arXiv subjects

Miguel A. Mendez

Publications and source records attributed to Miguel A. Mendez.

At least 19 recordsLinked to original sources

arXiv2026

Linear feedback control of liquid film on moving substrate via free-surface stresses

Liquid films on moving substrates are used in dip-coating processes to form uniform protective layers. Controlling free-surface waves is essential due to the film's inherent linear instability. Therefore, we develop a linear feedback controller to regulate the film toward a desired flat state by modulating the free-surface shear and pressure, with feedback gains derived analytically from linearised equations. Control performance is assessed for finite-amplitude waves using a Weighted Integral Boundary-Layer (WIBL) model at reduced Reynolds number $δ= 8$. We identify parameter regimes in which pressure feedback is linearly destabilising while shear is stabilising, and vice versa, with the control mechanisms determined by the balance between the kinematic and dynamic wave velocities. Both stabilising and destabilising combinations of feedback coefficients can drive finite-amplitude waves toward the flat state $\bar{h}=1.1$ in finite time. In pressure-unstable regimes, the control induces a limit-cycle behaviour, in which long waves decay slowly due to the interplay between thickness and slope terms. The travelling-wave solution, although it decays slowly, moves against gravity, whereas other combinations reduce the wave amplitude in the direction of uncontrolled propagation. These results provide a foundation for higher-Reynolds-number studies and the design of industrially feasible actuator layouts.

physics.flu-dyn↗

arXiv2026

A Fast Spectral Formulation of the Multiscale Proper Orthogonal Decomposition

Multiscale Proper Orthogonal Decomposition (mPOD) decomposes fluid flows into energy-optimal modes within prescribed frequency bands by combining Proper Orthogonal Decomposition with a multiresolution analysis (MRA). In its classical formulation, mPOD relies on a filter bank of finite impulse response (FIR) filters, enabling lossless reconstruction while mitigating Gibbs oscillations and temporal ringing. However, the smooth transition bands required for this purpose introduce partial spectral overlap between adjacent scales and require, for each band, the solution of an eigenvalue problem spanning the full temporal dimension. This work introduces a fast spectral formulation of the mPOD that substantially reduces the computational cost. The proposed approach replaces time-domain FIR filters with compact spectral masks enforcing strictly disjoint frequency supports, thereby exactly decoupling the problem across scales. This leads to a block-diagonal correlation operator in spectral space, so that each band can be treated independently. The resulting eigenvalue problems reduce to small systems whose size depends on the number of active frequencies per band rather than the full time dimension. The approach is validated on a synthetic dataset highlighting spectral windowing effects and on experimental particle image velocimetry (PIV) data of a cylinder wake at Reynolds number $\mbox{Re} \approx 5000$. In both cases, the proposed formulation accurately recovers the modal structures and singular values of the classical mPOD while reducing the computational cost by orders of magnitude.

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arXiv2026

Nonlinear System Identification of Variable-Pitch Propellers Using a Wiener Model

This work presents the system identification of a variable-pitch propeller (VPP) powertrain, encompassing the full actuation chain from PWM signals to thrust generation, with the aim of developing compact models suitable for real-time digital twinning and control applications. The identification is grounded in experimental data covering both static and dynamic responses of the system. The proposed model takes the form of a Wiener-like architecture, where the PWM inputs are first processed through linear first-order dynamics describing the motor and pitch actuation, and the resulting states are then mapped via a static nonlinear relation to the generated thrust. This structure naturally arises under the assumptions that the electronic actuation operates on a much faster time scale than the mechanical response, and that the contribution of the aerodynamically induced torque is negligible in the tested regime. The resulting parsimonious representation is shown to reproduce the measured dynamics with good accuracy while remaining interpretable and computationally light, thereby providing a practical basis for integration in control-oriented digital twin frameworks.

eess.SY↗

arXiv2026

A meshless data-tailored approach to compute statistics from scattered data with adaptive radial basis functions

Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements, particularly in image-based velocimetry. However, existing formulations based on isotropic kernels often suffer from spurious oscillations in regions with sharp gradients or strong flow anisotropy. This work introduces an anisotropic, gradient-informed, and adaptively sampled extension of the constrained RBF framework for regression of scattered data. Gradient information is estimated via local polynomial regression at collocation points, smoothed, and used to (1) re-sample data, maximizing sampling density near steep gradients while downsampling in smooth regions, and (2) construct a local anisotropic metric that shapes each basis function according to the flow directionality. In addition, a gradient-informed regularization is introduced by embedding observed gradients into the least-squares system as weighted soft constraints. The resulting formulation is fully meshless, linear, and computationally efficient, while significantly improving reconstruction quality in challenging regions. The method is evaluated on both synthetic and experimental datasets, including direct numerical simulation (DNS) data of a turbulent channel and time-resolved particle tracking velocimetry of a turbulent jet. Results show that the proposed approach outperforms isotropic and gradient-free RBF formulations in accuracy, smoothness, and physical consistency -- particularly near shear layers and boundaries -- while reducing the number of bases by an order of magnitude. To support the application, we have created a repository (https://github.com/mendezVKI/SPICY_VKI) that provides access to the investigated datasets.

physics.flu-dyn↗

arXiv2026

Integral modelling and Reinforcement Learning control of 3D liquid metal coating on a moving substrate

Metallic coatings are used to enhance the durability of metal surfaces by protecting them from corrosion. These protective layers are typically deposited in a fluid state via a liquid film. Controlling instabilities in the liquid film is crucial to achieving uniform, high-quality coatings. This study explores the possibility of controlling liquid films on a moving substrate using a combination of gas jets and electromagnetic actuators. To model the 3D liquid film, we extend existing integral models to incorporate the effects of electromagnetic actuators. The control strategy was developed within a reinforcement learning framework, in which the Proximal Policy Optimisation (PPO) algorithm interacts with the liquid film via pneumatic and electromagnetic actuators to optimise a reward function that accounts for instability-wave amplitude through a trial-and-error process. The PPO identified an optimal control law that reduced interface instabilities via a novel mechanism: gas jets push crests, and electromagnets raise troughs via the Lorentz force.

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arXiv2025

On the complex interplay of temperature, phase change and natural convection in self-pressurization-an investigation using segregated modeling

Accurate prediction of self-pressurization in cryogenic tanks requires resolving the coupled effects of heat ingress, natural convection, and phase change. This work introduces a segregated numerical framework in which the liquid and vapor phases are treated with incompressible and compressible solvers, respectively, and the liquid-vapor interface is modeled as a sharp boundary subject to energy-jump conditions derived from first principles, without accommodation or tuning coefficients. Conjugate heat transfer through the tank walls is accounted for by solving the heat-conduction equation in the solid domain rather than prescribing external heat-flux conditions. The framework is validated against laboratory-scale LN2 and large-scale LH2 experiments, reproducing the spatio-temporal evolution of pressure and temperature without adjustable parameters. In both settings, the simulations identify two distinct regimes in self-pressurization: an initial heating-driven phase that establishes a self-similar temperature profile in the vapor, followed by an evaporation-driven phase in which the pressure rise is governed by the saturation relation. The comparison between these largely different scales motivated a revised scaling for self-pressurization, based on ullage thermodynamics. Finally, the influence of buoyancy was examined by reducing the strength of the gravitational body force, which revealed that natural convection modifies the duration of the transient heating phase but has a limited impact on the long-term pressurization rate. This analysis also clarifies the mechanism controlling the development of thermal stratification in the liquid. Overall, the segregated approach provides a predictive, parameter-free tool for analyzing cryogenic storage and offers a physically grounded basis for scaling self-pressurization across fluids, geometries, and heat-flux conditions.

physics.flu-dyn↗

arXiv2025

Regime Maps for Sloshing in Horizontal Cylindrical Tanks Under Vertical Acceleration

Vertical sloshing in partially filled fuel tanks can significantly impact vehicle stability and structural integrity, particularly under harmonic accelerations near twice the sloshing natural frequency. In this regime, parametric resonance may arise, with nonlinear free-surface dynamics driving large-amplitude waves, interface break-up, and severe sloshing-induced mixing. In this work, we identify and characterize the distinct sloshing regimes associated with the lowest-frequency parametric instability, specifically when the external forcing frequency approaches twice the lowest natural frequency. Experiments were conducted in a transparent cylindrical tank with diameter D = 134.5 mm and length L = 336.3 mm. This work presents a data-driven approach for regime identification and classification that relies solely on high-speed video recordings and circumvents the need for interface tracking. The method combines prototype-based data labeling with dimensionality reduction via multiscale proper orthogonal decomposition (mPOD) and automatic kernel-based classification. The results are summarized in a dimensionless regime map across three fill ratios, where stable waves, longitudinal and transverse mode shapes, and mode-competition regimes are distinguished. The developed map provides a predictive tool for assessing sloshing-induced loads, supporting structural and operational optimization of fuel systems.

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arXiv2025

Learning with Physical Constraints

This chapter provides three tutorial exercises on physics-constrained regression. These are implemented as toy problems that seek to mimic grand challenges in (1) the super-resolution and data assimilation of the velocity field in image velocimetry, (2) data-driven turbulence modeling, and (3) system identification and digital twinning for forecasting and control. The Python codes for all exercises are provided in the course repository.

physics.flu-dyn↗

arXiv2025

Fundamentals of Regression

This chapter opens with a review of classic tools for regression, a subset of machine learning that seeks to find relationships between variables. With the advent of scientific machine learning this field has moved from a purely data-driven (statistical) formalism to a constrained or ``physics-informed'' formalism, which integrates physical knowledge and methods from traditional computational engineering. In the first part, we introduce the general concepts and the statistical flavor of regression versus other forms of curve fitting. We then move to an overview of traditional methods from machine learning and their classification and ways to link these to traditional computational science. Finally, we close with a note on methods to combine machine learning and numerical methods for physics

stat.ML↗

arXiv2025

On the choking mechanism in supersonic ejectors: a one-dimensional analysis of Reynolds-Averaged Navier Stokes simulations

Ejectors are passive devices used in refrigeration, propulsion, and process industries to compress a secondary stream without moving parts. The engineering modeling of choking in these devices remains an open question, with two mechanisms-Fabri and compound choking-proposed in the literature. This work develops a unified one-dimensional framework that implements both mechanisms and compares them with axisymmetric Reynolds-Averaged Navier Stokes (RANS) data processed by cross-sectional averaging. The compound formulation incorporates wall and inter-stream friction and a local pressure-equalization procedure that enables stable integration through the sonic point, together with a normal shock reconstruction. The Fabri formulation is assessed by imposing the dividing streamline extracted from RANS, isolating the sonic condition while avoiding additional modeling assumptions. The calibrated compound model predicts on-design secondary mass flow typically within 2 % with respect to the RANS simulations, rising to 5 % for a strongly under-expanded primary jet due to the equal-pressure constraint. The Fabri analysis attains less than 1 % error in on-design entrainment but exhibits high sensitivity to the dividing streamline and closure, which limits predictive use beyond on-design. Overall, the results show that Fabri and compound mechanisms can coexist within the same device and operating map, each capturing distinct aspects of the physics and offering complementary modeling value. Nevertheless, compound choking emerges as the more general mechanism governing flow rate blockage, as evidenced by choked flows with a subsonic secondary stream.

physics.flu-dyn↗

arXiv2025

POD-Based Sparse Stochastic Estimation of Wind Turbine Blade Vibrations

This study presents a framework for estimating the full vibrational state of wind turbine blades from sparse deflection measurements. The identification is performed in a reduced-order space obtained from a Proper Orthogonal Decomposition (POD) of high-fidelity aeroelastic simulations based on Geometrically Exact Beam Theory (GEBT). In this space, a Reduced Order Model (ROM) is constructed using a linear stochastic estimator, and further enhanced through Kalman fusion with a quasi-steady model of azimuthal dynamics driven by measured wind speed. The performance of the proposed estimator is assessed in a synthetic environment replicating turbulent inflow and measurement noise over a wide range of operating conditions. Results demonstrate the method's ability to accurately reconstruct three-dimensional deformations and accelerations using noisy displacement and acceleration measurements at only four spatial locations. These findings highlight the potential of the proposed framework for real-time blade monitoring, optimal sensor placement, and active load control in wind turbine systems.

eess.SY↗

arXiv2025

Statistical Methods and Modal Decompositions for Gridded and Scattered Data: Meshless Statistics and Meshless Data Driven Modal Analysis

Statistical tools are crucial for studying and modeling turbulent flows, where chaotic velocity fluctuations span a wide range of spatial and temporal scales. Advances in image velocimetry, especially in tracking-based methods, now allow for high-speed, high-density particle image processing, enabling the collection of detailed 3D flow fields. This lecture provides a set of tutorials on processing such datasets to extract essential quantities like averages, second-order moments (turbulent stresses) and coherent patterns using modal decompositions such as the Proper Orthogonal Decomposition (POD). After a brief review of the fundamentals of statistical and modal analysis, the lecture delves into the challenges of processing scattered data from tracking velocimetry, comparing it to traditional gridded-data approaches. It also covers research topics, including physics-based Radial Basis Function (RBF) regression for meshless computation of turbulent statistics and the definition of an RBF inner product, which enables meshless computation of data-driven decompositions. These include traditional methods like Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD), as well as advanced variants such as Spectral POD (SPOD) and Multiscale POD (mPOD). We refer to this approach as the "Meshless Data-Driven Decomposition" framework. All codes are available at https://github.com/mendezVKI/PIV_LS_2024_Signal

physics.flu-dyn↗

arXiv2025

A meshless and binless approach to compute statistics in 3D Ensemble PTV

We propose a method to obtain superresolution of turbulent statistics for three-dimensional ensemble particle tracking velocimetry (EPTV). The method is ''meshless'' because it does not require the definition of a grid for computing derivatives, and it is ''binless'' because it does not require the definition of bins to compute local statistics. The method combines the constrained radial basis function (RBF) formalism introduced Sperotto et al. (Meas Sci Technol, 33:094005, 2022) with a kernel estimate approach for the ensemble averaging of the RBF regressions. The computational cost for the RBF regression is alleviated using the partition of unity method (PUM). Three test cases are considered: (1) a 1D illustrative problem on a Gaussian process, (2) a 3D synthetic test case reproducing a 3D jet-like flow, and (3) an experimental dataset collected for an underwater jet flow at $\text{Re} = 6750$ using a four-camera 3D PTV system. For each test case, the method performances are compared to traditional binning approaches such as Gaussian weighting (Agüí and Jiménez, JFM, 185:447-468, 1987), local polynomial fitting (Agüera et al, Meas Sci Technol, 27:124011, 2016), as well as a binned version of the RBF statistics.

physics.flu-dyn↗

arXiv2024

On the unsteady aerodynamics of flapping wings under dynamic hovering kinematics

Hummingbirds and insects achieve outstanding flight performance by adapting their flapping motion to the flight requirements. Their wing kinematics can change from smooth flapping to highly dynamic waveforms, generating unsteady aerodynamic phenomena such as leading-edge vortices (LEV), rotational circulation, wing wake capture, and added mass. This article uncovers the interactions of these mechanisms in the case of a rigid semi-elliptical wing undergoing aggressive kinematics in the hovering regime at $Re\sim \mathcal{O}(10^3)$. The flapping kinematics were parametrized using smoothed steps and triangular functions and the flow dynamics were simulated by combining the overset method with Large Eddy Simulations (LES). The analysis of the results identifies an initial acceleration phase and a cruising phase. During the former, the flow is mostly irrotational and governed by the added mass effect. The added mass was shown to be responsible for a lift first peak due to the strong flapping acceleration. The dynamic pitching and the wing wake interaction generate a second lift peak due to a downwash flow and a vortex system on the proximal and distal parts of the wing's pressure side. Conversely, aerodynamic forces in the cruising phase are mainly governed by the growth and the establishment of the LEV. Finally, the leading flow structures in each phase and their impact on the aerodynamic forces were isolated using the extended Proper Orthogonal Decomposition (POD).

physics.flu-dyn↗

arXiv2024

Reinforcement Twinning: from digital twins to model-based reinforcement learning

Digital twins promise to revolutionize engineering by offering new avenues for optimization, control, and predictive maintenance. We propose a novel framework for simultaneously training the digital twin of an engineering system and an associated control agent. The twin's training combines adjoint-based data assimilation and system identification methods, while the control agent's training merges model-based optimal control with model-free reinforcement learning. The control agent evolves along two independent paths: one driven by model-based optimal control and the other by reinforcement learning. The digital twin serves as a virtual environment for confrontation and indirect interaction, functioning as an "expert demonstrator." The best policy is selected for real-world interaction and cloned to the other path if training stagnates. We call this framework Reinforcement Twinning (RT). The framework is tested on three diverse engineering systems and control tasks: (1) controlling a wind turbine under varying wind speeds, (2) trajectory control of flapping-wing micro air vehicles (FWMAVs) facing wind gusts, and (3) mitigating thermal loads in managing cryogenic storage tanks. These test cases use simplified models with known ground truth closure laws. Results show that the adjoint-based digital twin training is highly sample-efficient, completing within a few iterations. For the control agent training, both model-based and model-free approaches benefit from their complementary learning experiences. The promising results pave the way for implementing the RT framework on real systems.

eess.SY↗

arXiv2024

Capillary driven flows in microgravity

This work investigates the capillary rise dynamics of highly wetting liquids in a divergent U-tube in the microgravity conditions provided by 78th European Space Agency (ESA) parabolic flight. This configuration produces a capillary-driven channel flow. We use image recording in backlight illumination to characterize the interface dynamics and dynamic contact angle of HFE7200 and Di-Propylene Glycol (DPG). For the case of HF7200, we complement the interface measurements with Particle Tracking Velocimetry (PTV) to characterize the velocity fields underneath the moving meniscus. In the experiments with DPG, the liquid column reaches different heights within various experiments, and the measurements show a sharp reduction of the meniscus curvature when the contact line moves from a pre-wet to a dry substrate. In experiments with HFE7200, the interface always moves on a pre-wet surface. Yet a curvature reduction is observed due to the inertial forces on the underlying accelerating flow. The PTV measurements show that the distance from the interface within which the velocity profile adapts to the meniscus velocity shortens as the interface acceleration increases.

physics.flu-dyn↗

arXiv2023

Characterization of a capillary driven flow in microgravity by means of optical technique

The motion of a gas-liquid interface along a solid wall is influenced by the capillary forces resulting from the interface's shape and its interaction with the solid, where it forms a dynamic contact angle. Capillary models play a significant role in the management of cryogenic propellants in space, where surface tension dominates the behaviour of gas-liquid interfaces. Yet, most empirical models have been derived in configurations dominated by viscous forces. In this study, we experimentally investigate the wetting of a low-viscosity, highly wetting fluid in a reduced gravity environment. Our setup consisted of a transparent and diverging U-tube in which capillary forces sustain the liquid motion. Combining Particle Image Velocimetry (PIV) and high-speed backlighting visualization, the experimental campaign allowed for measuring the interface evolution and the velocity field within the liquid under varying gravity levels. This work reports on the preliminary results from the image velocimetry and shows that the velocity profile within the tube is close to parabolic until a short distance from the interface. Nevertheless, classic 1D models for capillary rise face difficulties reproducing the interface dynamics, suggesting that the treatment of the surface tension in these problems must be reviewed.

physics.flu-dyn↗

arXiv2023

On the coupling instability of a gas jet impinging on a liquid film

We investigate the dynamics of a gas jet impinging on a thin liquid film. This configuration is relevant to the jet-wiping process and is unstable. In particular, we complement previous works that focused on the wiping of liquids with low Kapitza numbers (highly viscous liquids) by numerically analyzing the wiping of liquids with much higher Kapitza numbers, more relevant to industrial processes. The simulations are carried out by combining Volume of Fluid (VOF) and Large Eddy Simulation (LES), and the dynamics of the gas-liquid interaction is analyzed using extended multiscale Proper Orthogonal Decomposition (emPOD). The resolution and flow details captured by the simulations are unprecedented. The results show that, despite the vastly different wiping conditions, the dynamics of the gas-liquid interaction is remarkably similar. This opens new avenues to the study and the scaling of the jet-wiping process.

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