ShuangheYang/rae2822-cst20-cfl3d-fine

RAE2822 Airfoil Aerodynamics: Paired CFD Data and Surrogate Models

12,000 airfoil geometries · 24,000 coarse/fine CFD results · trained MLP and Kriging models

This dataset contains 12,000 CST-parameterized airfoil geometries, each evaluated with CFL3D on coarse and fine structured meshes. Two independently sampled Latin hypercube designs share the same transonic flow condition. The accompanying benchmark compares a multilayer perceptron (MLP) with isotropic Matérn-5/2 Kriging across eight training-set sizes.

Use the data to study aerodynamic regression, sample efficiency, multi-fidelity learning, and error structure. The trained models predict lift and drag from 20 CST coefficients; the lift-to-drag ratio is derived from those predictions. The data-generation platform and numerical executables are not distributed.

Data at a glance

Design	Distinct production geometries	Coarse results	Fine results	Suggested role
LHS_10000	10,000	10,000	10,000	Training pool
LHS_2000	2,000	2,000	2,000	Independently sampled evaluation pool

The two pools contain no exactly repeated production CST vectors. Within each pool, every coarse result matches a fine result with exactly the same 20 coefficients. Four separate baseline provenance records represent one common RAE2822 geometry, excluded from the production counts. Paired tables are views of the same data, not additional independent samples.

Geometry and sampling

The input order is fixed:

$$\mathbf{a}=(U_0,\dots ,U_9,L_0,\dots ,L_9{)}^{\mathsf{T}}\mathrm{.}\backslash mathbf\; a=(U\_0,\backslash ldots,U\_9,L\_0,\backslash ldots,L\_9)^\{\backslash mathsf\; T\}.$$

With normalized chordwise coordinate $x\in[0,1]$, the two normalized surfaces are

$$\frac{y_u(x)}{c}=x^{1\mathrm{/}2}(1-x)\sum _{i=0}^9{U}_i\left(\genfrac{}{}{0px}{}{9}{i}\right)x^i(1-x{)}^{9-i},\backslash frac\{y\_u(x)\}\{c\}=x^\{1/2\}(1-x)\backslash sum\_\{i=0\}^\{9\}U\_i\backslash binom\{9\}\{i\}x^i(1-x)^\{9-i\},$$ $$\frac{y_l(x)}{c}=x^{1\mathrm{/}2}(1-x)\sum _{i=0}^9{L}_i\left(\genfrac{}{}{0px}{}{9}{i}\right)x^i(1-x{)}^{9-i}\mathrm{.}\backslash frac\{y\_l(x)\}\{c\}=x^\{1/2\}(1-x)\backslash sum\_\{i=0\}^\{9\}L\_i\backslash binom\{9\}\{i\}x^i(1-x)^\{9-i\}.$$

There is no extra trailing-edge thickness term. Lower-surface signs are already contained in $L_i$; do not negate them again. The baseline is a least-squares CST fit to RAE2822 measured ordinates.

Each coefficient is sampled in the box

$$a_j\in [a_j^0-0.1\mathrm{\mid }{a}_j^0\mathrm{\mid },a_j^0+0.1\mathrm{\mid }{a}_j^0\mathrm{\mid }]\mathrm{.}a\_j\backslash in[a\_j^0-0.1|a\_j^0|,\backslash \; a\_j^0+0.1|a\_j^0|].$$

Latin hypercube sampling stratifies each coordinate independently. Exact baseline coefficients, bounds and sampling details are supplied in the parameter table, machine-readable bounds and production methodology.

CFD conditions and mesh resolution

Quantity	Setting
Flow solver	CFL3D 6.4, Windows serial; steady two-dimensional compressible RANS
Turbulence model	Menter k–ω SST, IVISC=7
Mach number	0.73
Chord Reynolds number	6,500,000
Angle of attack	2.79°; Case 9 corrected computational condition
Freestream temperature	288.15 K, an engineering choice
Reference chord / area	1 m / 1 m² for unit span
Mesh generator and topology	cgrid; single-block structured C grid
Coarse mesh	7,360 quadrilaterals; 185 × 41 nodes per plane
Fine mesh	27,360 quadrilaterals; 361 × 77 nodes per plane
Farfield parameter / target wall y+	40 c / 0.5

The two fidelities share the geometry, flow condition, model, and acceptance criteria. Actual wall y+, mesh quality, iteration counts, and solver-call duration are recorded for each selected result. Both fidelity levels use CFL3D with structured C grids.

For unit span, the force coefficients and derived ratio are

$$C_L=\frac{L^{\mathrm{\prime }}}{\frac{1}{2}{\rho }_{\mathrm{\infty }}{U}_{\mathrm{\infty }}^{2}c},C_D=\frac{D^{\mathrm{\prime }}}{\frac{1}{2}{\rho }_{\mathrm{\infty }}{U}_{\mathrm{\infty }}^{2}c},K=\frac{C_L}{C_D}\mathrm{.}C\_L=\backslash frac\{L\text{'}\}\{\backslash tfrac12\backslash rho\_\backslash infty\; U\_\backslash infty^2c\},\backslash qquad\; C\_D=\backslash frac\{D\text{'}\}\{\backslash tfrac12\backslash rho\_\backslash infty\; U\_\backslash infty^2c\},\backslash qquad\; K=\backslash frac\{C\_L\}\{C\_D\}.$$

Labels are the last-100-iteration means of accepted final-grid lift and total drag coefficients. L_D is the ratio of the two means, not a third independently fitted quantity. These are numerical CFD labels, not wind-tunnel measurements.

Browse and load

Choose a configuration in the Dataset Viewer to browse records, column distributions, and pages. Typed Parquet files under parquet/ preserve string IDs and float64 coefficients. Identical numerical records remain available as JSONL under data/:

Configuration	Rows	Contents
lhs_10000_fine / lhs_10000_coarse	10,000 each	Main training-pool records
lhs_2000_fine / lhs_2000_coarse	2,000 each	Evaluation-pool records
paired_lhs_10000_coarse_fine	10,000	Shared CST, both fidelities, signed differences
paired_lhs_2000_coarse_fine	2,000	Shared CST, both fidelities, signed differences
baseline / baseline_coarse	2 each	Baseline provenance records
quality / quality_coarse	12,002 each	Mesh, y+, timing context and attempt sequence
convergence / convergence_coarse	12,002 each	Acceptance flags and numerical diagnostics

from datasets import load_dataset
import numpy as np

repo = "ShuangheYang/rae2822-cst20-cfl3d-fine"
data = load_dataset(repo, "lhs_10000_fine", split="train")
features = [f"U{i}" for i in range(10)] + [f"L{i}" for i in range(10)]
X = np.column_stack([data[name] for name in features])
y = np.column_stack([data["CL"], data["CD"]])

For paired-fidelity work, select paired_lhs_10000_coarse_fine and use CL_coarse, CD_coarse, CL_fine, CD_fine. The repository URL retains its original -fine suffix; the contents include both fidelities.

IDs are five-character strings. Use sample_key = dataset/fidelity/id for numerical records and geometry_key = dataset/id for geometry pairs. ID 00001 in LHS_10000 is different from ID 00001 in LHS_2000.

Surrogate-model benchmark

The fine-only benchmark uses all 10,000 training geometries, with 500 validation and 1,500 test geometries from LHS_2000. Twelve MLP configurations are screened; the top three receive additional initialization seeds. The selected configuration is then fixed for paired learning curves at 50, 100, 200, 500, 1,000, 2,000, 5,000 and 10,000 training samples.

The default MLP has a 20–64–64–64–2 Tanh branch and a trainable input-to-output linear bypass. Kriging fits two independent exact isotropic Matérn-5/2 Gaussian processes. Both predict CL and CD; the ratio is derived afterward.

Target	MLP MAPE (%)	Kriging MAPE (%)
CL	0.030353	0.059635
CD	0.061773	0.212512
L_D	0.046815	0.236063

These values describe the prespecified seed-11 models trained on 10,000 fine samples, evaluated on the same 1,500 test geometries. The exact values and other metrics are in research/results/evaluation.json. Kriging performs better at the tested small-data budgets; the mean learning curves cross between 2,000 and 5,000 training samples under this protocol. The benchmark does not establish a universal ranking of neural networks and Gaussian processes.

For a target $q$, the reported relative error is

$${\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}}_q=\frac{100\mathrm{\%}}{N}\sum _{i=1}^N\mid \frac{{\widehat{q}}_i-q_i}{q_i}\mid \mathrm{.}\backslash mathrm\{MAPE\}\_q=\backslash frac\{100\backslash \%\}\{N\}\backslash sum\_\{i=1\}^\{N\}\backslash left|\backslash frac\{\backslash widehat\; q\_i-q\_i\}\{q\_i\}\backslash right|.$$

The two-output aggregate is

$$E_2=\frac{100\mathrm{\%}}{2}(\frac{{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_{C_L}}{s_{C_L,\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}}}+\frac{{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_{C_D}}{s_{C_D,\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}}}),{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_q=\sqrt{\frac{1}{N}\sum _i({\widehat{q}}_i-q_i{)}^2}\mathrm{.}E\_2=\backslash frac\{100\backslash \%\}\{2\}\backslash left(\backslash frac\{\backslash mathrm\{RMSE\}\_\{C\_L\}\}\{s\_\{C\_L,\backslash mathrm\{test\}\}\}\; +\backslash frac\{\backslash mathrm\{RMSE\}\_\{C\_D\}\}\{s\_\{C\_D,\backslash mathrm\{test\}\}\}\backslash right),\backslash qquad\; \backslash mathrm\{RMSE\}\_q=\backslash sqrt\{\backslash frac1N\backslash sum\_i(\backslash widehat\; q\_i-q\_i)^2\}.$$

The test standard deviations are common to all models and use the population denominator. $E_2$ is not MAPE. Validation selection uses a separately documented score; see the benchmark guide.

Documentation and models

• Production methodology and detailed numerical protocol
• Coarse/fine pairing and multi-fidelity use
• Field dictionary, quality audit, and evaluation guidance
• Benchmark guide and hyperparameter comparison
• Research report (PDF) and experiment workbook
• MLP weights and inference
• Kriging weights and inference
• References and file checksums

Scope and evaluation

This is an in-domain dataset around RAE2822 at one flow condition. Fine denotes a mesh-resolution class, not experimentally certified truth. The release includes selected accepted results and their diagnostics, not complete failed-run history or full flow fields.

Split by geometry across fidelities when evaluating unseen shapes. If coarse labels are available for test geometries, describe that as a separate information and cost setting. Fit preprocessing only on training data. The external evaluation pool has prior research exposure; the benchmark is frozen for this study, not a historically untouched blind test. Existing model weights and reports use fine labels only.

Attribution and license

Maintained by ShuangheYang. Geometry and numerical-method sources are cited in References; NASA did not produce or endorse this dataset. No reuse license has yet been assigned to this release.