Evaluating boundary dependent errors in QM/MM simulations.

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations provide a powerful tool for studying chemical reactions, especially in complex biochemical systems. In most works to date, the quantum region is kept fixed throughout the simulation and is defined in an ad hoc way based on chemical intuition and available computational resources. The simulation errors associated with a given choice of the quantum region are, however, rarely assessed in a systematic manner. Here we study the dependence of two relevant quantities on the QM region size: the force error at the center of the QM region and the free energy of a proton transfer reaction. Taking lysozyme as our model system, we find that in an apolar region the average force error rapidly decreases with increasing QM region size. In contrast, the average force error at the polar active site is considerably higher, exhibits large oscillations and decreases more slowly, and may not fall below acceptable limits even for a quantum region radius of 9.0 A. Although computation of free energies could only be afforded until 6.0 A, results were found to change considerably within these limits. These errors demonstrate that the results of QM/MM calculations are heavily affected by the definition of the QM region (not only its size), and a convergence test is proposed to be a part of setting up QM/MM simulations.

Vortices, sound and flames - a damaging combination

The interaction between vortices, sound and combustion can lead to self-excited oscillations of such large amplitudes that structural damage is done. These occur because any small unsteadiness in the rate of combustion is a source of sound, generating pressure and velocity fluctuations. However, the velocity fluctuations perturb the flame, thereby altering the instantaneous rate of heat release. Instability is then possible because while acoustic waves perturb the combustion, the unsteady combustion generates yet more sound! Combustion oscillations can occur in afterburners and at idle in conventional aeroengine combustors. Lean premixed, prevapourized technology has tremendous potential to reduce NOx emissions, but is proving highly susceptible to self-excited oscillations. An overview of the physics of the interaction between vortices, sound and flames is presented, and illustrated by examples of instability in generic premixed ducted flames and in aeroengine combustors. The potential for both passive and active control is discussed.

Spray visualisation and acoustic analysis in a gas-turbine type burner

This paper presents the characterisation of self-excited oscillations in a kerosene burner. The combustion instability exhibits two different modes and frequencies depending on the air flow rate. Experimental results reveal the influence of the spray to shift between these two modes. Pressure and heat release fluctuations have been measured simultaneously and the flame transfer function has been calculated from these measurements. The Mie scattering technique has been used to record spray fluctuations in reacting conditions with a high speed camera. Innovative image processing has enabled us to obtain fluctuations of the Mie scattered light from the spray as a temporal signal acquired simultaneously with pressure fluctuations. This has been used to determine a transfer function relating the image intensity and hence the spray fluctuations to changes in air velocity. This function has identified the different role the spray plays in the two modes of instability. At low air flow rates, the spray responds to an unsteady air flow rate and the time varying spray characteristics lead to unsteady combustion. At higher air flow rates, effective evaporation means that the spray dynamics are less important, leading to a different flame transfer function and frequency of self-excited oscillation. In conclusion, the combustion instabilities observed are closely related with the fluctuations of the spray motion and evaporation.

Singing flames - The coupling of acoustics and combustion

An overview of the physics of the interaction between sound and flames is presented. The flame dynamics are investigated through experiment and computer modelling. The complementary rôles of wave analysis, low-order models for unsteady combustion, Computational Fluid Dynamics and experiment are illustrated by examples of oscillations in gas turbine combustors and in generic premixed ducted flames. The potential for 'antisound' and passive acoustic absorbers to eliminate the instability is also discussed.

Rhythm generation in monkey motor cortex explored using pyramidal tract stimulation.

We investigated whether stimulation of the pyramidal tract (PT) could reset the phase of 15-30 Hz beta oscillations observed in the macaque motor cortex. We recorded local field potentials (LFPs) and multiple single-unit activity from two conscious macaque monkeys performing a precision grip task. EMG activity was also recorded from the second animal. Single PT stimuli were delivered during the hold period of the task, when oscillations in the LFP were most prominent. Stimulus-triggered averaging of the LFP showed a phase-locked oscillatory response to PT stimulation. Frequency domain analysis revealed two components within the response: a 15-30 Hz component, which represented resetting of on-going beta rhythms, and a lower frequency 10 Hz response. Only the higher frequency could be observed in the EMG activity, at stronger stimulus intensities than were required for resetting the cortical rhythm. Stimulation of the PT during movement elicited a greatly reduced oscillatory response. Analysis of single-unit discharge confirmed that PT stimulation was capable of resetting periodic activity in motor cortex. The firing patterns of pyramidal tract neurones (PTNs) and unidentified neurones exhibited successive cycles of suppression and facilitation, time locked to the stimulus. We conclude that PTN activity directly influences the generation of the 15-30 Hz rhythm. These PTNs facilitate EMG activity in upper limb muscles, contributing to corticomuscular coherence at this same frequency. Since the earliest oscillatory effect observed following stimulation was a suppression of firing, we speculate that inhibitory feedback may be the key mechanism generating such oscillations in the motor cortex.

Resonance phenomena in a ferroelectric liquid crystals

In a surface stabilized ferroelectric liquid crystal cell, optical transmission oscillations have been revealed accompanying mechanical vibrations caused by fast field reversal. Special bookshelf textures, so-called "rainbow", were used in the experiments. Temperature dependences of the oscillation parameters have been studied. The temperature dependence of the oscillation frequency suggests that the some oscillation resonances correspond to modes of the liquid crystals.

Numerical simulations of unsteady wet steam flows with non-equilibrium condensation in the nozzle and the steam turbine

Numerical techniques for non-equilibrium condensing flows are presented. Conservation equations for homogeneous gas-liquid two-phase compressible flows are solved by using a finite volume method based on an approximate Riemann solver. The phase change consists of the homogeneous nucleation and growth of existing droplets. Nucleation is computed with the classical Volmer-Frenkel model, corrected for the influence of the droplet temperature being higher than the steam temperature due to latent heat release. For droplet growth, two types of heat transfer model between droplets and the surrounding steam are used: a free molecular flow model and a semi-empirical two-layer model which is deemed to be valid over a wide range of Knudsen number. The computed pressure distribution and Sauter mean droplet diameters in a convergent-divergent (Laval) nozzle are compared with experimental data. Both droplet growth models capture qualitatively the pressure increases due to sudden heat release by the non-equilibrium condensation. However the agreement between computed and experimental pressure distributions is better for the two-layer model. The droplet diameter calculated by this model also agrees well with the experimental value, whereas that predicted by the free molecular model is too small. Condensing flows in a steam turbine cascade are calculated at different Mach numbers and inlet superheat conditions and are compared with experiments. Static pressure traverses downstream from the blade and pressure distributions on the blade surface agree well with experimental results in all cases. Once again, droplet diameters computed with the two-layer model give best agreement with the experiments. Droplet sizes are found to vary across the blade pitch due to the significant variation in expansion rate. Flow patterns including oblique shock waves and condensation-induced pressure increases are also presented and are similar to those shown in the experimental Schlieren photographs. Finally, calculations are presented for periodically unsteady condensing flows in a low expansion rate, convergent-divergent (Laval) nozzle. Depending on the inlet stagnation subcooling, two types of self-excited oscillations appear: a symmetric mode at lower inlet subcooling and an asymmetric mode at higher subcooling. Plots of oscillation frequency versus inlet sub-cooling exhibit a hysteresis loop, in accord with observations made by other researchers for moist air flow. Copyright © 2006 by ASME.

Analysis of basic processes inside the keyhole during deep penetration ND-YAG CW laser welding

During laser welding, the keyhole is generated by the recoil pressure induced by the evaporation processes occurring mainly on the front keyhole wall (KW). In order to characterize the evaporation process, we have measured this recoil pressure by using a plume deflection technique, where the plume generated for static conditions (i. e. with no sample displacement) is deflected by a transverse side gas jet. From the measurement of the plume deflection angle, the recoil pressure can be determined as a function of incident intensity and sample material. From these data one can estimate the pressure generated on the front KW, during laser welding. Therefore, the corresponding dynamic pressure exerted by the vapor plume expansion on the rear KW, in contact with the melt pool, can be also estimated. These pressures appear to be in close agreement with those generated by an additional side jet that has been used in previous experiments, for stabilizing the observed melt pool oscillations or fluctuations.

Adaptive control of combustion instabilities for unknown sign of the high frequency gain

A type of adaptive, closed-loop controllers known as self-tuning regulators present a robust method of eliminating thermoacoustic oscillations in modern gas turbines. These controllers are able to adapt to changes in operating conditions, and require very little pre-characterisation of the system. One piece of information that is required, however, is the sign of the system's high frequency gain (or its 'instantaneous gain'). This poses a problem: combustion systems are infinite-dimensional, and so this information is never known a priori. A possible solution is to use a Nussbaum gain, which guarantees closed-loop stability without knowledge of the sign of the high frequency gain. Despite the theory for such a controller having been developed in the 1980s, it has never, to the authors' knowledge, been demonstrated experimentally. In this paper, a Nussbaum gain is used to stabilise thermoacoustic instability in a Rijke tube. The sign of the high frequency gain of the system is not required, and the controller is robust to large changes in operating conditions - demonstrated by varying the length of the Rijke tube with time. Copyright © 2008 by Simon J. Illingworth & Aimee S. Morgans.

VGs for a normal SBLI with a downstream diffuser

New types of vortex generators for boundary layer control were investigated experimentally in a flow field which contains a Mach 1.4 normal Shockwave followed by a subsonic diffuser. A parametric study of device height and distance upstream of the normal shock was undertaken with two novel devices: ramped-vanes and split-ramps. Flowfield diagnostics included high-speed Schlieren, oil flow visualization, and pitot-static pressure measurements. A number of flowfield parameters including flow separation, pressure recovery, centerline incompressible boundary layer shape factor, and shock stability were analyzed and compared to the baseline. All configurations tested yielded an elimination of centerline flow separation with the presence of the vortex generators. However, the devices also tended to increase the three-dimensionality of the flow with increased side-wall interaction. When located 25δo upstream of the normal shock, the largest ramped-vane device (whose height was about 0.75 the incoming uncontrolled boundary layer thickness, δo) yielded the smallest centerline incompressible shape factor and the least streamwise oscillations of the normal shock. However, additional studies are needed to better understand the corner interaction effects, which are substantial. © 2010 by the American Institute of Aeronautics and Astronautics, Inc.

Model-based thermoacoustic oscillation control via ℋ ∞ loop-shaping and integral quadratic constraints

Lean premixed prevaporized (LPP) technology has been widely used in the new generation of gas turbines in which reduced emissions are a priority. However, such combustion systems are susceptible to the damage of self-excited oscillations. Feedback control provide a way of preventing such dynamic stabilities. A flame dynamics assumption is proposed for a recently developed unsteady heat release model, the robust design technique, ℋ ∞ loop-shaping, is applied for the controller design and the performance of the controller is confirmed by simulations of the closed-loop system. The Integral Quadratic Constraints(IQC) method is employed to prove the stability of the closed-loop system. ©2010 IEEE.

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.

Transient growth and triggering in the horizontal Rijke tube Matthew

This theoretical paper examines a non-normal and non-linear model of a horizontal Rijke tube. Linear and non-linear optimal initial states, which maximize acoustic energy growth over a given time from a given energy, are calculated. It is found that non-linearity and non-normality both contribute to transient growth and that, for this model, linear optimal states are only a good predictor of non-linear optimal states for low initial energies. Two types of non-linear optimal initial state are found. The first has strong energy growth during the first period of the fundamental mode but loses energy thereafter. The second has weaker energy growth during the first period but retains high energy for longer. The second type causes triggering to self-sustained oscillations from lower energy than the first and has higher energy in the fundamental mode. This suggests, for instance, that low frequency noise will be more effective at causing triggering than high frequency noise.

Synchronization of modulated traveling baroclinic waves in a periodically forced, rotating fluid annulus.

Frequency entrainment and nonlinear synchronization are commonly observed between simple oscillatory systems, but their occurrence and behavior in continuum fluid systems are much less well understood. Motivated by possible applications to geophysical fluid systems, such as in atmospheric circulation and climate dynamics, we have carried out an experimental study of the interaction of fully developed baroclinic instability in a differentially heated, rotating fluid annulus with an externally imposed periodic modulation of the thermal boundary conditions. In quasiperiodic and chaotic amplitude-modulated traveling wave regimes, the results demonstrate a strong interaction between the natural periodic modulation of the wave amplitude and the externally imposed forcing. This leads to partial or complete phase synchronization. Synchronization effects were observed even with very weak amplitudes of forcing, and were found with both 1:1 and 1:2 frequency ratios between forcing and natural oscillations.