arXiv subjects

Maurizio Quadrio

Publications and source records attributed to Maurizio Quadrio.

At least 19 recordsLinked to original sources

arXiv2026

Drag reduction and subcritical turbulence in controlled pipe flows

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.

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arXiv2026

Energy transfer and scale organisation in dense canopy turbulence

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.

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arXiv2026

Direct numerical simulations of inhalation in a 23-generation lung model

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, while mass conservation requires flow rate oscillations to propagate through the airway bifurcations. To explain how these two competing effects shape the flow state in the deeper generations, we have performed the first high-fidelity numerical simulations of the air flow in a lung model including 23 successive bifurcations of a single planar airway. Turbulence modelling or assumptions on flow regimes are not required. The chosen flow rate is stationary (steady on average), and representative of the peak inspiratory flow reached by adult patients breathing through therapeutical 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.

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arXiv2026

On the optimal period of spanwise wall forcing for turbulent drag reduction

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 $δ$ is determined by the forcing period $T$. Although an optimal $T$ that maximizes 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, $δ$ 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 $δ$ 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.

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arXiv2025

A proposal for automated turbulence modelling

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.

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arXiv2025

Importance of the numerical schemes in the CFD of the human nose

Computational fluid dynamics of the air flow in the human nasal cavities, starting from patient-specific Computer Tomography (CT) scans, is an important tool for diagnostics and surgery planning. However, a complete and systematic assessment of the influence of the main modeling assumptions is still lacking. In designing such simulations, choosing the discretization scheme, which is the main subject of the present work, is an often overlooked decision of primary importance. We use a comparison framework to quantify the effects of the major design choices on the results. The reconstructed airways of a healthy, representative adult patient are used to set up a computational study where such effects are systematically measured. It is found that the choice of the numerical scheme is the most important aspect, although all varied parameters impact the solution noticeably. For a physiologically meaningful flow rate, changes of the global pressure drop up to more than 50\% are observed; locally, velocity differences can become extremely significant. Our results call for an improved standard in the description of this type of numerical studies, where way too often the order of accuracy of the numerical scheme is not mentioned.

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arXiv2025

A simple and efficient second-order immersed-boundary method for the incompressible Navier--Stokes equations

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 implemented alongside 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.

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arXiv2025

Understanding the mismatch between in-vivo and in-silico rhinomanometry

Numerical simulations and clinical measurements of nasal resistance are in quantitative disagreement. Bias introduced by the design of medical devices has not been considered until now as a possible explanation. The aim of present paper is to 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.

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arXiv2025

The aerodynamic performance of a transonic airfoil with spanwise forcing

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.

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arXiv2024

Turbulent skin-friction drag reduction via spanwise forcing at high Reynolds number

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 $1000 \le Re_τ\le 6000$, 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. (2016): 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. Comm. (2021), 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.

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arXiv2024

An adjoint-based approach for the surgical correction of nasal septal deviations

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.

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arXiv2024

Spatial discretization effects in spanwise forcing for turbulent drag reduction

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 e.g. 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.

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arXiv2023

Comparing flow-based and anatomy-based features in the data-driven study of nasal pathologies

In several problems involving fluid flows, Computational Fluid Dynamics (CFD) provides detailed quantitative information, and often allows the designer to successfully optimize the system, by minimizing a cost function. Sometimes, however, one cannot improve the system with CFD alone, because a suitable cost function is not readily available: one notable example is diagnosis in medicine. The field of interest considered here is rhinology: a correct air flow is key for the functioning of the human nose, yet the notion of a functionally normal nose is not available, and a cost function cannot be written. An alternative and attractive pathway to diagnosis and surgery planning is offered by data-driven methods. In this work, we consider the machine-learning study of nasal pathologies caused by anatomic malformations, with the aim of understanding whether fluid dynamic features, available after a CFD analysis, are more effective than purely geometric features in the training of a neural network for regression. Our experiments are carried out on an extremely simplified anatomic model and a correspondingly simple CFD approach; nevertheless, they demonstrate that flow-based features perform better than geometry-based ones, and allow the training of a neural network with fewer inputs, a crucial advantage in fields like medicine.

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arXiv2023

Turbulent drag reduction with streamwise travelling waves in the compressible regime

The ability of streamwise-travelling waves of spanwise velocity to reduce the turbulent skin friction drag is assessed in the compressible regime. Direct numerical simulations are carried out to compare drag reduction in subsonic, transonic and supersonic channel flows. Compressibility improves the benefits of the travelling waves, in a way that depends on the control parameters: drag reduction becomes larger than the incompressible one for small frequencies and wavenumbers. However, the improvement depends on the specific procedure employed for comparison. When the Mach number is varied and, at the same time, wall friction is changed by the control, the bulk temperature in the flow can either evolve freely in time until the aerodynamic heating balances the heat flux at the walls, or be constrained such that a fixed percentage of kinetic energy is transformed into thermal energy. Physical arguments suggest that, in the present context, the latter approach should be preferred. Not only it provides a test condition in which the wall-normal temperature profile more realistically mimics that in an external flow, but also leads to a much better scaling of the results, over both the Mach number and the control parameters. Under this comparison, drag reduction is only marginally improved by compressibility.

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arXiv2023

Linear stability of Poiseuille flow over a steady spanwise Stokes layer

The temporal linear stability of plane Poiseuille flow modified by spanwise forcing applied at the walls is considered. The forcing consists of a stationary streamwise distribution of spanwise velocity that generates a steady transversal Stokes layer, known to reduce skin-friction drag in a turbulent flow with little energetic cost. A large numerical study is carried out, where the effects of both the physical and the discretization parameters are thoroughly explored, for three representative subcritical values of the Reynolds number Re. Results show that the spanwise Stokes layer significantly affects the linear stability of the system. For example, at Re=2000 the wall forcing is found to more than double the negative real part of the least-stable eigenvalue, and to decrease by nearly a factor of four the maximum transient growth of perturbation energy. These observations are Re-dependent and further improve at higher $Re$. Comments on the physical implications of the obtained results are provided, suggesting that spanwise forcing might be effective to obtain at the same time a delayed transition to turbulence and a reduced turbulent friction.

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arXiv2023

On the comparison between pre- and post-surgery nasal anatomies via computational fluid dynamics

Nasal breathing difficulties (NBD) are widespread and difficult to diagnose; the failure rate of their surgical corrections is high. Computational Fluid Dynamics (CFD) enables diagnosis of NBD and surgery planning, by comparing a pre-operative (pre-op) situation with the outcome of virtual surgery (post-op). An equivalent comparison is involved when considering distinct anatomies in the search for the functionally normal nose. Currently, this comparison is carried out in more than one way, under the implicit assumption that results are unchanged, which reflects our limited understanding of the driver of the respiratory function. The study describes how to set up a meaningful comparison. A pre-op anatomy, derived via segmentation from a CT scan, is compared with a post-op anatomy obtained via virtual surgery. State-of-the-art numerical simulations for a steady inspiration carry out the comparison under three types of global constraints, derived from the field of turbulent flow control: a constant pressure drop (CPG) between external ambient and throat, a constant flow rate (CFR) through the airways and a constant power input (CPI) from the lungs can be enforced. A significant difference in the quantities of interest is observed depending on the type of comparison. Global quantities (flow rate, pressure drop, nasal resistance) as well as local ones are affected. The type of flow forcing affects the outcome of the comparison between pre-op and post-op anatomies. Among the three available options, we argue that CPG is the least adequate. Arguments favouring either CFR or CPI are presented.

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arXiv2023

Curvature effects on the structure of near-wall turbulence

The interaction between near-wall turbulence and wall curvature is described for the incompressible flow in a plane channel with a small concave-convex-concave bump on the bottom wall, with height comparable to the wall-normal location of the main turbulent structures. The analysis starts from a database generated by a direct numerical simulation and hinges upon the anisotropic generalised Kolmogorov equations, i.e. the exact budget equations for the second-order structure function tensor. The influence of the bump on the wall cycle and on the energy production, redistribution and transfers is described in the physical and scale spaces. Over the upstream side of the bump, the energy drained from the mean flow to sustain the streamwise fluctuations decreases, and the streaks of high and low streamwise velocity weaken and are stretched spanwise. After the bump tip, instead, the production of streamwise fluctuations grows and the streaks intensify, progressively recovering their characteristic spanwise scale. The wall-normal fluctuations, and thus the quasi-streamwise vortices, are sustained by the mean flow over the upstream side of the bump, while energy flows from the vertical fluctuations to the mean field over the downstream side. On the concave portion of the upstream side, the near-wall fluctuations form structures of spanwise velocity which are consistent with Taylor-Görtler vortices at an early stage of development. Their evolution is described by analysing the scale-space pressure-strain term. A schematic description of the bump flow is presented, in which various regions are identified according to the signs of curvature and streamwise pressure gradient.

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arXiv2023

On-off pumping for drag reduction in a turbulent channel flow

We show that the energy required by a turbulent flow to displace a given amount of fluid through a straight duct in a given time interval can be reduced by modulating in time the pumping power. The control strategy is hybrid: it is passive, as it requires neither a control system nor control energy, but it manipulates how pumping energy is delivered to the system (as in active techniques) to increase the pumping efficiency. Our control employs a temporally periodic pumping pattern, where a short and intense acceleration (in which the pumping system is on) followed by a longer deceleration (in which the pumping system is off) makes the flow alternately visit a quasi-laminar and a turbulent state. The computational study is for a plane channel flow, and employs direct numerical simulations, which present specific computational challenges, for example the highly varying instantaneous value of the Reynolds number, and the importance of discretisation effects. Particular care is devoted to a meaningful definition of drag reduction in the present context. The ability of the forcing to yield significant savings is demonstrated. Since only a small portion of the parameter space is investigated, the best performance of the control technique remains to be assessed.

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