Wave propagation in a slowly-varying duct with mean vortical swirling flow

The propagation of unsteady disturbances in a slowlyvarying cylindrical duct carrying mean swirling flow is investigated using a multiple-scales technique. This is applicable to turbomachinery flow behind a rotor stage when the swirl and axial velocities are of the same order. The presence of mean vorticity couples acoustic and vorticity equations which produces an eigenvalue problem that is not self-adjoint unlike that for irrotational mean flow. In order to determine the amplitude variation along the duct, an adjoint solution for the coupled system of equations is derived. The solution breaks down where a mode changes from cut on to cut off. In this region the amplitude is governed by a form of Airy's equation, and the effect of swirl is to introduce a small shift in the origin of the Airy function away from the turning-point location. The variation of axial wavenumber and amplitude along the duct is calculated. In hard-walled ducts mean swirl is shown to produce much larger amplitude variation along the duct compared with a nonswirling flow. Mean swirl also has a large effect in ducts with finite-impedance walls which differs depending on whether modes are co-rotating with the swirl or counter rotating. © 2001 by A.J. Cooper, Published by the American Institute of Aeronautics and Astronautics, Inc.

On the laminar-turbulent transition of the rotating-disk flow: The role of absolute instability

© 2014 Cambridge University Press. This paper describes a detailed experimental study using hot-wire anemometry of the laminar-turbulent transition region of a rotating-disk boundary-layer flow without any imposed excitation of the boundary layer. The measured data are separated into stationary and unsteady disturbance fields in order to elaborate on the roles that the stationary and the travelling modes have in the transition process. We show the onset of nonlinearity consistently at Reynolds numbers, R, of ∼ 510, i.e. at the onset of Lingwood's (J. Fluid Mech., vol. 299, 1995, pp. 17-33) local absolute instability, and the growth of stationary vortices saturates at a Reynolds number of ∼ 550. The nonlinear saturation and subsequent turbulent breakdown of individual stationary vortices independently of their amplitudes, which vary azimuthally, seem to be determined by well-defined Reynolds numbers. We identify unstable travelling disturbances in our power spectra, which continue to grow, saturating at around R=585, whereupon turbulent breakdown of the boundary layer ensues. The nonlinear saturation amplitude of the total disturbance field is approximately constant for all considered cases, i.e. different rotation rates and edge Reynolds numbers. We also identify a travelling secondary instability. Our results suggest that it is the travelling disturbances that are fundamentally important to the transition to turbulence for a clean disk, rather than the stationary vortices. Here, the results appear to show a primary nonlinear steep-fronted (travelling) global mode at the boundary between the local convectively and absolutely unstable regions, which develops nonlinearly interacting with the stationary vortices and which saturates and is unstable to a secondary instability. This leads to a rapid transition to turbulence outward of the primary front from approximately R=565 to 590 and to a fully turbulent boundary layer above 650.

Minimalistic models of an energy-efficient vertical-hopping robot

The use of free vibration in elastic structure can lead to energy-efficient robot locomotion, since it significantly reduces the energy expenditure if properly designed and controlled. However, it is not well understood how to harness the dynamics of free vibration for the robot locomotion, because of the complex dynamics originated in discrete events and energy dissipation during locomotion. From this perspective, the goals of this paper are to propose a design strategy of hopping robot based on elastic curved beams and actuated rotating masses and to identify the minimalistic model that can characterize the basic principle of robot locomotion. Since the robot mainly exhibits vertical hopping, three 1-D models are examined that contain different configurations of simple spring-damper-mass components. The real-world and simulation experiments show that one of the models best characterizes the robot hopping, through analyzing the basic kinematics and negative works in actuation. Based on this model, the self-stability of hopping motion under disturbances is investigated, and design and control parameters are analyzed for the energy-efficient hopping. In addition, further analyses show that this robot can achieve the energy-efficient hopping with the variation in payload, and the source of energy dissipation of the robot hopping is investigated. © 1982-2012 IEEE.

Trajectory control based on discrete full-range dynamics

There has been an increasing interest in the use of mechanical dynamics, (e.g., assive, Elastic, And viscous dynamics) for energy efficient and agile control of robotic systems. Despite the impressive demonstrations of behavioural performance, The mechanical dynamics of this class of robotic systems is still very limited as compared to those of biological systems. For example, Passive dynamic walkers are not capable of generating joint torques to compensate for disturbances from complex environments. In order to tackle such a discrepancy between biological and artificial systems, We present the concept and design of an adaptive clutch mechanism that discretely covers the full-range of dynamics. As a result, The system is capable of a large variety of joint operations, including dynamic switching among passive, actuated and rigid modes. The main innovation of this paper is the framework and algorithm developed for controlling the trajectory of such joint. We present different control strategies that exploit passive dynamics. Simulation results demonstrate a significant improvement in motion control with respect to the speed of motion and energy efficiency. The actuator is implemented in a simple pendulum platform to quantitatively evaluate this novel approach.

Learning legged locomotion

Legged locomotion of biological systems can be viewed as a self-organizing process of highly complex system-environment interactions. Walking behavior is, for example, generated from the interactions between many mechanical components (e.g., physical interactions between feet and ground, skeletons and muscle-tendon systems), and distributed informational processes (e.g., sensory information processing, sensory-motor control in central nervous system, and reflexes) [21]. An interesting aspect of legged locomotion study lies in the fact that there are multiple levels of self-organization processes (at the levels of mechanical dynamics, sensory-motor control, and learning). Previously, the self-organization of mechanical dynamics was nicely demonstrated by the so-called Passive Dynamic Walkers (PDWs; [18]). The PDW is a purely mechanical structure consisting of body, thigh, and shank limbs that are connected by passive joints. When placed on a shallow slope, it exhibits natural bipedal walking dynamics by converting potential to kinetic energy without any actuation. An important contribution of these case studies is that, if designed properly, mechanical dynamics can generate a relatively complex locomotion dynamics, on the one hand, and the mechanical dynamics induces self-stability against small disturbances without any explicit control of motors, on the other. The basic principle of the mechanical self-stability appears to be fairly general that there are several different physics models that exhibit similar characteristics in different kinds of behaviors (e.g., hopping, running, and swimming; [2, 4, 9, 16, 19]), and a number of robotic platforms have been developed based on them [1, 8, 13, 22]. © 2009 Springer London.

Bipedal walking and running with compliant legs

Passive dynamics plays an important role in legged locomotion of the biological systems. The use of passive dynamics provides a number of advantages in legged locomotion such as energy efficiency, self-stabilization against disturbances, and generating gait patterns and behavioral diversity. Inspired from the theoretical and experimental studies in biomechanics, this paper presents a novel bipedal locomotion model for walking and running behavior which uses compliant legs. This model consists of three-segment legs, two servomotors, and four passive joints that are constrained by eight tension springs. The self-organization of two gait patterns (walking and running) is demonstrated in simulation and in a real-world robot. The analysis of joint kinematics and ground reaction force explains how a minimalistic control architecture can exploit the particular leg design for generating different gait patterns. Moreover, it is shown how the proposed model can be extended for controlling locomotion velocity and gait patterns with the simplest control architecture. © 2007 IEEE.

Mass chains with passive interconnection: Complex iterative maps and scalability

This paper introduces the problem of passive control of a chain of N identical masses in which there is an identical passive connection between neighbouring masses and a similar connection to a movable point. The problem arises in the design of multi-storey buildings which are subjected to earthquake disturbances, but applies in other situations, for example vehicle platoons. The paper will study the scalar transfer functions from the disturbance to a given intermass displacement. It will be shown that these transfer functions can be conveniently represented in the form of complex iterative maps and that these maps provide a method to establish boundedness in N of the H ∞-norm of these transfer functions for certain choices of interconnection impedance. © 2013 IEEE.