The transition to electric vehicles is bringing about significant changes in automobile design, particularly in terms of aerodynamics. The absence of a combustion engine has opened up new possibilities for modifying vehicle geometries. However, optimizing vehicle aerodynamics through traditional methods requires a large amount of computational and experimental studies, which are expensive. In this work, we analyze a dataset of industry-quality automobile geometries and their associated aerodynamic performance obtained from experimentally validated, high-fidelity large-eddy simulations. We show that a low-dimensional relationship between these geometries and their aerodynamics can be extracted using a nonlinear autoencoder. By leveraging this relationship, we perform aerodynamic design optimization of vehicle designs and demonstrate that the optimized geometries show agreement with validation simulations.

Unlock the potential of data-driven aerodynamics for electric vehicle design

Automobile aerodynamic analysis

Our dataset includes a wide range of industry-quality automobile geometries with different unsteady wake behaviors and aerodynamic performances. The baseline car designs come from various production models, and parametric modifications are made to produce a variety of geometries. The flow around the vehicles is computed using a large-eddy simulation with a moving mesh validated by industry wind-tunnel experiments. The time-averaged flow around automobiles has several salient features, such as three-dimensional separated flow regions and recirculation regions. These wake structures create regions of low and high pressure, which contribute to the drag force. However, the wide range of vehicle parameters and the nonlinear nature of fluid flow make it challenging to formulate aerodynamic prediction models. We aim to capture the relationship between vehicle geometry and drag coefficient using a small number of latent variables.

For example, the box car has larger separated flow regions and a larger low-pressure wake compared to other geometries. But some box cars in the dataset can have a lower drag coefficient than some SUV and hatchback designs due to differences in the front geometry. Other flow interactions, such as ground effects, require careful aerodynamic analysis.

Latent manifold discovery

When directly learning the relationship between vehicle geometries and drag coefficient, we can obtain multiple models with similar accuracy, which makes shape optimization difficult. Therefore, we seek low-dimensional coordinates that capture the relationship between input geometries and drag coefficient while reconstructing the geometry. We use a nonlinear autoencoder to learn a curvilinear coordinate system that parameterizes the manifold representation of our dataset. The autoencoder consists of an encoder and a decoder. The encoder reduces the dimension of the input data into a lower-dimensional latent space, and the decoder reconstructs the input from the encoded representation. We also use an observable-augmented nonlinear autoencoder that is trained to estimate the drag coefficient from the compressed representation of the vehicle geometries. This allows us to observe geometric similarities and identify relevant features for design optimization.

The discovered three-dimensional latent space manifold represents the relationship between vehicle geometries and their estimated drag coefficients. Each point in the low-dimensional space corresponds to a vehicle geometry, and vehicles cluster based on geometric similarity and estimated drag coefficient. The average percent absolute error of estimated drag values is within 2% of the reference value.

Data-driven shape optimization

With the identified latent space manifold, we can modify existing vehicle geometries to improve aerodynamic performance. Optimization is performed directly in the low-dimensional latent space to accelerate computations. By computing the gradient of drag at a given latent space point, we obtain a direction in the latent space corresponding to a decrease in drag coefficient. We can then modify the latent space coordinate and observe changes in the decoded geometry to identify regions to modify. However, we must ensure that the optimized geometries are physically realizable. We consider a soft distance constraint based on the latent space distance between the optimized design and the training data to avoid moving too far from the training data.

We demonstrate data-driven vehicle shape optimization on the discovered manifold. For example, starting from a high-drag SUV case, we optimize the geometry to reduce the drag coefficient by 11%. The optimized geometry has a boattail-like effect, reduces the pressure gradient at the spoiler, and tapers the trailing wake vortices. The edges of the front geometry are smoothed, reducing the size of the high-pressure zone and allowing the flow to transition smoothly. The validation cases show that the model has learned the trend between geometric features and aerodynamic performance.

Discussion

In this study, we perform a data-driven analysis of the aerodynamic performance of production vehicle geometries using experimentally validated large-eddy simulations. We use a data-driven vehicle shape optimization approach with an observable-augmented nonlinear autoencoder to identify a low-dimensional latent space manifold. The approach effectively compresses voxelized geometries and reconstructs the geometry while estimating the drag coefficient. This allows us to observe the relationship between different vehicle geometries and their aerodynamic performance and perform optimization. We decode various geometries along the optimization trajectory and validate the trend of estimated drag with large-eddy simulations.

For the current autoencoder architecture, we use a combination of PCA and a nonlinear multi-layer perceptron to improve the tractability and convergence of the model. We choose to use voxel data instead of mesh geometry because it offers a compromise between computational feasibility and geometric fidelity. While the PCA autoencoder approach makes the current approach computationally tractable, it would be interesting to explore alternative methods to exploit local features.

The current study explores the potential of machine learning in expediting industrial aerodynamic design. The use of data-driven methods shows promise in accelerating industrial design optimization and streamlining the production of more efficient vehicles.