Linear stability of miscible two-fluid flow down an incline

We show that miscible two-layer free-surface flows of varying viscosity down an inclined substrate are different in their stability characteristics from both immiscible two-layer flows, and flows with viscosity gradients spanning the entire flow. New instability modes arise when the critical layer of the viscosity transport equation overlaps the viscosity gradient. A lubricating configuration with a less viscous wall layer is identified to be the most stabilizing at moderate miscibility (moderate Peclet numbers). This also is in contrast with the immiscible case, where the lubrication configuration is always destabilizing. The co-existence that we find under certain circumstances, of several growing overlap modes, the usual surface mode, and a Tollmien-Schlichting mode, presents interesting new possibilities for nonlinear breakdown. © 2013 AIP Publishing LLC.

Global linear stability of the boundary-layer flow over a rotating sphere

We consider the linear global stability of the boundary-layer flow over a rotating sphere. Our results suggest that a self-excited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°-65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotating-sphere flow may be different to that for the rotating disk. © 2014 Elsevier Masson SAS. All rights reserved.

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.

Global nonlinear dynamics of thin aerofoil wakes

In the present investigation of thin aerofoil wakes we compare the global nonlinear dynamics, obtained by direct numerical simulations, to the associated local instability features, derived from linear stability analyses. A given configuration depends on two control parameters: the Reynolds number Re and the adverse pressure gradient m (with m < 0) prevailing at the aerofoil trailing edge. Global instability is found to occur for large enough Re and |m|; the naturally selected frequency is determined by the local absolute frequency prevailing at the trailing edge. © 2010 Springer Science+Business Media B.V.

Combustion rumble prediction with integrated computational-fluid-dynamics/ low-order-model methods

The pressure oscillation within combustion chambers of aeroengines and industrial gas turbines is a major technical challenge to the development of high-performance and low-emission propulsion systems. In this paper, an approach integrating computational fluid dynamics and one-dimensional linear stability analysis is developed to predict the modes of oscillation in a combustor and their frequencies and growth rates. Linear acoustic theory was used to describe the acoustic waves propagating upstream and downstream of the combustion zone, which enables the computational fluid dynamics calculation to be efficiently concentrated on the combustion zone. A combustion oscillation was found to occur with its predicted frequency in agreement with experimental measurements. Furthermore, results from the computational fluid dynamics calculation provide the flame transfer function to describe unsteady heat release rate. Departures from ideal one-dimensional flows are described by shape factors. Combined with this information, low-order models can work out the possible oscillation modes and their initial growth rates. The approach developed here can be used in more general situations for the analysis of combustion oscillations. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Friction-induced vibration: Model development and comparison with large-scale experimental tests

This paper presents a comparison between theoretical predictions and experimental results from a pin-on-disc test rig exploring friction-induced vibration. The model is based on a linear stability analysis of two systems coupled by sliding contact at a single point. Predictions are compared with a large volume of measured squeal initiations that have been post-processed to extract growth rates and frequencies at the onset of squeal. Initial tests reveal the importance of including both finite contact stiffness and a velocity-dependent dynamic model for friction, giving predictions that accounted for nearly all major clusters of squeal initiations from 0 to 5 kHz. However, a large number of initiations occurred at disc mode frequencies that were not predicted with the same parameters. These frequencies proved remarkably difficult to destabilise, requiring an implausibly high coefficient of friction. An attempt has been made to estimate the dynamic friction behaviour directly from the squeal initiation data, revealing complex-valued frequency-dependent parameters for a new model of linearised dynamic friction. These new parameters readily destabilised the disc modes and provided a consistent model that could account for virtually all initiations from 0 to 15 kHz. The results suggest that instability thresholds for a wide range of squeal-type behaviour can be predicted, but they highlight the central importance of a correct understanding and accurate description of dynamic friction at the sliding interface. © 2013 Elsevier Ltd. All rights reserved.

Absolute and convective instability in gas turbine fuel injectors

Hydrodynamic instabilities in gas turbine fuel injectors help to mix the fuel and air but can sometimes lock into acoustic oscillations and contribute to thermoacoustic instability. This paper describes a linear stability analysis that predicts the frequencies and strengths of hydrodynamic instabilities and identifies the regions of the flow that cause them. It distinguishes between convective instabilities, which grow in time but are convected away by the flow, and absolute instabilities, which grow in time without being convected away. Convectively unstable flows amplify external perturbations, while absolutely unstable flows also oscillate at intrinsic frequencies. As an input, this analysis requires velocity and density fields, either from a steady but unstable solution to the Navier-Stokes equations, or from time-averaged numerical simulations. In the former case, the analysis is a predictive tool. In the latter case, it is a diagnostic tool. This technique is applied to three flows: a swirling wake at Re = 400, a single stream swirling fuel injector at Re - 106, and a lean premixed gas turbine injector with five swirling streams at Re - 106. Its application to the swirling wake demonstrates that this technique can correctly predict the frequency, growth rate and dominant wavemaker region of the flow. It also shows that the zone of absolute instability found from the spatio-temporal analysis is a good approximation to the wavemaker region, which is found by overlapping the direct and adjoint global modes. This approximation is used in the other two flows because it is difficult to calculate their adjoint global modes. Its application to the single stream fuel injector demonstrates that it can identify the regions of the flow that are responsible for generating the hydrodynamic oscillations seen in LES and experimental data. The frequencies predicted by this technique are within a few percent of the measured frequencies. The technique also explains why these oscillations become weaker when a central jet is injected along the centreline. This is because the absolutely unstable region that causes the oscillations becomes convectively unstable. Its application to the lean premixed gas turbine injector reveals that several regions of the flow are hydrodynamically unstable, each with a different frequency and a different strength. For example, it reveals that the central region of confined swirling flow is strongly absolutely unstable and sets up a precessing vortex core, which is likely to aid mixing throughout the injector. It also reveals that the region between the second and third streams is slightly absolutely unstable at a frequency that is likely to coincide with acoustic modes within the combustion chamber. This technique, coupled with knowledge of the acoustic modes in a combustion chamber, is likely to be a useful design tool for the passive control of mixing and combustion instability. Copyright © 2012 by ASME.