airfoil_design

Airfoil Design

The airfoil design is aimed to minimize the drag coefficient ($C_D$) while keeping lift coefficient ($C_L$) greater than a given value, thus improving the lift-drag ratio.

The airfoil dataset is based on UIUC dataset which contain more than 1,600 real-world airfoil design. We use the open-source script to remove abnormal airfoils and obtain 1,433 airfoils, which are stored in data_bs/pts.

We construct two distinct cubic B-spline curves with 34 control points for the upper surface and lower surface of the airfoil, respectively. The two end control points of each B-spline curve are fixed at the leading edge (0, 0) and the trailing edge (1, 0). The control points data are stored in data_bs/controls. Finally, all control points data are concatenated in a numpy array bs_datas.npy.

Shape Sampling

Firstly, we shall enrich the control points data. We apply WGAN-GP to do it. Run the following code

python main_gan.py --lr 1e-4 --batch_size 128 --lambda_gp 10 --regular 0.3 --nEpoch 100000 --wass

The trained generator are stored in resultsWGAN. We use this generator to obtain more data, finally, the generated data and origin data are stored in data_extend_wgan.npy, with a total of 46,286 items.

High-fidelity Physical Model Learning

There two kinds of fluid conditions are considered:

• incompressible: $Re=6.5e6, Ma=0.150$, angel of attack $\alpha$ ranges over $[0^\circ, 10^\circ]$ with $0.1^\circ$ gridsizes.

• compressible: $Re=6.5e6, Ma=0.150$, angel of attack $\alpha$ ranges over $[0^\circ, 3^\circ]$ with $0.03^\circ$ gridsizes.

Therefore, there are a total of 4,628,600 items need to be labeled under each fluid condition. For each item, we use Xfoil to calculate the corresponding $C_L, C_D$. Usually, the cost of labelling is huge. Consequently, we apply mean-teacher-based active learning algorithm to select 500,000 items for labeling and learn a physical model. For the convenience, all items are labelled at once and stored in remake_data_v2_ma150.npy and remake_data_v2_ma734.npy, corresponding to fluid condition $Ma=0.150$ and $Ma=0.734$. These corresponding codes are located in mean-teacher-al.

Run the following code under the directory mean-teacher-al

python main.py --ma 150 # incompressible fluid case

python main.py --ma 734 # compressible fluid case

The corresponding network's parameters are stored in results-al-semi-150 and results-al-semi-734, respectively. And the learning results are as follows.

$Ma$	$\text{RMAE}_{C_L}$	$\text{RMAE}_{C_D}$
0.150	5.193E-3	2.156E-2
0.734	1.058E-2	6.690E-2

Shape Anomaly Detection

The critical factor impacting the performance of auto-encoder training is the choice of the dimension of the latent space. So run the following code.

python lpca.py

The result should be 5(round up). This give a lower bound of the dimension of latent space. For verifying that the value is sufficient, we examine the reconstruction error as a function of the dimension of latent space, which are shown as follows.

In our experiment, we choose 16. Run the following code to train the auto-encoder.

python main_ae.py --embed-dim 16

The corresponding parameters are stored in resultsAE_ID=16_wgan. And the result are as follows.

index	value
ReconErr mean	2.283E-3
ReconErr variance	2.199E-5

Numerical Optimization

We use naca2412 as the initial airfoil. Run the following code.

python shapeOptALSSL.py --ma 150 # 734

And the optimized results are located in optimize_results, which are shown as follows.

mach = 0.150 mach = 0.734