Wakes instability

If Re increases beyond 20 the separation ring moves forward so that the attached re-circulating wake widens and lengthens. The separation angle measured in degrees from the front stagnation point is well approximated by 0 = 180-42.5 (ln(Re/20)) at 20 < Re < 400. The steady wake region appears at 20[Pg.364]

It has also been shown, using visual illustrative methods, that accumulation can occur in the wake of people or objects, provided that the contaminants are emitted in the vortex region. Special consideration must be taken with instabilities and vortices generated by the working person. Vortices can also occur in empty open unidirectional airflow benches. 

For the hydrodynamic instability model, Lienhard and Dhir (1973b) extended the Zuber model to the CHF on finite bodies of several kinds (see Sec. 2.3.1, Fig. 2.18). Lienhard and Hasan (1979) proposed a mechanical energy stability criterion The vapor-escape wake system in a boiling process remains stable as long as the net mechanical energy transfer to the system is negative. They concluded that there is no contradiction between this criterion and the hydrodynamic instability model. 

Sleepiness in narcolepsy has also been considered a subjective phenomenon associated with the instability of boundaries between behavioral states and the constant intrusion of sleep episodes into wakefulness. Under baseline conditions, 0X2R, orexin , and orexin/ataxin-3 transgenic mice have normal amounts of wakefulness and non-REM sleep during the light and dark phases and over 24 h (Chemelli et al, 1999 Hara et al, 2001 Mochizuki et al, 2004 Willie... 

As predicted, MCH l orexin mice displayed an intermediate body weight phenotype, indicating independent and opposing neuromodulatory actions of MCH and orexin on metabolism. Surprisingly, however, rather than expressing an attenuated narcoleptic phenotype, MCHr orexin l mice exhibited more severe behavioral state instability during the active phase. When compared with orexin mice, the double null mice had about twice as many cataplectic episodes (Fig. 15.7A), they were less able to maintain wakefulness, and... 

Fig. 3a indicates that the bubble-rise velocity measured based on the displacement of the top surface of the bubble ( C/bt) quickly increases and approaches the terminal bubble rise velocity in 0.02 s. The small fluctuation of Ubt is caused by numerical instability. The bubble-rise velocity measured based on the displacement of the bottom surface of the bubble (Ubb) fluctuates significantly with time initially and converges to Ubt after 0.25 s. The overshooting of Ubb can reach 45-50 cm/s in Fig. 3a. The fluctuation of Ubb reflects the unsteady oscillation of the bubble due to the wake flow and shedding at the base of the bubble. Although the relative deviation between the simulation results of the 40 X 40 x 80 mesh and 100 x 100 x 200 mesh is notable, the deviation is insignificant between the results of the 80 x 80 x 160 mesh and those of the 100 X 100 x 200 mesh. The agreement with experiments at all resolutions is generally reasonable, although the simulated terminal bubble rise velocities ( 20 cm/s) are slightly lower than the experimental results (21 25 cm/s). A lower bubble-rise velocity obtained from the simulation is expected due to the no-slip condition imposed at the gas-liquid interface, and the finite thickness for the gas-liquid interface employed in the computational scheme.

As Re increases, skin friction becomes proportionately less and, at values greater than about 20, flow separation occurs with the formation of vortices in the wake of the sphere. At high Reynolds numbers, the size of the vortices progressively increases until, at values of between 100 and 200, instabilities in the flow give rise to vortex shedding. The effect of these changes in the nature of the flow on the force exerted on the particle is now considered. 

At Re = 130, a weak long-period oscillation appears in the tip of the wake (T2). Its amplitude increases with Re, but the flow behind the attached wake remains laminar to Re above 200. The amplitude of oscillation at the tip reaches 10% of the sphere diameter at Re = 270 (GIO). At about this Re, large vortices, associated with pulsations of the fluid circulating in the wake, periodically form and move downstream (S6). Vortex shedding appears to result from flow instability, originating in the free surface layer and moving downstream to affect the position of the wake tip (Rll, R12, S6). 

Above inviscid mechanism of instability is often encountered in free shear layers and jets. A fundamental difference between flows having an inflection point (such as in free shear layer, jets and wakes and the cross flow component of some three-dimensional boundary layers) and flows without inflection points (as in wall bounded flows in channel or in boundary layers) exists. Flows with inflection points are susceptible to temporal instabilities for very low Reynolds numbers. One can find detailed accounts of invis-... 

Instead of using this equation, in the literature, there are few models proposed by which the frequency or Strouhal number of the shedding is fixed. Koch (1985) proposed a resonance model that fixes it for a particular location in the wake by a local linear stability analysis. Upstream of this location, flow is absolutely unstable and downstream, the flow displays convective instability. Nishioka Sato (1973) proposed that the frequency selection is based on maximum spatial growth rate in the wake. The vortex shedding phenomenon starts via a linear instability and the limit cycle-like oscillations result from nonlinear super critical stability of the flow, describ-able by Eqn. (5.3.1). 

Koch, W. (1985). Local instability characteristics and frequency determination of self excited wake flow. J. Sound and vib., 99, 53-83. 

Large-diameter solid particles in a three-phase fluidized-bed system cause bubbles to be small, whereas, in a fine particle slurry, the bubbles can become large. Henriksen and Ostergaard40 showed that the large bubbles in the latter case can break as a result of Taylor instability at the root of the bubble. The wake properties of bubbles in a three-phase fluidized-bed system have been studied by Rigby and Capes.115 They showed that bubble wakes in a three-phase system consist not only of a stable portion carried with the bubbles but also of vortices shed by the bubbles. 

It is of interest that the onset of circulation of liquid drops is associated with deformation of the spherical drop into an ellipsoid (R8, C6, G2). Deformation of the spherical drops was found to be associated with oscillations and with higher transfer rates (C6) even in highly viscous fluids where stagnant drop characteristics are generally assumed. Garner (GI2), who studied the wake behind the deformed drops, concluded that the higher transfer rates were due to the onset of instability and oscillation of the wake at this relatively low Reynolds number (200) compared with 400 to 450 for solid spheres. However, no quantitative relationship is available. 

Nakaya, C. Instability of the near wake behind a circular cylinder. 

On the contrary, in polymer solutions, the fluctuations start at much smaller Re values than in water (about 30 times below between B and C Figure 5). However, the f values are equal ( C f 0.6 Hz) or higher ( D -> F, f 2 Hz) than that measured in water. A reasonable assumption which implies a smaller 6 value can then be put forward. Since the Karman vortices cannot be established in this creeping flow (Re 0.3), one must assume that the instabilities are not generated in the wake, but actually in the upstream region where the local 6 value is small. This hypothesis is consistent with the above interpretation based on the onset of a conformation change upstream. 

The continuous increase of the flame speed after the grid with increasing distance x, which is obvious from Fig. 10, cannot be explained by the turbulence structure in the wake of the rods as measured in the isothermal experiments, since under those circumstances the turbulent fluctuation velocity decreases rather fast due to dissipation (x/d 20-25). The continuous acceleration must be due to other mechanisms, presumably turbulence generating instabilities in the reaction zone. It was found from hot wire measure-... 

The analysis of the measured burning velocities in the wake of different grid structures show that, contrary to the predictions on the basis of wind tunnel measurements, the flame front is continuously accelerated after the passage of a grid structure. This acceleration must be due to turbulence generating gasdynamic instabilities in or near the reaction zone. Despite this, a nondimensionalized correlation was found, indicating that the turbulent... 

In the wake of the researches for oscillatory reactions more than a dozen pH-autoactivated reactions were shown to produce bistability when operated in a CSTR [57]. Theoretical calculations and experiments demonstrate that such systems readily give rise to spatial bistability when conducted in an OSFR. They would provide a large choice of reaction systems to test the chemomechanical instabilities theoretically described above. However, in our selection criteria, we have to take into account that many of these reactions can already exhibit kinetic oscillations over more or less wide ranges of feed parameters. Such complication can make it difficult to discriminate between kinetic and chemomechanic oscillatory instabilities. Furthermore, it has also been shown that in the case of proton-autoactivated system the natural faster diffusion of this species can lead to another source of oscillatory instability in an OSFR, the long range activation instability [58]. 

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