19 research outputs found
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 arrangements within the two-dimensional interaction
plane. It is discovered that there is a \textit{two-dimensionally} stable
equilibrium point for a side-by-side arrangement. In fact, this arrangement is
super-stable, meaning that hydrodynamic forces will passively maintain this
arrangement even under external perturbations and the school as a whole has no
net forces acting on it, causing 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 arrangement and the stable equilibrium is
further verified for freely-swimming foils where dynamic recoil motions are
present. When constrained, the swimmers experience a collective thrust and
efficiency increase up to 100\% and 40\%, respectively, in a side-by-side
arrangement, whereas the staggered arrangements output an even higher
efficiency improvement of 87\% with a 94\% increase in thrust. For
freely-swimming foils, the recoil motion attenuates the improvements at the
stable equilibrium, showing a more modest speed and efficiency enhancement of
up to 9\% and 6\%, 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.Comment: Revised version of the manuscript upon first peer revie
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.Comment: Main body: 10 pages & 3 figures; supplementary material: 6 pages & 5
figures. Submitted to JFM Rapid
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
Hydrodynamic Performance of Aquatic Flapping: Efficiency of Underwater Flight in the Manta
The manta is the largest marine organism to swim by dorsoventral oscillation (flapping) of the pectoral fins. The manta has been considered to swim with a high efficiency stroke, but this assertion has not been previously examined. The oscillatory swimming strokes of the manta were examined by detailing the kinematics of the pectoral fin movements swimming over a range of speeds and by analyzing simulations based on computational fluid dynamic potential flow and viscous models. These analyses showed that the fin movements are asymmetrical up- and downstrokes with both spanwise and chordwise waves interposed into the flapping motions. These motions produce complex three-dimensional flow patterns. The net thrust for propulsion was produced from the distal half of the fins. The vortex flow pattern and high propulsive efficiency of 89% were associated with Strouhal numbers within the optimal range (0.2β0.4) for rays swimming at routine and high speeds. Analysis of the swimming pattern of the manta provided a baseline for creation of a bio-inspired underwater vehicle, MantaBot
Kinematics of swimming of the manta ray: three-dimensional analysis of open water maneuverability
For aquatic animals, turning maneuvers represent a locomotor activity that may not be confined to a single coordinate plane, making analysis difficult particularly in the field. To measure turning performance in a three-dimensional space for the manta ray (Mobula birostris), a large open-water swimmer, scaled stereo video recordings were collected. Movements of the cephalic lobes, eye and tail base were tracked to obtain three-dimensional coordinates. A mathematical analysis was performed on the coordinate data to calculate the turning rate and curvature (1/turning radius) as a function of time by numerically estimating the derivative of manta trajectories through three-dimensional space. Principal component analysis (PCA) was used to project the three-dimensional trajectory onto the two-dimensional turn. Smoothing splines were applied to these turns. These are flexible models that minimize a cost function with a parameter controlling the balance between data fidelity and regularity of the derivative. Data for 30 sequences of rays performing slow, steady turns showed the highest 20% of values for the turning rate and smallest 20% of turn radii were 42.65+16.66 deg s-1 and 2.05+1.26 m, respectively. Such turning maneuvers fall within the range of performance exhibited by swimmers with rigid bodies
Flow interactions of two- and three-dimensional networked bio-inspired control elements in an in-line arrangement
We present experiments that examine the modes of interaction, the collective performance and the role of three-dimensionality in two pitching propulsors in an in-line arrangement. Both two-dimensional foils and three-dimensional rectangular wings of ARββ=ββ2 are examined. In contrast to previous work, two interaction modes distinguished as the coherent and branched wake modes are not observed to be directly linked to the propulsive efficiency, although they are linked to peak thrust performance and minimum power consumption as previously described (Boschitsch et al 2014 Phys. Fluids 26 051901). In fact, in closely-spaced propulsors peak propulsive efficiency of the follower occurs near its minimum power and this condition reveals a branched wake mode. Alternatively, for propulsors spaced far apart peak propulsive efficiency of the follower occurs near its peak thrust and this condition reveals a coherent wake mode. By examining the collective performance, it is discovered that there is an optimal spacing between the propulsors to maximize the collective efficiency. For two-dimensional foils the optimal spacing of X*ββ=ββ0.75 and the synchrony of Οββ=ββ2Οβ/β3 leads to a collective efficiency and thrust enhancement of 42% and 38%, respectively, as compared to two isolated foils. In comparison, for ARββ=ββ2 wings the optimal spacing of X*ββ=ββ0.25 and the synchrony of Οββ=ββ7 Οβ/β6 leads to a collective efficiency and thrust enhancement of 25% and 15%, respectively. In addition, at the optimal conditions the collective lateral force coefficients in both the two- and three-dimensional cases are negligible, while operating off these conditions can lead to non-negligible lateral forces. Finally, the peak efficiency of the collective and the follower are shown to have opposite trends with increasing spacing in two- and three-dimensional flows. This is correlated to the breakdown of the impinging vortex on the follower wing in three-dimensions. These results can aid in the design of networked bio-inspired control elements that through integrated sensing can synchronize to three-dimensional flow interactions