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.

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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.

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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.

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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.

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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.@en

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. @en

This paper introduces an approach for parameterizing airfoil geometries using a Variational Auto encoder (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 air foils 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 theVAE 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.

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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.@en

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.@en

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.

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Turbulence is characterised by chaotic dynamics and a high-dimensional state space, which make this phenomenon challenging to predict. However, turbulent flows are often characterised by coherent spatiotemporal structures, such as vortices or large-scale modes, which can help obtain a latent description of turbulent flows. However, current approaches are often limited by either the need to use some form of thresholding on quantities defining the isosurfaces to which the flow structures are associated or the linearity of traditional modal flow decomposition approaches, such as those based on proper orthogonal decomposition. This problem is exacerbated in flows that exhibit extreme events, which are rare and sudden changes in a turbulent state. The goal of this paper is to obtain an efficient and accurate reduced-order latent representation of a turbulent flow that exhibits extreme events. Specifically, we employ a three-dimensional multiscale convolutional autoencoder (CAE) to obtain such latent representation. We apply it to a three-dimensional turbulent flow. We show that the Multiscale CAE is efficient, requiring less than 10% degrees of freedom than proper orthogonal decomposition for compressing the data and is able to accurately reconstruct flow states related to extreme events. The proposed deep learning architecture opens opportunities for nonlinear reduced-order modeling of turbulent flows from data.@en

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.@en

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.

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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.@en

Multi-scale analysis of turbulence-flame interaction is performed using experimental data sets from three methane- and propane-fired premixed, turbulent V-flames, at an approach flow turbulent Reynolds number of 450 and a ratio of r.m.s. fluctuating velocity from the mean to laminar flame speed of between 2.1 and 3.0, straddling the border between corrugated flamelets and thin reaction zone in the Borghi-Peters diagram. The measurements were made in the plane of a single laser sheet using stereo particle image velocimetry SPIV and planar laser-induced fluorescence to measure three orthogonal components of velocity and flame OH. Methods to approximate the remaining, unmeasured, out of plane derivatives are described. The instantaneous SPIV images were bandpass filtered at user-specified characteristic length scales L_ω and L_s (for vorticity and strain rate, respectively) resulting in instantaneous bandpass-filtered velocity fields, u̲_b^L_ω and u̲_b^L_s, which were further analysed to give the bandpass filtered vorticity field, ω̲^L_ω=∇×u̲_b^L_ω, the strain-rate field, e_ij^L_s, and the tangential strain rate field a_T^L_s. This work quantifies two aspects of turbulence-flame interaction. The first aspect is that of the flame interaction of eddies of size L_s on the turbulence, as found by the statistics of the alignment of vorticity with strain rate. We find that vortical eddies with scale about L_ω=2δ_th (where δ_th is the flame thickness) are stretched by L_s structures which are larger than about 2 L_ω, with this factor broadly true also for vortical eddies of scales L_ω=4δ_th and L_ω=6δ_th. Within the limitations of the data set, these findings are consistent with those in the literature on reacting and non-reacting flows, suggesting that the premixed flame has had little influence on the vortex stretching mechanism. The second aspect of turbulence-flame interaction examined is that of flame surface-averaged tangential strain rate imparted by eddies. Eddies with length scales L_s smaller than 3 or 4δ_th are likely to have the strongest individual contribution but eddies of this length scale and smaller may contribute only about 1/5th of the total tangential strain rate. This is to be compared with the value of 10% that has been reported in the literature based on analysis of DNS predictions of premixed flames at turbulent Reynolds numbers up to 110. Eddies with length scale L_s larger than about 20δ_th contribute a negligible amount to the total tangential strain rate. We have found no evidence that the Lewis number up to about 1.8 has an observable effect, but this may reflect the limitations of the current experiment. In the context of large eddy simulations (LES) of premixed combustion, these results are preliminary experimental evidence supporting the suggestion that resolving turbulence scales down to a few multiples of δ_th might be adequate to capture much of the flame straining caused by turbulence.

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In this chapter, the research dedicated to moderate or intense low-oxygen dilution (MILD) combustion (also called flameless combustion) that relied on direct numerical simulations (DNS) is summarized. In particular, the various DNS carried out are detailed and three different configurations are considered: the autoigniting mixing layer between fuel and hot and diluted oxidizer, the premixed MILD combustion resulting from internal exhaust gas recirculation, and the nonpremixed MILD combustion with internal exhaust gas recirculation. Focus is placed here on different aspects of MILD combustion. First, works that relate to the onset of MILD combustion and the apparition of the initial ignition kernels are discussed, in particular, a summary is provided on the findings that show the particular physics of MILD combustion, where the initial ignition kernels are mostly related to the distribution of mixture fraction and recirculating radicals. Subsequently, the identified physical mechanisms involved in the development of those ignition kernels are summarized. In particular, focus is placed on the balance between ignition and deflagrative mechanisms. Using different analysis methods, the works summarized here show that, while there is a coexistence between ignition and deflagration, ignition is the main contributor to the overall heat release. Finally, the implications of these findings on the modeling of MILD combustion are discussed through various studies that assessed a priori different modeling frameworks for MILD combustion. In those, models that capture this essential and dominant ignition behavior of MILD combustion were shown to be more accurate.

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Pool fires are canonical representations of many accidental fires which can exhibit an unstable unsteady behavior, known as puffing, which involves a strong coupling between the temperature and velocity fields. Despite their practical relevance to fire research, their experimental study can be limited due to the complexity of measuring relevant quantities in parallel. In this work, we analyze the use of a recent physics-informed machine learning approach, called hidden fluid mechanics (HFM), to reconstruct unmeasured quantities in a puffing pool fire from measured quantities. The HFM framework relies on a physics-informed neural network (PINN) for this task. A PINN is a neural network that uses both the available data, here the measured quantities, and the physical equations governing the system, here the reacting Navier-Stokes equations, to infer the full fluid dynamic state. This framework is used to infer the velocity field in a puffing pool fire from measurements of density, pressure, and temperature. In this work, the dataset used for this test was generated from numerical simulations. It is shown that the PINN is able to reconstruct the velocity field accurately and to infer most features of the velocity field. In addition, it is shown that the reconstruction accuracy is robust with respect to noisy data, and a reduction in the number of measured quantities is explored and discussed. This study opens up the possibility of using PINNs for the reconstruction of unmeasured quantities from measured ones, providing the potential groundwork for their use in experiments for fire research.

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A neural network (NN) aided model is proposed for the filtered reaction rate in moderate or intense low-oxygen dilution (MILD) combustion. The framework of the present model is based on the partially stirred reactor (PaSR) approach, and the fraction of the reactive structure appearing in the PaSR is predicted using different NN's, to consider both premixed and non-premixed conditions while allowing the use of imbalanced training data between premixed and non-premixed combustion direct numerical simulation (DNS) data. The key ingredient in the present model is the use of local combustion mode prediction performed by using another NN, which is developed in a previous study. The trained model was then assessed by using two unknown combustion DNS cases, which yields much higher dilution level (more intense MILD condition) and higher Karlovitz number than the DNS cases used as training data. The model performance assessment has been carried out by means of the Pearson's correlation coefficient and mean squared error. For both the present model and zeroth-order approximated reaction rate, the correlation coefficient with the target values shows relatively high values, suggesting that the trend of predicted field, by the present model and zeroth-order approximation, is well correlated with the actual reaction rate field. This suggests that the use of PaSR equation is promising if the fraction of the reactive structure is appropriately predicted, which is the objective in the present study. On the other hand, substantially lower mean squared error is observed for a range of filter sizes for the present model than that for the zeroth-order approximation. This suggests that the present filtered reaction rate model can account for the SGS contribution reasonably well.

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Multi-layer perceptrons with different numbers of hidden layers and variable neurons were investigated to model the nonlinear flame response of a Bunsen-type flame. The neural network models demonstrate the ability to learn the flame describing function (FDF) for a laminar premixed flame, while using only one computational fluid dynamics (CFD) simulation. The system is excited with a broadband, low-pass filtered velocity signal that exhibits a uniform distribution of amplitudes within a predetermined range. The obtained time series of flow velocity upstream of the flame and heat release rate fluctuations are used to train the nonlinear model using a multi-layer perceptron. Several models with varying hyperparameters are trained and the dropout strategy is used as a regularizer to avoid overfitting. The best performing model is subsequently used to compute the FDF using mono-frequent excitations. In addition to accurately predicting the FDF, the trained neural network model also captures the presence of higher harmonics in the flame response. As a result, when coupled with an acoustic solver, the obtained neural network model is better suited than a classical FDF model to predict limit cycle oscillations characterized by more than one frequency. The RMS value of the predicted acoustic oscillations, together with the associated dominant frequencies are in excellent agreement with CFD reference data.

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