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Two models based on convolutional neural networks are trained to predict the two-dimensional instantaneous velocity-fluctuation fields at different wall-normal locations in a turbulent open-channel flow, using the wall-shear-stress components and the wall pressure as inputs. The first model is a fully convolutional neural network (FCN) which directly predicts the fluctuations, while the second one reconstructs the flow fields using a linear combination of orthonormal basis functions, obtained through proper orthogonal decomposition (POD), and is hence named FCN-POD. Both models are trained using data from direct numerical simulations at friction Reynolds numbers $Re_{\tau } = 180$ and 550. Being able to predict the nonlinear interactions in the flow, both models show better predictions than the extended proper orthogonal decomposition (EPOD), which establishes a linear relation between the input and output fields. The performance of the models is compared based on predictions of the instantaneous fluctuation fields, turbulence statistics and power-spectral densities. FCN exhibits the best predictions closer to the wall, whereas FCN-POD provides better predictions at larger wall-normal distances. We also assessed the feasibility of transfer learning for the FCN model, using the model parameters learned from the $Re_{\tau }=180$ dataset to initialize those of the model that is trained on the $Re_{\tau }=550$ dataset. After training the initialized model at the new $Re_{\tau }$ , our results indicate the possibility of matching the reference-model performance up to $y^{+}=50$ , with $50\,\%$ and $25\,\%$ of the original training data. We expect that these non-intrusive sensing models will play an important role in applications related to closed-loop control of wall-bounded turbulence.

Abstract. A method to extract turbulent statistics from three-dimensional (3D) PIV measurements via ensemble averaging is presented. The proposed technique is a 3D extension of the ensemble particle tracking velocimetry methods, which consist in summing distributions of velocity vectors calculated on low image density samples and then extract the statistical moments from the velocity vectors within sub-volumes, with the size of the sub-volume depending on the desired number of particles and on the available number of snapshots.The extension to 3D measurements poses the additional difficulty of sparse velocity vectors distributions, thus requiring a large number of snapshots to achieve high resolution measurements with a sufficient degree of accuracy. At the current state, this hinders the achievement of single-voxel measurements, unless millions of samples are available. Consequently, one has to give up spatial resolution and live with still relatively large (if compared to the voxel) sub-volumes. This leads to the further problem of the possible occurrence of a residual mean velocity gradient within the subvolumes, which significantly contaminates the computation of second order moments.In this work, we propose a method to reduce the residual gradient effect, allowing to reach high resolution even with relatively large interrogation spots, therefore still retrieving a large number of particles on which it is possible to calculate turbulent statistics. The method consists in applying a polynomial fit to the velocity distributions within each sub-volume trying to mimic the residual mean velocity gradient.

State-of-art preprocessing methods for Particle Image Velocimetry (PIV) are severely challenged by time-dependent light reflections and strongly non-uniform background. In this work, a novel image preprocessing method is proposed. The method is based on the Proper Orthogonal Decomposition (POD) of the image recording sequence and exploits the different spatial and temporal coherence of background and particles. After describing the theoretical framework, the method is tested on synthetic and experimental images, and compared with well-known pre-processing techniques in terms of image quality enhancement, improvements in the PIV interrogation and computational cost. The results show that, unlike existing techniques, the proposed method is robust in the presence of significant background noise intensity, gradients, and temporal oscillations. Moreover, the computational cost is one to two orders of magnitude lower than conventional image normalization methods. A downloadable version of the preprocessing toolbox has been made available at http://seis.bris.ac.uk/~aexrt/PIVPODPreprocessing/.

This work evaluates the applicability of super-resolution generative adversarial networks (SRGANs) as a methodology for the reconstruction of turbulent-flow quantities from coarse wall measurements. The method is applied both for the resolution enhancement of wall fields and the estimation of wall-parallel velocity fields from coarse wall measurements of shear stress and pressure. The analysis has been carried out with a database of a turbulent open-channel flow with a friction Reynolds number [Formula: see text] generated through direct numerical simulation. Coarse wall measurements have been generated with three different downsampling factors [Formula: see text] from the high-resolution fields, and wall-parallel velocity fields have been reconstructed at four inner-scaled wall-normal distances [Formula: see text]. We first show that SRGAN can be used to enhance the resolution of coarse wall measurements. If compared with the direct reconstruction from the sole coarse wall measurements, SRGAN provides better instantaneous reconstructions, in terms of both mean-squared error and spectral-fractional error. Even though lower resolutions in the input wall data make it more challenging to achieve highly accurate predictions, the proposed SRGAN-based network yields very good reconstruction results. Furthermore, it is shown that even for the most challenging cases, the SRGAN is capable of capturing the large-scale structures that populate the flow. The proposed novel methodology has a great potential for closed-loop control applications relying on non-intrusive sensing.

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In the last two decades, several techniques have been introduced that are capable to extract three-dimensional three-components velocity fields in fluid flows. Fast-paced developments in both hardware and processing algorithms have generated a diverse collection of methods, with a growing range of application in flow diagnostics. The context has been further enriched by an increasingly marked trend of hybridization, in which the boundaries between different techniques are fading. In this review, we carry out a survey of the prominent methods, including optical techniques and approaches based on medical imaging. Each one is outlined through a sample application from the recent literature, focusing on respective strengths and challenges. A framework for the evaluation of the velocimetry performance in terms of dynamic spatial range is discussed, along with technological trends and emerging strategies to exploit 3D data. While critical challenges still exist, these observations highlight how volumetric techniques are transforming experimental fluid mechanics, and that the possibilities they offer have just begun to be explored.

The extension of the well-assessed high-accuracy algorithms for two-dimensional-two components particle image velocimetry (PIV) to the case of three-dimensional (3D) data involves a considerable increase of the computational cost. Tomographic PIV is strongly affected by this issue, relying on 3D cross-correlation to estimate the velocity field. In this study, a number of solutions are presented, enabling a more efficient calculation of the velocity field without any significant loss of accuracy. A quick estimation of the predictor displacement field is proposed, based on voxels binning in the first steps of the process. The corrector displacement field is efficiently computed by restricting the search area of the correlation peak. In the initial part of the process, the calculation of a reduced cross-correlation map by using Fast Fourier Transform on blocks is suggested, in order to accelerate the processing by avoiding redundant calculations in case of overlapping interrogations windows. Eventually, direct cross-correlations with a search radius of only 1 pixel in the neighborhood of the estimated peak are employed; the final iterations are consistently faster, since direct correlations can better enjoy the sparsity of the distributions, reducing the number of operations to be performed. Furthermore, three different approaches to reduce the number of redundant calculations for overlapping windows are presented, based on pre-calculations of the contributions to the cross-correlations coefficients along segments, planes or blocks. The algorithms are tested both on synthetic and real images, showing that a potential speed-up of up to 800 times can be obtained, depending on the complexity of the flow field to be analyzed. The challenging application on a real swirling jet results in a speed-up of an order of magnitude