Naturally occurring oscillations

Model instability is demonstrated by many of the simulation examples and leads to very interesting phenomena, such as multiple steady states, naturally occurring oscillations, and chaotic behaviour. In the case of a model which is inherently unstable, nothing can be done except to completely reformulate the model into a more stable form... 

Natural cause and effect 175 Naturally occurring oscillations 126 Negative feedback 158 Nelder-Mead search algorithm 108 Newton s gradient method 108 Nitrogen 572 Non-equilibrium... 

Both practical combustors had pilot streams carr 4ng a fuel-air mixture richer than that of the main flow. These could also serve as a convenient location for the addition of oscillations to the fuel flow to control naturally occurring oscillations. Oscillation of fuel in the main flow will be more effective if it is applied close to the entry to the burner. Hence the present study examined the possibility of control by oscillation of fuel at locations corresponding to both portions of the combustor in-flow. 

The flammability and stability limits of Fig. 19.7 were obtained using fuel-air mixtures with the same equivalence ratio in the radial and tangential inlets, and without an axial jet. The lean flammability limit decreased from 0.57 to 0.4 as the swirl number was increased from 0.6 to 3.75, and the region of high-heat release moved closer to the swirler which represented an acoustic pressure antinode for the naturally occurring oscillations associated with a quarter wave in the entire duct, with frequency close to 200 Hz. Thus, swirl led to an increase in the amplitude of oscillations and to an earlier transition from smooth to rough combustion with antinodal RMS pressures up to 10 kPa, and initiated at an equivalence ratio of 0.5 for a swirl number of 3.75... 

Active control of naturally occurring oscillations in the two flow arrangements resulted in levels of attenuation which were generally less than those achieved in premixed flames stabilized behind simple bluff bodies. Difficulties were experienced in controlling pressure oscillations over certain ranges of equivalence ratio for different reasons and the experiments confirmed the importance of the location of fuel addition. 

The tendency of premixed flames to detach from the flame holder to stabilize further downstream has also been reported close to the flammability limit in a two-dimensional sudden expansion flow [27]. The change in flame position in the present annular flow arrangement was a consequence of flow oscillations associated with rough combustion, and the flame can be particularly susceptible to detachment and possible extinction, especially at values of equivalence ratio close to the lean flammability limit. Measurements of extinction in opposed jet flames subject to pressure oscillations [28] show that a number of cycles of local flame extinction and relight were required before the flame finally blew off. The number of cycles over which the extinction process occurred depended on the frequency and amplitude of the oscillated input and the equivalence ratios in the opposed jets. Thus the onset of large amplitudes of oscillations in the lean combustor is not likely to lead to instantaneous blow-off, and the availability of a control mechanism to respond to the naturally occurring oscillations at their onset can slow down the progress towards total extinction and restore a stable flame. 

To demonstrate liquid-fueled active combustion control, instability suppression experiments were performed under several conditions. Figure 21.6 shows the dump combustor set-up used in the demonstration experiments. Three configurations in which naturally unstable oscillations were observed are shown. Table 21.1 lists the specific flow conditions where instabilities occurred. The case number in the table corresponds to the combustor configuration used. 

The frequency a> itself can be regarded as a complex variable. We are not restricted to thinking about only sinusoidal oscillations of fields but we can use frequency language to talk about fields that shrink or grow exponentially. The language must be able to talk about real materials in which electric fields or charge fluctuations occur, oscillate with natural frequencies of the substance, and die away over time. 

The unfiltered OLED shows a deep absorption peak due to the Fabry-Perot resonance of the naturally-occurring weak microcavity, and the filtered OLED shows oscillations in the reflectance due to the same effect. Lower reflectance filters could be designed with more layers in the DBR, at the expense of added complexity. 

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