surface |
| | Mw-D | |
| | X-A | The position of the highest wall Mach number behind the shock wave |
| | x-tmax | The position of maximum thickness |
| | c-tmax | The camber at maximum thickness |
| | t0.2, t0.8 | relative thickness at 0.2, 0.8 chord |
| | c0.2, c0.5, c0.8 | camber at 0.2, 0.5, 0.8 chord |
| | vol | volume of airfoil |
| | RLE | leading edge radius |
| | TEA | tailing edge angle |
| | U1~U10 | upper surface CST coefficients |
| | L1~L10 | lower surface CST coefficients |
| |
| ## Meta for each dataset (`index.npy`) |
| |
| | Dataset | `FT` | `VT-BUF` | `VT-DD` | `VT-GU` | |
| | ---------- | ----------- | -------------- | ----------- | ---------- | |
| | array size | (16478, 10) | (25607, 13) | (17386, 13) | (16031, 13)| |
| | 0 | airfoil index | |
| | 1 | condition index | |
| | 2 | ref index for the airfoil| |
| | 3 | aoa | aoa | ma | aoa |
| | 4 | ref aoa | ref aoa | ref ma | ref aoa |
| | 5 | ref ma | ref ma | ref aoa | ref ma |
| | 6 | ref cl | ref cl | ref cl | ref cl |
| | 7 | cl | buffet aoa (estimated) | / | / |
| | 8 | cd | sepearation aoa | / | / |
| | 9 | running idx | cl | " | " |
| |10 | / | cd | " | " |
| |11 | / | running idx | " | " |
| |12 | / | tmax | " | " |
| |
| ## Volumetric flow field |
| |
| The field is described with a structured grid for simulation. The `i`-direction is circling the airfoil, from far-field at wake to the trailing edge, then |
| from the trailing edge through the lower surface to the leading edge; then go back through the upper surface. The `j`-direction is wall-normal from the airfoil surface |
| to the farfield. We truncated the grid in `j` direction at 75 and in `i` direction from 25 to -25. This leads to a final grid size of \\(331 \times 75\\) |
| |
| <img src="https://cdn-uploads.huggingface.co/production/uploads/6878e482bd4380c813fd99de/WT41XY0b-TTuk9PEArtEp.png" alt="volume" width="40%"> |
| |
| At each grid point, 6 channels are provided. The first two are coordinates (`x`, `y`) of the cell vertex. The rest are four flow quantities |
| (`p`, `T`, `u`, and `v`). They are NON-DIMENSIONAL with freestream condition (in CFL3D.prt way), and interpolated to the vertices. |
| |
| $$ |
| p = \frac{\tilde p}{\tilde p_\infty}, T = \frac{\tilde T}{\tilde T_\infty}, u = \frac{\tilde u}{\tilde u_\infty}, v = \frac{\tilde v}{\tilde v_\infty}, |
| $$ |
| where ~ stands for dimensional values. |
| |
| ## Surface flow field |
| |
| The surface pressure and skin-friction distributions are critical for analyzing aerodynamic coefficients and extracting key flow features. They are defined with |
| |
| $$ |
| C_p = \frac{p - p_\infty}{0.5\rho V_\infty^2}, \quad C_{f} = \frac{\tau_w}{0.5\rho_\infty V_\infty^2}, \quad \tau_w=\mu \frac{\partial u_t}{\partial s_n} |
| $$ |
| where \\(\bm{u_t}\\) is the tangential velocity at the wall surface, while \\(s_n\\) is the wall-normal coordinate. The positive value of \\(C_f\\) indicates that the flow |
| is aligned with the flow for both surfaces. |
|
|
| The two quantities are interpolated and reported on a series of 401 \\(x\\) reference points as |
|
|
| $$ |
| x_i = \frac{\cos a_0\pi - \cos\left( a_0 (1-k_i)+a_1 k_i\right)\pi}{\cos a_0\pi - cos a_1\pi},\quad k_i = \frac{i}{n-1}. |
| $$ |
| |
| The final data consists of three channels: the \\(y\\) coordinates of these reference points and the two coefficients. |
| |
| <img src="https://cdn-uploads.huggingface.co/production/uploads/6878e482bd4380c813fd99de/hUT54BHUNk5egT_qQXvOL.png" alt="surface" width="40%"> |
| |
| |
| |
