
Autoencoder-Based Dimensionality Reduction of Turbulent Channel Flow Under Spanwise Wall Oscillations
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Turbulent flows play an important role in determining the performance of many industrial systems and environmental processes. While Direct Numerical Simulation (DNS) offers highly accurate results by resolving all scales of turbulence, its computational cost becomes prohibitively high, especially at large Reynolds numbers. To reduce this expense, Reduced Order Models (ROMs) are introduced to simplify the flow dynamics while retaining essential features, significantly lowering the computational resources required. To reduce the dimensionality a more compact coordinate system describing the flow has to be identified. Proper Orthogonal Decomposition (POD), a linear technique, has been widely used for this purpose. However, non-linear methods like Autoencoder Neural Networks (AEs) have recently gained popularity for their ability to capture more complex flow features in a more compact space, leveraging the non-linear relations between phenomena [1]. After reducing dimensionality, the flow dynamics are predicted within the low-dimensional (latent) space, offering an efficient alternative to full-scale simulations [2]. To explore the efficiency of POD and AE and its variants, they are applied to an actuated heated turbulent channel flow at Reτ = 200. The flow is controlled using spanwise wall oscillations (SWO) [3], where the spanwise velocity at the walls oscillates as W sin (2ᴨt/T). The period is here fixed to T+ = 500. The dataset is composed of 20 Large Eddy Simulations (LES), with different oscillation amplitudes, uniformly distributed in W+ ∈ [0,30], where 16 simulations are used for training and the remaining 4 for validation. The train-test split verifies the model's ability to interpolate on unseen oscillation amplitudes, ensuring robustness to changes in this control parameter. Convolutional Autoencoders (CAE) are compared to the benchmark POD to assess flow complexity and quantify the improvement in reconstruction achieved by the CAE. To further refine the results, β-Variational Autoencoders (β-VAE) [5,6] are employed to improve the orthogonality of the latent space, aiming to approach the uncorrelated modes of extended POD [7]. Finally, following the approach of [8], a friction-augmented CAE is proposed, where friction coefficient (Cf) and Nusselt number (Nu) are reconstructed from the latent space using a Multi Layer Perception (MLP), in order to enhance the physical insights captured by the model (see Fig. 1).