Scaling trends of bird's alular feathers in connection to leading-edge vortex flow over hand-wing.

An aerodynamic structure ubiquitous in Aves is the alula; a small collection of feathers muscularized near the wrist joint. New research into the aerodynamics of this structure suggests that its primary function is to induce leading-edge vortex (LEV) flow over bird's outer hand-wing to enhance wing lift when manuevering at slow speeds. Here, we explore scaling trends of the alula's spanwise position and its connection to this function. Specifically, we test the hypothesis that the relative distance of the alula from the wing tip is that which maximizes LEV-lift when the wing is spread and operated in a deep-stall flight condition. To test this, we perform experiments on model wings in a wind tunnel to approximate this distance and compare our results to positional measurements of the alula on spread-wing specimens. We found the position of the alula on non-aquatic birds selected for alula optimization to be located at or near the lift-maximizing position predicted by wind tunnel experiments. These findings shed new light on avian wing anatomy and the role of unconventional aerodynamics in shaping it.

Transient pressure modeling in jetting animals.

There are many marine animals that employ a form of jet propulsion to move through the water, often creating the jets by expanding and collapsing internal fluid cavities. Due to the unsteady nature of this form of locomotion and complex body/nozzle geometries, standard modeling techniques prove insufficient at capturing internal pressure dynamics, and hence swimming forces. This issue has been resolved with a novel technique for predicting the pressure inside deformable jet producing cavities (M. Krieg and K. Mohseni, J. Fluid Mech., 769, 2015), which is derived from evolution of the surrounding fluid circulation. However, this model was only validated for an engineered jet thruster with simple geometry and relatively high Reynolds number (Re) jets. The purpose of this manuscript is twofold: (i) to demonstrate how the circulation based pressure model can be used to analyze different animal body motions as they relate to propulsive output, for multiple species of jetting animals, (ii) and to quantitatively validate the pressure modeling for biological jetting organisms (typically characterized by complicated cavity geometry and low/intermediate Re flows). Using jellyfish (Sarsia tubulosa) as an example, we show that the pressure model is insensitive to complex cavity geometry, and can be applied to lower Re swimming. By breaking down the swimming behavior of the jellyfish, as well as that of squid and dragonfly larvae, according to circulation generating mechanisms, we demonstrate that the body motions of Sarsia tubulosa are optimized for acceleration at the beginning of pulsation as a survival response. Whereas towards the end of jetting, the velar morphology is adjusted to decrease the energetic cost. Similarly, we show that mantle collapse rates in squid maximize propulsive efficiency. Finally, we observe that the hindgut geometry of dragonfly larvae minimizes the work required to refill the cavity. Date Received: 10-18-2019, Date Accepted: 99-99-9999 *kriegmw@hawaii.edu, UHM Ocean and Res Eng, 2540 Dole St, Honolulu, HI 96822.

A Soft End Effector Inspired by Cephalopod Suckers and Augmented by a Dielectric Elastomer Actuator.

This article describes a soft suction cup end effector with squid-inspired suction generation and an octopus-inspired cup design that uses a dielectric elastomer actuator (DEA) to generate suction for adhesion. The fabrication process for the end effector is described in detail, and a mechanical model for generated pressure differential as a function of voltage is presented. When actuated, the DEA exerts an electrostatic stress on the walls of the end effector, resulting in pressure reduction in its water-filled cavity. The actuator is soft, flexible, and creates suction without a reliance on typical DEA elements such as rigid supporting structures and elastomer prestrain. It does not require net fluid flux out of the sucker, allowing faster attachment and easier release. It can be actuated underwater and has been validated with pull-off tests. The sucker generates a pressure differential of 3.63 ± 0.07 kPa (±SD) when driven at 10.75 kV in water and should reach a 4.90 kPa pressure differential when energized at its theoretical failure point of 12.4 kV. Data normalized by the input voltage show that 90% of the maximum pressure differential can be achieved within 50 ms of voltage application. Weighing less than 30 g in air, this elastomer end effector is capable of pulling with a force of 8.34 ± 0.10 N (±SD) and reversibly lifting 26.7 times its own mass underwater when actuated at 10.75 kV.

A vortex model for forces and moments on low-aspect-ratio wings in side-slip with experimental validation.

This paper studies low-aspect-ratio ([Formula: see text]) rectangular wings at high incidence and in side-slip. The main objective is to incorporate the effects of high angle of attack and side-slip into a simplified vortex model for the forces and moments. Experiments are also performed and are used to validate assumptions made in the model. The model asymptotes to the potential flow result of classical aerodynamics for an infinite aspect ratio. The [Formula: see text] → 0 limit of a rectangular wing is considered with slender body theory, where the side-edge vortices merge into a vortex doublet. Hence, the velocity fields transition from being dominated by a spanwise vorticity monopole ([Formula: see text] ≫ 1) to a streamwise vorticity dipole ([Formula: see text] ∼ 1). We theoretically derive a spanwise loading distribution that is parabolic instead of elliptic, and this physically represents the additional circulation around the wing that is associated with reattached flow. This is a fundamental feature of wings with a broad-facing leading edge. The experimental measurements of the spanwise circulation closely approximate a parabolic distribution. The vortex model yields very agreeable comparison with direct measurement of the lift and drag, and the roll moment prediction is acceptable for [Formula: see text] ≤ 1 prior to the roll stall angle and up to side-slip angles of 20°.

Unified slip boundary condition for fluid flows.

Determining the correct matching boundary condition is fundamental to our understanding of several everyday problems. Despite over a century of scientific work, existing velocity boundary conditions are unable to consistently explain and capture the complete physics associated with certain common but complex problems, such as moving contact lines and corner flows. The widely used Maxwell and Navier slip boundary conditions make an implicit assumption that velocity varies only in the wall normal direction. This makes their boundary condition inapplicable in the vicinity of contact lines and corner points, where velocity gradient exists both in the wall normal and wall tangential directions. In this paper, by identifying this implicit assumption we are able to extend Maxwell's slip model. Here, we present a generalized velocity boundary condition that shows that slip velocity is a function of not only the shear rate but also the linear strain rate. In addition, we present a universal relation for slip length, which shows that, for a general flow, slip length is a function of the principal strain rate. The universal relation for slip length along with the generalized velocity boundary condition provides a unified slip boundary condition to model a wide range of steady Newtonian fluid flows. We validate the unified slip boundary for simple Newtonian liquids by using molecular dynamics simulations and studying both the moving contact line and corner flow problems.

Design considerations for an underwater soft-robot inspired from marine invertebrates.

This article serves as an overview of the unique challenges and opportunities made possible by a soft, jellyfish inspired, underwater robot. We include a description of internal pressure modeling as it relates to propulsive performance, leading to a desired energy-minimizing volume flux program. Strategies for determining optimal actuator placement derived from biological body motions are presented. In addition a feedback mechanism inspired by the epidermal line sensory system of cephalopods is presented, whereby internal pressure distribution can be used to determine pertinent deformation parameters.

Identifying and modeling motion primitives for the hydromedusae Sarsia tubulosa and Aequorea victoria.

The movements of organisms can be thought of as aggregations of motion primitives: motion segments containing one or more significant actions. Here, we present a means to identify and characterize motion primitives from recorded movement data. We address these problems by assuming that the motion sequences can be characterized as a series of dynamical-system-based pattern generators. By adopting a nonparametric, Bayesian formalism for learning and simplifying these pattern generators, we arrive at a purely data-driven model to automatically identify breakpoints in the movement sequences. We apply this model to swimming sequences from two hydromedusa. The first hydromedusa is the prolate Sarsia tubulosa, for which we obtain five motion primitives that correspond to bell cavity pressurization, jet formation, jetting, cavity fluid refill, and coasting. The second hydromedusa is the oblate Aequorea victoria, for which we obtain five motion primitives that correspond to bell compression, vortex separation, cavity fluid refill, vortex formation, and coasting. Our experimental results indicate that the breakpoints between primitives are correlated with transitions in the bell geometry, vortex formation and shedding, and changes in derived dynamical quantities. These dynamics quantities include terms like pressure, power, drag, and thrust. Such findings suggest that dynamics information is inherently present in the observed motions.

A model of the lateral line of fish for vortex sensing.

In this paper, the lateral line trunk canal (LLTC) of a fish is modeled to investigate how it is affected by an external flow field. Potential flow theory is adopted to model the flow field around a fish's body in the presence of a Karman vortex street. Karman and reverse Karman streets represent the flow patterns behind a bluff body and a traveling fish, respectively. An analytical solution is obtained for a flat body, while a fish-like body is modeled using a Joukowski transformation and the corresponding equations are solved numerically. The pressure distribution on the body surface is then computed employing Bernoulli's equation. For a known external flow, the flow inside the LLTC is driven by the pressure gradient between a pair of consecutive pores, which can be solved analytically. Governing dimensionless parameters are obtained from this analytical solution, and the effects of these numbers on the amplitude or features of the velocity distribution inside the canal are studied. The results show that the main characteristics of a vortex street including the magnitude of vortices, their translational speed, their spacing, their distance from the fish's body and the angle of the vortex street axis can all be recovered by measuring the velocity distribution along the canal and its changes with time. To this end, the proposed LLTC model could explain how a fish identifies the characteristics of a Karman vortex street shed by a nearby object or a traveling fish. It is also demonstrated that while this model captures the ac (alternating current) component of the external velocity signal, the dc (direct current) component of the signal is filtered out. Based on the results of our model, the role of the LLTC in a fish's schooling and its evolutionary impact on fish sensing are discussed.

New perspectives on collagen fibers in the squid mantle.

The squid mantle is a complex structure which, in conjunction with a highly sensitive sensory system, provides squid with a wide variety of highly controlled movements. This article presents a model describing systems of collagen fibers that give the mantle its shape and mechanical properties. The validity of the model is verified by comparing predicted optimal fiber angles to actual fiber angles seen in squid mantle. The model predicts optimal configurations for multiple fiber systems. It is found that the tunic fibers (outer collagen layers) provide optimal jetting characteristics when oriented at 31°, which matches empirical data from previous studies. The model also predicted that a set of intramuscular fibers (IM-1) are oriented relative to the longitudinal axis to provide optimal energy storage capacity within the limiting physical bounds of the collagen fibers themselves. In addition, reasons for deviations from the predicted values are analyzed. This study illustrates how the squid's reinforcing collagen fibers are aligned to provide several locomotory advantages and demonstrates how this complex biological process can be accurately modeled with several simplifying assumptions.

A ridge tracking algorithm and error estimate for efficient computation of Lagrangian coherent structures.

A ridge tracking algorithm for the computation and extraction of Lagrangian coherent structures (LCS) is developed. This algorithm takes advantage of the spatial coherence of LCS by tracking the ridges which form LCS to avoid unnecessary computations away from the ridges. We also make use of the temporal coherence of LCS by approximating the time dependent motion of the LCS with passive tracer particles. To justify this approximation, we provide an estimate of the difference between the motion of the LCS and that of tracer particles which begin on the LCS. In addition to the speedup in computational time, the ridge tracking algorithm uses less memory and results in smaller output files than the standard LCS algorithm. Finally, we apply our ridge tracking algorithm to two test cases, an analytically defined double gyre as well as the more complicated example of the numerical simulation of a swimming jellyfish. In our test cases, we find up to a 35 times speedup when compared with the standard LCS algorithm.

The numerical comparison of flow patterns and propulsive performances for the hydromedusae Sarsia tubulosa and Aequorea victoria.

The thrust-generating mechanism of a prolate hydromedusa Sarsia tubulosa and an oblate hydromedusa Aequorea victoria was investigated by solving the incompressible Navier-Stokes equations in the swirl-free cylindrical coordinates. The calculations clearly show the vortex dynamics related to the thrust-generating mechanism, which is very important for understanding the underlying propulsion mechanism. The calculations for the prolate jetting hydromedusa S. tubulosa indicate the formation of a single starting vortex ring for each pulse cycle with a relatively high vortex formation number. However, the calculations for the oblate jet-paddling hydromedusa A. victoria indicate shedding of the opposite-signed vortex rings very close to each other and the formation of large induced velocities along the line of interaction as the vortices move away from the hydromedusa in the wake. In addition to this jet propulsion mechanism, the hydromedusa's bell margin acts like a paddle and the highly flexible bell margin deforms in such a way that the low pressure leeward side of the bell margin has a projected area in the direction of motion. This thrust is particularly important during refilling of the subumbrella cavity where the stopping vortex causes significant pressure drag. The swimming performances based on our numerical simulations, such as swimming velocity, thrust, power requirement and efficiency, were computed and support the idea that jet propulsion is very effective for rapid body movement but is energetically costly and less efficient compared with the jet-paddling propulsion mechanism.

Flow structures and fluid transport for the hydromedusae Sarsia tubulosa and Aequorea victoria.

The flow structures produced by the hydromedusae Sarsia tubulosa and Aequorea victoria are examined using direct numerical simulation and Lagrangian coherent structures (LCS). Body motion of each hydromedusa is digitized and input to a CFD program. Sarsia tubulosa uses a jetting type of propulsion, emitting a single, strong, fast-moving vortex ring during each swimming cycle while a secondary vortex of opposite rotation remains trapped within the subumbrellar region. The ejected vortex is highly energetic and moves away from the hydromedusa very rapidly. Conversely, A. victoria, a paddling type hydromedusa, is found to draw fluid from the upper bell surface and eject this fluid in pairs of counter-rotating, slow-moving vortices near the bell margins. Unlike S. tubulosa, both vortices are ejected during the swimming cycle of A. victoria and linger in the tentacle region. In fact, we find that A. victoria and S. tubulosa swim with Strouhal numbers of 1.1 and 0.1, respectively. This means that vortices produced by A. victoria remain in the tentacle region roughly 10 times as long as those produced by S. tubulosa, which presents an excellent feeding opportunity during swimming for A. victoria. Finally, we examine the pressure on the interior bell surface of both hydromedusae and the velocity profile in the wake. We find that S. tubulosa produces very uniform pressure on the interior of the bell as well as a very uniform jet velocity across the velar opening. This type of swimming can be well approximated by a slug model, but A. victoria creates more complicated pressure and velocity profiles. We are also able to estimate the power output of S. tubulosa and find good agreement with other hydromedusan power outputs. All results are based on numerical simulations of the swimming jellyfish.

Force characterization of dielectrophoresis in droplet transport.

Transporting microdroplets using electric fields can be accomplished with several mechanisms, the primary methods being dielectrophoresis (DEP) for electrically insulating liquids, and electrowetting on dielectric for conducting fluids. In both cases, an electric field is applied near the leading edge of the droplet using patterned electrodes, giving rise to an electrostatic pressure that induces droplet transport. This paper examines the nature of the force distribution for DEP-actuated droplets in several electrode configurations, calculated using a numerical method designed for handling jump conditions in the Poisson equation. The numerical method is described and verified by comparison with known analytical results. The net force acting upon a DEP droplet is investigated, with the effect of electrode configuration presented for several cases, demonstrating some beneficial aspects for engineering applications.

An electrowetting microvalve: numerical simulation.

Numerical simulation of a zero-leakage microvalve is investigated where a liquid droplet is used as a gate to regulate the flow in a T junction. The droplet gate is activated by changing its surface tension via an applied electric field. Numerical simulation of the droplet actuation is considered where the effect of electrowetting is imposed in the form of a modified boundary condition at the contact line. Numerical simulation is used to predict the droplet behavior and to design the valve. It is found that the pressure breakdown of the microvalve is significantly affected by the geometry of the T junction corners. It is expected that such a microvalve design will improve the sensitivity and performance of a wide variety of microfluidic devices.

A formulation for calculating the translational velocity of a vortex ring or pair.

Cephalopods, among other marine animals, use jet propulsion for swimming. A simple actuator is designed to loosely mimic pulsatile jet formation in squid and jellyfish. The actuator is comprised of a cavity with an oscillating diaphragm and an exit orifice. Periodic oscillation of the diaphragm results in the formation of an array of vortex rings and eventually could generate a periodic pulsatile jet. A general formulation for calculating the velocity of a steadily translating vortical structure in two-dimensional and axi-symmetric shear flows is presented. This technique is based on taking the variational derivative of an energetic function at its critical point. This technique is general, applicable to vortices in liquid and gas media, with no limitation on the relative size of the vortex core. The technique is then implemented to estimate the translational velocity of a vortex ring in a Helmholtz vortex ring generator.