An Investigation of instabilities characteristic of liquid propellant rocket motors :

"February 1952."

Analysis of chaotic instabilities in a rotating body with internal energy dissipation

Melnikov's method is used to analytically predict the onset of chaotic instability in a rotating body with internal energy dissipation. The model has been found to exhibit chaotic instability when a harmonic disturbance torque is applied to the system for a range of forcing amplitude and frequency. Such a model may be considered to be representative of the dynamical behavior of a number of physical systems such as a spinning spacecraft. In spacecraft, disturbance torques may arise under malfunction of the control system, from an unbalanced rotor, from vibrations in appendages or from orbital variations. Chaotic instabilities arising from such disturbances could introduce uncertainties and irregularities into the motion of the multibody system and consequently could have disastrous effects on its intended operation. A comprehensive stability analysis is performed and regions of nonlinear behavior are identified. Subsequently, the closed form analytical solution for the unperturbed system is obtained in order to identify homoclinic orbits. Melnikov's method is then applied on the system once transformed into Hamiltonian form. The resulting analytical criterion for the onset of chaotic instability is obtained in terms of critical system parameters. The sufficient criterion is shown to be a useful predictor of the phenomenon via comparisons with numerical results. Finally, for the purposes of providing a complete, self-contained investigation of this fundamental system, the control of chaotic instability is demonstated using Lyapunov's method.

Prediction of chaotic instabilities in a dragline bucket swing

The occurrence of chaotic instabilities is investigated in the swing motion of a dragline bucket during operation cycles. A dragline is a large, powerful, rotating multibody system utilised in the mining industry for removal of overburden. A simplified representative model of the dragline is developed in the form of a fundamental non-linear rotating multibody system with energy dissipation. An analytical predictive criterion for the onset of chaotic instability is then obtained in terms of critical system parameters using Melnikov's method. The model is shown to exhibit chaotic instability due to a harmonic slew torque for a range of amplitudes and frequencies. These chaotic instabilities could introduce irregularities into the motion of the dragline system, rendering the system difficult to control by the operator and/or would have undesirable effects on dragline productivity and fatigue lifetime. The sufficient analytical criterion for the onset of chaotic instability is shown to be a useful predictor of the phenomenon under steady and unsteady slewing conditions via comparisons with numerical results. (c) 2005 Elsevier Ltd. All rights reserved.

Modulational instabilities in fibres with periodic dispersion

We analytically and numerically analyze the occurrence of modulational instability in fibers with periodic changes in the group-velocity dispersion. For small variations, a set of resonances occurs in the gain spectrum. However, large dispersion variations eliminate these resonances and restrict the bandwidth of the fundamental gain spectrum. This research has been motivated by the adoption of dispersion management techniques in long-haul optical communications.

In situ studies of phase separation and crystallization directed by Marangoni instabilities during spin-coating

Results of a pioneering study are presented in which for the first time, crystallization, phase separation and Marangoni instabilities occurring during the spin-coating of polymer blends are directly visualized, in real-space and real-time. The results provide exciting new insights into the process of self-assembly, taking place during spin-coating, paving the way for the rational design of processing conditions, to allow desired morphologies to be obtained. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

From rogue waves to random walks:nonlinear instabilities in supercontinuum generation

The noise properties of supercontinuum generation continue to be a subject of wide interest within both pure and applied physics. Aside from immediate applications in supercontinuum source development, detailed studies of supercontinuum noise mechanisms have attracted interdisciplinary attention because of links with extreme instabilities in other physical systems, especially the infamous and destructive oceanic rogue waves. But the instabilities inherent in supercontinuum generation can also be interpreted in terms of natural links with the general field of random processes, and this raises new possibilities for applications in areas such as random number generation. In this contribution we will describe recent work where we interpret supercontinuum intensity and phase fluctuations in this way.

Modulational instabilities in fibres with periodic dispersion

We analytically and numerically analyze the occurrence of modulational instability in fibers with periodic changes in the group-velocity dispersion. For small variations, a set of resonances occurs in the gain spectrum. However, large dispersion variations eliminate these resonances and restrict the bandwidth of the fundamental gain spectrum. This research has been motivated by the adoption of dispersion management techniques in long-haul optical communications.

Convection induced by instabilities in the presence of a transverse seepage

The transition of laterally heated flows in a vertical layer and in the presence of a streamwise pressure gradient is examined numerically for the case of different values Prandtl number. The stability analysis of the basic flow for the pure hydrodynamic case ( Pr = 0 ) was reported in [1]. We find that in the absence of transverse pumping the previously known critical parameters are recovered [2], while as the strength of the Poiseuille flow component is increased the convective motion is delayed considerably. Following the linear stability analysis for the vertical channel flow our attention is focused on a study of the finite am- plitude secondary travelling-wave (TW) solutions that develop from the perturbations of the transverse roll type imposed on the basic flow and temperature profiles. The linear stability of the secondary TWs against three-dimensional perturbations is also examined and it is shown that the bifurcating tertiary flows are phase-locked to the secondary TWs.

Non-radial instabilities and progenitor asphericities in core-collapse supernovae

Since core-collapse supernova simulations still struggle to produce robust neutrino-driven explosions in 3D, it has been proposed that asphericities caused by convection in the progenitor might facilitate shock revival by boosting the activity of non-radial hydrodynamic instabilities in the post-shock region. We investigate this scenario in depth using 42 relativistic 2D simulations with multigroup neutrino transport to examine the effects of velocity and density perturbations in the progenitor for different perturbation geometries that obey fundamental physical constraints (like the anelastic condition). As a framework for analysing our results, we introduce semi-empirical scaling laws relating neutrino heating, average turbulent velocities in the gain region, and the shock deformation in the saturation limit of non-radial instabilities. The squared turbulent Mach number, 〈Ma2〉, reflects the violence of aspherical motions in the gain layer, and explosive runaway occurs for 〈Ma2〉 ≳ 0.3, corresponding to a reduction of the critical neutrino luminosity by ∼25∼25 per cent compared to 1D. In the light of this theory, progenitor asphericities aid shock revival mainly by creating anisotropic mass flux on to the shock: differential infall efficiently converts velocity perturbations in the progenitor into density perturbations δρ/ρ at the shock of the order of the initial convective Mach number Maprog. The anisotropic mass flux and ram pressure deform the shock and thereby amplify post-shock turbulence. Large-scale (ℓ = 2, ℓ = 1) modes prove most conducive to shock revival, whereas small-scale perturbations require unrealistically high convective Mach numbers. Initial density perturbations in the progenitor are only of the order of Ma2progMaprog2 and therefore play a subdominant role.

Asymmetric hydrogen flame in a heated micro-channel: role of Darrieus-Landau and thermal-diffusive instabilities

Present work examines numerically the asymmetric behavior of hydrogen/air flame in a micro-channel subjected to a non-uniform wall temperature distribution. A high resolution (with cell size of 25 μm × 25 μm) of two-dimensional transient Navier–Stokes simulation is conducted in the low-Mach number formulation using detailed chemistry evolving 9 chemical species and 21 elementary reactions. Firstly, effects of hydrodynamic and diffusive-thermal instabilities are studied by performing the computations for different Lewis numbers. Then, the effects of preferential diffusion of heat and mass transfer on the asymmetric behavior of the hydrogen flame are analyzed for different inlet velocities and equivalence ratios. Results show that for the flames in micro-channels, interactions between thermal diffusion and molecular diffusion play major role in evolution of a symmetric flame into an asymmetric one. Furthermore, the role of Darrieus–Landau instability found to be minor. It is also found that in symmetric flames, the Lewis number decreases behind the flame front. This is related to the curvature of flame which leads to the inclination of thermal and mass fluxes. The mass diffusion vectors point toward the walls and the thermal diffusion vectors point toward the centerline. Asymmetric flame is observed when the length of flame front is about 1.1–1.15 times of the channel width.