Porous media are a promising technology to reduce turbulent boundary layer trailing edge noise. However, the fact that the porous material is grazed by turbulent flow on both sides makes its characterization not trivial. This paper describes the modifications resulting from the interaction between the grazing flows through the porous medium, defined as communication. To this end, lattice-Boltzmann simulations of two communicating turbulent channel flows separated by a fully resolved porous medium are carried out. The porous medium is realized as a 75% porous triply periodic minimal surface of type Schwarz’ P. Results are compared against the case with porous medium backed by a solid wall and the smooth wall channel flow. When communication between the two channel flows is allowed, spanwise coherent structures appear that are assimilated to a shear instability at a non-dimensional frequency of. Instantaneous flow through the porous medium is observed and is driven by a time-dependent pressure differential between the channels (with a zero mean and 7.8 Pa standard deviation). This leads to a decrease in energy in turbulent scales smaller than 2.5δ and for bulk scaled frequencies greater than. These flow modifications are not observed in the non-communicating case, with the wall preventing flow through, where the topology of the fluctuating statistics is similar to the smooth wall case. Finally, the drag is found to increase by over 200% with respect to the non-communicating case and 650% with respect to a smooth turbulent channel flow. The drag increase is found to be driven by the velocity fluctuations impinging on the porous topology. The communication does not follow the asymptotic drag relation for the same equivalent roughness, thus entering a different drag regime.

Chaotic systems with extreme events present significant challenges in terms of prediction and control due to their complex nonlinear dynamics and potential high dimensionality. We investigate here the use of cluster-based reduced-order modelling (ROM) and control techniques applied to such systems. In this approach, we first model the dynamics of the system by identifying clusters of similar states and only model the transition between clusters. Then, based on those identified clusters, we define a per-cluster control parameter. This effectively neglects the specific dynamics within a given cluster while retaining the main dynamics of the full-order model. The considered test case is the Moehlis-Faisst-Eckhart (MFE) system which exhibits extreme events in the form of quasi-relaminarization events. The influence of the number of clusters and the order of modelling on the accuracy of the resulting reduced-order cluster-based model is explored. A cluster-based control strategy is also proposed and applied to the MFE system to prevent extreme events. This strategy manages to achieve the objectives with a large reduction in extreme events in the controlled MFE system, decreasing the amount of time spent in extreme state by 90% and the mean kinetic energy by 20%. This work highlights the potential of cluster-based reduced-order modelling and control.

This study presents a compact data-driven Reynolds-averaged Navier-Stokes (RANS) model for wind turbine wake prediction, built as an enhancement of the standard - formulation. Several candidate models were discovered using the symbolic regression framework Sparse Regression of Turbulent Stress Anisotropy (SpaRTA), trained on a single Large Eddy Simulation (LES) dataset of a standalone wind turbine. The leading model was selected by prioritizing simplicity while maintaining reasonable accuracy, resulting in a novel linear eddy viscosity model. This selected leading model reduces eddy viscosity in high-shear regions—particularly in the wake—to limit turbulence mixing and delay wake recovery. This addresses a common shortcoming of the standard - model, which tends to overpredict mixing, leading to unrealistically fast wake recovery. Moreover, the formulation of the leading model closely resembles that of the established -- model. Consistent with this resemblance, the leading and -- models show nearly identical performance in predicting velocity fields and power output, but they differ in their predictions of turbulent kinetic energy. In addition, the generalization capability of the leading model was assessed using three unseen six-turbine configurations with varying spacing and alignment. Despite being trained solely on a standalone turbine case, the model produced results comparable to LES data. These findings demonstrate that data-driven methods can yield interpretable, physically consistent RANS models that are competitive with traditional modeling approaches while maintaining simplicity and achieving generalizability.

This paper investigates water injection effects in a simplified Ansaldo GT36 reheat system under realistic conditions of 20 atm using large eddy simulation (LES) coupled with thickened flame modeling and adaptive mesh refinement. The water injection conditions are optimized by performing a parametric study based on global sensitivity analysis (GSA) with a surrogate model based on Gaussian process (GP) to reduce computational cost. In particular, the influence of four design parameters, namely, Sauter mean diameter (SMD), water mass flow, and the angles of the spray's hollow cone, is tested to achieve an optimized solution. In the "dry"case, the LES simulations show several flashback events attributed to compressive pressure waves resulting from auto-ignition in the core flow near the crossover temperature. The use of water injection is found to be effective in suppressing the flashback occurrence. In particular, the global sensitivity analysis shows that the external angle of the spray cone and the mass flow of water are the most important design parameters for flashback prevention. NOx emissions are reduced by about 17% with water injection. Once an optimized condition with water injection is found, a recently proposed method to downscale the combustor to lower pressures is applied and tested. Additional LESs are performed for this purpose at the dry, unstable condition and the "wet,"stable condition. Results show that similar dynamics are predicted at 1 atm, validating the method's robustness. This provides avenues for experimentally testing combustion dynamics at simplified conditions which are still representative of high-pressure practical configurations.

Recent research [Porcarelli et al., Int. J Hydrogen Energy 49, 2024] shows NOx can be suppressed in lean premixed hydrogen flames at high levels of strain without loss of efficiency. However, the thermoacoustic response of such flames in high strain regimes remains unexplored. The present work addresses this by investigating the thermoacoustic characteristics of very lean premixed hydrogen flames under increasing levels of applied strain rates. High-fidelity simulations are conducted in a counterflow, reactants-to-products configuration, where strain rate is controlled by inlet velocities. Several simulations are conducted under a range of different strain rates and forcing frequencies. The simulations are run using a modified version of the reactingFOAM solver within OpenFOAM-9 that accounts for the different diffusivities in hydrogen flames and uses the low-Mach formulation of the Navier–Stokes equations. The forcing was imposed by applying sinusoidal oscillations on top of the uniform velocity of the reactants at the inlet boundary with a specific frequency and an amplitude of 10% of the mean value. Results indicate that above a threshold, increasing strain raises the gain and shifts its peak to higher frequencies. This behaviour stems from the flame speed response to strain at negative Markstein lengths and can be leveraged for the development of ultralow-emission combustion devices where applied strain can be used as an additional mechanism to shift an unstable flame response to different frequencies. Moreover, the highest applied strain rate investigated triggers an inversion of the Markstein length, leading to a 180 phase shift in the flame dynamic response. This aspect and further implications are discussed in the paper.

We present a data-driven approach to Reynolds-averaged Navier-Stokes (RANS) turbulence closure modelling in magnetohydrodynamic (MHD) flows. In these flows the magnetic field interacting with the conductive fluid induces unconventional turbulence states such as quasi two-dimensional (2D) turbulence, and turbulence suppression, which are poorly represented by standard Boussinesq models. Our data-driven approach uses time-averaged Large Eddy Simulation (LES) data of annular pipe flows, at different Hartmann numbers, to derive corrections for the - SST model. Correction fields are obtained by injecting time averaged LES fields into the MHD RANS equations, and examining the remaining residuals. The correction to the Reynolds-stress anisotropy is approximated with a modified Tensor Basis Neural Network (TBNN). We extend the generalised eddy hypothesis with a traceless antisymmetric tensor representation of the Lorentz force to obtain MHD flow features, thus keeping Galilean and frame invariance while including MHD effects in the turbulence model. The resulting data-driven models are shown to reduce errors in the mean flow, and to generalise to annular flow cases with different Hartmann numbers from those of the training cases.

Direct numerical simulations (DNS) are conducted for reactants-to-products counterflow configurations at turbulent conditions to understand how strain affects the structure and NOx emissions of lean premixed hydrogen flames. Two nominal equivalence ratio conditions, 0.5 and 0.7, are investigated. Under unstretched conditions, the Markstein length is negative for the former and slightly positive for the latter, indicating distinct responses of heat release rate and flame consumption speed to strain in each case. For each equivalence ratio condition, three levels of applied strain rate are considered, resulting in a total of six DNS. Results indicate that overall NOx emissions decrease with increasing strain at turbulent conditions, consistent with recent results for laminar conditions presented in Porcarelli et al. (2024). However, the relative decrease of NOx with strain is faster under turbulent conditions because turbulent mixing limits the occurrence of super-adiabatic temperatures. Moreover, the decrease of NOx is strongly correlated only to the mean applied tangential strain rate, while local fluctuations of strain due to vortices exhibit more stochastic behaviour. The detailed analysis presented in this article indicates that the applied strain can be used to substantially decrease NOx emissions in premixed hydrogen flames under practical conditions. Novelty and Significance statement: This work examines for the first time in detail the coupled effects of strain and turbulence in hydrogen flames, for various conditions spanning different signs of the Markstein length and increasing applied strain levels. In particular, it clarifies the different roles of applied strain, turbulence-driven strain, and curvature on both flame structure and NOx generation. Results further show for the first time that both in-flame and post-flame NOx can be suppressed at high strain levels under turbulent conditions. This result is of paramount importance as it implies that NOx can be suppressed at combustor-relevant conditions by straining the flame.

The implementation of the Particle Swarm Optimization (PSO) algorithm is investigated to optimize the active attenuation of Tollmien–Schlichting (TS) waves developing in a two-dimensional zero pressure gradient boundary layer. This is done numerically, where the PSO algorithm optimizes the characteristics of harmonic suction and blowing jets, in a feedforward control framework. The PSO-based controller selects and modifies the phase and amplitude of the jets to minimize the pressure fluctuation amplitude downstream of the actuator. To allow for efficient simulation, the 2-dimensional incompressible Navier–Stokes equations are expanded in a harmonic perturbation form and solved in linear and nonlinear variants using harmonic balancing. This study explores the performance of control in both linear and nonlinear development regimes of TS waves through control of single and multi-frequency ensembles of instabilities. Respectively, linear and nonlinear controller design approaches are employed. The findings reveal that the integration of PSO into the control design produces an effective suppression of TS waves through opposition control. The linearly designed controller effectively attenuates single and multi-frequency disturbances. However, when applied in regions of strong nonlinear interactions among instability modes, performance degradation is observed. On the contrary, the nonlinearly designed controller proves effective in mitigating nonlinear multi-frequency instabilities dominating the later stages of growth. A near-complete elimination of TS waves is achieved by accounting for nonlinear interactions among harmonic modes detected by an input sensor. This highlights the benefit of integrating the PSO algorithm in control of TS waves, particularly in the nonlinear growth regime, where classical control methods are generally ineffective.

Phase-resolved volumetric velocity measurements of a pulsed jet are conducted by means of three-dimensional particle tracking velocimetry (PTV). The resulting scattered and relatively sparse data are densely reconstructed by adopting physics-informed neural networks (PINNs), here regularized by the Navier-Stokes equations. It is shown that the assimilation remains robust even at low particle densities ( ppp < 10 − 3 ) where the mean particle distance is larger than 10% of the outlet diameter. This is achieved by enforcing compliance with the governing equations, thereby leveraging the spatiotemporal evolution of the measured flow field. Thus, the PINN reconstructs unambiguously velocity, vorticity, and pressure fields, enabling a robust identification of vortex structures with a level of detail not attainable with conventional methods (binning) or more advanced data assimilation techniques (vortex-in-cell). The results of this article suggest that the PINN methodology is inherently suited to the assimilation of PTV data, in particular under conditions of severe data sparsity encountered in experiments with limited control of the seeding concentration and/or distribution.

Phase-resolved volumetric velocity measurements of a pulsed jet are conducted by means of three-dimensional particle tracking velocimetry (PTV). The resulting scattered and relatively sparse data are densely reconstructed by adopting physics-informed neural networks (PINNs), here regularized by the Navier-Stokes equations. It is shown that the assimilation yields a higher spatial resolution, and the process remains robust, even at low particle densities ( 𝑝𝑝𝑝 < 0.001). This is achieved by enforcing compliance with the governing equations, thus leveraging the spatiotemporal evolution of the measured flow field. The results indicate that the PINN reconstructs unambiguously velocity, vorticity and pressure fields with a level of detail not attainable with conventional methods (binning) or more advanced data assimilation techniques (vortex-in-cell). The results of this article support the findings of Clark di Leoni (2023) suggesting that the PINN methodology is inherently suited to the assimilation of PTV data, in particular under conditions of severe sparsity or during experiments with limited control of seeding concentration.

In this work, we propose a data-driven framework to identify precursors of extreme events in turbulent reacting flows. Specifically, we tackle the problem of flashback prediction in a lean hydrogen reheat combustor. Our framework is composed of two parts. The first consists in the use of a co-kurtosis based approach to identify the components of the thermochemical and flow state which are the most relevant for the onset of flashback. This allows for an efficient low-dimensional representation. From this reduced representation, a modularity-based clustering algorithm is then employed to segregate between clusters which contain normal and extreme (flashbacking) states, and the cluster located in-between these states, which are the precursor states of extreme events. We show that this method is able to identify the most important features at the onset of flashback in the considered reheat combustor and then provide precursor states based on those. The prediction time obtained with the identified precursors is relatively large when compared to the duration over which the combustor is stable. Additional analyses on the specific choice of features for the precursor identification and the sampling locations are made. The robustness of the method when using shorter time series to identify the precursor is also investigated. Results show that the method is generally robust with respect to such changes. A first step towards practical measurements is also attempted with wall pressure measurements, which shows only a moderate reduction in prediction time. This work proposes for the first time a data-driven technique to automatically identify precursors of flashback in hydrogen combustion opening the path for such applications on other extreme events in reacting flows.

Permeable materials are a promising trailing edge noise reduction technique. The noise reduction is a result of the unsteady interaction between the two communicating boundary layers, in a process referred to as the pressure release mechanism. However, in practice the aeroacoustic performance of permeable trailing edges degrades under lifting conditions, i.e. with a pressure and velocity differential. This study aims at investigating such flow physics using the Lattice Boltzmann Method through 3DS Power FLOW. A numerical setup was created to explore the impact of velocity and pressure differentials between two communicating boundary layers and relate them to the aeroacoustic performance of porous media. The proposed numerical setup consists of two vertically stacked temporally developing channel flows separated by a porous medium (6δ × (4δ + t) × 2 δ), where δ and t are the half-channel height and the porous medium thickness respectively. The two channel flows communicate through fully resolved porous media, here, 75% porous triply periodic minimal surfaces. A large drag increase is observed for all geometries. An increase in anti-correlation between the pressure fluctuations between the channels is found to be related to a drag increase. It was concluded that the spanwise coherent turbulent structures drive the increase in drag. These structures are also affected by the geometry of the porous medium at the surface of the grazing flows. The presence of large coherent turbulent structures leads to a shift in turbulent energy scales. This is related to the modification of the wall pressure spectrum, where it was observed that less energy is present at low frequencies, whereas a peak was observed at a higher frequency. The crossover frequency is between 150Hz and 600Hz.

This paper introduces an approach for parameterizing airfoil geometries using a Variational Autoencoder (VAE) with a focus on achieving a low-dimensional and interpretable model. The primary focus is to facilitate efficient use in design optimization environments by capturing essential airfoil features in a minimal number of latent dimensions. To address the black-box nature of VAEs and enhance interpretability, a correlation analysis is performed to uncover the relationships between the airfoil properties and these inferred latent dimensions. Key to this research is the incorporation of both geometric and aerodynamic properties in this analysis, enabling the generation of airfoils with desired aerodynamic characteristics through manual tuning of the latent vector by a designer. The method is evaluated using the extensive UIUC airfoil database, which includes a diverse range of airfoil categories. The VAE is trained on airfoil surface coordinate points, and the generated output geometries are refined using a composite Bezier curve to smooth out local imperfections. Results demonstrate that the VAE can successfully extract and parameterize key airfoil features using a limited number of interpretable latent parameters. These parameters show clear correlations with geometric and aerodynamic airfoil properties, providing a practical and understandable parameterization model that facilitates the intuitive generation of new airfoil designs through smooth interpolation of the training data.

A design can only be as good as its mathematical representation. In engineering design optimization, the chosen method of parameterization can have significant impact on the outcomes. This paper introduces a novel methodology for airfoil design parameterization utilizing variational autoencoders (VAEs), a class of neural networks known for their proficiency in reducing dimensionality. However, a significant challenge with VAEs is the interpretability of the encoded latent space. This work aims to address this issue by creating a network with an interpretable latent space, yielding parameters that are understandable to humans. The effectiveness of this approach is evaluated using the comprehensive UIUC airfoil database, which offers a diverse range of airfoil shapes for analysis. We show that a VAE can successfully extract key features of airfoil geometries and parameterize them using six parameters, which show a clear correlation with airfoil properties in a way that remains understandable by the designer. Additionally, it smoothly interpolates the data points, allowing the generation of new airfoils and thus offering a practical and interpretable airfoil parameterization.

This paper presents an investigation of the effects of water injection within a simplified version of the Ansaldo GT36 reheat system. The investigation is carried out under realistic operating conditions of 20 atm and using large eddy simulation (LES) coupled with the thickened flame model (TFM) and an adaptive mesh refinement. The water injection conditions are optimized by performing a parametric study based on global sensitivity analysis and a surrogate model based on Gaussian process is employed as a way to reduce computational cost. In particular, the influence on the system performance of four design parameters, namely Sauter mean diameter, water mass flow and the angles of the spray's hollow cone, is tested to achieve an optimized solution. In the 'dry' case, the LES simulations show several flashback events, which are a defining aspect of the considered conditions, and attributed to compressive pressure waves resulting from autoignition in the core flow near the crossover temperature. The use of water injection is found to be effective in suppressing the flashback occurrence. In particular, the global sensitivity analysis shows that the external angle of the spray cone and the mass flow of water are the most important design parameters for flashback prevention. Moreover, NOx was shown to be reduced by about 17% by the use of the water injection at the tested conditions. Once an optimised condition with water injection is found, a recently proposed method to downscale the combustor to lower pressures is applied and tested. Additional LES are performed for this purpose at the 'dry', unstable condition and the 'wet', stable condition. Results show that similar dynamics, respectively unstable and stable, is predicted at 1 atm, suggesting the robustness of the method. This provides avenues for experimentally testing combustion dynamics at simplified conditions which are still representative of high-pressure practical configurations.

This work focuses on the suppression of Tollmien-Schlichting (TS) waves in a two-dimensional laminar boundary layer using optimized unsteady suction and blowing jets as an Active Flow Control (AFC) method. The suppression of TS waves via this AFC system is enabled through two artificial intelligence-based optimization methodologies: Single-Step Deep Reinforcement Learning (SDRL) and Particle Swarm Optimization (PSO). The primary aim of this research is to assess the performance of these methods in optimizing the AFC parameters with respect to convergence rate, computational efficiency, and ability to find an optimum control state. The findings demonstrate the success of both methods in finding appropriate control parameters resulting in TS wave attenuation by up to 40 dB in the maximum convective instability amplitude for the linear and nonlinear stages of development. The comparative study in this paper presents the effectiveness of the SDRL algorithm in optimizing the AFC system for TS waves’ suppression and demonstrates that it can outperform PSO in terms of convergence rate and computational efficiency alongside a better performance in finding an improved optimum for linear control cases. However, the advantage of the SDRL-based controller over the PSO-based one diminishes in multi-frequency nonlinear control cases where the controller is located downstream and attempting to control highly amplified multi-modal TS waves.

A lean premixed ethylene-air flame in a backstep configuration is simulated on multiple grids using both direct numerical simulations (DNS) with reduced order kinetic mechanism and large eddy simulations (LES) with flamelet-based thermochemistry. The configuration includes preheated reactants and a recirculation zone that provides radicals and high temperature gases to stabilize the flame. Heat losses are present due to the proximity of cooled walls. The reacting flow obtained from DNS at different resolutions is first analyzed to investigate the property of heat transfer within the recirculation region. LES based on adiabatic flamelets with a correction of the heat capacity is then tested, and its ability to account for heat losses is compared to results obtained using a three-dimensional non-adiabatic flamelet approach. Mean fields and subgrid properties are compared to those obtained from DNS to assess the capability of the LES models. The results show that the non-adiabatic flamelet approach can predict recirculation region and temperature fields with good accuracy. The model with heat capacity correction is able to effectively correct the heat capacity behavior as observed by a priori comparisons. However, in the a posteriori context, it is observed to overestimate the temperature field, although the correct size of the recirculation region is predicted. The combined a priori and a posteriori analyses on the same configuration and at different mesh resolutions allow for a precise separation of modeling effects due to heat transfer at the wall and combustion closure, thus providing indications on the LES performance in the context of flamelets.

The dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear decomposition of the turbulent state to predict the flow based on a reduced-order representation of the dynamics. We divide the turbulent flow into a spatial problem and a temporal problem. First, we compute the latent space, which is the manifold onto which the turbulent dynamics live. The latent space is found by a series of nonlinear filtering operations, which are performed by a convolutional autoencoder (CAE). The CAE provides the decomposition in space. Second, we predict the time evolution of the turbulent state in the latent space, which is performed by an echo state network (ESN). The ESN provides the evolution in time. Third, by combining the CAE and the ESN, we obtain an autonomous dynamical system: The CAE-ESN. This is the reduced-order model of the turbulent flow. We test the CAE-ESN on the two-dimensional Kolmogorov flow and the three-dimensional minimal flow unit. We show that the CAE-ESN: (i) finds a latent-space representation of the turbulent flow that has of the degrees of freedom than the physical space; (ii) time-accurately and statistically predicts the flow at different Reynolds numbers; and (iii) takes computational time to predict the flow with respect to solving the governing equations. This work opens possibilities for nonlinear decomposition and reduced-order modelling of turbulent flows from data.

Modeling complex dynamical systems with only partial knowledge of their physical mechanisms is a crucial problem across all scientific and engineering disciplines. Purely data-driven approaches, which only make use of an artificial neural network and data, often fail to accurately simulate the evolution of the system dynamics over a sufficiently long time and in a physically consistent manner. Therefore, we propose a hybrid approach that uses a neural network model in combination with an incomplete partial differential equations (PDEs) solver that provides known, but incomplete physical information. In this study, we demonstrate that the results obtained from the incomplete PDEs can be efficiently corrected at every time step by the proposed hybrid neural network—PDE solver model, so that the effect of the unknown physics present in the system is correctly accounted for. For validation purposes, the obtained simulations of the hybrid model are successfully compared against results coming from the complete set of PDEs describing the full physics of the considered system. We demonstrate the validity of the proposed approach on a reactive flow, an archetypal multi-physics system that combines fluid mechanics and chemistry, the latter being the physics considered unknown. Experiments are made on planar and Bunsen-type flames at various operating conditions. The hybrid neural network—PDE approach correctly models the flame evolution of the cases under study for significantly long time windows, yields improved generalization and allows for larger simulation time steps.

Abrupt and rapid high-amplitude changes in a dynamical system’s states known as extreme events appear in many processes occurring in nature, such as drastic climate patterns, rogue waves, or avalanches. These events often entail catastrophic effects, therefore their description and prediction is of great importance. However, because of their chaotic nature, their modelling represents a great challenge up to this day. The applicability of a data-driven modularity-based clustering technique to identify precursors of rare and extreme events in chaotic systems is here explored. The proposed identification framework based on clustering of system states, probability transition matrices and state space tessellation was developed and tested on two different chaotic systems that exhibit extreme events: the Moehliss-Faisst-Eckhardt model of self-sustained turbulence and the 2D Kolmogorov flow. Both exhibit extreme events in the form of bursts in kinetic energy and dissipation. It is shown that the proposed framework provides a way to identify pathways towards extreme events and predict their occurrence from a probabilistic standpoint. The clustering algorithm correctly identifies the precursor states leading to extreme events and allows for a statistical description of the system’s states and its precursors to extreme events.