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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 elasto-viscoplasticity 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 phenomena of bursting bubbles. We investigate how bursting dynamics depends on capillary, elastic, and yield stresses by exploring the parameter space of the Deborah number $De$ (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 elasto-viscoplastic medium is shown to affect primarily the jet evolution only at faster relaxation times (low $De$). The role of elastic stresses on jet development is elucidated with the support of energy budgets identifying different modes of energy transfer within the elasto-viscoplastic 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., Comment: 35 pages, 20 figures

Designing active-flow-control (AFC) strategies for three-dimensional (3D) bluff bodies is a challenging task with critical industrial implications. In this study we explore the potential of discovering novel control strategies for drag reduction using deep reinforcement learning. We introduce a high-dimensional AFC setup on a 3D cylinder, considering Reynolds numbers ($Re_D$) from $100$ to $400$, which is a range including the transition to 3D wake instabilities. The setup involves multiple zero-net-mass-flux jets positioned on the top and bottom surfaces, aligned into two slots. The method relies on coupling the computational-fluid-dynamics solver with a multi-agent reinforcement-learning (MARL) framework based on the proximal-policy-optimization algorithm. MARL offers several advantages: it exploits local invariance, adaptable control across geometries, facilitates transfer learning and cross-application of agents, and results in a significant training speedup. For instance, our results demonstrate $21\%$ drag reduction for $Re_D=300$, outperforming classical periodic control, which yields up to $6\%$ reduction. To the authors' knowledge, the present MARL-based framework represents the first time where training is conducted in 3D cylinders. This breakthrough paves the way for conducting AFC on progressively more complex turbulent-flow configurations., Comment: Under review in Nature Engineering Communications

This study presents novel active-flow-control (AFC) strategies aimed at achieving drag reduction for a three-dimensional cylinder immersed in a flow at a Reynolds number based on freestream velocity and cylinder diameter of (Re_D=3900). The cylinder in this subcritical flow regime has been extensively studied in the literature and is considered a classic case of turbulent flow arising from a bluff body. The strategies presented are explored through the use of deep reinforcement learning. The cylinder is equipped with 10 independent zero-net-mass-flux jet pairs, distributed on the top and bottom surfaces, which define the AFC setup. The method is based on the coupling between a computational-fluid-dynamics solver and a multi-agent reinforcement-learning (MARL) framework using the proximal-policy-optimization algorithm. Thanks to the acceleration in training facilitated by exploiting the local invariants with MARL, a drag reduction of (8\%) was achieved, with a mass cost efficiency two orders of magnitude lower than those of the existing classical controls in the literature. This development represents a significant advancement in active flow control, particularly in turbulent regimes critical to industrial applications., Comment: Under review in "Special Issue": Progress in Engineering Turbulence Modelling, Simulation and Measurements

In this work we compare different drag-reduction strategies that compute their actuation based on the fluctuations at a given wall-normal location in turbulent open channel flow. In order to perform this study, we implement and describe in detail the reinforcement-learning interface to a computationally-efficient, parallelized, high-fidelity solver for fluid-flow simulations. We consider opposition control (Choi, Moin, and Kim, Journal of Fluid Mechanics 262, 1994) and the policies learnt using deep reinforcement learning (DRL) based on the state of the flow at two inner-scaled locations ($y^+ = 10$ and $y^+ = 15$). By using deep deterministic policy gradient (DDPG) algorithm, we are able to discover control strategies that outperform existing control methods. This represents a first step in the exploration of the capability of DRL algorithm to discover effective drag-reduction policies using information from different locations in the flow., Comment: 6 pages, 5 figures

This paper presents for the first time successful results of active flow control with multiple independently controlled zero-net-mass-flux synthetic jets. The jets are placed on a three-dimensional cylinder along its span with the aim of reducing the drag coefficient. The method is based on a deep-reinforcement-learning framework that couples a computational-fluid-dynamics solver with an agent using the proximal-policy-optimization algorithm. We implement a multi-agent reinforcement-learning framework which offers numerous advantages: it exploits local invariants, makes the control adaptable to different geometries, facilitates transfer learning and cross-application of agents and results in significant training speedup. In this contribution we report significant drag reduction after applying the DRL-based control in three different configurations of the problem., Comment: ETMM14 2023 conference proceeding paper

We introduce a reinforcement learning (RL) environment to design and benchmark control strategies aimed at reducing drag in turbulent fluid flows enclosed in a channel. The environment provides a framework for computationally-efficient, parallelized, high-fidelity fluid simulations, ready to interface with established RL agent programming interfaces. This allows for both testing existing deep reinforcement learning (DRL) algorithms against a challenging task, and advancing our knowledge of a complex, turbulent physical system that has been a major topic of research for over two centuries, and remains, even today, the subject of many unanswered questions. The control is applied in the form of blowing and suction at the wall, while the observable state is configurable, allowing to choose different variables such as velocity and pressure, in different locations of the domain. Given the complex nonlinear nature of turbulent flows, the control strategies proposed so far in the literature are physically grounded, but too simple. DRL, by contrast, enables leveraging the high-dimensional data that can be sampled from flow simulations to design advanced control strategies. In an effort to establish a benchmark for testing data-driven control strategies, we compare opposition control, a state-of-the-art turbulence-control strategy from the literature, and a commonly-used DRL algorithm, deep deterministic policy gradient. Our results show that DRL leads to 43% and 46% drag reduction in a minimal and a larger channel (at a friction Reynolds number of 180), respectively, outperforming the classical opposition control by around 20 percentage points., Comment: 19 pages, 4 figures

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)], 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 $Pr = \nu/\alpha = (1,2,4,6)$ are considered (where $\nu$ is the kinematic viscosity and $\alpha$ 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., Comment: 13 pages, 9 figures

In this chapter we extend earlier work (Vinuesa et al., Nature Communications 11, 2020) on the potential of artificial intelligence (AI) to achieve the 17 Sustainable Development Goals (SDGs) proposed by the United Nations (UN) for the 2030 Agenda. The present contribution focuses on three SDGs related to healthy and sustainable societies, i.e. SDG 3 (on good health), SDG 11 (on sustainable cities) and SDG 13 (on climate action). This chapter extends the previous study within those three goals, and goes beyond the 2030 targets. These SDGs are selected because they are closely related to the coronavirus disease 19 (COVID-19) pandemic, and also to crises like climate change, which constitute important challenges to our society.

Conditional averages are used to evaluate the effect of sweeps and ejections on amplitude modulation. This is done numerically with a direct numerical simulation (DNS) of a channel flow at friction Reynolds number $Re_{\tau} = 1000$ in a minimal stream-wise unit (MSU). The amplitude-modulation map of such DNS is also compared to the one of a regular channel flow in a longer streamwise domain (LSD), in order to assess its validity for this study. The cheaper MSU is found to provide a good representation of the modulation phenomena in the LSD. As for conditional averages, the amplitude-modulation coefficient is conditioned on the sign of the large-scale fluctuations. Care must be exerted in defining such a coefficient, as the conditioned large-scale fluctuation has non-zero average, indeed as a consequence of conditioning. Both sweeps and ejections (positive and negative large-scale fluctuation events) are found to have a positive contribution to amplitude modulation in the buffer layer, and a negative one in the outer layer. The negative-modulation region is found to shrink in case of ejections, so that the positive-modulation region extends farther away from the wall. Two more conditional statistics are used to provide an alternative representation of amplitude modulation and insights into the characteristics of the large-scale structures.

Adaptive mesh refinement (AMR) in the high-order spectral-element method code Nek5000 is demonstrated and validated with well-resolved large-eddy simulations (LES) of the flow past a wing profile. In the present work, the flow around a NACA 4412 profile at a chord-based Reynolds number $Re_c=200,000$ is studied at two different angles of attack: 5 and 11 degrees. The mesh is evolved from a very coarse initial mesh by means of volume-weighted spectral error indicators, until a sufficient level of resolution is achieved at the boundary and wake regions. The non-conformal implementation of AMR allows the use of a large domain avoiding the need of a precursor RANS simulation to obtain the boundary conditions (BCs). This eliminates the effect of the steady Dirichlet BCs on the flow, which becomes a relevant source of error at higher angles of attack (specially near the trailing edge and wake regions). Furthermore, over-refinement in the far field and the associated high-aspect ratio elements are avoided, meaning less pressure-iterations of the solver and a reduced number of elements, which leads to a considerable computational cost reduction. Mean flow statistics are validated using experimental data obtained for the same profile in the Minimum Turbulence Level (MTL) wind tunnel at KTH, as well as with a previous DNS simulation, showing excellent agreement. This work constitutes an important step in the direction of studying stronger pressure gradients and higher Reynolds complex flows with the high fidelity that high-order simulations allow to achieve. Eventually, this database can be used for the development and improvement of turbulence models, in particular wall models., Comment: ETMM13 conference paper

Modelling the near-wall region of wall-bounded turbulent flows is a widespread practice to reduce the computational cost of large-eddy simulations (LESs) at high Reynolds number. As a first step towards a data-driven wall-model, a neural-network-based approach to predict the near-wall behaviour in a turbulent open channel flow is investigated. The fully-convolutional network (FCN) proposed by Guastoni et al. [preprint, arXiv:2006.12483] is trained to predict the two-dimensional velocity-fluctuation fields at $y^{+}_{\rm target}$, using the sampled fluctuations in wall-parallel planes located farther from the wall, at $y^{+}_{\rm input}$. The data for training and testing is obtained from a direct numerical simulation (DNS) at friction Reynolds numbers $Re_{\tau} = 180$ and $550$. The turbulent velocity-fluctuation fields are sampled at various wall-normal locations, i.e. $y^{+} = \{15, 30, 50, 80, 100, 120, 150\}$. At $Re_{\tau}=550$, the FCN 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 less than 20% error in prediction of streamwise-fluctuations intensity. These results are an encouraging starting point to develop a neural-network based approach for modelling turbulence at the wall in numerical simulations., Comment: Proc. 13th ERCOFTAC Symp. on Engineering Turbulence Modeling and Measurements (ETMM13), Rhodes, Greece, September 15-17, 2021

Bayesian optimization (BO) based on Gaussian process regression (GPR) is applied to different CFD (computational fluid dynamics) problems which can be of practical relevance. The problems are i) shape optimization in a lid-driven cavity to minimize or maximize the energy dissipation, ii) shape optimization of the wall of a channel flow in order to obtain a desired pressure-gradient distribution along the edge of the turbulent boundary layer formed on the other wall, and finally, iii) optimization of the controlling parameters of a spoiler-ice model to attain the aerodynamic characteristics of the airfoil with an actual surface ice. The diversity of the optimization problems, independence of the optimization approach from any adjoint information, the ease of employing different CFD solvers in the optimization loop, and more importantly, the relatively small number of the required flow simulations reveal the flexibility, efficiency, and versatility of the BO-GPR approach in CFD applications. It is shown that to ensure finding the global optimum of the design parameters of the size up to 8, less than 90 executions of the CFD solvers are needed. Furthermore, it is observed that the number of flow simulations does not significantly increase with the number of design parameters. The associated computational cost of these simulations can be affordable for many optimization cases with practical relevance.

Two models based on convolutional neural networks are trained to predict the two-dimensional 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), hence named FCN-POD. Both models are trained using data from two direct numerical simulations (DNS) at friction Reynolds numbers $Re_{\tau} = 180$ and $550$. Thanks to their ability to predict the nonlinear interactions in the flow, both models show a better prediction performance than the extended proper orthogonal decomposition (EPOD), which establishes a linear relation between input and output fields. The performance of the various models is compared based on predictions of the instantaneous fluctuation fields, turbulence statistics and power-spectral densities. The FCN exhibits the best predictions closer to the wall, whereas the FCN-POD model provides better predictions at larger wall-normal distances. We also assessed the feasibility of performing transfer learning for the FCN model, using the weights from $Re_{\tau}=180$ to initialize those of the $Re_{\tau}=550$ case. Our results indicate that it is possible to obtain a performance similar to that of the reference model up to $y^{+}=50$, with $50\%$ and $25\%$ of the original training data. These non-intrusive sensing models will play an important role in applications related to closed-loop control of wall-bounded turbulence., Comment: 31 pages, 17 figures

A fully-convolutional neural-network model is used to predict the streamwise velocity fields at several wall-normal locations by taking as input the streamwise and spanwise wall-shear-stress planes in a turbulent open channel flow. The training data are generated by performing a direct numerical simulation (DNS) at a friction Reynolds number of $Re_{\tau}=180$. Various networks are trained for predictions at three inner-scaled locations ($y^+ = 15,~30,~50$) and for different time steps between input samples $\Delta t^{+}_{s}$. The inherent non-linearity of the neural-network model enables a better prediction capability than linear methods, with a lower error in both the instantaneous flow fields and turbulent statistics. Using a dataset with higher $\Delta t^+_{s}$ improves the generalization at all the considered wall-normal locations, as long as the network capacity is sufficient to generalize over the dataset. The use of a multiple-output network, with parallel dedicated branches for two wall-normal locations, does not provide any improvement over two separated single-output networks, other than a moderate saving in training time. Training time can be effectively reduced, by a factor of 4, via a transfer learning method that initializes the network parameters using the optimized parameters of a previously-trained network.

In the present work we assess the capabilities of neural networks to predict temporally evolving turbulent flows. In particular, we use the nine-equation shear flow model by Moehlis et al. [New J. Phys. 6, 56 (2004)] to generate training data for two types of neural networks: the multilayer perceptron (MLP) and the long short-term memory (LSTM) network. We tested a number of neural network architectures by varying the number of layers, number of units per layer, dimension of the input, weight initialization and activation functions in order to obtain the best configurations for flow prediction. Due to its ability to exploit the sequential nature of the data, the LSTM network outperformed the MLP. The LSTM led to excellent predictions of turbulence statistics (with relative errors of 0.45% and 2.49% in mean and fluctuating quantities, respectively) and of the dynamical behavior of the system (characterized by Poincar\'e maps and Lyapunov exponents). This is an exploratory study where we consider a low-order representation of near-wall turbulence. Based on the present results, the proposed machine-learning framework may underpin future applications aimed at developing accurate and efficient data-driven subgrid-scale models for large-eddy simulations of more complex wall-bounded turbulent flows, including channels and developing boundary layers.

Reynolds-number effects in the adverse-pressure-gradient (APG) turbulent boundary layer (TBL) developing on the suction side of a NACA4412 wing section are assessed in the present work. To this end, we analyze four cases at Reynolds numbers based on freestream velocity and chord length ranging from Rec = 100, 000 to 1,000,000, all of them with 5 degree angle of attack. The results of four well-resolved large-eddy simulations (LESs) are used to characterize the effect of Reynolds number on APG TBLs subjected to approximately the same pressure-gradient distribution (defined by the Clauser pressure-gradient parameter beta). Comparisons of the wing profiles with zero-pressure-gradient (ZPG) data at matched friction Reynolds numbers reveal that, for approximately the same beta distribution, the lower-Reynolds-number boundary layers are more sensitive to pressure-gradient effects. This is reflected in the values of the inner-scaled edge velocity Ue+ , the shape factor H, the components of the Reynolds-stress tensor in the outer region and the outer-region production of turbulent kinetic energy. This conclusion is supported by the larger wall-normal velocities and outer-scaled fluctuations observed in the lower-Rec cases.Thus, our results suggest that two complementing mechanisms contribute to the development of the outer region in TBLs and the formation of large-scale energetic structures: one mechanism associated with the increase in Reynolds number, and another one connected to the APG. Future extensions of the present work will be aimed at studying the differences in the outer-region energizing mechanisms due to APGs and increasing Reynolds number.

The scope of the present project is to quantify the effects of uniform blowing and body-force damping on turbulent boundary layers subjected to a non-uniform adverse-pressure-gradient distribution. To this end, well-resolved large-eddy simulations are employed to describe the flow around the NACA4412 airfoil at moderate Reynolds number 200, 000 based on freestream velocity and chord length. In the present paper we focus on uniform blowing and the conference presentation will include a comparison with body-force damping applied in the same region. The inner-scaled profiles of the mean velocity and of selected components of the Reynolds-stress tensor are examined and compared with the uncontrolled cases. It is known that uniform blowing and adverse-pressure gradients share some similarities in their effect on the boundary layers, and our results will show that these effects are not independent. The behaviour of the skin-friction coefficient is analyzed through the FIK decomposition, and the impact of this control strategy on the aerodynamic efficiency of the airfoil is discussed., Comment: Proc. 12th ERCOFTAC Symp. on Engineering Turbulence Modeling and Measurements (ETMM12), Montpellier, France, September 26-28, 2018

The characteristics of complex turbulent boundary layers under adverse pressure gradients are assessed through well-resolved large-eddy simulations (LES) with the spectral-element code Nek5000. Two wing sections are analysed: a NACA0012 at 0 degree angle of attack which presents a mild adverse-pressure gradient (APG) along the chord and a NACA4412 at 5 degree angle of attack with a strong adverse pressure gradient on the suction side, both profiles at Rec = 400,000. The turbulent statistics show that the mild-APG turbulent boundary layer (TBL) of the NACA0012 presents a slight deviation of the velocity fluctuations in the outer region while the strong-APG TBL of the NACA4412 shows significantly larger fluctuations throughout the wall-normal direction with respect to the zero-pressure-gradient (ZPG) TBL. These differences are more substantial in the outer region of the boundary layer. Spectral analyses show that the APG has a significant impact on the largest scales in the boundary layer. Our results indicate that the APG increases the turbulent kinetic energy (TKE) of the TBL, more prominently in the outer layer, and suggest a different mechanism than the one related to high Re in ZPGs., Comment: Proc. 12th ERCOFTAC Symp. on Engineering Turbulence Modeling and Measurements (ETMM12), Montpellier, France, September 26-28, 2018

The present study revisits the amplitude modulation phenomenon, specifically for the robustness in its quantification. To achieve this, a well-resolved large-eddy simulation (LES) data set at Re_theta= 8200 is used. First, the fluctuating streamwise velocity signal is decomposed into its small- and large-scale components using both Fourier filters and empirical mode decomposition (EMD), allowing the comparison among different separation filters. The effects of these filters on various definitions for quantifying the amplitude modulation have been discussed. False positive identification of the amplitude modulation has also been tested using a randomised signal. Finally, the impact of the inclination angle of the large-scale structures on the modulation quantification has been assessed., Comment: Proc. 12th ERCOFTAC Symp. on Engineering Turbulence Modeling and Measurements (ETMM12), Montpellier, France, September 26-28, 2018

Turbulent boundary layers under adverse pressure gradients are studied using well-resolved large-eddy simulations (LES) with the goal of assessing the influence of the streamwise pressure development. Near-equilibrium boundary layers were identified with the Clauser parameter $\beta$. The pressure gradient is imposed by prescribing the free-stream velocity. In order to fulfill the near-equilibrium conditions, the free-stream velocity has to follow a power-law distribution. The turbulence statistics pertaining to cases with a constant Clauser pressure-gradient parameter ? were compared with cases with a non-constant pressure distribution at matched ? and friction Reynolds number Re_tau . It was noticed that the non-constant cases appear to approach far downstream a certain state of the boundary layer, which is uniquely characterised by beta? and Re_tau. The investigations on the flat plate were extended to the flow around a wing section. Comparisons with the flat-plate cases at matched Re_tau and ? revealed some interesting features: In turbulent boundary layers with strong pressure gradients in the development history the energy-carrying structures in the outer region are strongly enhanced, which can be detected by the pronounced wake in the mean velocity as well as the large second peak in the Reynolds stresses. Furthermore, a scaling law suggested by Kitsios et al. (2015), proposing the edge velocity and displacement thickness as scaling parameters, was tested on a constant pressure gradient case. The mean velocity and Reynolds stress profiles were found to be dependent on the downstream development, indicating that their conclusion might be the result of a too short constant pressure gradient region., Comment: Proc. 11th ERCOFTAC Symp. on Engineering Turbulence Modeling and Measurements (ETMM11), Palermo (Italy), September 21-23, 2016

The results of a DNS of the flow around a wing section represented by a NACA4412 profile, with Rec = 400, 000 and 5 degree angle of attack, are presented in this study. The high-order spectral element code Nek5000 was used for the computations. The Clauser pressure-gradient parameter ? ranges from 0 and 85 on the suction side, and the maximum Re_theta and Re_tau values are around 2,800 and 373, respectively. Comparisons between the suction side with ZPG TBL data show a more prominent wake, a steeper logarithmic region and lower velocities in the buffer region. The APG also leads to a progressively increasing value of the inner peak in the tangential velocity fluctuations, as well as the development of an outer peak, which is also observed in the other components of the Reynolds stress tensor. Other effects of strong APGs are increased production and dissipation profiles across the boundary layer, together with enhanced viscous diffusion and velocity-pressure-gradient correlation values near the wall. All these effects are connected to the fact that the large-scale motions of the flow become energized due to the APG, as apparent from spanwise premultiplied power spectral density plots., Comment: Proc. 11th ERCOFTAC Symp. on Engineering Turbulence Modeling and Measurements (ETMM11), Palermo (Italy), September 21-23, 2016