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.

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 $R{e}_{\tau }=180$ generated through direct numerical simulation. Coarse wall measurements have been generated with three different downsampling factors $f_d=[4,\hspace{0.17em}8,\hspace{0.17em}16]$ from the high-resolution fields, and wall-parallel velocity fields have been reconstructed at four inner-scaled wall-normal distances $y^{+}=[15,\hspace{0.17em}30,\hspace{0.17em}50,\hspace{0.17em}100]$ . 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.

This study assesses the capability of extended proper orthogonal decomposition (EPOD) and convolutional neural networks (CNNs) to reconstruct large-scale and very-large-scale motions (LSMs and VLSMs respectively) employing wall-shear-stress measurements in wall-bounded turbulent flows. Both techniques are used to reconstruct the instantaneous LSM evolution in the flow field as a combination of proper orthogonal decomposition (POD) modes, employing a limited set of instantaneous wall-shear-stress measurements. Due to the dominance of nonlinear effects, only CNNs provide satisfying results. Being able to account for nonlinearities in the flow, CNNs are shown to perform significantly better than EPOD in terms of both instantaneous flow-field estimation and turbulent-statistics reconstruction. CNNs are able to provide a more effective reconstruction performance employing more POD modes at larger distances from the wall and employing lower wall-measurement resolutions. Furthermore, the capability of tackling nonlinear features of CNNs results in estimation capabilities that are weakly dependent on the distance from the wall.

Different types of neural networks have been used to solve the flow sensing problem in turbulent flows, namely to estimate velocity in wall-parallel planes from wall measurements. Generative adversarial networks (GANs) are among the most promising methodologies, due to their more accurate estimations and better perceptual quality. This work tackles this flow sensing problem in the vicinity of the wall, addressing for the first time the reconstruction of the entire three-dimensional (3-D) field with a single network, i.e. a 3-D GAN. With this methodology, a single training and prediction process overcomes the limitation presented by the former approaches based on the independent estimation of wall-parallel planes. The network is capable of estimating the 3-D flow field with a level of error at each wall-normal distance comparable to that reported from wall-parallel plane estimations and at a lower training cost in terms of computational resources. The direct full 3-D reconstruction also unveils a direct interpretation in terms of coherent structures. It is shown that the accuracy of the network depends directly on the wall footprint of each individual turbulent structure. It is observed that wall-attached structures are predicted more accurately than wall-detached ones, especially at larger distances from the wall. Among wall-attached structures, smaller sweeps are reconstructed better than small ejections, while large ejections are reconstructed better than large sweeps as a consequence of their more intense footprint.

This work presents an experimental setup for acquiring synchronized wall and flow field measurements in a turbulent boundary layer (TBL). Instantaneous measurements of the convective heat transfer distribution at the wall and of the flow field are carried out simultaneously, using synchronized wall-parallel planar particle image velocimetry and infrared thermography. A low-thermal-inertia heated-thin-foil sensor is embedded in the wall beneath the TBL to measure the wall temperature maps with enough temporal resolution. The unsteady energy balance of the heated foil can be solved to restore the instantaneous value of the convective heat transfer coefficient on the wall. A detailed description of the sensor design is included. Furthermore, owing to the relatively low signal-to-noise ratio of instantaneous temperature fluctuation measurements, a recipe for data processing is proposed. A study to characterize the uncertainty of the experimental setup design is also performed. The overall agreement in the correlation between wall heat transfer and velocity fields with the literature supports the validity of the proposed approach. This solution is potentially interesting for flow control purposes, where sensing is performed at the wall.