In a paper published in the journal Scientific Reports, researchers evaluated a convolutional neural network's (CNN) ability to predict velocity and pressure aerodynamic fields in heavy vehicles. They conducted various Computational Fluid Dynamics (CFD) simulations using different vehicle geometries and a dataset derived from these simulations to train, validate, and assess the CNN.
Study: Efficient Aerodynamic Field Predictions in Heavy Vehicle Design: A CNN Approach. Image credit: Generated using DALL.E.3
The CNN achieved impressive accuracy by discretizing field representations based on expected velocity gradients, closely matching numerical results with minimal errors. Notably, this approach drastically reduced computational time by four orders of magnitude, showcasing promising prospects for efficient aerodynamic field predictions in vehicle design.
Background
Recent attention in heavy vehicle design emphasizes aerodynamics, driven by fuel costs, European decarbonization policies, and engine electrification. The aerodynamic drag's crucial role in reducing fuel consumption and emissions, especially for electric vehicles, is clear. While improvements quickly transfer among similar goods transportation models, customizing aerodynamics for diverse heavy vehicles like coaches is challenging. Challenges with CFD tools—high costs, limited access to resources, and complexity—have prompted the exploration of alternative methods, like CNNs in Deep Learning, for cost-effective and efficient aerodynamic optimization in heavy vehicle design.
Methodology Overview: Aerodynamic Flow Prediction
This study's methodology involved utilizing three primary 2D geometries for CFD and CNN investigations: the Sunsundegui Coach model 5 (SC5) and SC7 bus models from Sunsundegui and a scaled Ahmed Body. Scaling up by a factor of 12 replicated the conditions of the Langley Full-Scale Tunnel to accommodate the CNN. This adjustment aimed to resemble the geometries' dimensions and maintain a blockage ratio consistent with wind tunnel conditions, as observed in Fu et al. and Bayraktar et al. studies. Different variants of these geometries, especially the Ahmed body with varied slant angles and leading radii, were generated to provide a diverse training dataset for the CNN.
Researchers explored diffuser length and height variations across 200 configurations for the SC5 and SC7 bus models. The computational setup for the numerical simulations involved Star Computational Continuum Mechanics version 2020.3.117 (Star-CCM+v2020.3.117) software, focusing on steady-state solutions with specific boundary conditions, such as an inlet velocity of 95 km/h and a Reynolds number of around 4.3 million for result validation. The meshing strategy employed an exemplary mesh configuration based on a sensitivity study, ensuring accuracy while optimizing computational resources.
Turbulence modeling adopted the k-ω SST model due to its versatility and accuracy in resolving adverse pressure gradients. Researchers chose this model due to its capability to blend k–ω and k–ϵ models based on specific wall distance criteria. Acknowledging the potential variability in results, researchers noted the impact of configuration variations on different slant angles. Validation included comparing the simulated drag coefficient (Cd) with experimental and numerical data from previous studies.
Despite some discrepancies attributed to the inherent limitations of 2D simulations, such as neglecting specific vortex systems and ignoring unsteady effects, the general trends in Cd were consistent, validating the simulations' capability to predict flow characteristics.
The CNN utilized a U-Net architecture, proven effective in fluid dynamics problems, with inputs comprising flow region channel (FRC) and signed distance function (SDF) layers representing boundary conditions and geometry distances, respectively. The output layers were generated by interpolating and normalizing velocity and pressure fields obtained from CFD simulations. Researchers proposed an alternative CNN mesh to balance the computational cost and resolution limitations inherent in neural networks, resembling the resolution of CFD meshes.
The CNN architecture consisted of four encoder/decoder blocks with convolutional layers, ReLU activation functions, and pooling layers designed to predict velocity and pressure fields around heavy vehicles. Using MATLAB 2022b and its Deep Learning Toolbox, researchers trained the network, following the structure of previous successful CNNs used in fluid dynamics problems, like the U-Net architectures employed in similar studies by different researchers.
Comparing CFD and CNN Predictions
The researchers compared the predictive accuracy of CNN against CFD simulations across 22 test cases. The CNN demonstrates adeptness in forecasting velocity and pressure fields around SC5, SC7, and Ahmed body geometries through qualitative analysis. Though minor disparities like boundary layer depiction and slight wake size underestimation in SC5 arise, they are considered insignificant. More significant errors in the Ahmed body's predictions, attributed to geometric differences and limited training cases, do not impede the accurate depiction of major flow characteristics, especially within wake regions.
A deeper dive into velocity profiles along vehicle wakes reveals consistent depictions by both CFD and CNN. Despite nuanced differences—more pronounced with the Ahmed body—the CNN closely mirrors patterns, with acceptable maximum absolute errors, notably considering the geometric variability of the Ahmed body.
Quantitative assessment of data distribution highlights a close alignment between CFD and CNN, particularly in arithmetic mean and standard deviation across analyzed magnitudes. Although variations exist in predicting extreme values—where the CNN tends to underpredict, notably in velocity fields—the overarching trends remain consistent.
Assessing CNN meshes unveils their accuracy in predicting the entire test set, where the alternative mesh notably diminishes maximum and mean errors across cases, except for mean error in pressure fields. It resonates with earlier observations, showcasing the alternative mesh's superior resolution in boundary layers, enhancing accuracy, and minimizing mistakes.
Performance-wise, CNN's efficiency stands out in computational time, with CFD simulations requiring an average of 27,528.21 seconds compared to a mere 56.46 seconds for the CNN across the 22 geometries. This staggering efficiency positions the CNN as 10,711 times faster than CFD simulations. However, it's crucial to note the requisite 24-hour training time for the CNN, utilizing a single Intel Xeon Gold 5120 CPU core.
Conclusion
To sum up, this study conducted CFD simulations on bus geometries and trains a CNN to predict flow fields, aiming to evaluate the CNN's capacity against CFD outcomes while conserving computational resources. The CNN demonstrated proficiency in forecasting flow phenomena but encounters errors in boundary layer depiction, excelling in wake predictions despite geometric variations.
Analysis reveals alignment in data trends between CFD and CNN but highlights challenges in predicting extreme values. An alternative CNN mesh reduces errors, primarily in boundary layers, and significantly cuts computation time. However, limitations persist in domain resolution and boundary layer modeling within the current neural network model.
Deep Learning Secures IoT with Federated Learning