arXiv subjects

Keith W. Moored

Publications and source records attributed to Keith W. Moored.

13 recordsLinked to original sources

arXiv2025

Tuna-Like Swimmers Experience a Fluid-Mediated Stable Side-by-Side Formation

New free-swimming experiments and simulations are conducted on a pair of three-dimensional, bio-robotic swimmers composed of a body and tail section based on Yellowfin tuna, Thunnus albacares. It is discovered that the pair converges spontaneously to a side-by-side schooling formation that is stable to perturbations in the swimming direction at a fixed lateral spacing. We reveal that for close lateral spacings of 43% of the body length and thick, tuna-like bodies with a 22% thickness-to-length ratio, the flow between the swimmers is accelerated in a "channeling effect" due to flow constriction. Consequently, this creates a low-pressure zone that is the primary mechanism generating a fluid-mediated restorative force, thereby making the side-by-side formation hydrodynamically stable. This quasi-steady mechanism makes the stability of the formation insensitive to the phase synchronization between the bio-robots in contrast to previous results for schooling foils. Moreover, in the side-by-side formation tunalike swimmers are seen to have only a small reduction in their swimming speed and a concurrent small rise in their cost of transport. By leveraging this channeling effect, bio-robotic schools may be able to maintain a schooling formation with little or no control. This flow mechanism may also be present in biological schools of tuna-like fish where it may sculpt the formations observed in nature.

physics.flu-dyn↗

arXiv2025

Wavenumber affects the lift of ray-inspired fins near a substrate

Rays and skates tend to have different fin kinematics depending on their proximity to a ground plane such as the seafloor. Near the ground, rays tend to be more undulatory (high wavenumber), while far from the ground, rays tend to be more oscillatory (low wavenumber). It is unknown whether these differences are driven by hydrodynamics or other biological pressures. Here we show that near the ground, the time-averaged lift on a ray-like fin is highly dependent on wavenumber. We support our claims using a ray-inspired robotic rig that can produce oscillatory and undulatory motions on the same fin. Potential flow simulations reveal that lift is always negative because quasisteady forces overcome wake-induced forces. Three-dimensional flow measurements demonstrate that oscillatory wakes are more disrupted by the ground than undulatory wakes. All these effects lead to a suction force toward the ground that is stronger and more destabilizing for oscillatory fins than undulatory fins. Our results suggest that wavenumber plays a role in the near-ground dynamics of ray-like fins, particularly in terms of dorsoventral accelerations. The fact that lower wavenumber is linked with stronger suction forces offers a new way to interpret the depth-dependent kinematics of rays and ray-inspired robots.

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arXiv2024

Tailoring formations of self-organizing hydrofoil schools towards high-efficiency

We present new unconstrained simulations and constrained experiments of a pair of pitching hydrofoils in a leader-follower in-line arrangement. Free-swimming simulations of foils with $matched$ pitching amplitudes show self-organization into stable formations at a constant gap distance without any control. Leading-edge separation on the follower foil plays a crucial role in creating these formations by acting as an additional dynamic drag source on the follower, which depends on the gap spacing and phase synchronization. Over a wide range of phase synchronization, amplitude, and Lighthill number typical of biology, we discover that the stable gap distance scales with the actual wake wavelength of an isolated foil $rather$ $than$ the nominal wake wavelength. A scaling law for the actual wake wavelength is derived and shown to collapse data across a wide Reynolds number range of $200 \leq Re < \infty$. Additionally, in both simulations and experiments $mismatched$ foil amplitudes are discovered to increase the efficiency of hydrofoil schools by 70% while maintaining a stable formation without closed-loop control. This occurs by (1) increasing the stable gap distance between foils such that they are pushed into a high-efficiency zone and (2) raising the level of efficiency in these zones. This study bridges the gap between constrained and unconstrained studies of in-line schooling by showing that constrained-foil measurements can be used as a map of the potential efficiency benefits of schooling. These findings can aid in the design of high-efficiency bio-robot schools and may provide insights into the energetics and behaviour of fish schools.

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arXiv2023

Two-dimensionally stable self-organization arises in simple schooling swimmers through hydrodynamic interactions

We present new constrained and free-swimming experiments and simulations of a pair of pitching hydrofoils interacting in a minimal school. The hydrofoils have an out-of-phase synchronization and they are varied through in-line, staggered, and side-by-side formations within the two-dimensional interaction plane. It is discovered that there is a \textit{two-dimensionally} stable equilibrium point for a side-by-side formation. In fact, this formation is super-stable, meaning that hydrodynamic forces will passively maintain this formation even under external perturbations and the school as a whole has no net forces acting on it that cause it to drift to one side or the other. Moreover, previously discovered \textit{one-dimensionally} stable equilibria driven by wake vortex interactions are shown to be, in fact, two-dimensionally \textit{unstable}, at least for an out-of-phase synchronization. Additionally, it is discovered that a trailing-edge vortex mechanism provides the restorative force to stabilize a side-by-side formation. The stable equilibrium is further verified by experiments and simulations for freely-swimming foils where dynamic recoil motions are present. When constrained, swimmers in compact side-by-side formations experience collective efficiency and thrust increases up to 40\% and 100\%, respectively, whereas slightly staggered formations output an even higher efficiency improvement of 84\% with a 87\% increase in thrust. Freely-swimming foils in a stable side-by-side formation show an efficiency and speed enhancement of up to 9\% and 15\%, respectively. These newfound schooling performance and stability characteristics suggest that fluid-mediated equilibria may play a role in the control strategies of schooling fish and fish-inspired robots.

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arXiv2023

Revealing the mechanism and scaling laws behind equilibrium altitudes of near-ground pitching hydrofoils

A classic lift decomposition (von Kármán & Sears 1938) is conducted on potential flow simulations of a near-ground pitching hydrofoil. It is discovered that previously observed stable and unstable equilibrium altitudes are generated by a balance between positive wake-induced lift and negative quasi-steady lift while the added mass lift doesn't play a role. Using both simulations and experiments, detailed analyses of each lift component's near-ground behavior provide further physical insights. When applied to three-dimensional pitching hydrofoils the lift decomposition reveals that the disappearance of equilibrium altitudes for AR < 1.5 occurs due to the magnitude of the quasi-steady lift outweighing the magnitude of the wake-induced lift at all ground distances. Scaling laws for the quasi-steady lift, wake-induced lift and the stable equilibrium altitude are discovered. A simple scaling law for the lift of a steady foil in ground effect is derived. This scaling shows that both circulation enhancement and the velocity induced at a foil's leading edge by the bound vortex of its ground image foil are the essential physics to understand steady ground effect. The scaling laws for unsteady pitching foils can predict the equilibrium altitude to within 20% of its value when St < 0.45. For St equal to or greater than 0.45 there is a wake instability effect, not accounted for in the scaling relations, that significantly alters the wake-induced lift. These results not only provide key physical insights and scaling laws for steady and unsteady ground effect, but also for two schooling hydrofoils in a side-by-side formation with an out-of-phase synchronization.

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arXiv2020

Scaling Laws for the Propulsive Performance of a Purely Pitching Foil in Ground Effect

Scaling laws for the thrust production and power consumption of a purely pitching hydrofoil in ground effect are presented. For the first time, ground effect scaling laws based on physical insights capture the propulsive performance over a wide range of biologically-relevant Strouhal numbers, dimensionless amplitudes, and dimensionless ground distances. This is achieved by advancing previous scaling laws (Moored & Quinn 2018) with physics-driven modifications to the added mass and circulatory forces to account for ground distance variations. The key physics introduced are the increase in the added mass of a foil near the ground and the reduction in the influence of a wake vortex system due to the influence of its image system. The scaling laws are found to be in good agreement with new inviscid simulations and viscous experiments, and can be used to accelerate the design of bio-inspired hydrofoils that oscillate near a ground plane or two out-of-phase foils in a side-by-side arrangement.

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arXiv2020

Intermittent Unsteady Propulsion with a Combined Heaving and Pitching Foil

Inviscid computations are presented of a self-propelled virtual body connected to a combined heaving and pitching foil that uses continuous and intermittent motions. It is determined that intermittent swimming can improve efficiency when the dimensionless heave ratio is $h^* < 0.7$ while it degrades efficiency for $h^* \geq 0.7$. This is a consequence of the physical origins of the force production for pitch-dominated ($h^* < 0.5$) and heave-dominated ($h^* > 0.5$) motions. Based on insight derived from classic unsteady thin airfoil theory, it is discovered that pitch-dominated motions are driven by added-mass-based thrust production where self-propelled efficiency is maximized for high reduced frequencies, while heave-dominated motions are driven by circulatory-based thrust production where self-propelled efficiency is maximized by low reduced frequencies. Regardless of the dimensionless heave ratio the reduced frequency is high for small amplitude motions, high Lighthill numbers, and low duty cycles and vice versa. Moreover, during intermittent swimming, the stopping vortex that is shed at the junction of the bursting and coasting phases becomes negligibly weak for $h^* < 0.5$ and small amplitude motions of $A^* = 0.4$. This study provides insight into the mechanistic trade-offs that occur when biological or bio-inspired swimmers continuously or intermittently use combined heaving and pitching hydrofoils.

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arXiv2020

Scaling Laws for Three-Dimensional Combined Heaving and Pitching Propulsors

We present new scaling laws for the thrust production and power consumption of three-dimensional combined heaving and pitching hydrofoils by extending the three-dimensional pitching scaling laws introduced by Ayancik et al. (2019). New self-propelled inviscid simulations and previously published experimental data are used to validate the scaling laws over a wide range of motion amplitudes, Strouhal numbers, heave ratios, aspect ratios, and pitching axis locations. The developed scaling laws are shown to predict inviscid numerical data and experimental data well, within $\pm$ 25% and $\pm$ 16% of the thrust and power data, respectively. The scaling laws reveal that both the circulatory and added mass forces are important when considering a wide range of motion amplitudes and that nonlinear corrections to the classic linear theory are essential to modeling the performance across this wide amplitude range. By using the scaling laws as a guide, it is determined that peak efficiencies occur when $A^*$ > 1 and for these large-amplitude motions, there is an optimal $h^*$ that maximizes the efficiency in the narrow range of 0.75 < $h^*$ < 0.94. Finally, the scaling laws show that to further improve efficiency in this high-efficiency regime, the aspect ratio, and dimensionless amplitude should be increased, while the Lighthill number should be decreased (lower drag and/or a larger propulsor planform area to wetted surface area ratio), and the pitch axis should be located behind the leading edge. This scaling model can be used to guide the design of the next generation of high-efficiency bio-inspired machines.

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arXiv2019

Exact solutions for ground effect

"Ground effect" refers to the enhanced performance enjoyed by fliers or swimmers operating close to the ground. We derive a number of exact solutions for this phenomenon, thereby elucidating the underlying physical mechanisms involved in ground effect. Unlike previous analytic studies, our solutions are not restricted to particular parameter regimes such as "weak" or "extreme" ground effect, and do not even require thin aerofoil theory. Moreover, the solutions are valid for a hitherto intractable range of flow phenomena including point vortices, uniform and straining flows, unsteady motions of the wing, and the Kutta condition. We model the ground effect as the potential flow past a wing inclined above a flat wall. The solution of the model requires two steps: firstly, a coordinate transformation between the physical domain and a concentric annulus, and secondly, the solution of the potential flow problem inside the annulus. We show that both steps can be solved by introducing a new special function which is straightforward to compute. Moreover, the ensuing solutions are simple to express and offer new insight into the mathematical structure of ground effect. In order to identify the missing physics in our potential flow model, we compare our solutions against new experimental data. The experiments show that boundary layer separation on the wing and wall occurs at small angles of attack, and we suggest ways in which our model could be extended to account for these effects.

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arXiv2018

Scaling Laws for the Propulsive Performance of Three-Dimensional Pitching Propulsors

Scaling laws for the thrust production and energetics of self-propelled or fixed-velocity three-dimensional rigid propulsors undergoing pitching motions are presented. The scaling relations extend the two-dimensional scaling laws presented in Moored & Quinn (2018) by accounting for the added mass of a finite-span propulsor, the downwash/upwash effects from the trailing vortex system of a propulsor, and the elliptical topology of shedding trailing-edge vortices. The novel three-dimensional scaling laws are validated with self-propelled inviscid simulations and fixed-velocity experiments over a range of reduced frequencies, Strouhal numbers and aspect ratios relevant to bio-inspired propulsion. The scaling laws elucidate the dominant flow physics behind the thrust production and energetics of pitching bio-propulsors, and they provide guidance for the design of bio-inspired propulsive systems.

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arXiv2017

Inviscid scaling laws of a self-propelled pitching airfoil

Inviscid computational results are presented on a self-propelled virtual body combined with an airfoil undergoing pitch oscillations about its leading-edge. The scaling trends of the time-averaged thrust forces are shown to be predicted accurately by Garrick's theory. However, the scaling of the time-averaged power for finite amplitude motions is shown to deviate from the theory. Novel time-averaged power scalings are presented that account for a contribution from added-mass forces, from the large-amplitude separating shear layer at the trailing-edge, and from the proximity of the trailing-edge vortex. Scaling laws for the self-propelled speed, efficiency and cost of transport ($CoT$) are subsequently derived. Using these scaling relations the self-propelled metrics can be predicted to within 5% of their full-scale values by using parameters known a priori. The relations may be used to drastically speed-up the design phase of bio-inspired propulsion systems by offering a direct link between design parameters and the expected $CoT$. The scaling relations also offer one of the first mechanistic rationales for the scaling of the energetics of self-propelled swimming. Specifically, the cost of transport is shown to scale predominately with the added mass power. This suggests that the $CoT$ of organisms or vehicles using unsteady propulsion will scale with their mass as $CoT \propto m^{-1/3}$, which is indeed shown to be consistent with existing biological data.

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arXiv2017

Unsteady Propulsion by an Intermittent Swimming Gait

Inviscid computational results are presented on a self-propelled swimmer modeled as a virtual body combined with a two-dimensional hydrofoil pitching intermittently about its leading edge. Lighthill (1971) originally proposed that this burst-and-coast behavior can save fish energy during swimming by taking advantage of the viscous Bone-Lighthill boundary layer thinning mechanism. Here, an additional inviscid Garrick mechanism is discovered that allows swimmers to control the ratio of their added mass thrust-producing forces to their circulatory drag-inducing forces by decreasing their duty cycle, DC, of locomotion. This mechanism can save intermittent swimmers as much as 60% of the energy it takes to swim continuously at the same speed. The inviscid energy savings are shown to increase with increasing amplitude of motion, increase with decreasing Lighthill number, Li, and switch to an energetic cost above continuous swimming for sufficiently low DC. Intermittent swimmers are observed to shed four vortices per cycle that form into groups that are self-similar with the DC. In addition, previous thrust and power scaling laws of continuous self-propelled swimming are further generalized to include intermittent swimming. The key is that by averaging the thrust and power coefficients over only the bursting period then the intermittent problem can be transformed into a continuous one. Furthermore, the intermittent thrust and power scaling relations are extended to predict the mean speed and cost of transport of swimmers. By tuning a few coefficients with a handful of simulations these self-propelled relations can become predictive. In the current study, the mean speed and cost of transport are predicted to within 3% and 18% of their full-scale values by using these relations.

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arXiv2017

Unsteady three-dimensional boundary element method for self-propelled bio-inspired locomotion

An unsteady three-dimensional boundary element method is developed to provide fast calculations of biological and bio-inspired self-propelled locomotion. The approach uniquely combines an unsteady three-dimensional boundary element method, a boundary layer solver and self-propelled equations of motion. This novel implementation allows for the self-propelled speed, power, efficiency and economy to be accurately calculated. A Dirichlet formulation is used with a combination of constant strength source and doublet elements to represent a deforming body with a nonlinearly deforming wake. The wake elements are desingularized to numerically stabilize the evolution of the wake vorticity. Weak coupling is used in solving the equations of motion and in the boundary layer solution. The boundary layer solver models both laminar and turbulent behavior along the deforming body to estimate the total skin friction drag acting on the body. The results from the method are validated with analytical solutions, computations and experiments. Finally, a bio-inspired self-propelled undulatory fin is modeled. The computed self-propelled speeds and wake structures agree well with previous experiments. The computations go beyond the experiments to gain further insight into the propulsive efficiency for self-propelled undulating fins. It is found that the undulating fin produces a time-averaged momentum jet at 76% of the span that accelerates fluid in the streamwise direction and in turn generates thrust. Additionally, it is discovered that high amplitude motions suppress the formation of a bifurcating momentum jet and instead form a single core jet. Consequently, this maximizes the amount of streamwise momentum compared to the amount of wasted lateral momentum and leads to a propulsive efficiency of 78% during self-propelled locomotion.

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