This study identifies the scale-dependent processes that sustain turbulence in dense submerged canopy flows. Using a scale-resolved energy budget, we determine where in space and at which scales production, pressure-strain redistribution, and inter-scale transfer predominantly occur, and how they link the canopy layer to the overlying shear flow. We show that energy production is localised at the interfacial shear layer, over a narrow range of streamwise and spanwise scales, while fluctuations within the canopy are primarily maintained through inter-scale transfer and pressure-strain redistribution. The dynamically active scales in the canopy are largely imposed by outer-layer structures, with their organisation and coherence mediated by these inherited motions. Energy exchange across the canopy interface is asymmetric but not unidirectional: although the dominant transfer is from the outer layer towards the canopy, intermittent reverse interactions occur at all scales. The most intense cross-interface exchanges are associated with finer-scale motions rather than large-scale structures, indicating that extreme interfacial energy fluxes are governed predominantly by small-scale dynamics. The flexibility of the canopy weakens the coherence of outer-layer structures and reduces the efficiency of inter-layer energy transfer, thereby altering both the organisation and scale of the fluctuations within the canopy. These results clarify how turbulence in dense canopies is organised and sustained, providing a unified energetic interpretation that links coherent structures to scale-dependent mechanisms.

Pipe flow controlled by streamwise-travelling waves of azimuthal wall velocity is studied using direct numerical simulations at a bulk Reynolds number Re_b=4900. A comprehensive analysis of drag reduction shows that the flow response differs fundamentally from that of channel flow. Under suitable forcing, pipe flow relaminarizes, whereas channel flow does not. Depending on the control parameters, the flow exhibits the spatially localized turbulent state characteristic of transitional pipe flow, with turbulent puffs persisting at bulk Reynolds numbers up to three times higher than in the uncontrolled case. The bulk Reynolds number alone does not determine the onset of localization. Moreover, drag reduction, which alters the natural relation between bulk and friction velocities, is insufficient to identify a universal onset criterion. An intermittency indicator based on the spatial variance of the cross-sectional turbulent kinetic energy relates the emergence of localized turbulence to the low wall friction produced by the control, although the correspondence is not one-to-one. Despite their qualitative resemblance to canonical turbulent puffs, the controlled puffs exhibit distinct properties; for example, their fronts may propagate faster than the bulk flow. Overall, this work provides a comprehensive characterization of the subcritical turbulent state and its turbulent puffs in controlled pipe flow, and offers a new perspective on control strategies that aim at flow relaminarization.

Accurate analysis of conjugate heat transfer (CHT) is of primary importance in many engineering applications and biological flows where it is crucial to implement a reliable model that couples thermal conduction in the solid boundary with convection in the fluid. CHT simulations entail higher computational costs to well resolve the smooth/rough solid layers and to generate high-quality meshes for complex finite-thickness wall geometries. This work adopts upscaled boundary conditions capable of modeling the heat transfer at a fraction of the cost of the full conjugate-forced-convection analysis. The effective velocity and temperature conditions are applied to pressure-driven, developing flows through ducts with different types of wall roughness down to the smooth limit. The results are compared against fully resolving CHT simulations, and the good agreement demonstrates suitability of the macroscopic approach as a cheaper alternative. The model is finally applied to the flow within the human nose, where CHT is mandatory because of the physiological importance of thermal exchange processes. Despite the simplifying assumptions made to the physics in this case, the results obtained are fairly encouraging for future use of the model, possibly with relevant adjustments and extensions, in typical biomedical contributions.

In this work, direct numerical simulations are used to investigate which physical effects of active flow control are most relevant for improving the aerodynamic performance of airfoils. To this end, two active flow control strategies based on inherently different physical mechanisms are systematically compared on the upper surface of the supercritical V2C airfoil in compressible transonic flow. The first strategy consists of streamwise-travelling waves of spanwise wall velocity (StTW), a skin-friction drag reduction technique that locally decreases wall shear stress in the region of application. The second strategy is uniform wall-normal suction, which locally increases skin-friction drag. One strength of the present study is that the control configurations are evaluated at matched lift coefficients to isolate the impact of the control mechanisms on drag components, boundary-layer development, shock position, and energetic cost. Despite their opposite local effects on skin-friction drag, both control strategies yield comparable and significant improvements in global aerodynamic efficiency. The analysis reveals that, for both approaches, the dominant mechanism responsible for the efficiency increase is a downstream displacement of the shock, accompanied by a reduction in boundary-layer momentum thickness. These results highlight the central role of shock–boundary-layer interaction control in enhancing transonic aerodynamic performance and demonstrate that skin-friction drag reduction alone is not a sufficient metric for assessing the effectiveness of active flow control strategies.

Abstract This work explores the application of control theory to turbulent channel flow. We use linear optimal control theory to design estimators and controllers that use real-time wall measurements to either reconstruct the internal flow field or compute control inputs to reduce drag. A peculiar feature of this study is the use of Wiener filtering, formulated in the frequency domain, which provides a computationally efficient alternative to conventional time-domain design approaches. The proposed framework integrates the best possible (linear) description of both system noise, representing the effect of nonlinear terms neglected by linearization, and linear model of the channel flow. Notwithstanding the highly preliminary nature of this work, we already demonstrate with DNS an interesting amount of drag reduction at Re τ = 200, and discuss several avenues to further improve control performance.

Turbulent channel flow controlled by spanwise wall oscillations is studied using direct numerical simulations to improve how spanwise forcing reduces skin-friction drag. Harmonic wall oscillations generate a periodic transverse Stokes layer whose thickness $\delta$ is determined by the forcing period $T$ . Although an optimal $T$ that maximises drag reduction is known to exist, its physical significance remains unclear. To elucidate it, we extend the spanwise Stokes layer by augmenting wall oscillation with an additional spanwise body force. In this formulation, $\delta$ and $T$ become decoupled and can be varied independently. The oscillating wall thus appears as a special and suboptimal case of spanwise forcing. Optimal performance is obtained for substantially smaller $T$ and larger $\delta$ than those of the classical Stokes layer. For the conditions examined, with Reynolds number and forcing amplitude held fixed, the maximum drag reduction increases by approximately one third, while the maximum net energy saving improves markedly from $-35\,\%$ to $+16\,\%$ . These findings suggest that drag-reduction strategies based on spanwise forcing deserve renewed scrutiny: wall oscillation represents only one possible actuation method, and not necessarily the most effective one.

The air flows in the proximal and distal portions of the human lungs are interconnected: the lower Reynolds number in the deeper generations causes a progressive flow regularization, but mass conservation requires flow rate oscillations to propagate through the airway bifurcations. To explain how these competing effects shape the flow state in the deeper generations, we have performed the first high-fidelity numerical simulation of the air flow in a lung model that includes 23 successive bifurcations of a single planar airway. Turbulence modeling or assumptions on flow regimes are not required. The chosen flow rate is steady on average, and representative of the peak inspiratory flow reached by adult patients breathing through therapeutic inhalers. As expected, advection becomes progressively less important after each bifurcation, until a time-dependent Stokes regime governed solely by viscous diffusion is established in the smallest generations. However, fluctuations in this regime are relatively fast and large with respect to the mean flow, which is in contrast with the commonly agreed picture that only the breathing frequency is relevant at the scale of the alveoli. We demonstrate that the characteristic frequency and amplitude of these fluctuations are linked to the flow in the upper part of the bronchial tree, as they originate from the time-dependent flow splitting in the upper bifurcations. Even though these fluctuations are observed here in an idealized, rigid lung model, our findings suggest that the assumptions usually adopted in many of the current lung models might need to be revised.

Spanwise wall forcing in the form of streamwise-travelling waves is applied to the suction side of a transonic airfoil with a shock wave to reduce aerodynamic drag. The study, conducted using direct numerical simulations, extends earlier findings by Quadrio et al. (J. Fluid Mech. vol. 942, 2022, R2) and confirms that the wall manipulation shifts the shock wave on the suction side towards the trailing edge of the profile, thereby enhancing its aerodynamic efficiency. A parametric study over the parameters of wall forcing is carried out for the Mach number set at 0.7 and the Reynolds number at 300,000. Similarities and differences with the incompressible plane case are discussed; for the first time, we describe how the interaction between the shock wave and the boundary layer is influenced by flow control via spanwise forcing. With suitable combinations of control parameters, the shock is delayed, and results in a separated region whose length correlates well with friction reduction. The analysis of the transient process following the sudden application of control is used to link flow separation with the intensification of the shock wave.

An immersed-boundary method for the incompressible Navier-Stokes equations is presented. It employs discrete forcing for a sharp discrimination of the solid-fluid interface, and achieves second-order accuracy, demonstrated in examples with highly complex three-dimensional geometries. The method is implicit, meaning that the point in the solid which is nearest to the interface is accounted for implicitly, which benefits stability and convergence properties; the correction is also implicit in time (without requiring a matrix inversion), although the temporal integration scheme is fully explicit. The method stands out for its simplicity and efficiency: when integrated with second-order finite differences, only the weight of the center point of the Laplacian stencil in the momentum equation is modified, and no corrections for the continuity equation and the pressure are required. The immersed-boundary method, its performance and its accuracy are first verified on simple problems, and then put to test on a simple laminar, two-dimensional flow and on two more complex examples: the turbulent flow in a channel with a sinusoidal wall, and the flow in a human nasal cavity, whose extreme anatomical complexity mandates an accurate treatment of the boundary.

The high dimensionality and variability of Computational Fluid Dynamics (CFD) data pose a significant challenge for Machine Learning (ML) models. The only solutions in the literature addressing inference from CFD flow fields are based on expert-driven features, which consist of fluid dynamic quantities averaged on specific regions of the entire computational domain. However, using handcrafted features can limit the scalability and portability of existing methods, and result in the loss of critical flow field information that might be essential for capturing non-linear patterns inherent in the CFD data. We propose a method to replace handcrafted features with features defined on regions obtained by clustering. Our approach combines: i) physics-based clustering, to identify meaningful regions within the flow field, ii) cluster-based feature extraction, to capture localized fluid dynamics properties, and iii) set-learning models to process the extracted information. Our solution allows integrating physics-based modeling with ML, and provides a portable and flexible pipeline capable of effectively dealing with the variability and dimensionality of CFD flow fields. We validate our method on publicly available CFD datasets (from the aerospace domain) and apply it to a realistic scenario, that is, the classification of pathologies in real 3D human upper airways extracted from CT scans, acquired in collaboration with a medical hospital. Experimental results demonstrate the accuracy and scalability of our method, and highlight its potential for leveraging CFD data in ML frameworks for other scientific and engineering applications.

We address the Reynolds number dependence of the turbulent skin-friction drag reduction induced by streamwise-travelling waves of spanwise wall oscillations. The study relies on direct numerical simulations of drag-reduced flows in a plane open channel at friction Reynolds numbers in the range $1000 \leqslant Re_\tau \leqslant 6000$ , which is the widest range considered so far in simulations with spanwise forcing. Our results corroborate the validity of the predictive model proposed by Gatti & Quadrio (J. Fluid Mech. vol. 802, 2016, pp. 553-558): regardless of the control parameters, the drag reduction decreases monotonically with $Re$ at a rate that depends on the drag reduction itself and on the skin-friction of the uncontrolled flow. We do not find evidence in support of the results of Marusic et al. (Nat. Commun. vol. 12, no. 1, 2021, pp. 5805), which instead report by experiments an increase of the drag reduction with $Re$ in turbulent boundary layers, for control parameters that target low-frequency, outer-scaled motions. Possible explanations for this discrepancy are provided, including obvious differences between open channel flows and boundary layers, and possible limitations of laboratory experiments.

The transonic airflow around a supercritical wing with a shock wave is described via direct numerical simulations. Flow control for turbulent drag reduction is applied via streamwise traveling waves of spanwise velocity applied on a finite portion of the suction side. The near-field modifications caused by the forcing are studied via the analysis of the wake profile downstream of the trailing edge. Moreover, for the first time, the effects of spanwise forcing on aeroacoustic noise are considered to establish whether active flow control for drag reduction could possibly increase noise. By extracting the acoustic signals on a circumference placed in the near-field around the wing and by studying them in terms of sound intensity and frequency content, it is found that noise intensity is not significantly increased by spanwise forcing and that frequency content is only minimally altered. Furthermore, if the angle of attack is reduced to take into account the increased lift and the reduced drag made possible by the control action, changes in the noise characteristics become negligible.

Solving the Reynolds-averaged Navier-Stokes equations (RANS) closed with an eddy viscosity computed through a turbulence model is still the leading approach for Computational Fluid Dynamics simulations. Unfortunately, universal models with good predictive capabilities over a wide range of flows are not available. In this work, we propose the use of machine learning to improve existing RANS models. The approach does not require high-fidelity training data. A convolutional neural network is used to identify and segment at runtime the flow field into different zones, each resembling one item of a predefined list of elementary flows. The turbulence model applied in each zone is taken from an equally predefined set of classic models, each specifically tuned to work best for one elementary flow, free from the requirement of universality. The idea is first presented in general terms, and then demonstrated via a preliminary implementation, where only three elementary flows are considered, and three turbulence models are used. Test cases show that, already in this oversimplified form, automated zonal modelling outperforms the baseline RANS models without computational overhead.

The high dimensionality of flow fields obtained from Computational Fluid Dynamics (CFD) poses major challenges for Machine Learning (ML), especially when the scarcity of training data combines with strong geometric variability. Most existing ML approaches for inference from CFD data rely on expert-defined features, primarily quantities computed over manually selected regions. However, this strategy does not scale well, since regions must be redefined for each new geometry, requiring expert knowledge and significant effort. To overcome this limitation, we introduce two complementary methods to extract features from CFD flow fields: the first identifies meaningful flow regions by clustering features derived from the governing equations; the second employs mesh morphing to align each flow field onto a common reference geometry, enabling consistent use of expert-defined regions across cases. Both require minimal human intervention on new samples and ensure scalability across diverse CFD scenarios. We validate our methods on two distinct applications: first, by accurately identifying airfoil shapes and geometric defects; second, by classifying nasal pathologies from 3D CFD simulations of human upper airways reconstructed from CT scans. Both methods show robustness and high accuracy, highlighting their potential for automated, generalizable, and scalable CFD analysis within ML frameworks.

Numerical simulations and clinical measurements of nasal resistance are in quantitative disagreement. The order of magnitude of this mismatch, that sometimes exceeds 100%, is such that known sources of uncertainty cannot explain it. The goal of the present work is to examine a source of bias introduced by the design of medical devices, which has not been considered until now as a possible explanation. We study the effect of the location of the probe on the rhinomanometer that is meant to measure the ambient pressure. Rhinomanometry is carried out on a 3D silicone model of a patient-specific anatomy; a clinical device and dedicated sensors are employed side-by-side for mutual validation. The same anatomy is also employed for numerical simulations, with approaches spanning a wide range of fidelity levels. We find that the intrinsic uncertainty of the numerical simulations is of minor importance. To the contrary, the position of the pressure tap intended to acquire the external pressure in the clinical device is crucial, and can cause a mismatch comparable to that generally observed between in-silico and in-vivo rhinomanometry data. A source of systematic bias may therefore exist in rhinomanometers, designed under the assumption that measurements of the nasal resistance are unaffected by the flow development within the instruments.

The application of Machine Learning (ML) to Computational Fluid Dynamics (CFD) has gained significant attention due to its potential in speeding up simulations and approximating numerical solutions of physical equations. Still, the dominant role of ML, which is to infer expert labels that cannot be calculated from explicit equations, has received much less attention in CFD. A major challenge in this direction is the scarcity of large, annotated datasets required to train robust ML models for flow field classification. In this work, we address the problem of training a ML model to classify CFD flow fields, inferring pathologies affecting the human upper airways. We propose a novel data augmentation method to address this limitation which involves an automated pipeline to extract CFD-ready surfaces from CT scans and a computational geometry technique to generate synthetic training samples. By defining deformation functions for specific pathologies on a reference surface and mapping these to healthy anatomical surfaces, we create a large and diverse training set with minimal expert supervision. This method allows for the generation of a dataset with high anatomical variability and well-defined labels, enhancing the model's ability to generalize to unseen geometries. We demonstrate that a Neural Network (NN) can accurately classify two common nasal pathologies, septal deviation and turbinate hypertrophy, achieving strong performance on real pathological patient data despite being trained solely on synthetic samples.

Deviations of the septal wall are widespread anatomic anomalies of the human nose; they vary significantly in shape and location, and often cause the obstruction of the nasal airways. When severe, septal deviations need to be surgically corrected by ear-nose-throat (ENT) specialists. Septoplasty, however, has a low success rate, owing to the lack of suitable standardized clinical tools for assessing type and severity of obstructions, and for surgery planning. Moreover, the restoration of a perfectly straight septal wall is often impossible and possibly unnecessary. This paper introduces a procedure, based on advanced patient-specific Computational Fluid Dynamics (CFD) simulations, to support ENT surgeons in septoplasty planning. The method hinges upon the theory of adjoint-based optimization, and minimizes a cost function that indirectly accounts for viscous losses. A sensitivity map is computed on the mucosal wall to provide the surgeon with a simple quantification of how much tissue removal at each location would contribute to easing the obstruction. The optimization procedure is applied to three representative nasal anatomies, reconstructed from CT scans of patients affected by complex septal deviations. The computed sensitivity consistently identifies all the anomalies correctly. Virtual surgery, i.e. morphing of the anatomies according to the computed sensitivity, confirms that the characteristics of the nasal airflow improve significantly after small anatomy changes derived from adjoint-based optimization.

Nasal Breathing Difficulties (NBD) consist of pathologies which are difficult to diagnose, heal and affect a high percentage of the population; the only way to treat these diseases is, most of the times, by surgery but the success rate is not very high since many patients have no relief from it. This should be attributed to the variety of the nose’s functions, which is far more complex than a simple duct to connect the environment to the lungs. CFD is emerging as an innovative approach to study these problems systematically; in this contribution the target is to use a method based on adjoint equations to get senstivity maps whose purpose is to provide surgeons with more informations on which are the regions, inside the nose, to focus on. This work focuses only on the reduction of the pressure drop across the nose, therefore a single objective function is used. Three different frameworks, with two formulations of the continuous adjoint equation method, are compared: in two cases topological sensitivities were used while in the latter the surface sensitivity was evaluated.

The two most common shape-optimization methods for fluid mechanics problems are based on topology modifications and surface modifications. When the number of design parameters is large compared to the number of objective functions the most efficient way to evaluate the sensitivity derivatives is using the solution from adjoint equations. In external aerodynamics such as aircraft wings, cars, and trains, surface sensitivities are commonly applied since the topology remains the same and the surface quality and precision are important factors. In internal flows, such as ducts and tubes, the choice between topology and surface modifications is not trivial. Both methods can lead to useful optimal solutions, but either possesses its own pros and cons. Changing the topology might be admissible, and even adding material (duct thickness) can lead to unexpected topologically different solutions. This is also true in many bio-mechanical applications such as surgery of the upper airways (UA). In this paper, topological and surface sensitivities are evaluated and compared in OpenFOAM by solving the adjoint equations for a simple geometry first, and and then for the upper airways. Two different geometries of the UA are investigated: the first consists of only the nasal cavity and the sensitivity analysis is applied to the inner geometry and the surrounding walls. In the second case, a tissue of a certain thickness is added to the first to simulate a tissue removal around the existing airways. The different geometries are analyzed and discussed, evidencing also pros and cons of the different processes.

Wall-based spanwise forcing has been experimentally used with success by Auteri et al. (Phys. Fluids, vol. 22, 2010, 115103) to obtain large reductions of turbulent skin-friction drag and considerable energy savings in a pipe flow. The spatial distribution of the azimuthal wall velocity used in the experiment was not continuous, but piecewise constant. The present study is a numerical replica of the experiment, based on a set of direct numerical simulations (DNS); its goal is the identification of the effects of spatially discrete forcing, as opposed to the idealized sinusoidal forcing considered in the majority of numerical studies. Regardless of the discretization, with DNS the maximum drag reduction is found to be larger: the flow easily reaches complete relaminarization, whereas the experiment was capped at 33 % drag reduction. However, the key result stems from the observation that, for the piecewise-constant forcing, the apparent irregularities of the experimental data appear in the simulation data too. They derive from the rich harmonic content of the discontinuous travelling wave, which alters the drag reduction of the sinusoidal forcing. A detailed understanding of the contribution of each harmonic reveals that, whenever for example technological limitations constrain one to work far from the optimal forcing parameters, a discrete forcing may perform very differently from the corresponding ideal sinusoid, and in principle can outperform it. However, care should be exercised in comparison, as discrete and continuous forcing have different energy requirements.