1. Introductory .—This is the third of a series of papers dealing with the stability or instability of certain forms of vortex motion associated with the wake of a body moving in a fluid. In the earlier papers we examined the case of a system of equal vortex rings in parallel planes, as they might form in the rear of a sphere in steady motion. Nisi and Porter have shown that the lowest speed at which the vortex ring forms is 8·14 v / d where v is the kinematic viscosity of the fluid and d is the diameter of the sphere. Such a system of vortices has been proved to be only partially stable, and it is therefore to be inferred that their production occurs at a transition stage to a more stable type of flow. Now it is well known that in the case of two dimensional flow past a cylinder of any cross-sectional shape, eddies are formed in symmetrical pairs at low values of Reynolds' number, whereas at higher values asymmetry sets in and the eddying is formed alternately at one side of the cylinder and then at the other with regular periodicity. This latter stage occurs over a range of values of Reynolds’ number extending from about 70 to 105. Detailed explorations of the field for some distance behind the cylinder have established that the centres of eddying approximately assume the stable formation which has come to be known as the “Karman vortex street."

The Steady Motion and Sabilily of a Helical Vortex

Numerical analysis of the wake dynamics of a propeller

The work in this paper focuses on the examination of the effect of variable stiffness distributions on the kinematics and propulsion performance of a tuna-like swimmer. This is performed with the use of a recently developed fully coupled fluid-structure interaction solver. The two different scenarios considered in the present study are the stiffness varied along the fish body and the caudal fin, respectively. Our results show that it is feasible to replicate the similar kinematics and propulsive capability to that of the real fish via purely passive structural deformations. In addition, propulsion performance improvement is mainly dependent on the better orientation of the force near the posterior part of swimmers towards the thrust direction. Specifically, when a variable body stiffness scenario is considered, the bionic body stiffness profile results in better performance in most cases studied herein compared with a uniform stiffness commonly investigated in previous studies. Given the second scenario, where the stiffness is varied only in the spanwise direction of the tail, similar tail kinematics to that of the live scombrid fish only occurs in association with the heterocercal flexural rigidity profile. The resulting asymmetric tail conformation also yields performance improvement at intermediate stiffness in comparison to the cupping and uniform stiffness.

https://iopscience.iop.org/article/10.1088/1748-3190/abb3b6/pdf

The effect of variable stiffness of tuna-like fish body and fin on swimming performance

Understanding the connection between physiology and kinematics of natural swimmers is of great importance to design efficient bio-inspired underwater vehicles. This study looks at high-fidelity three-dimensional numerical simulations for flows over an undulating American eel with prescribed anguilliform kinematics. Particularly, our work focuses on why natural anguilliform swimmers employ wavelengths shorter than their bodylengths while performing wavy kinematics. For this purpose, we vary the undulatory wavelength for a range of values generally observed in different aquatic animals at Strouhal numbers 0.30 and 0.40. We observe that our anguilliform swimmer is able to demonstrate more suitable hydrodynamic performance for wavelengths of 0.65 and 0.80. For longer wavelengths, the swimmer experiences large frictional drag, which deteriorates its performance. The wake topology was dominated by hairpin-like structures, which are closely linked with the underlying physics of anguilliform swimming found in nature.

Why do anguilliform swimmers perform undulation with wavelengths shorter than their bodylengths

The effect of non-uniform chordwise stiffness distribution on the self-propulsive performance of three-dimensional flexible plates is studied numerically. Some typical stiffness distributions, including uniform, declining, and growing distribution, are considered. First, the normalized bending stiffness K is derived, which can well represent the overall bending stiffness of the non-uniform plates. For different non-uniformly distributed plates with the same K, the maximum displacement difference between the trailing and leading edges of the plate during the flapping is almost identical. There exists a common optimal K at which all the plates achieve their optimal performance, i.e., the highest cruising speed and efficiency. Second, we reveal what kind of non-uniform distribution could be the best at a specific K in terms of the propulsive performance. The force analysis indicates that a larger bending deformation in the anterior part for the growing distribution leads to a larger thrust. Hence, the large local slope along the anterior flexible plate is preferred to enhance the propulsive performance. The results obtained in this study may shed some light on a better understanding of the hydrodynamic effect on the self-propulsion of the non-uniform stiffness wings or fins of animals.

Optimal chordwise stiffness distribution for self-propelled heaving flexible plates

A numerical analysis based on detached eddy simulations is conducted to investigate vortex instabilities in the wake of a preswirl pumpjet propulsor. Three models are established to separate the roles that the rotor, stator, and duct play in the vortex structure of the pumpjet propulsor. In this paper, only the vortex structure of the rotor is considered. The results show that the vortex system of the rotor is mainly composed of the tip vortices, a hub vortex, the trailing tip vortices, and the trailing root vortices. The trailing tip vortices are generated by the premature shedding of the tip vortices in the rotor model compared with a normal single propeller. The existence of trailing root vortices increases the stability of the hub vortex. Furthermore, a unique multi-inductance instability mode of the tip vortex, called the “overlap–forward” phenomenon, is found for low values of the advance coefficient J. It is found that the instability of the tip vortex depends not only on the spiral-to-spiral distance but also on the highest-efficiency point of the propeller. The instability inception point of the tip vortex moves farther downstream with increasing J, whereas when J is greater than the highest-efficiency point of the propeller, the stable length of the tip vortices drops sharply. The energy transfer process from blade harmonics to shaft harmonics of the tip vortices depends on J and is related to the spatial evolution of the tip vortices.

/pdf/numerical-simulation-of-vortex-instabilities-in-the-wake-of-17b378mn3v.pdf

Numerical simulation of vortex instabilities in the wake of a preswirl pumpjet propulsor

A fluid─structure interaction solver for the study on a passively deformed fish fin with non-uniformly distributed stiffness

An inflation-deflation propulsion system inspired by the jet propulsion mechanism of squids and other cephalopods is proposed. The two-dimensional squid-like swimmer has a flexible mantle body with a pressure chamber and a nozzle that serves as the inlet and outlet of water. The fluid-structure interaction simulation results indicate that larger mean thrust production and higher efficiency can be achieved in high Reynolds number scenarios compared with the cases in laminar flow. The improved performance at high Reynolds number is attributed to stronger jet-induced vortices and highly suppressed external body vortices, which are associated with drag force. Optimal efficiency is reached when the jet vortices start to dominate the surrounding flow. The mechanism of symmetry-breaking instability under the turbulent flow condition is found to be different from that previously reported in laminar flow. Specifically, this instability in turbulent flow stems from irregular internal body vortices, which cause symmetry breaking in the wake. A higher Reynolds number or smaller nozzle size would accelerate the formation of this symmetry-breaking instability.

Pulsed-jet propulsion of a squid-inspired swimmer at high Reynolds number

A numerical study based on detached eddy simulations is conducted to investigate the effects of the odd and even number of rotor/stator blades, that is, nr/ ns, on the hydrodynamic performance of a pre-swirl pumpjet propulsor (PJP). In this paper, six PJPs, the PJP 6-4 ( ns– nr), 8-6, 10-8, 7-5, 9-7, and 11-9, are created. The hydrodynamic performance, the unsteady force of blades, and the wake structure of the PJPs are compared. The results show that the frequency of the fluctuating force of the whole rotor highly depends on the number or, more specifically, the parity of nr. When the parameter nr is the even number, it can be found that the total unsteady force of the rotor blades will be strengthened at the k-order stator-blades-passing frequency ([Formula: see text]). Moreover, it indicates that the superposition-enhancement coefficient (is defined as [Formula: see text]) at [Formula: see text] equals to nr, at least from the present tests. In terms of both the rotor and stator numbers are even, a phenomenon of the rotor–stator resonance occurs at [Formula: see text], where fn represents the hub rotational frequency. This work is expected to give some insight in the design of a PJP.

/pdf/effect-of-the-odd-and-even-number-of-blades-on-the-3st6l9mu.pdf

Yang Luo

Papers

Numerical simulation of vortex instabilities in the wake of a preswirl pumpjet propulsor

A fluid─structure interaction solver for the study on a passively deformed fish fin with non-uniformly distributed stiffness

The effect of variable stiffness of tuna-like fish body and fin on swimming performance

Pulsed-jet propulsion of a squid-inspired swimmer at high Reynolds number

Effect of the odd and even number of blades on the hydrodynamic performance of a pre-swirl pumpjet propulsor