Fully-convolutional neural networks (FCN) were proven to be effective for predicting the instantaneous state of a fully-developed turbulent flow at different wall-normal locations using quantities measured at the wall. In Guastoni et al. (J Fluid Mech 928:A27, 2021. https://doi.org/10.1017/jfm.2021.812), we focused on wall-shear-stress distributions as input, which are difficult to measure in experiments. In order to overcome this limitation, we introduce a model that can take as input the heat-flux field at the wall from a passive scalar. Four different Prandtl numbers Pr=ν/α=(1,2,4,6) are considered (where ν is the kinematic viscosity and α is the thermal diffusivity of the scalar quantity). A turbulent boundary layer is simulated since accurate heat-flux measurements can be performed in experimental settings: first we train the network on aptly-modified DNS data and then we fine-tune it on the experimental data. Finally, we test our network on experimental data sampled in a water tunnel. These predictions represent the first application of transfer learning on experimental data of neural networks trained on simulations. This paves the way for the implementation of a non-intrusive sensing approach for the flow in practical applications.

A gas bubble sitting at a liquid-gas interface can burst following the rupture of the thin liquid film separating it from the ambient, owing to the large surface energy of the resultant cavity. This bursting bubble forms capillary waves, a Worthington jet and subsequent droplets for a Newtonian liquid medium. However, rheological properties of the liquid medium like elastoviscoplasticity can greatly affect these dynamics. Using direct numerical simulations, this study exemplifies how the complex interplay between elasticity (in terms of elastic stress relaxation) and yield stress influences the transient interfacial phenomenon of bursting bubbles. We investigate how bursting dynamics depends on capillary, elastic and yield stresses by exploring the parameter space of the Deborah number ${{\textit {De}}}$ (dimensionless relaxation time of elastic stresses) and the plastocapillary number $\mathcal {J}$ (dimensionless yield-stress of the medium), delineating four distinct characteristic behaviours. Overall, we observe a non-monotonic effect of elastic stress relaxation on the jet development while plasticity of the elastoviscoplastic (EVP) medium is shown to affect primarily the jet evolution only at faster relaxation times (low ${{\textit {De}}}$). The role of elastic stresses on jet development is elucidated with the support of energy budgets identifying different modes of energy transfer within the EVP medium. The effects of elasticity on the initial progression of capillary waves and droplet formation are also studied. In passing, we study the effects of solvent-polymer viscosity ratio on bursting dynamics and show that polymer viscosity can increase the jet thickness apart from reducing the maximum height of the jet.

The objective of the present study is to provide a numerical database of thermal boundary layers and to contribute to the understanding of the dynamics of passive scalars at different Prandtl numbers. In this regard, a direct numerical simulation (DNS) of an incompressible zero-pressure-gradient turbulent boundary layer is performed with the Reynolds number based on momentum thickness Re-theta ranging up to 1080. Four passive scalars, characterized by the Prandtl numbers Pr=1,2,4,6 are simulated using the pseudo-spectral code SIMSON (Chevalier et al., SIMSON : a pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. TRITA-MEK 2007:07. KTH Mechanics, Stockholm, Sweden, 2007). To the best of our knowledge, the present DNS provides the thermal boundary layer with the highest Prandtl number available in the literature. It corresponds to that of water at similar to 24(degrees)C, when the fluid temperature is considered as a passive scalar. Turbulence statistics for the flow and thermal fields are computed and compared with available numerical simulations at similar Reynolds numbers. The mean flow and scalar profiles, root-mean-squared velocity and scalar fluctuations, turbulent heat flux, turbulent Prandtl number and higher-order statistics agree well with the numerical data reported in the literature. Furthermore, the pre-multiplied two-dimensional spectra of the velocity and of the passive scalars are computed, providing a quantitative description of the energy distribution at the different length scales for various wall-normal locations. The energy distribution of the heat-flux fields at the wall is concentrated on longer temporal structures with increasing Prandtl number. This is due to the thinner thermal boundary layer as thermal diffusivity decreases and, thereby, the longer temporal structures exhibit a different footprint at the wall.

The objective of this study is to assess the capability of convolution-based neural networks to predict the wall quantities in a turbulent open channel flow, starting from measurements within the flow. Gradually approaching the wall, the first tests are performed by training a fully-convolutional network (FCN) to predict the two-dimensional velocity-fluctuation fields at the inner-scaled wall-normal location ytarget+, using the sampled velocity fluctuations in wall-parallel planes located farther from the wall, at yinput+. The predictions from the FCN are compared against the predictions from a proposed R-Net architecture as a part of the network investigation study. Since the R-Net model is found to perform better than the FCN model, the former architecture is optimized to predict the two-dimensional streamwise and spanwise wall-shear-stress components and the wall pressure from the sampled velocity-fluctuation fields farther from the wall. The data for training and testing is obtained from direct numerical simulation (DNS) of open channel flow at friction Reynolds numbers Reτ=180 and 550. The turbulent velocity-fluctuation fields are sampled at various inner-scaled wall-normal locations, i.e. y+={15,30,50,100,150}, along with the wall-shear stress and the wall pressure. At Reτ=550, both FCN and R-Net can take advantage of the self-similarity in the logarithmic region of the flow and predict the velocity-fluctuation fields at y+=50 using the velocity-fluctuation fields at y+=100 as input with about 10% error in prediction of streamwise-fluctuations intensity. Further, the network model trained in this work is also able to predict the wall-shear-stress and wall-pressure fields using the velocity-fluctuation fields at y+=50 with around 10% error in the intensity of the corresponding fluctuations at both Reτ=180 and 550. These results are an encouraging starting point to develop neural-network-based approaches for modelling turbulence near the wall in numerical simulations, especially large-eddy simulations (LESs).

Flow-control techniques are extensively studied in fluid mechanics, as a means to reduce energy losses related to friction, both in fully-developed and spatially-developing flows. These techniques typically rely on closed-loop control systems that require an accurate representation of the state of the flow to compute the actuation. Such representation is generally difficult to obtain without perturbing the flow. For this reason, in this work we propose a fully-convolutional neural-network (FCN) model trained on direct-numerical-simulation (DNS) data to predict the instantaneous state of the flow at different wall-normal locations using quantities measured at the wall. Our model can take as input the heat-flux field at the wall from a passive scalar with Prandtl number Pr = ν/α = 6 (where ν is the kinematic viscosity and α is the thermal diffusivity of the scalar quantity). The heat flux can be accurately measured also in experimental settings, paving the way for the implementation of a non-intrusive sensing of the flow in practical applications.

Turbulent flow of purely viscoelastic fluids has gained attention in the drag-reduction and flow control communities since a tiny amount of polymer has proven efficient in reducing friction drag in pipe flows. Drag reduction by polymers (elasticity) is related to their ability to modify coherent structures in wall-bounded turbulence. When it comes to practical flows of interest, numerical simulations of such flows become challenging due to the associated computational cost of capturing the multiple physical mechanisms that drive the flow. On the other hand, experimental investigations of drag reduction in viscoelastic flows are limited by the near-wall measurements and the capability of the experimental techniques to accurately quantify the flow, without disturbing it. A complete description of viscoelastic turbulence would require the characterization of both velocity and polymeric stresses. However, the polymer deformation cannot be accessed directly from the experiments. Hence, in the objective of the present study, the idea of non-intrusive sensing has been applied to viscoelastic channel flow to predict the velocity fluctuations and polymeric stress components near the wall using the quantities measured at the wall. To this aim, the convolutional neural network (CNN) models are trained to predict the two-dimensional velocity fluctuation and polymeric shear stress fluctuation and elongation fields at different wall-normal distances in a viscoelastic channel flow. The present work would highlight the capability of a data-driven approach to model turbulence in complex fluid flows and in addition also finds useful applications in experimental settings.

The objective of the present study is to provide a numerical database of thermal boundary layers and to contribute to the understanding of the dynamics of passive scalars at different Prandtl numbers. In this regard, a direct numerical simulation (DNS) of an incompressible zero-pressure-gradient turbulent boundary layer is performed with the Reynolds number based on momentum thickness Re_θ up to 1080. Four passive scalars, characterized by the Prandtl numbers Pr = 1,2,4,6 are simulated with constant Dirichlet boundary conditions, using the pseudo-spectral code SIMSON (Chevalier et al. 2007). To the best of our knowledge, the present direct numerical simulation provides the thermal boundary layer with the highest Prandtl number available in the literature. It corresponds to that of water at ≈24°C, when the fluid temperature is considered as a passive scalar. Turbulence statistics for the flow and thermal fields are computed and compared with available numerical simulations at similar Reynolds numbers. The mean flow and temperature profiles, root-mean squared (RMS) velocity and temperature fluctuations, turbulent heat flux, turbulent Prandtl number and higher-order statistics agree well with the numerical data reported in the literature. Furthermore, the pre-multiplied two-dimensional spectra of the velocity and of the passive scalars are computed, providing a quantitative description of the energy distribution at the different lengthscales for various wall-normal locations. The energy distribution of the heat flux fields at the wall is concentrated on longer temporal structures and exhibits different footprint at the wall, with increasing Prandtl number.

Fully-convolutional neural networks (FCN) were proven to be effective for predicting the instantaneous state of a fully-developed turbulent flow at different wall-normal locations using quantities measured at the wall. In Guastoni et al. (2021), we focused on wall-shear-stress distributions as input, which are difficult to measure in experiments. In order to overcome this limitation, we introduce a model that can take as input the heat-flux field at the wall from a passive scalar. Four different Prandtl numbers Pr = ν/α = (1,2,4,6) are considered (where ν is the kinematic viscosity and α is the thermal diffusivity of the scalar quantity). A turbulent boundary layer is simulated since accurate heat-flux measurements can be performed in experimental settings, paving the way for the implementation of a non-intrusive sensing approach for the flow in practical applications. This is particularly important for closed-loop flow control, which requires an accurate representation of the state of the flow to compute the actuation.

The objective of this study is to assess the capability of convolution-based neural networks to predict wall quantities in a turbulent open channel flow. The first tests are performed by training a fully-convolutional network (FCN) to predict the 2D velocity-fluctuation fields at the inner-scaled wall-normal location y⁺ target, using the sampled velocity fluctuations in wall-parallel planes located farther from the wall, at y⁺ input. The predictions from the FCN are compared against the predictions from a proposed R-Net architecture. Since the R-Net model is found to perform better than the FCN model, the former architecture is optimized to predict the 2D streamwise and spanwise wall-shear-stress components and the wall pressure from the sampled velocity-fluctuation fields farther from the wall. The dataset is obtained from DNS of open channel flow at Re_τ=180 and 550. The turbulent velocity-fluctuation fields are sampled at various inner-scaled wall-normal locations, along with the wall-shear stress and the wall pressure. At Re_τ=550, both FCN and R-Net can take advantage of the self-similarity in the logarithmic region of the flow and predict the velocity-fluctuation fields at y⁺=50 using the velocity-fluctuation fields at y⁺=100 as input with about 10% error in prediction of streamwise-fluctuations intensity. Further, the R-Net is also able to predict the wall-shear-stress and wall-pressure fields using the velocity-fluctuation fields at y⁺=50 with around 10% error in the intensity of the corresponding fluctuations at both Re_τ=180 and 550. These results are an encouraging starting point to develop neural-network-based approaches for modelling turbulence near the wall in large-eddy simulations.