Behaviour of unsteady transonic shock / boundary layer interactions with three-dimensional effects

An experimental investigation into the response of transonic SBLIs to periodic down-stream pressure perturbations in a parallel walled duct has been conducted. Tests have been carried out with a shock strength of M ∞ = 1.5 for pressure perturbation frequencies in the range 16-90 Hz. Analysis of the steady interaction at M∞ = 1.5 has also been made. The principle measurement techniques were high speed schlieren photography and laser Doppler anemometry. The structure of the steady SBLI was found to be highly three-dimensional, with large corner flows and sidewall SBLIs. These aspects are thought to influence the upstream transmission of pressure information through the interaction by affecting the post-shock flow field, including the extent of regions of secondary supersonic flow. At low frequency, the dynamics of shock motion can be predicted using an inviscid analytical model. At increased frequencies, viscous effects become significant and the shock exhibits unexpected dynamic behaviour, due to a phase lag between the upstream transmission of pressure information in the core flow and in the viscous boundary layers. Flow control in the form of micro-vane vortex generators was found to have a small impact on shock dynamics, due to the effect it had on the post-shock flow field outside the viscous boundary layer region. The relationship between inviscid and viscous effects is developed and potential destabilising mechanisms for SBLIs in practical applications are suggested. Copyright © 2009 by Paul Bruce and Holger Babinsky.

Triggering in a thermoacoustic system with stochastic noise

This paper explores the mechanism of triggering in a simple thermoacoustic system, the Rijke tube. It is demonstrated that additive stochastic perturbations can cause triggering before the linear stability limit of a thermoacoustic system. When triggering from low noise amplitudes, the system is seen to evolve to self-sustained oscillations via an unstable periodic solution of the governing equations. Practical stability is introduced as a measure of the stability of a linearly stable state when finite perturbations are present. The concept of a stochastic stability map is used to demonstrate the change in practical stability limits for a system with a subcritical bifurcation, once stochastic terms are included. The practical stability limits are found to be strongly dependent on the strength of noise.

Fem modeling of periodic arrays of multi-walled carbon nanotubes

Multiwalled carbon nanotubes display dielectric properties similar to those of graphite, which can be calculated using the well known Drude-Lorentz model. However, most computational softwares lack the capacity to directly incorporate this model into the simulations. We present the finite element modeling of optical propagation through periodic arrays of multiwalled carbon nanotubes. The dielectric function of nanotubes was incorporated into the model by using polynomial curve fitting technique. The computational analysis revealed interesting metamaterial filtering effects displayed by the highly dense square lattice arrays of carbon nanotubes, having lattice constants of the order few hundred nanometers. The curve fitting results for the dielectric function can also be used for simulating other interesting optical applications based on nanotube arrays.

Measurements of triggering and transient growth in a model lean-premixed gas turbine combustor

Instability triggering and transient growth of thermoacoustic oscillations were experimentally investigated in combination with linear/nonlinear flame transfer function (FTF) methodology in a model lean-premixed gas turbine combustor operated with CH 4 and air at atmospheric pressure. A fully premixed flame with 10kW thermal power and an equivalence ratio of 0.60 was chosen for detailed characterization of the nonlinear transient behaviors. Flame transfer functions were experimentally determined by simultaneous measurements of inlet velocity fluctuations and heat release rate oscillations using a constant temperature anemometer and OH */CH * chemiluminescence emissions, respectively. The phase-resolved variation of the local flame structure at a limit cycle was measured by planar laser-induced fluorescence of OH. Simultaneous measurements of inlet velocity, OH */CH * emission, and acoustic pressure were performed to investigate the temporal evolution of the system from a stable to a limit cycle operation. This measurement allows us to describe an unsteady instability triggering event in terms of several distinct stages: (i) initiation of a small perturbation, (ii) exponential amplification, (iii) saturation, (iv) nonlinear evolution of the perturbations towards a new unstable periodic state, (v) quasi-steady low-amplitude periodic oscillation, and (vi) fully-developed high-amplitude limit cycle oscillation. Phase-plane portraits of instantaneous inlet velocity and heat release rate clearly show the presence of two different attractors. Depending on its initial position in phase space at infinitesimally small amplitude, the system evolves towards either a high-amplitude oscillatory state or a low-amplitude oscillatory state. This transient phenomenon was analyzed using frequency- and amplitude-dependent damping mechanisms, and compared to subcritical and supercritical bifurcation theories. The results presented in this paper experimentally demonstrate the hypothesis proposed by Preetham et al. based on analytical and computational solutions of the nonlinear G-equation [J. Propul. Power 24 (2008) 1390-1402]. Good quantitative agreement was obtained between measurements and predictions in terms of the conditions for the onset of triggering and the amplitude of triggered combustion instabilities. © 2011 The Combustion Institute.

Stiffness and strength of tridimensional periodic lattices

This paper presents a method for the linear analysis of the stiffness and strength of open and closed cell lattices with arbitrary topology. The method hinges on a multiscale approach that separates the analysis of the lattice in two scales. At the macroscopic level, the lattice is considered as a uniform material; at the microscopic scale, on the other hand, the cell microstructure is modelled in detail by means of an in-house finite element solver. The method allows determine the macroscopic stiffness, the internal forces in the edges and walls of the lattice, as well as the global periodic buckling loads, along with their buckling modes. Four cube-based lattices and nine cell topologies derived by Archimedean polyhedra are studied. Several of them are characterized here for the first time with a particular attention on the role that the cell wall plays on the stiffness and strength properties. The method, automated in a computational routine, has been used to develop material property charts that help to gain insight into the performance of the lattices under investigation. © 2012 Elsevier B.V.

Rhythmic stabilization of periodic orbits in a wedge

The paper addresses the rhythmic stabilization of periodic orbits in a wedge billiard with actuated edges. The output feedback strategy, based on the sole measurement of impact times, results from the combination of a stabilizing state feedback control law and a nonlinear deadbeat state estimator. It is shown that the robustness of both the control law and the observer leads to a simple rhythmic controller achieving a large basin of attraction. Copyright © 2005 IFAC.

Stabilization of periodic orbits in a wedge billiard

This paper introduces a stabilization problem for an elementary impact control system in the plane. The rich dynamical properties of the wedge billiard, combined to the relevance of the associated stabilization problem for feedback control issues in legged robotics make it a valuable benchmark for energy-based stabilization of impact control systems.

Some remarks about periodic feedback stabilization

Periodic feedback stabilization is a very natural solution to overcome the topological obstructions which may occur when one tries to asymptotically (locally) stabilize a (locally) controllable nonlinear system around an equilibrium point. The object of this paper is to give a simple geometric interpretation of this fact, to show that one obtains a weakened form of those obstructions when periodic feedback is used, and to illustrate the success of periodic feedback stabilization on a representative system which contains a drift.