yunplus/SuperWing

SuperWing, a comprehensive benchmark dataset of transonic swept wings comprising 4239 wing shapes and nearly 30,000 flow fields across diverse geometries and operating conditions. Unlike previous efforts that rely on perturbations of a baseline wing, SuperWing is generated using a simplified yet expressive parameterization scheme. By incorporating spanwise-varying dihedral, twist, and airfoil characteristics, the dataset captures realistic design complexity and ensures greater diversity than existing ones. Please refer to our arXiv paper for more details on the dataset.

The simulations are conducted on the 160-core high-performance computing cluster at AeroLab, Tsinghua University

Features

1. Focusing on the "kink" wings (with two segments instead of one in the spanwise direction) under transonic regime (Mach number between 0.75 and 0.90), which bring more complex flow features and are closer to the industry.
2. More diversity on the wing shape by generating them from basic parameters instead of perturbing from a baseline wing shape
3. RANS simulation with well-validated solver ADflow and structural computational mesh.

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Data overview

Files

(N=28856, Nshape=4239)

Type	File	Description	Shape	Size
Metadata	config.dat	shape parameters	$N_{\mathrm{s}\mathrm{h}\mathrm{a}\mathrm{p}\mathrm{e}}\times 56N\_\{\backslash mathrm\{shape\}\}\; \backslash times\; 56$	5.0 MB
	index.npy	indexing, operating conditions, and aerodynamic coefficients	$N_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}}\times 12N\_\{\backslash mathrm\{sample\}\}\; \backslash times\; 12$	2.8 MB
	training_samples_index.txt	training sample split	--	0.1 MB
Shape / Surface flow	data_surf.npy.zst	surface simulation mesh and flow quantities on mesh points (cell center)	$N_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}}\times 10\times \mathrm{44,096}N\_\{\backslash mathrm\{sample\}\}\; \backslash times\; 10\; \backslash times\; 44\{,\}096$	26.7 GB (85.3 GB)
	origingeom.npy	[STRUCTURED] reference surface mesh (grid points)	$N_{\mathrm{s}\mathrm{h}\mathrm{a}\mathrm{p}\mathrm{e}}\times 3\times 129\times 257N\_\{\backslash mathrm\{shape\}\}\; \backslash times\; 3\; \backslash times\; 129\; \backslash times\; 257$	3.3 GB
	geom0.npy	[STRUCTURED] reference surface mesh (cell center)	$N_{\mathrm{s}\mathrm{h}\mathrm{a}\mathrm{p}\mathrm{e}}\times 3\times 128\times 256N\_\{\backslash mathrm\{shape\}\}\; \backslash times\; 3\; \backslash times\; 128\; \backslash times\; 256$	3.3 GB
	data.npy	[STRUCTURED] surface flow quantities at reference mesh (cell center)	$N_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}}\times 3\times 128\times 256N\_\{\backslash mathrm\{sample\}\}\; \backslash times\; 3\; \backslash times\; 128\; \backslash times\; 256$	22.7 GB
Volumetric flow	data_vol.xx.npy.zst	coordinates and flow quantities at near-field volumetric simulation mesh (cell center)	$N_{\mathrm{s}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}}\times 8\times \mathrm{3,086,720}N\_\{\backslash mathrm\{sample\}\}\; \backslash times\; 8\; \backslash times\; 3\{,\}086\{,\}720$	3.2 TB (5.3 TB)

Channels (for geometry and flow)

Index	data_surf.npy	data_vol.npy	Index	origingeom.npy, geom0.npy
0	Coordinate $xx$	Coordinate $xx$	0	Coordinate $xx$
1	Coordinate $yy$	Coordinate $yy$	1	Coordinate $yy$
2	Coordinate $zz$	Coordinate $zz$	2	Coordinate $zz$
3	Density $\tilde{\rho }\backslash tilde\; \backslash rho$	Density $\tilde{\rho }\backslash tilde\; \backslash rho$		data.npy
4	Pressure coef. $C_{p}C\_\{p\}$	Pressure $\tilde{p}\backslash tilde\; p$	0	Pressure coef. $C_{p,\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{d}}C\_\{p,\backslash mathrm\{scaled\}\}$
5	$xx$ skin friction coef. $C_{f,x}C\_\{f,x\}$	$xx$ velocity ${\tilde{V}}_x\backslash tilde\; V\_x$	1	Streamwise skin friction coef. $C_{f,\tau ,\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{d}}C\_\{f,\backslash tau,\backslash mathrm\{scaled\}\}$
6	$yy$ skin friction coef. $C_{f,y}C\_\{f,y\}$	$yy$ velocity ${\tilde{V}}_y\backslash tilde\; V\_y$	2	$zz$ skin friction coef. $C_{f,z,\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{d}}C\_\{f,z,\backslash mathrm\{scaled\}\}$
7	$zz$ skin friction coef. $C_{f,z}C\_\{f,z\}$	$zz$ velocity ${\tilde{V}}_z\backslash tilde\; V\_z$
8	Temperature $\tilde{T}\backslash tilde\; T$

• $\widetilde{(\cdot )}\backslash tilde\{(\backslash cdot)\}$ means the relative value to the freestream condition ( ${\rho }_{\mathrm{\infty }},p_{\mathrm{\infty }},T_{\mathrm{\infty }},V_{\mathrm{\infty }}\backslash rho\_\backslash infty,\; p\_\backslash infty,\; T\_\backslash infty,\; V\_\backslash infty$ )
• $(\cdot {)}_{\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{d}}(\backslash cdot)\_\{\backslash mathrm\{scaled\}\}$ means they are scaled to have a similar magnitude. The scaling factor for the three channels are 1, 150, 300.

Coefficients definition

• Pressure coefficient: $C_p=\frac{p-p_{\mathrm{\infty }}}{0.5{\rho }_{\mathrm{\infty }}{V}_{\mathrm{\infty }}^2}C\_p\; =\; \backslash frac\{p-p\_\backslash infty\}\{0.5\backslash rho\_\backslash infty\; V\_\backslash infty^2\}$
• Friction coefficient: (vector) $C_{\mathit{f}}=[C_{f,x},C_{f,y},C_{f,z}{]}^T=\frac{}{0.5{\rho }_{\mathrm{\infty }}{V}_{\mathrm{\infty }}^2},=\mu \frac{\mathrm{\partial }}{\mathrm{\partial }{s}_n}C\_\{\backslash bm\; f\}\; =\; [C\_\{f,x\},\; C\_\{f,y\},\; C\_\{f,z\}]^T\; =\; \backslash frac\{\backslash bm\{\backslash tau\_w\}\}\{0.5\backslash rho\_\backslash infty\; V\_\backslash infty^2\},\; \backslash quad\; \backslash bm\{\backslash tau\_w\}=\backslash mu\; \backslash frac\{\backslash partial\; \backslash bm\; \{u\_t\}\}\{\backslash partial\; s\_n\}$
  • $C_{f,\tau ,\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{d}}C\_\{f,\backslash tau,\backslash mathrm\{scaled\}\}$ means the component in the $xx$ - $yy$ surface.

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Data format

Meta Data

The metadata include the wing geometry parameters, operating conditions, aerodynamic coefficients, group identifiers, and predefined train/test splits used in this work.

configs.dat

configs.dat stores the parametric definition of each wing geometry and can be used to reconstruct the geometry from scratch. It contains:

• Columns 1–7: Global planform parameters, including:

  • sweep angle ${\mathrm{\Lambda }}_{\mathrm{L}\mathrm{E}}\backslash Lambda\_\backslash mathrm\{LE\}$
  • tip/kink dihedral angles ${\mathrm{\Gamma }}_{\mathrm{L}\mathrm{E},\mathrm{t}\mathrm{i}\mathrm{p}}\backslash Gamma\_\backslash mathrm\{LE,tip\}$, ${\mathrm{\Gamma }}_{\mathrm{L}\mathrm{E},\mathrm{k}\mathrm{i}\mathrm{n}\mathrm{k}}\backslash Gamma\_\backslash mathrm\{LE,kink\}$
  • aspect ratio $ARAR$
  • taper ratio $TRTR$
  • kink location ${\eta }_k\backslash eta\_k$
  • root parameter ${\kappa }_{\mathrm{r}\mathrm{o}\mathrm{o}\mathrm{t}}\backslash kappa\_\backslash mathrm\{root\}$

• Columns 8–17: Spanwise variation parameters:

  • thickness ratios $r_{t}r\_t$ ( $\times 3\backslash times\; 3$)
  • deformation parameters $r_{\delta }r\_\backslash delta$ ( $\times 4\backslash times\; 4$)
  • twist angles ${\alpha }_{\mathrm{t}\mathrm{w}}\backslash alpha\_\backslash mathrm\{tw\}$ ( $\times 4\backslash times\; 4$)

• Columns 18–38: Baseline airfoil shape:

  • CST coefficients for upper surface ( $\times 10\backslash times\; 10$)
  • CST coefficients for lower surface ( $\times 10\backslash times\; 10$)

• Columns 39–56: Operating conditions:

  • eight pairs of Mach number $MaMa$ and angle of attack $\alpha \backslash alpha$

Some operating conditions may be missing in the final dataset if CFD simulations fail to converge.

index.npy

index.npy provides metadata for each flow-field sample. Each row corresponds to one sample. It includes:

• Geometry mapping

  • Column 1: geometry index (linked to configs.dat)
  • Column 2: operating-condition index within the geometry

• Operating conditions

  • Column 3: angle of attack $\alpha \backslash alpha$
  • Column 4: Mach number $MaMa$

• Reference quantities

  • Column 5: half reference area $S_{1\mathrm{/}2}S\_\{1/2\}$
  • Column 6: half span $b_{1\mathrm{/}2}b\_\{1/2\}$

• Aerodynamic coefficients

  • lift coefficient $C_{L}C\_L$
  • drag coefficient $C_{D}C\_D$
  • pitching moment coefficient $C_{M,z}C\_\{M,z\}$

  These coefficients are computed from pressure coefficient and skin-friction vector by surface integration:

  $>C_{\mathit{F}}=[C_x,C_y,C_z{]}^T=\frac{1}{S_{1\mathrm{/}2}}{\sum }_{i=1}^{N_{\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}}}[C_p^{(i)}{\mathit{n}}^{(i)}+(C_{\mathit{f}}^{(i)}-(C_{\mathit{f}}^{(i)}\cdot {\mathit{n}}^{(i)}){\mathit{n}}^{(i)})]A^{(i)}>>\; C\_\{\backslash bm\; F\}=[C\_x,C\_y,C\_z]^T\; =\backslash frac\{1\}\{S\_\{1/2\}\}\; \backslash sum\_\{i=1\}^\{N\_\{\backslash mathrm\{cell\}\}\}\; \backslash left[\; C\_p^\{(i)\}\backslash bm\; n^\{(i)\}\; +\; \backslash left(C\_\{\backslash bm\; f\}^\{(i)\}\; -\; (C\_\{\backslash bm\; f\}^\{(i)\}\backslash cdot\; \backslash bm\; n^\{(i)\})\backslash bm\; n^\{(i)\}\; \backslash right)\; \backslash right]\; A^\{(i)\}\; >$

  Lift and drag are obtained by rotating the force vector according to the angle of attack:

  $>[C_L,C_D,C_z{]}^T={\mathit{R}}_{\alpha }{C}_{\mathit{F}}>>\; [C\_L,C\_D,C\_z]^T=\backslash bm\; R\_\backslash alpha\; C\_\{\backslash bm\; F\}\; >$

  The pitching moment coefficient is:

  $>C_{M,z}=\frac{1}{S_{1\mathrm{/}2}{c}_{\mathrm{r}\mathrm{e}\mathrm{f}}}{\sum }_{i=1}^{N_{\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}}}{\mathit{r}}^{(i)}\times \left([C_p^{(i)}{\mathit{n}}^{(i)}+(C_{\mathit{f}}^{(i)}-(C_{\mathit{f}}^{(i)}\cdot {\mathit{n}}^{(i)}){\mathit{n}}^{(i)})]A^{(i)}\right)>>\; C\_\{M,z\}=\backslash frac\{1\}\{S\_\{1/2\}c\_\backslash mathrm\{ref\}\}\backslash sum\_\{i=1\}^\{N\_\{\backslash mathrm\{cell\}\}\}\backslash bm\; r^\{(i)\}\backslash times\backslash left(\backslash left[C\_p^\{(i)\}\backslash bm\; n^\{(i)\}+\backslash left(C\_\{\backslash bm\; f\}^\{(i)\}-(C\_\{\backslash bm\; f\}^\{(i)\}\backslash cdot\backslash bm\; n^\{(i)\})\backslash bm\; n^\{(i)\}\backslash right)\backslash right]A^\{(i)\}\backslash right)\; >$

  where: ${\mathit{n}}^{(i)}\backslash bm\; n^\{(i)\}$: outward normal vector, $A^{(i)}A^\{(i)\}$: surface-cell area, ${\mathit{r}}^{(i)}\backslash bm\; r^\{(i)\}$: position vector from the reference point, $c_{\mathrm{r}\mathrm{e}\mathrm{f}}=1.0c\_\backslash mathrm\{ref\}=1.0$: reference chord length

  Two sets of aerodynamic coefficients are provided:

  • Columns 7–9: coefficients computed on the original CFD mesh using ADflow
  • Columns 10–12: coefficients evaluated on the structured reference mesh for machine-learning applications

training_samples_index.txt

training_samples_index.txt stores the indices of training samples used in technical validation.

The dataset is split by wing shape to evaluate generalization:

• 90% of wing shapes are randomly selected for training
• the remaining shapes are used for testing

Training sample indices are recorded in this file.

Parquet Files

train.parquet and test.parquet provide metadata organized into training and test splits for convenient visualization and loading in HuggingFace.

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Surface shape and flow

Original data [NEW]

data_surf/data_surf.npy.zst provides the centric coordinates of the exact surface mesh for the simulations, and the surface flow values on the surface mesh centers. To enable compact storage, we flatten the original multi-block structured mesh into a one-dimensional sequence of 44,096 points.

Structured surface shape and flow

origingeom.npy, geom0.npy, data.npy

Besides the raw multi-block solver output, we also prepare the surface mesh and flow fields in a format suitable for ML models with structured inputs and outputs.

The reference mesh geom0 contains the cell-centric coordinates of the reference surface mesh with size $256\times 128\times 3256\; \backslash times\; 128\; \backslash times\; 3$, and the three channels stand for $x,y,zx,\; y,\; z$. The surface physical quantities data.npy are on the same reference mesh with size $256\times 128\times 3256\; \backslash times\; 128\; \backslash times\; 3$, and the three channels stand for $C_p,C_{f,\tau },C_{f,z}C\_p,\; C\_\{f,\backslash tau\},\; C\_\{f,z\}$. (the latter two are the decomposed friction coefficients on the streamwise and spanwise directions).

reference mesh: The simulation mesh on the wing surface is first interpolated to a reference mesh. In the spanwise ($j$-direction), 128 cross-sectional planes are sampled with even spacing, and tips are excluded. For each cross-section (i-direction), a fixed set of normalized chordwise positions $\{(x\mathrm{/}c{)}_i\}\backslash \{(x/c)\_i\backslash \}$ s is used for both the upper and lower surfaces, and the tail edge is represented only with one cell. The reference mesh along the wing surface is then unfolded as shown below, resulting in a final vertex surface grid of $257\times 129257\; \backslash times\; 129$ points per wing (origingeom.npy). This is useful when we need to calculate coefficients from the surface flow outputs. The cell-centric grid for the mesh is obtained just by averaging the coordinates at the four vertices.

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Volumetric flow quantities on the near-field simulation mesh

data\_vol/data\_vol.xx.npy.zst provides the volumetric flow, including the cell-centric coordinates and five core flow quantities at each simulation cell. They are again defined as the relative value to the freestream. Similar to the surface data, we flatten and concatenate the multi-block mesh into a one-dimensional point cloud sequence.

Given that it requires a large far field, the flow variables at far-field mesh points show only negligible deviations from the freestream values. To avoid this redundancy, we include the first 71 layers of mesh in the wall-normal dimension for each block. This produces 3,086,720 points per volumetric flow field.

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Postprocess

Aerodynamic coefficients

One can integrate surface flow (formatted as in data.npy) to get the aerodynamic coefficients (i.e., the lift coefficient $C_L$, the drag coefficient $C_D$, the pitching moment coefficient $C_{M,z}$) with the code in floGen (flogen.post). We also provide the post.py file here for simple download.

Remark.

1. It uses pytorch.
2. The geometric information should be with the grid point mesh (origingeom.npy), not the cell-centric mesh (geom0.npy).
3. The values in data.npy are already non-dimensionalized with the freestream condition

import post
geom = torch.from_numpy(np.load('origingeom.npy'))[i_shape]).float().to(device)
aoa = 3.0
ref_area = np.load('index.npy')[i_sample, 4]

output = <your_model_output> # with shape (H, W, 3)

cf_xyz = post._get_xz_cf_t(geom, output[..., 1:]) # transfer to xyz coordinates

force_coefficients = post.get_force_2d_t(geom=geom, aoa=aoa, cp=output[..., 0], cf=cf_xyz) / ref_area  # returns: CD, CL, CZ
moment_coefficients = post.get_moment_2d_t(geom=geom, cp=output[..., 0], cf=cf_xyz, ref_point=[0.25, 0, 0]) / ref_area   # returns: CMx, CMy, CMz

One can also use the cfdpost repo (https://github.com/YangYunjia/cfdpost).

from cfdpost.wing.basic import BasicWing

geom = torch.from_numpy(np.load('origingeom.npy'))[i_shape]).float().to(device)
geom_infos = {}
geom_infos['ref_area'] = np.load('index.npy')[i_sample, 4]
aoa = 3.0

output = <your_model_output> # with shape (H, W, 3)

wg1 = BasicWing(paras=geom_infos, aoa=aoa, iscentric=True)
wg1.read_formatted_surface(geometry=geom, data=output, isinitg=False, isnormed=False)
wg1.aero_force()
cl_real = wg1.coefficients # CL, CD, CMz

Visualization

To visualize the wing surface field, we provide a brief code that gives a not bad looking.

import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl

def color_map(data, c_map, alpha, dmin=None, dmax=None):
    dmin = np.nanmin(data) if dmin is None else dmin
    dmax = np.nanmax(data) if dmax is None else dmax
    _c_map = mpl.colormaps.get_cmap(c_map)

    norm = mpl.colors.Normalize(vmin=dmin, vmax=dmax)
    _sm = mpl.cm.ScalarMappable(norm=norm, cmap=_c_map)
    _colors = _sm.to_rgba(data)
    _colors[..., -1] = alpha
    
    return _colors, _sm

geom = np.load('data/ppn2norigingeom.npy')[0]
output = <your_model_output> # with shape (H, W, 3)

fig = plt.figure(figsize=(10, 4), dpi=200)
ax = fig.add_subplot(projection='3d')

elev = 68; azim =120 

colors, sm = color_map(output[..., 0], 'gist_rainbow', alpha=1, dmin=-1, dmax=1)    # cp
ax.plot_surface(*geom[[0,2,1]], facecolors=colors, edgecolor='none', rstride=1, cstride=3, shade=True)
ax.view_init(elev=elev, azim=azim)
ax.set_axis_off()
ax.grid(False)
ax.xaxis.pane.set_visible(False)
ax.yaxis.pane.set_visible(False)
ax.zaxis.pane.set_visible(False)

plt.show()

This should gives sth. like: