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.

Global modes with multiple saddle points

Significant progress has been made towards understanding the global stability of slowly-developing shear flows. The WKBJ theory developed by Patrick Huerre and his co-authors has proved absolutely central, with the result that both the linear and the nonlinear stability of a wide range of flows can now be understood in terms of their local absolute/convective instability properties. In many situations, the local absolute frequency possesses a single dominant saddle point in complex X-space (where X is the slow streamwise coordinate of the base flow), which then acts as a single wavemaker driving the entire global linear dynamics. In this paper we consider the more complicated case in which multiple saddles may act as the wavemaker for different values of some control parameter. We derive a frequency selection criterion in the general case, which is then validated against numerical results for the linearized third-order Ginzburg-Landau equation (which possesses two saddle points). We believe that this theory may be relevant to a number of flows, including the boundary layer on a rotating disk and the eccentric Taylor-Couette-Poiseuille flow. © 2014 Elsevier Masson SAS. All rights reserved.

An energy-efficient hopping robot based on free vibration of a curved beam

This paper explores a design strategy of hopping robots, which makes use of free vibration of an elastic curved beam. In this strategy, the leg structure consists of a specifically shaped elastic curved beam and a small rotating mass that induces free vibration of the entire robot body. Although we expect to improve energy efficiency of locomotion by exploiting the mechanical dynamics, it is not trivial to take advantage of the coupled dynamics between actuation and mechanical structures for the purpose of locomotion. From this perspective, this paper explains the basic design principles through modeling, simulation, and experiments of a minimalistic hopping robot platform. More specifically, we show how to design elastic curved beams for stable hopping locomotion and the control method by using unconventional actuation. In addition, we also analyze the proposed design strategy in terms of energy efficiency and discuss how it can be applied to the other forms of legged robot locomotion. © 1996-2012 IEEE.

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.

Hopping robot based on free vibration of an elastic curved beam

This study presents a novel approach to the design of low-cost and energy-efficient hopping robots, which makes use of free vibration of an elastic curved beam. We found that a hopping robot could benefit from an elastic curved beam in many ways such as low manufacturing cost, light body weight and small energy dissipation in mechanical interactions. A challenging problem of this design strategy, however, lies in harnessing the mechanical dynamics of free vibration in the elastic curved beam: because the free vibration is the outcome of coupled mechanical dynamics between actuation and mechanical structures, it is not trivial to systematically design mechanical structures and control architectures for stable locomotion. From this perspective, this paper investigates a case study of simple hopping robot to identify the design principles of mechanics and control. We developed a hopping robot consisting of an elastic curved beam and a small rotating mass, which was then modeled and analyzed in simulation. The experimental results show that the robot is capable of exhibiting stable hopping gait patterns by using a small actuation with no sensory feedback owing to the intrinsic stability of coupled mechanical dynamics. Furthermore, an additional analysis shows that, by exploiting free vibration of the elastic curved beam, cost of transport of the proposed hopping locomotion can be in the same rage of animals' locomotion including human running. © 2011 IEEE.

Development of a turning mid turbine frame with embedded design-part II: Unsteady measurements

© 2014 by ASME. This paper, the second of two parts, presents a new setup for the two-stage two-spool facility located at the Institute for Thermal Turbomachinery and Machine Dynamics (ITTM) of Graz University of Technology. The rig was designed to reproduce the flow behavior of a transonic turbine followed by a counter-rotating low pressure stage such as those in high bypass aero-engines. The meridional flow path of the machine is characterized by a diffusing S-shaped duct between the two rotors. The role of wide chord vanes placed into the mid turbine frame is to lead the flow towards the low pressure (LP) rotor with appropriate swirl. Experimental and numerical investigations performed on this setup showed that the wide chord struts induce large wakes and extended secondary flows at the LP inlet flow. Moreover, large deterministic fluctuations of pressure, which may cause noise and blade vibrations, were observed downstream of the LP rotor. In order to minimize secondary vortices and to damp the unsteady interactions, the mid turbine frame was redesigned to locate two zero-lift splitters into each vane passage. While in the first part of the paper the design process of the splitters and the time-averaged flow field were presented, in this second part the measurements performed by means of a fast response probe will support the explanation of the time-resolved field. The discussion will focus on the comparison between the baseline case (without splitters) and the embedded design.

Development of a turning mid turbine frame with embedded design-part I: Design and steady measurements

© 2014 by ASME. The paper presents a new setup for the two-stage two-spool facility located at the Institute for Thermal Turbomachinery and Machine Dynamics (ITTM) of Graz University of Technology. The rig was designed in order to simulate the flow behavior of a transonic turbine followed by a counter-rotating low pressure (LP) stage like the spools of a modern high bypass aeroengine. The meridional flow path of the machine is characterized by a diffusing S-shaped duct between the two rotors. The role of turning struts placed into the mid turbine frame is to lead the flow towards the LP rotor with appropriate swirl. Experimental and numerical investigations performed on the setup over the last years, which were used as baseline for this paper, showed that wide chord vanes induce large wakes and extended secondary flows at the LP rotor inlet flow. Moreover, unsteady interactions between the two turbines were observed downstream of the LP rotor. In order to increase the uniformity and to decrease the unsteady content of the flow at the inlet of the LP rotor, the mid turbine frame was redesigned with two zero-lifting splitters embedded into the strut passage. In this first part of the paper the design process of the splitters and its critical points are presented, while the time-averaged field is discussed by means of five-hole probe measurements and oil flow visualizations. The comparison between the baseline case and the embedded design configuration shows that the new design is able to reduce the flow gradients downstream of the turning struts, providing a more suitable inlet condition for the low pressure rotor. The improvement in the flow field uniformity is also observed downstream of the turbine and it is, consequently, reflected in an enhancement of the LP turbine performance. In the second part of this paper the influence of the embedded design on the time-resolved field is investigated.