2025 Archive

Abstract: Typical unsteady vortex-dominated flows like those involved in bio-inspired propulsion, airfoil separation, bluff body wakes, and vortex-induced vibrations can be prohibitively expensive to simulate and impossible to measure comprehensively. These examples are governed by non-linear interactions, and often involve moving boundaries, high-dimensional parameter spaces, and multi-scale flow structures. The classical way to get around these challenges is to reduce the experimental complexity by using canonical motions or simplified unsteady inflow conditions. To complement these canonical experiments, we can design self-exploring automated experiments that combine the automation of the experimental pipeline with data-science tools to increase experimental throughput and expedite scientific discovery. Such automated experiments can explore and exploit higher-dimensional parameter spaces and potentially cover more realistic and technically relevant unsteady conditions compared to what is traditionally feasible with supervised canonical experiments. 

In this tutorial, we will provide examples and share experiences on how to design and improve your own self-exploring automated experiment, with special attention to cyber-physical systems. 

Biography: Karen Mulleners is an associate professor in the institute of mechanical engineering in the school of engineering at EPFL. She is the head of the unsteady flow diagnostics laboratory (UNFoLD). She is an experimental fluid dynamicist who focuses on unfolding the origin and development of unsteady flow separation and vortex formation. Karen studied physics in Belgium (Hasselt University, previously Limburgs Universitair Centrum) and the Netherlands (TU Eindhoven). She received her PhD in mechanical engineering from the Leibniz Universität Hannover in Germany in 2010 for her work on dynamic stall on pitching airfoils that she conducted as a member of the German aerospace centre (DLR) in Göttingen. Before joining EPFL in 2016, Karen was a (non-tenure track) assistant professor at the Leibniz Universität Hannover in Germany.

Abstract: Phononic materials (PMs) are periodic structures known for their unique elastodynamic properties. Beyond their traditional role in vibration mitigation, recent investigations have revealed their ability to passively and adaptively influence flow behavior through fluid–structure interaction (FSI). For instance, PMs can delay laminar–turbulent transition and reduce unsteadiness in shock–boundary-layer interactions. Despite these advances, there remains no systematic framework linking specific PM behaviors to the resulting FSI dynamics, an essential step toward understanding and designing coupled fluid–solid systems. Moreover, dynamical quantities often overlooked in conventional PM modeling, such as vibration amplitude, become critical in FSI contexts.

To address this gap, we introduce a behavioral framework for PM–FSI systems that identifies key parameters governing the coupled response. These behavioral parameters, distinct from, yet mappable to, the PM’s structural descriptors, capture the effective stiffness, truncation resonance frequency, dynamic displacement amplitude, and unit-cell mass of the material. Using high-fidelity, strongly coupled simulations of laminar flow past a flat plate embedded with a PM section, we quantify how these parameters modulate the spectral features of the vortex-shedding process. The results reveal clear relationships between each behavioral parameter and the corresponding lift-coefficient signatures in the FSI response. While this study focuses on aerodynamic configurations, the proposed framework provides a general foundation for investigating and designing phononic materials in fluid environments.

Abstract: The vortex-dominant wake of a transverse cylinder has been extensively studied. Among various configurations, the spinning of the cylinder about its axis shows prominent changes in the behavior of the vortex street due to the asymmetric influence of rotation on the flow passing the cylinder. Vortex shedding can be modulated or even suppressed at certain rotation rates, thereby altering the drag and lift. This study focuses on a rotating cylinder subjected to a uniform incoming flow with periodic temporal variations, a more realistic condition than the idealized assumption of steady flow often used in engineering design and analysis. Wall-resolved large-eddy simulations are performed for a cylinder at ReD = U∞D/ν = 2580, where U∞ is the mean incoming flow velocity. The inflow velocity is modulated sinusoidally around the mean by 10% or 20% (peak to trough). For cylinder rotation, the linear velocity on the cylinder surface (Us) is set to 0, 1.36U∞, and 2.72U∞ for the stationary, slow-spinning, and fast-spinning cases, respectively. Previous studies showed that Us = 1.91U∞ is a threshold beyond which vortex shedding ceases to occur, but such stabilization is disrupted by the pulsation in the present study. Results show that pulsation does not alter the mean lift generated by the cylinder. However, rotation suppresses the unsteady lift response induced by pulsation relative to that of a stationary cylinder. While pulsation enhances both the mean and fluctuating components of drag, rotation significantly reduces the mean drag penalty but has little influence on the pulsating fluctuation. These results shed light on the unsteady aerodynamic behavior of rotating cylinders, which is relevant to engineering applications such as thrust generation in rotor ships, stabilization of spinning projectiles, and vibration control in rotating propulsion shafts.

Abstract: Kirigami-inspired surfaces passively deform in fluid flows, offering a novel approach for applications in adaptive aerodynamic control, drag reduction, and renewable energy harvesting. We experimentally investigate how the cutting pattern can be used to control aerodynamic forces.  First, the cutting pattern and base material’s Young’s modulus govern the sheet’s effective stiffness, which sets its resistance to fluid-induced deformation, as quantified by the Cauchy number. As the kirigami opens, the resulting flow permeability causes the drag to fall below the quadratic force-velocity scaling typical of rigid bodies.  Second, specific cutting patterns trigger out-of-plane buckling of the elements created by the cuts. We show that by strategically designing the pattern to control the rotation and orientation of these buckled elements, we can generate and finely tune lift forces. Critically, we demonstrate independent control over lift and drag: drag on a kirigami can be varied by more than a factor of two at a constant lift, and lift can be adjusted with minimal change in drag. This work establishes a direct link between kirigami geometry, its resulting flow-induced deformations, and the aerodynamic performance, paving the way for smart, adaptive surfaces for flow manipulation.

Abstract: Flapping-wing turbines (FWTs) – oscillating wings rather than radial rotors – represent an innovative clean renewable source and have shown competitive power extraction efficiencies relative to conventional rotary turbines, as demonstrated in literature with high-fidelity simulations and limited experiments on physical prototypes. Although interest in FWTs is growing, design optimization, adaptability and reliability have proven difficult for field implementation due to the high-order parameter design space that defines interactions between aerodynamics, wing motion, and energy extraction. Current engineering design approaches involve extensive computer simulations coupled with optimization solvers or trial-and-error experiments which are both time and resource intensive tools. The motivation for the current work was to provide insights into the governing dynamics informing practical design guidelines. An experimental setup was developed and equipped with synchronized high precision force measurements along with streaked particle imaging for Leading Edge Vortex (LEV) evolution observations. A parameter space sweep across varied reduced frequencies, pitch amplitudes, Reynolds numbers, and blockage ratios was conducted to assess the impact of LEV and kinematic motion synchronization on performance. Complementing the experimental study, a low-order unsteady flow solver was used to predict performance trends between optimal cases with LEVs present versus cases with attached flow as Reynolds number increased. Results from the solver were compared against the experiments instantaneous force data and streaked particle images to validate the methodology before extending the parameter space to higher simulated Reynolds numbers. The results indicate that while overall optimum performance often coincides with the presence of an LEV, comparable performance can be achieved under attached flow conditions, which is desirable for practical design and implementation of these systems.

Abstract: Wall-bounded flows in nature and engineering applications are often modulated by near-wall structures through the vortices shed in their wakes. In this study, we investigate the influence of a small circular cylinder placed with its axis aligned in the spanwise direction of a turbulent boundary layer (TBL). Direct numerical simulations are conducted with either a stationary or a rotating cylinder. The cylinder has diameter D=0.1δ (where δ is the TBL thickness) and is centered at y=0.1δ, following the experimental setup in Ribeiro et al. (2023). At the friction Reynolds number of 220, this setup is designed to disturb both the buffer layer and the upper part of the log layer. The cylinder rotates opposite to the mean-shear vorticity, thereby counteracting it. Preliminary results show periodic vortex shedding from the cylinder that substantially energizes the TBL. The rotation produces a Kármán vortex street with a shedding frequency different from the stationary case. As expected from wall proximity (ground effect) and spanwise inhomogeneity associated with ambient TBL structures, the wake is asymmetric. Its impact on the characterization of the TBL is discussed via statistics and temporal-spatial analysis. 

Abstract: Geophysical fluid dynamics (GFD) refers to fluid dynamics on a rotating sphere where the rotation plays an important role in the behavior of the fluid. GFD is important in understand the atmosphere and ocean, as well as planetary science. In this talk, I discuss a use of the vortex semi-Lagrangian method for the barotropic vorticity equation on a rotating sphere and some applications to understanding atmospheric phenomenon. 

Abstract: Understanding the physics of flow-structure interactions (FSI) is crucial to developing next-level passive, adaptive flow control strategies for unmanned aerial vehicles operating in vortex-dominated, low Reynolds number regimes. High-fidelity simulation tools that compute the nonlinearly coupled flow-surface interplay are key to enabling this understanding. Developing a robust, high-fidelity simulation framework for FSI presents several challenges that remain an area of active research. An important challenge revolves around the treatment of the body within the flow grid, potentially involving complex modifications to the underlying flow solver, such as altering stencils or embedding costly linear solves that can significantly increase the cost compared with body-less solvers. To overcome these challenges, we present a new immersed method, Interface-manifold aware projection (IMAP). This technique provides a fast, novel, non-intrusive simulation framework for complex flow-structure interactions. IMAP's approach is rooted in viewing the no-slip constraint as a manifold within which the flow evolves. The method centers on constructing projections to constrain the dynamics to this manifold before time advancement. These projection steps leverage standard immersed-boundary operators and are built from small, surface-local operators that do not involve large-dimensional linear systems. IMAP eliminates the need for costly embedded solves inherent to many projection-based immersed boundary methods, as well as stencil modifications associated with other immersed boundary methods. In this talk, we introduce the methodology behind the approach and demonstrate results for two-dimensional channel flow past a cylinder.

Abstract: Flow reattachment is the final stage of the dynamic stall cycle, where the lift coefficient recovers to its quasi-static value after being lost due to flow separation. In this study, we analyze the reattachment process of a sinusoidally pitching airfoil using pressure and flow field data to identify the dynamics of the unsteady reattachment process. In unsteady conditions, decreasing angle of attack below critical stall angle is insufficient to trigger recovery. We identify a necessary condition for recovery onset by analyzing the leading-edge suction parameter. The recovery consistently begins after the leading edge suction parameter exceeds a critical threshold independent of the pitch rate. Once the critical leading edge suction parameter is reached, the shear layer reattaches to the airfoil in a wave-like motion from the leading to the trailing edge. Shear layer reattachment ends when the wave reaches the trailing edge, followed by boundary layer reattachment. The boundary layer reattachment concludes the recovery process, and the lift coefficient recovers to its quasi-static value. The wave propagation onset is delayed relative to when the angle of attack falls below the critical stall angle. The onset delay depends on the pitch rate, but the durations of wave propagation and boundary layer reattachment states are independent of the pitch rate. Understanding the characteristic timescales of the recovery process can lead to more accurate reattachment predictions and better control strategies for dynamic stall.

Abstract: A flow control framework based on linear stability analysis is proposed focusing on reducing the aerodynamic drag due to dynamic stall through a finite-window temporal actuation. The methodology is applied on a periodically plunging SD7003 airfoil. Finite-time Lyapunov exponent (FTLE) fields reveal a saddle point near the  airfoil leading edge, where a shear layer forms and feeds a dynamic stall vortex (DSV).  A local stability analysis conducted at this saddle point identifies a Kelvin-Helmholtz instability, and the most unstable eigenvalue frequencies remain constant when the variation in the effective angle of attack is minimal. The findings from the FTLE fields and the stability analysis are used to inform the position and finite duty cycle of a periodic blowing and suction actuation applied in a wall-resolved large eddy simulation (LES). The present framework reduces the actuation duty cycle by 77.5\% during the airfoil plunging motion, while maintaining the same performance as a continuous actuation throughout the entire cycle. The LES results demonstrate that disturbances from the stability-analysis-informed actuation modify the leading-edge dynamics, preventing the formation of the coherent DSV and significantly reducing the drag.

Abstract: This study investigates the impact of surface indentations, shaped as dimples, on the flow dynamics of a pitching foil under zero-freestream conditions. A series of systematic experiments were conducted employing flow field measurements using Particle Image Velocimetry. The dimple depth ratio (d/D, where d is the dimple depth and D is the dimple diameter) was varied from 0.022 to 0.088 across Reynolds numbers (defined based on the maximum trailing edge velocity and foil chord) of 3700, 10000 and 20000. The impact of dimples on the wake characteristics was evaluated by analyzing the time-averaged jet behavior and vortex dynamics. The results reveal that the deepest dimpled case modified the far wake of the pitching foil, particularly at higher Reynolds numbers. Under these conditions, the vortices shed from the trailing edge persisted longer, and the jet exhibited greater coherence. The dimples appear to influence dipole interactions in the wake, reducing the jet deflection. These findings suggest that surface roughness can be strategically employed to modulate wake dynamics and improve the stability of the jet, potentially enhancing the propulsion efficiency of bio-inspired flapping foil systems.

Abstract: The role of (active) dynamic wing twist on aerodynamic performance of three-dimensional hovering flapping flight is explored using numerical simulations. A variety of cases with different pitch angles and with (flexible wings) or without (rigid wings) dynamic twist are compared.In some cases dynamic twist yields enhanced time-averaged efficiency. Using the force and power partitioning method (an adaptation of FMPM), it is shown that this enhancement results from the absence of vortical structures near the wing root lower surface and to the presence of an extended leading edge vortex on the wing upper surface, when compared to the most efficient rigid wing case. These differences in flow topology lead to enhanced lift during the early phase of the strokes without changes in power consumption.

Abstract: Ocean monitoring tools yield extensive data for understanding climate change but energy consumption is a limiting factor for mission duration. In contrast, Aurelia aurita jellyfish have a cost of transport 97% lower than some underwater vehicles and are adaptable to a wide range of ocean environments. Here we explore mechanically modifying jellyfish bells with added forebodies to reduce hydrodynamic drag on swimming animals. By equipping jellyfish with microelectronic swim controllers, we create an ocean monitoring tool capitalizing on jellyfish regenerative capabilities paired with inexpensive electronics. Previous work has demonstrated stimulated jellyfish vertical swimming speeds of 2.8 times baseline speeds without swim controllers. We found that the combination of external swimming control and the addition of the mechanical forebody resulted in an increase in swimming speeds to 4.5 times natural jellyfish locomotion. Moreover, the biohybrid jellyfish were capable of carrying a payload volume up to 105% of the jellyfish body volume. The added payload decreased the intracycle acceleration of the biohybrid robots relative to natural jellyfish, which could also facilitate more precise measurements by onboard sensors that depend on consistent platform motion. While many robotic exploration tools are limited by cost, energy expenditure, and varying oceanic environmental conditions, this platform is inexpensive, highly efficient, and benefits from the widespread natural habitats of jellyfish. The demonstrated performance of these biohybrid robots suggests an opportunity to expand the set of robotic tools for comprehensive monitoring of the changing ocean.

Abstract: In this study, we numerically investigate the mechanism of the oscillatory flow dynamics associated with the tip vortex cavitation (TVC) over an elliptical hydrofoil section. Using our in-house three-dimensional variational multiphase flow solver, we investigate the TVC phenomenon via dynamic subgrid-scale modelling and the homogeneous mixture theory. To begin, we examine the grid resolution requirements and introduce a length scale considering both the tip vortex strength and the core radius. This length-scale is then employed to non-dimensionalize the spatial resolution in the tip vortex region, the results of which serve as a basis for estimation of the required mesh resolution in large eddy simulations of TVC. We next perform simulations to analyze the dynamical modes of tip vortex cavity oscillation at different cavitation numbers, and compare them with the semi-analytical solution. The breathing mode of cavity surface oscillation is extracted from the spatial-temporal evolution of the cavity's effective radius. The temporally averaged effective radius demonstrates that the columnar cavity experiences a growth region followed by decay as it progresses away from the tip. Further examination of the characteristics of local breathing mode oscillations in the growth and decay regions indicates the alteration of the cavity's oscillatory behavior as it travels from the growth region to the decay region, with the oscillations within the growth region being characterized by lower frequencies. For representative cavitation numbers  σ∈[1.2,2.6], we find that pressure fluctuations exhibit a shift of the spectrum towards lower frequencies as the cavitation number decreases, similar to its influence on breathing mode oscillations. The results indicate the existence of correlations between the breathing mode oscillations and the pressure fluctuations. While the low-frequency pressure fluctuations are found to be correlated with the growth region, the breathing mode oscillations within the decay region are related to higher-frequency pressure fluctuations.

Abstract: Accurate estimation of transient aerodynamic states is crucial for understanding unsteady flow dynamics and controlling aerodynamic performance. In this study, we investigate the use of machine learning to estimate the underlying low-order state-space representation of strongly disturbed aerodynamics from sparse, noisy pressure measurements recorded by sensors on a NACA airfoil. The uncertainty in the predicted states, affected by measurement noise, is also quantified.

Two complementary approaches are explored. In one framework, a neural network approximation is employed to directly infer a statistical representation of the aerodynamic state from surface pressure observations while accounting for model uncertainty. This approach captures the probabilistic nature of state estimation. In another framework, an online data assimilation methodology is pursued using learned surrogate models for the dynamics in a low-dimensional latent space. The models are then integrated with sequential filtering to improve state estimates using sequences of pressure observations.

Both approaches provide insight into the role of sensor placement, measurement noise, and model uncertainty in aerodynamic state estimation. The figure below illustrates the general overview of the estimation task using either approach, including pressure-to-state inference, uncertainty quantification, and reconstructed flow fields. This study contributes to advancing data-driven aerodynamic state estimation and uncertainty modeling in unsteady flows.

Abstract: As the drone delivery market grows, the need for higher payload capacity is driving the adoption of compact drone designs, including co-axial propellers. While overlapping propellers offer significant benefits, they also present challenges, particularly the noise they generate, which impacts public acceptance and drone adoption. To design efficient and quiet multi-rotor propulsion systems, a deeper understanding of aerodynamic noise sources is essential. In this study, we experimentally investigate the effect of axial separation distance on the interaction between coaxial counter-rotating propellers during hover conditions. Our measurements were conducted in a semi-anechoic room at the University of Southampton. Using a modular rig equipped with two two-bladed 16-inch diameter rotors, we varied the axial separation distance while maintaining a constant total thrust of 16 N and zero total torque. Our research focused on how separation distance influences the aerodynamic response of the system. We utilized force and phase-locked high-resolution low-speed Particle Image Velocimetry (PIV) measurements for both upstream and downstream rotors. In this presentation, we examine the wake of the upstream propeller for various separation distances to better understand the noise sources. Using the Γ₂ criteria, we identified the tip vortex positions and analyzed their meandering across different separation distances. Additionally, we assessed the strength and velocity profiles of these tip vortices. Finally, we compared rotor wakes with the Kocurek-Tangler wake model to quantify the impact of the added pressure gradient from the second rotor. Our results indicate that separation distance is a key factor influencing vortex meandering. For a given early wake age (within the first blade passing), our findings show that as the separation distance decreases, vortices convect faster to a more radially inward position, become weaker, and aperiodicity increases. 

Abstract: The wake of a wing undergoes a transition from two- to three-dimensional state via mode C instability along with the formation of hairpin vortex structures. The mode C instability exhibits a period-doubling mechanism and neither odd- nor even-RT symmetry. The spanwise wavelength is in good agreement with those from earlier studies for bluff body flows. The hairpin vortices are uniformly distributed along the span at the onset of three-dimensionality and interspersed at large Reynolds numbers (Re). The shear layer vortices interact with the flow close to the surface of the airfoil, leading to its reattachment and the formation of the Laminar Separation Bubble (LSB). The airfoil experiences a very significant increase in lift and decrease in drag at the formation of LSB. The flow past a finite wing is associated with a strong streamwise "wing-tip" vortex. The modification of vortex shedding and other flow structures due to wing-tip vortex is investigated. The flow is steady for low aspect ratio (AR) wings. Vortex shedding occurs in cells for high aspect ratio wings. Dislocations are of fork-, connected fork-, and mixed-type. A combination of fork- and reverse fork-type is formed as a consequence of splitting and reconnection of vortices. Unlike Prandtl's lifting line theory, the drag at low Re increases with an increase in AR. Viscous and pressure drag dominate for low and high AR, respectively. The streamwise vortices result in non-monotonic spanwise variation of local force coefficients and increased strength of wing-tip vortex. A discrete vortex model is proposed to explain this behaviour of the sectional lift coefficient. Rankine and Lamb–Oseen models are used to determine the core radius of wing-tip vortex. The geometric twist of a finite wing can be utilized to control the number of vortex shedding cells. Dislocations at the junction of neighbouring cells are of fork-type for wash-in and of reverse fork-type for wash-out. Despite a significant effect of the twist on the flow and spanwise variation of the local force coefficients, low to moderate twist of the wing has a relatively minor effect on the span-integrated force coefficients. Wash-in results in a decrease in unsteadiness in the flow and increased strength of wing-tip vortex. On the other hand, wash-out offers lower strength of wing-tip vortex and increased unsteadiness. The rate of increase of strength of wing-tip vortex with twist angle depends on the angle of attack at the wing-root. The wake of a nominally two-dimensional geometry of various cross sections, including airfoils and cylinders, is associated with similar three-dimensional instabilities. Flow past a cylinder in the presence of side walls is investigated numerically for various combinations of Re and aspect ratio. Various attributes such as cellular shedding, dislocations, oblique angle of vortices, and their structure near the end wall are studied. The vortices near the end wall diffuse for low Re, whereas linkages form between adjacent vortices of opposite polarity at larger Re. The end conditions and nonlinear mechanisms play a significant role in the evolution of cellular shedding. 

Abstract: Using the optimally time-dependent (OTD) mode analysis, we study the transient perturbation dynamics for a NACA0012 airfoil interacting with a vortex gust. The transient flow resulting from the vortex-airfoil interaction is taken to be the unsteady base flow.  Here, the gust ratio is taken to be G = {-1, -0.5, 0.5, 1}. The impingement of a vortex gust leads to massive flow separation and the formation of large-scale vortices near the airfoil within two convective time units. The highly unsteady nature of these interactions calls for the use of OTD mode analysis to capture the most amplified coherent structures with respect to the time-evolving base flow. For each gust ratio, the OTD modes highlight the most amplified region to perturbations, revealing its transient behaviors as the wake develops. With a moderate positive gust (G = 0.5), the region of the largest amplification shifts from the leading-edge vortex sheet to the nascent leading-edge vortex and subsequently resides in the wake near the airfoil trailing edge. On the other hand, strong gust-airfoil interactions (G = {-1,1}) show the most amplified area to reside near the core of the shed vortices. This study demonstrates the utility of OTD mode analysis for vortex gust-airfoil interactions and provides fundamental insights into the complex perturbation dynamics of unsteady aerodynamics problems.

Abstract: Flags are flexible membranes in a free stream, that align with the flow at low velocities. Beyond a critical velocity, the flag experiences fast deformations and an increase in drag. We experimentally investigate the flapping dynamics of different aspect ratio flags in the post critical regime. In this regime, time-resolved deformation measurements from event-based imaging reveal that the flag deflection propagates as a travelling wave toward the free end of the flag with a speed close to the free stream velocity. At the free end, the transverse motion of the tip reaches a peak-to-peak amplitude around 60% of the flag's length, and the flapping period ranges from 1.8 to 2.5 convective times. The fast motion of the tip leads to the flow deflection and the formation of coherent vortices in the wake. We show how aspect ratio affects the timescales of the flapping. Lower aspect ratio flags have a slower wave propagation speed and lower flapping frequency. Overall, the mean drag coefficient increases linearly with the squared tip velocity and goes from 0.05 to 0.5. When the tip velocity is lower, less shear is generated, and the vortices are weaker. The effect of the aspect ratio on the evolution of the cycle-averaged circulation can be accounted for by scaling the circulation using the ratio between the area of the flag and its perimeter. A better understanding of the link between aspect ratio and unsteady vortex formation can help better account for three-dimensional effects in applications, such as aortic valve design or fish-like propulsion.

Abstract: Hydrofoils are lifting surfaces used to reduce the resistance of a ship by lifting its hull out of the water. A common shape of 3D hydrofoil is the “(inverted) T-shaped hydrofoil”, made from a vertical shaft, the hydrofoil’s mast, which could be the rudder of a boat, and at its tip a horizontal wing which produces lift. The interaction between the mast and the wing of a T-foil is sparsely documented but has important consequence on the hydrofoil’s performance. For two flow regimes (Re = 6 500 and Re = 20 000) and two angles of attack (6° and 12°), the three velocity components were measured in a volume downstream of the hydrofoil through Lagrangian Particle Tracking. Those data were combined with Prandtl’s lifting line theory in order to estimate the spanwise lift distribution of the wing based on the downstream vorticity. This method highlighted the modified distribution due to the mast-wing interaction of a T-shaped hydrofoil, with an important loss of lift near the mast. This should be taken into account when designing a hydrofoil as the lift distribution need to be optimised to reduce induced drag. Moreover, this method allowed us to evaluate the hydrofoil’s lift which was then compared to data from a load sensor.

Abstract: We present a series of experiments on streamwise free-swimming hydrofoils with non-uniform flexibility, aimed at understanding their self-organizational behavior and associated schooling benefits. Utilizing two custom-developed, wirelessly controllable platforms supported by air bearings, we conducted tests with hydrofoils driven by servo motors executing sinusoidal pitching motions. Each platform was equipped with a motion controller and a real-time data acquisition system to monitor energetics, swimming speed, and trajectories. Our investigation focuses on whether non-uniformly flexible foils can self-organize into stable formations and what performance benefits are conferred by these formations. Additionally, we examine the role of fluid-structural coupling in these flexible foils, exploring how it may alter the self-organizational principles previously observed in rigid foils. These findings contribute to the broader understanding of collective behavior and efficiency in aquatic locomotion.