FR3D: Three-dimensional Flow Reconstruction and Force Estimation for Unsteady Flows Around Extruded Bluff Bodies via Conformal Mapping Aided Convolutional Autoencoders

Since typical experiments in fluids involve only point measurements of the flow via simple and inexpensive methods such as pitot tubes, FR techniques can provide researchers additional insight into flows when more advanced techniques such as particle image velocimetry (PIV) are not available. Various statistical tools have been applied to FR such as linear stochastic estimation (LSE) [1], gappy proper orthogonal decomposition (gappy POD) [2], extended proper orthogonal decomposition (EPOD) [3], and sparse representation [4]. Though these techniques are time-tested and have been applied in practical experiments, for instance to estimate and control the flow in a backward-facing step case via LSE [5], their linear nature limit their capability to deal with complex flows. Neural networks, owing to their universal approximation capabilities [6], are capable of learning arbitrary non-linear and high-dimensional relationships in datasets. This capability makes them very attractive for FR tasks. As a result, the recent explosion of interest in neural networks (NNs) - enabled by substantial increases in computing power, theoretical advances, and the availability of open-source deep learning software - has coincided with a shift towards NN-based FR, and substantial strides were made recently with the application of NNs to the field. Notably, Erichson et al. [7] produced a seminal study exploring the usage of neural networks to reconstruct flows past cylinders. A number of works followed Erichson et al., a selection of which are presented: Fukami et al. [8] demonstrated that NN-based methods can outperform linear FR methods for the reconstruction of flows past cylinders and flapped airfoils [9], and also coupled NN-based FR with Voronoi tessellations to achieve flexibility in terms of the sensor setup [8]. Sun and Wang [10] investigated the application of physics-informed Bayesian NNs in FR, demonstrating high robustness to noise when reconstructing flows in simulated vascular structures.