Multiple time scale analysis of pressure oscillations in solid rocket motors

A two-inlet, side dump ramjet combustor configuration was tested in a connected-pipe setup using uncooled and uninsulated chamber walls. High amplitude combustion induced pressure oscillations were observed during most test conditions with a predominant frequency of around 300 Hz. Special efforts were made to relate the oscillations to longitudinal acoustic modes. A simplified no flow, uniform temperature acoustic cavity prediction method (NASTRAN) was utilized to model the longitudinal acoustic modes. This model was verified via room temperature laboratory tests using the actual test hardware and a loudspeaker as an input forcing function to excite the acoustic modes. During combustion tests, the measured oscillation modes were tentatively identified as second or third longitudinal modes or a bulk mode, depending on the test conditions.

The combustion instabilities in solid rocket motor (SRM) are abiding predicament since their inception seven decades ago. The availability of large amount of energy in SRM combustion in comparison to small amount required to generate the combustion instabilities ensue the likely occurrence of the problem. This entails the SRM combustion instability prediction. This paper deals with the prediction of acoustic longitudinal mode linear combustion instabilities in 3D grain SRM. The stability history of SRM is predicted during motor burn time. This necessitates the performance (pressure/thrust) analysis. The FEA based solver is employed for the acoustic analysis of the grain port cavity as the grain burns. This is followed by determination of propellant response function. The computer code developed using approximate stability analysis results based on spatial and temporal averaging of the equations of two phase flow is used to predict the stability history. The results are presented and discussed for various longitudinal acoustic modes of SRM. The study evinces the decrease in stability margin with time and increase with mode number.

The "criticality hypothesis," based on observed scale-free correlations in neural activity, posits that the brain operates at a critical point of transition between two phases. However, the validity of this hypothesis is still debated. Here, employing a commonly used model of cortical dynamics, we find that a phase of long-range order (LRO) in neural activity may be induced by memory (time nonlocality) without invoking criticality. The cortical-dynamics model contains fast and slow time scales that govern the neural and resource (memory) dynamics, respectively. When the resource dynamics are sufficiently slow, we observe an LRO phase, which manifests in avalanche size and duration probability distributions that are fit well by power laws. When the slow and fast time scales are no longer sufficiently distinct, LRO is destroyed. Since this LRO phase spans a wide range of parameters, it is robust against perturbations, unlike critical systems.

A three-dimensional high-fidelity numerical simulation of a small-scale solid rocket motor is carried out adopting the implicit large-eddy simulation (ILES) approach to investigate the coupling between vortex shedding and the acoustic modes of the motor chamber. The ONERA C1xb laboratory-scale model is considered at a firing time close to ignition, corresponding to a 3-mm-grain burned layer. The analysis focuses on the characterization of the unsteady pressure signature on the motor wall, with emphasis on the role played by turbulence on the level of pressure oscillations. It is found that the root mean square of the wall-pressure fluctuations obtained by ILES along the motor wall is in excellent agreement with the experimental data, which is contrary to the prediction of axisymmetric simulations. Fourier spectral analysis reveals that, for this grain geometry, the first three longitudinal modes are weakly excited at the motor head end and most of the energy is concentrated in the shear layer detaching from the grain edge, whose development in the motor chamber is characterized by the rollers breakup with subsequent transition to fine-scale turbulence. The spectrum highlights that the coupling between vortex shedding and pressure oscillations is locked on the third acoustic mode, in agreement with previous experimental observations and with the frequency predicted by a simple acoustic feedback loop model.

The paper considers the eighth-order proton exchange membrane (PEM) fuel-cell mathematical model and shows that it has a multi-time scale property, indicating that the dynamics of three model state space variables operate in the slow time scale and the dynamics of five state variables operate in the fast time scale. This multi-scale nature allows independent controllers to be designed in slow and fast time scales using only corresponding reduced-order slow (of dimension three) and fast (of dimension five) sub-models. The presented design facilitates the design of hybrid controllers, for example, the linear-quadratic optimal controller for the slow subsystem and the eigenvalue assignment controller for the fast subsystem. The design efficiency and its high accuracy are demonstrated via simulation on the considered PEM fuel cell model.

Experimental investigation of frequency and amplitude of density wave oscillations in vertical upflow boiling

Meta-equilibrium state of multi-species ambipolar diffusion and its relevance to polar mesopheric summer echoes

An investigation of the self-excitation of low frequency (100-600 Hz), longitudinal acoustic modes of a rearward-facing step combustor has been performed. As in combustion instabilities of air breathing propulsion systems, the pressure oscillations are excited by a fluctuating heat release from a flame that is stabilized in a recirculation zone. Flow visualization results and flame radiation intensity data reveal that large vortex structures are responsible for this fluctuating heat release. The vortices are shed at frequencies corresponding to longitudinal acoustic modes of the system or to the first subharmonic of one of the modes. A series of parametric studies were performed to determine the dependence of the vortex shedding frequency upon the step height, mean flow speed, fuel type, and equivalence ratio. It was discovered that the vortex shedding frequency can shift between modes as a result of changes in the chemical reaction time of the reactants or as a result of changes in the mixing process of the cold reactants with the hot products. Detailed investigations into the mechanism of sustenance of the oscillations during instability were performed for several operating conditions. The distribution of the combustion associated with vortex shedding was investigated by measuring the radiation intensity from the flame region. These results were used in Rayleigh's Criterion to determine regions of driving and damping of the oscillations. A one-dimensional linearized acoustic model is used to predict the natural modes of the system and a fluctuating volumetric source is used to model the oscillatory heat release. First, independent driving is applied to determine the system response to driving at different frequencies. One important result is that, the phase difference between the pressure oscillations and the velocity oscillations at the flameholder is very sensitive to the frequency of driving near natural modes of the system. Finally, a velocity-sensitive volumetric source with a time delay is included as feedback to determine the linear stability characteristics of the system. Various mechanisms leading to nonlinear limit cycle behavior are then discussed and compared to experimental data obtained during transition to instability.

In recent years technology development for the design of electric and hybrid-electric vehicle systems has reached a peak, due to ever increasing restrictions on fuel economy and reduced vehicle emissions. An international race among car manufacturers to bring production hybrid-electric vehicles to market has generated a great deal of interest in the scientific community. The design of these systems requires development of new simulation and optimization tools. In this paper, a description of a real-time numerical environment for Virtual Proving Grounds studies for hybrid-electric vehicles is presented. Within this environment, vehicle models are developed using a recursive multibody dynamics formulation that results in a set of Differential-Algebraic Equations (DAE), and vehicle subsystem models are created using Ordinary Differential Equations (ODE). Based on engineering knowledge of vehicle systems, two time scales are identified. The first time scale, referred to as slow time scale, contains generalized coordinates describing the mechanical vehicle system that includs the chassis, steering rack, and suspension assemblies. The second time scale, referred to as fast time scale, contains the hybrid-electric powertrain components and vehicle tires. Multirate techniques to integrate the combined set of DAE and ODE in two time scales are used to obtain computational gains that will allow solution of the system’s governing equations for state derivatives, and efficient numerical integration in real time.

In this paper, we present a review about mathematical models of population and community dynamics incorporating individual behaviour. The considered models consist in coupling a game theoretic model, going on at a fast time scale and that describes the change of tactics among individuals in a population or in a community to a model going on at a slow time scale describing the effects in the long term of individual tactics on reproduction and mortality of the populations. As application, an extension of a stage-structured population with intra-individual behavioural variability is presented. Individuals can adopt three different tactics: hawk, dove and bully. We consider a stage-structured population with immature and mature individuals. A mature individual experiences the different tactics in his life and it is assumed that the game is played at a fast time scale in comparison to population dynamics. This fast part of the model is coupled to a slow part, which describes the growth of each sub-population. By use of aggregation of variables methods, we obtain a reduced system of two differential equations governing immature and total mature sub-populations at the slow time scale. The analysis of the model shows that when the cost of fightings is smaller, the proportion of hawks is larger. The total population size equilibrium shows a maximum with respect to the gain of the game.

We examined the role of the cerebellum in patients with tremor-dominant cervical dystonia by measuring the adaptive capacity of rapid reflexive eye movements (saccades). We chose the saccade adaptation paradigm because, unlike other motor learning paradigms, the real-time modification of saccades cannot "wait" for the sensory (visual) feedback. Instead, saccades rely primarily on the internal reafference modulated by the cerebellum. The saccade adaptation happens over fast and slow timescales. The fast timescale has poor retention of learned response, while the slow timescale has strong retention. Cerebellar defects resulting in loss of function affect the fast timescale but the slow timescale of saccade adaptation is retained. In contrast, maladaptive cerebellar disorders feature the absence of both fast and slow timescales. We were able to measure both timescales using noninvasive oculography in 6 normal individuals. In contrast, both timescales were absent in 12 patients with tremor-dominant cervical dystonia. These findings are consistent with maladaptive cerebellar outflow as a putative pathophysiological basis for tremor-dominant cervical dystonia.

Integrating scheduling and control for economic MPC of buildings with energy storage

Long-range effects, such as allostery, have evolved in proteins as a means of regulating function via communication between distal sites. An NMR-based perturbation mapping approach was used to more completely probe the dynamic response of the core mutation V54A in the protein eglin c by monitoring changes in picosecond to nanosecond aromatic side-chain dynamics and H/D exchange stabilities. Previous side-chain dynamics studies on this mutant were limited to methyl-bearing residues, most of which were found to rigidify on the picosecond to nanosecond time scale in the form of a contiguous "network". Here, high precision (13)C relaxation data from 13 aromatic side chains were acquired by applying canonical relaxation experiments to a newly developed carbon labeling scheme [Teilum et al. (2006) J. Am. Chem. Soc. 128, 2506-2507]. The fitting of model-free parameters yielded S (2) variability which is intermediate with respect to backbone and methyl-bearing side-chain variability and tau e values that are approximately 1 ns. Inclusion of the aromatic dynamic response results in an expanded network of dynamically coupled residues, with some aromatics showing increases in flexibility, which partially offsets the rigidification in methyl side chains. Using amide hydrogen exchange, dynamic propagation on a slower time scale was probed in response to the V54A perturbation. Surprisingly, regional stabilization (slowed exchange) 10-12 A from the site of mutation was observed despite a global destabilization of 1.5 kcal x mol (-1). Furthermore, this unlikely pocket of stabilized residues colocalizes with increases in aromatic flexibility on the faster time scale. Because the converse is also true (destabilized residues colocalize with rigidification on the fast time scale), a plausible entropy-driven mechanism is discussed for relating colocalization of opposing dynamic trends on vastly different time scales.

Aqueous hydroxyl group as the vibrational probe to access the hydrophobicity of amide derivatives

A full-vectorial finite-element-based approach is used to find accurate modal solutions for the acoustic modes in a Ge-doped planar silica optical waveguide. To enhance accuracy of the solution, the existing structural symmetry is exploited, and rigorous analyses of the interactions between the guided acoustic and optical modes are performed. The stimulated Brillouin scattering frequency and the overlaps between the fundamental and the higher-order transverse and longitudinal acoustic modes and the fundamental quasi-TE optical mode are presented.