Oscillations, flow dynamic

Fig. 2.4 Flow dynamics of normal jet impingement with an oscillating diaphragm. Reprinted from Lasance and Simons (2005) with permission...

Bergles, A. E., P. Goldberg, and J. S. Maulbetsch, 1967a, Acoustic Oscillations in a High Pressure Single Channel Boiling System, EUR ATOM Rep., Proc. Symp. on Two-Phase Flow Dynamics, Eindhoven, pp. 525-550. (6)... 

The results of Fig. 19.8 for a swirl number of 1.35 show that the attenuation increased to 10 dB with the velocity of the axial jet up to 42 m/s, and further increase to 47 m/s caused the amplitude to fall from around 6 kPa to less than 1.5 kPa and the attenuation to decrease from 10 dB to almost zero. Similar results were observed with the swirl number of 0.6 the attenuation improved with axial jet velocity up to 60 m/s, after which the amplitude and attenuation decreased. The decline in the amplitude of oscillation and its attenuation by active control was due to the interaction between the axial jet with a large velocity and the central recirculation zone, which caused the flame to move further downstream of the swirler and heat release to occur further from the pressure antinode. The consequent increase in the distance between the point of entry of the oscillated fuel and the active burning zone reduced the effectiveness of the oscillated input due to increased fluid dynamic damping and development of a large difference in phase between different parts of the oscillated flow, especially with swirl surrounding the oscillated axial jet. 

An account of the behavior of acoustic wave propagation in a gas-solid suspension or particle movement in a turbulent eddy requires comprehensive knowledge of the dynamics of particle motion in an oscillating flow field. This oscillating flow can be analyzed in terms of one-dimensional simple harmonic oscillation represented by... 

An additional complication that occurs with oscillating flow is the existence of several regimes of laminar and turbulent flow that are functions of frequency as well as Reynolds number, as shown in Figure 3 for the case of smooth circular tubes [2]. These flow regimes are the subject of much research [3]. They are shown as a function of the peak Reynolds number Nr,peak and the ratio of channel radius R to the viscous penetration depth Sv This ratio is sometimes referred to as the dynamic Reynolds number and is similar to the Womersley number Wo = D 28y). In the weakly turbulent regime... 

Dynamic shear rheology involves measuring the resistance to dynamic oscillatory flows. Dynamic moduli such as the storage (or solid-like) modulus (G ), the loss (or fluid-like) modulus (G"), the loss tangent (tan 8 = G"IG ) and the complex viscosity ( / ) can all be used to characterize deformation resistance to dynamic oscillation of a sinusoidally imposed deformation with a characteristic frequency of oscillation (o). 

Mathematical formalism has been developed using semi-empirical considerations [36, 37]. Computer simulation smdies show that resulting equation predicts oscillations. Attempt has been made to provide justification on the bases of Navier-Stokes equation but it is open to question. Dimensional analysis has recently been employed for investigating the phenomena [31]. Flow dynamics and stability in a density oscillator have been examined by Steinbock and co-workers [38], They have related it to Rayleigh-Taylor instability of two different dense viscous liquids. A theoretical description has been presented which is based on a one-fluid model and a steady state approximation for a two-dimensional flow using Navier-Stokes equation. However, the treatment is quite complex and cannot explain the generation of electric potential oscillations. 

Although at low shear rates and low frequencies, respectively, the non-Newtonian viscosity v and the dynamic viscosity rf reflect similar characteristic times, it would not be expected that and j/(-y) should be similar functions at large values of their respective arguments, since steady flow at a high shear rate involves very different molecular motions from oscillating flow at low amplitudes where escape from topological restraints is not required. However, it has been frequently observed that 1j7 ( ) closely resembles v y). Here j (< )) = = (7 /(d,... 

Most chemically reacting systems tliat we encounter are not tliennodynamically controlled since reactions are often carried out under non-equilibrium conditions where flows of matter or energy prevent tire system from relaxing to equilibrium. Almost all biochemical reactions in living systems are of tliis type as are industrial processes carried out in open chemical reactors. In addition, tire transient dynamics of closed systems may occur on long time scales and resemble tire sustained behaviour of systems in non-equilibrium conditions. A reacting system may behave in unusual ways tliere may be more tlian one stable steady state, tire system may oscillate, sometimes witli a complicated pattern of oscillations, or even show chaotic variations of chemical concentrations. 

Another instability mode of interest is due to the flow regime itself. For example, it is well known that the slug flow regime is periodic and that its occurrence in an adiabatic riser can drive a dynamic oscillation (Wallis and Hearsley, 1961). In a BWR system, one must guard against this type of instability in components such as steam separation standpipes. The design of the BWR steam separator complex is normally given a full-scale, out-of-core proof test to demonstrate that both static and dynamic performance are stable. 

In Chapter 3 the steady-state hydrodynamic aspects of two-phase flow were discussed and reference was made to their potential for instabilities. The instability of a system may be either static or dynamic. A flow is subject to a static instability if, when the flow conditions change by a small step from the original steady-state ones, another steady state is not possible in the vicinity of the original state. The cause of the phenomenon lies in the steady-state laws hence, the threshold of the instability can be predicted only by using steady-state laws. A static instability can lead either to a different steady-state condition or to a periodic behavior (Boure et al., 1973). A flow is subject to a dynamic instability when the inertia and other feedback effects have an essential part in the process. The system behaves like a servomechanism, and knowledge of the steady-state laws is not sufficient even for the threshold prediction. The steady-state may be a solution of the equations of the system, but is not the only solution. The above-mentioned fluctuations in a steady flow may be sufficient to start the instability. Three conditions are required for a system to possess a potential for oscillating instabilities ... 

Compound dynamic instabilities as secondary phenomena. Pressure-drop oscillations are triggered by a static instability phenomenon. They occur in systems that have a compressible volume upsteam of, or within, the heated section. Maul-betsch and Griffith (1965, 1967), in their study of instabilities in subcooled boiling water, found that the instability was associated with operation on the negative-sloping portion of the pressure drop-versus-flow curve. Pressure drop oscillations were predicted by an analysis (discussed in the next section), but because of the... 

In the droplet drag sub-modelT572 598 the effects of droplet distortion and oscillation due to droplet-gas relative motion on droplet drag coefficient are taken into account. Dynamical changes of the drag coefficient with flow conditions can be calculated with this submodel. Applications of the sub-models to diesel sprays showed that... 

Although most of the reported gas-phase experiments do not investigate the temporal evolution of alcohol clusters explicitly, the frequency-domain spectral information can nevertheless be translated into the time domain, making use of some elementary and robust relationships between spectral and dynamical features [289]. According to this, the 10-fs period of the hydrogen-bonded O—H oscillator is modulated and damped by a series of other phenomena. Energy flow into doorway states is certainly slower than for aliphatic C—H bonds [290] but on a time scale of a few picoseconds, energy will nevertheless have... 

The experiments and the simulation of CSTR models have revealed a complex dynamic behavior that can be predicted by the classical Andronov-Poincare-Hopf theory, including limit cycles, multiple limit cycles, quasi-periodic oscillations, transitions to chaotic dynamic and chaotic behavior. Examples of self-oscillation for reacting systems can be found in [4], [17], [18], [22], [23], [29], [30], [32], [33], [36]. The paper of Mankin and Hudson [17] where a CSTR with a simple reaction A B takes place, shows that it is possible to drive the reactor to chaos by perturbing the cooling temperature. In the paper by Perez, Font and Montava [22], it has been shown that a CSTR can be driven to chaos by perturbing the coolant flow rate. It has been also deduced, by means of numerical simulation, that periodic, quasi-periodic and chaotic behaviors can appear. 

It is well known that a nonlinear system with an external periodic disturbance can reach chaotic dynamics. In a CSTR, it has been shown that the variation of the coolant temperature, from a basic self-oscillation state makes the reactor to change from periodic behavior to chaotic one [17]. On the other hand, in [22], it has been shown that it is possible to reach chaotic behavior from an external sine wave disturbance of the coolant flow rate. Note that a periodic disturbance can appear, for instance, when the parameters of the PID controller which manipulates the coolant flow rate are being tuned by using the Ziegler-Nichols rules. The chaotic behavior is difficult to obtain from normal... 

From the study presented in this chapter, it has been demonstrated that a CSTR in which an exothermic first order irreversible reaction takes place, can work with steady-state, self-oscillating or chaotic dynamic. By using dimensionless variables, and taking into account an external periodic disturbance in the inlet stream temperature and coolant flow rate, it has been shown that chaotic dynamic may appear. This behavior has been analyzed from the Lyapunov exponents and the power spectrum. 

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