README.md

metadata

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.	$(t\mathrm{/}c{)}_{\max }(t/c)\_\{\backslash max\}$	$M{a}_{\mathrm{\infty }}Ma\_\{\backslash infty\}$	$C_{L}C\_L$	$AoAAoA$(deg.)	$N_{\mathrm{A}\mathrm{i}\mathrm{r}\mathrm{f}\mathrm{o}\mathrm{i}\mathrm{l}\mathrm{s}}N\_\{\backslash mathrm\{Airfoils\}\}$	$N_{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{f}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{d}\mathrm{s}}N\_\{\backslash mathrm\{flowfileds\}\}$	Comment
FT	A-1	$C_{L}C\_L$	0.095	0.76	ls(0.6, 1.0, 0.04)	/	1498	16478	FIX MAX. THICKNESS
VT/BUF	A-3-1 (n3; 5)	$AoAAoA$	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)	$MaMa$	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)	$C_{L}C\_L$	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

$$y_{\text{u,b}}(x)=C(x)\cdot \sum _{i=0}^9{u}_i\cdot {\mathrm{\Phi }}_i(x),y_{\text{l,b}}(x)=C(x)\cdot \sum _{i=0}^9{l}_i\cdot {\mathrm{\Phi }}_i(x),y\_\backslash text\{u,b\}(x)\; =\; C(x)\; \backslash cdot\; \backslash sum\_\{i=0\}^\{9\}\; u\_i\; \backslash cdot\; \backslash Phi\_i(x),\backslash quad\; y\_\backslash text\{l,b\}(x)\; =\; C(x)\; \backslash cdot\; \backslash sum\_\{i=0\}^\{9\}\; l\_i\; \backslash cdot\; \backslash Phi\_i(x),$$ where $C(x)=x^{0.5}(1-x{)}^{1.0}C(x)\; =\; x^\{0.5\}(1-x)^\{1.0\}$ is the class function, and where ${\varphi }_i(x)=\left(\genfrac{}{}{0px}{}{n}{i}\right)x^i(1-x{)}^{n-i}\backslash phi\_i(x)=\backslash binom\{n\}\{i\}x^i(1-x)^\{n-i\}$ denotes the $ii$-th Bernstein basis polynomial of degree $nn$.

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 $M{a}_{\mathrm{\infty }}Ma\_\{\backslash infty\}$ and $C_{L}C\_L$. 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 $331\times 75331\; \backslash times\; 75$

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.

$$p=\frac{\tilde{p}}{{\tilde{p}}_{\mathrm{\infty }}},T=\frac{\tilde{T}}{{\tilde{T}}_{\mathrm{\infty }}},u=\frac{\tilde{u}}{{\tilde{u}}_{\mathrm{\infty }}},v=\frac{\tilde{v}}{{\tilde{v}}_{\mathrm{\infty }}},p\; =\; \backslash frac\{\backslash tilde\; p\}\{\backslash tilde\; p\_\backslash infty\},\; T\; =\; \backslash frac\{\backslash tilde\; T\}\{\backslash tilde\; T\_\backslash infty\},\; u\; =\; \backslash frac\{\backslash tilde\; u\}\{\backslash tilde\; u\_\backslash infty\},\; v\; =\; \backslash frac\{\backslash tilde\; v\}\{\backslash tilde\; v\_\backslash infty\},$$ 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

$$C_p=\frac{p-p_{\mathrm{\infty }}}{0.5\rho V_{\mathrm{\infty }}^2},C_f=\frac{{\tau }_w}{0.5{\rho }_{\mathrm{\infty }}{V}_{\mathrm{\infty }}^2},{\tau }_w=\mu \frac{\mathrm{\partial }{u}_t}{\mathrm{\partial }{s}_n}C\_p\; =\; \backslash frac\{p\; -\; p\_\backslash infty\}\{0.5\backslash rho\; V\_\backslash infty^2\},\; \backslash quad\; C\_\{f\}\; =\; \backslash frac\{\backslash tau\_w\}\{0.5\backslash rho\_\backslash infty\; V\_\backslash infty^2\},\; \backslash quad\; \backslash tau\_w=\backslash mu\; \backslash frac\{\backslash partial\; u\_t\}\{\backslash partial\; s\_n\}$$ where $\backslash bm\{u\_t\}$ is the tangential velocity at the wall surface, while $s_{n}s\_n$ is the wall-normal coordinate. The positive value of $C_{f}C\_f$ indicates that the flow is aligned with the flow for both surfaces.

The two quantities are interpolated and reported on a series of 401 $xx$ reference points as

$$x_i=\frac{\cos a_0\pi -\cos (a_0(1-k_i)+a_1{k}_i)\pi }{\cos a_0\pi -cos{a}_1\pi },k_i=\frac{i}{n-1}\mathrm{.}x\_i\; =\; \backslash frac\{\backslash cos\; a\_0\backslash pi\; -\; \backslash cos\backslash left(\; a\_0\; (1-k\_i)+a\_1\; k\_i\backslash right)\backslash pi\}\{\backslash cos\; a\_0\backslash pi\; -\; cos\; a\_1\backslash pi\},\backslash quad\; k\_i\; =\; \backslash frac\{i\}\{n-1\}.$$

The final data consists of three channels: the $yy$ coordinates of these reference points and the two coefficients.