In this work a cephalopod-like deformable body that fills an internal cavity with fluid and expels it to propel an escape manoeuvre, while undergoing a drastic external shape change through shrinking, is shown to employ viscous as well as mainly inviscid hydrodynamic mechanisms to power an impressively fast start. First, we show that recovery of added-mass energy enables a shrinking rocket in a dense inviscid flow to achieve greater escape speed than an identical rocket in a vacuum. Next, we extend the shrinking body results of Weymouth & Triantafyllou (J. Fluid Mech., vol. 702, 2012, pp. 470-487) to three-dimensional bodies and show that three hydrodynamic mechanisms must be combined to achieve rapid escape performance in a viscous fluid: added-mass energy recovery; flow separation elimination; and an optimized energy storage and recovery. In particular, we show that the mechanism of separation elimination achieved through rapid body shrinking, coordinated with the mechanism of recovering the initially imparted added-mass energy, is critical to achieving a high escape speed. Hence a flexible, collapsing body can be vastly superior to a rigid-shell jet-propelled body.
a b s t r a c tA new robust and accurate Cartesian-grid treatment for the immersion of solid bodies within a fluid with general boundary conditions is described. The new approach, the Boundary Data Immersion Method (BDIM), is derived based on a general integration kernel formulation which allows the field equations of each domain and the interfacial conditions to be combined analytically. The resulting governing equation for the complete domain preserves the behavior of the original system in an efficient Cartesian-grid method, including stable and accurate pressure values on the solid boundary. The kernel formulation allows a detailed analysis of the method, and it is demonstrated that BDIM is consistent, obtains second-order convergence relative to the kernel width, and is robust with respect to the grid and boundary alignment. Formulation for no-slip and free slip boundary conditions are derived and numerical results are obtained for the flow past a cylinder and the impact of blunt bodies through a free surface. The BDIM predictions are compared to analytic, experimental and previous numerical results confirming the properties, efficiency and efficacy of this new boundary treatment for Cartesian grid methods.
Abstract. We design and test an octopus-inspired flexible hull robot that demonstrates outstanding fast-starting performance. The robot is hyper-inflated with water, and then rapidly deflates to expel the fluid so as to power the escape maneuver. Using this robot we verify for the first time in laboratory testing that rapid size-change can substantially reduce separation in bluff bodies traveling several body lengths, and recover fluid energy which can be employed to improve the propulsive performance. The robot is found to experience speeds over ten body lengths per second, exceeding that of a similarly propelled optimally streamlined rigid rocket. The peak net thrust force on the robot is more than 2.6 times that on an optimal rigid body performing the same maneuver, experimentally demonstrating large energy recovery and enabling acceleration greater than 14 body lengths per second squared. Finally, over 53% of the available energy is converted into payload kinetic energy, a performance that exceeds the estimated energy conversion efficiency of fast-starting fish. The Reynolds number based on final speed and robot length is Re ≈ 700, 000. We use the experimental data to establish a fundamental deflation scaling parameter σ * which characterizes the mechanisms of flow control via shape change. Based on this scaling parameter, we find that the fast-starting performance improves with increasing size.
The extinct ocean-going plesiosaurs were unique within vertebrates because they used two flipper pairs identical in morphology for propulsion. Although fossils of these Mesozoic marine reptiles have been known for more than two centuries, the function and dynamics of their tandem-flipper propulsion system has always been unclear and controversial. We address this question quantitatively for the first time in this study, reporting a series of precisely controlled water tank experiments that use reconstructed plesiosaur flippers scaled from well-preserved fossils. Our aim was to determine which limb movements would have resulted in the most efficient and effective propulsion. We show that plesiosaur hind flippers generated up to 60% more thrust and 40% higher efficiency when operating in harmony with their forward counterparts, when compared with operating alone, and the spacing and relative motion between the flippers was critical in governing these increases. The results of our analyses show that this phenomenon was probably present across the whole range of plesiosaur flipper motion and resolves the centuries-old debate about the propulsion style of these marine reptiles, as well as indicating why they retained two pairs of flippers for more than 100 million years.
An accurate Cartesian-grid treatment for intermediate Reynolds number fluid-solid interaction problems is described. We first identify the inability of existing immersed boundary methods to handle intermediate Reynolds number flows to be the discontinuity of the velocity gradient at the interface. We address this issue by generalizing the Boundary Data Immersion Method (BDIM, Weymouth and Yue, J. Comp. Phys., vol. 230, 2011), in which the field equations of each domain are combined analytically, through the addition of a higher order term to the integral formulation. The new method, featuring a second-order convolution, retains the desirable simplicity of direct forcing methods and smoothes the velocity field at the fluid-solid interface while removing its bias. This results in accurate flow predictions and pressure fields without spurious fluctuations, even at high Reynolds number where the method is second order in the L 2 norm. A treatment for sharp corners is also derived that significantly improves the flow predictions near the trailing edge of thin airfoils. The second-order BDIM is applied to unsteady problems relevant to ocean energy extraction as well as animal and vehicle locomotion for Reynolds numbers up to 10 5 .
The propulsive performance of a pair of tandem flapping foils is sensitively dependent on the spacing and phasing between them. Large increases in thrust and efficiency of the hind foil are possible, but the mechanisms governing these enhancements remain largely unresolved. Two-dimensional numerical simulations of tandem and single foils oscillating in heave and pitch at a Reynolds number of 7,000 are performed over a broad and dense parameter space, allowing the effects of inter-foil spacing (S) and phasing (ϕ) to be investigated over a range of non-dimensional frequencies (or Strouhal number, St). Results indicate that the hind foil can produce from no thrust, to twice the thrust of a single foil depending on its spacing and phasing with respect to the fore foil, which is consistent with previous studies that were carried out over a limited parameter space. Examination of instantaneous flowfields indicate that high thrust occurs when the hind foil weaves in between the vortices that have been shed by the fore foil, and low thrust occurs when the hind foil intercepts these vortices. Contours of high thrust and minimal thrust appear as inclined bands in the S − ϕ parameter space and this behaviour is apparent over the entire range of Strouhal numbers considered (0.2 St 0.5). A novel quasi-steady model that utilises kinematics of a virtual hind foil together with data obtained from simulations of a single flapping foil shows that performance augmentation is primarily determined through modification of the instantaneous angle of attack of the hind foil by the vortex street established by the fore foil. This simple model provides estimates of thrust and efficiency for the hind foil, which is consistent with data obtained through full simulations. The limitations of the virtual hind foil method and its physical significance is also discussed.
The fluid mechanics employed by aquatic animals in their escape or attack maneuvers, what we call survival hydrodynamics, are fascinating because the recorded performance in animals is truly impressive. Such performance forces us to pose some basic questions on the underlying flow mechanisms that are not in use yet in engineered vehicles. A closely related issue is the ability of animals to sense the flow velocity and pressure field around them in order to detect and discriminate threats in environments where vision or other sensing is of limited or no use. We review work on animal flow sensing and actuation as a source of inspiration, and in order to formulate a number of basic problems and investigate the flow mechanisms that enable animals develop their remarkable performance. We describe some intriguing mechanisms of actuation and sensing.
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