Oscillating flow pattern

The surface tension effects are negligible for the case (a), but simulation without them would again cause oscillation. Flow pattern is shown in Fig. 16 for reduced front advance. Surface tension smoothes the interfacial shape in any case and thus it should be always included, sometimes only to improve the numerical performance. 

In vertical flow, axial symmetry exists and flow patterns tend to be somewhat more stable. However, with slug flow in particular, oscillations in the flow can occur as a result of sudden changes in pressure as liquid slugs are discharged from the end of the pipe. 

The flow patterns (expansion of the bubbly, slug and annular regions of flow) affect the local pressure drop, as well as the pressure oscillations in micro-channels (Kandlikar et al. 2001 Wu and Cheng 2003a,b, 2004 Qu and Mudawar 2003 Hetsroni et al. 2005 Lee and Mudawar 2005a). 

The experimental investigations of boiling instability in parallel micro-channels have been carried out by simultaneous measurements of temporal variations of pressure drop, fluid and heater temperatures. The channel-to-channel interactions may affect pressure drop between the inlet and the outlet manifold as well as associated temperature of the fluid in the outlet manifold and heater temperature. Figure 6.37 illustrates this phenomenon for pressure drop in the heat sink that contains 13 micro-channels of d = 220 pm at mass flux G = 93.3kg/m s and heat flux q = 200kW/m. The temporal behavior of the pressure drop in the whole boiling system is shown in Fig. 6.37a. The considerable oscillations were caused by the flow pattern alternation, that is, by the liquid/two-phase alternating flow in the micro-channels. The pressure drop FFT is presented in Fig. 6.37b. Under... 

Check the static instabilities by steady-state correlations, to avoid or alleviate the primary phenomenon of a potential static instability, namely, boiling crisis, vapor burst, flow pattern transition, and the physical conditions that extend the static instability into repetitive oscillations. 

The Presumed Probability Density Function method is developed and implemented to study turbulent flame stabilization and combustion control in subsonic combustors with flame holders. The method considers turbulence-chemistry interaction, multiple thermo-chemical variables, variable pressure, near-wall effects, and provides the efficient research tool for studying flame stabilization and blow-off in practical ramjet burners. Nonreflecting multidimensional boundary conditions at open boundaries are derived, and implemented into the current research. The boundary conditions provide transparency to acoustic waves generated in bluff-body stabilized combustion zones, thus avoiding numerically induced oscillations and instabilities. It is shown that predicted flow patterns in a combustor are essentially affected by the boundary conditions. The derived nonreflecting boundary conditions provide the solutions corresponding to experimental findings. 

Figure 1.174 Experimental image of the intricate, periodic flow patterns generated by the oscillating injection via adjacent channels into a main stream [48] (by courtesy ofSpringer-Verlag).

Fig. 12.18 Flow patterns above the oscillating region of HDPE. (a) Microtome cut along the cylinder axis of HDPE solidified inside a capillary die showing that the flow patterns are formed at the die entrance, (b) Microtome cut of the HDPE extrudate resulting under the same conditions as in (a). [Reprinted by permission from N. Bergem, Visualization Studies of Polymer Melt Flow Anomalies in Extruders, Proceedings of the Seventh International Congress on Rheology, Gothenberg, Sweden, 1976, p. 50.]...

Although in general the calculation of 8hm for modulation is difficult, a simplistic understanding can be obtained through consideration of the flow pattern above an oscillating infinite plate [13]. The velocity profile u(y,t) parallel to the wall, at a distance y above the wall, is a lagged, damped simple-harmonic motion ... 

For sufficiently large electrodes with a small vibration amplitude, aid < 1, a solution of the hydrodynamic problem is possible [58, 59]. As well as the periodic flow pattern, a steady secondary flow is induced as a consequence of the interaction of viscous and inertial effects in the boundary layer [13] as shown in Fig. 10.10. It is this flow which causes the enhancement of mass-transfer. The theory developed by Schlichting [13] and Jameson [58] applies when the time of oscillation, w l is small in comparison with the time taken for a species to diffuse across the hydrodynamic boundary layer (thickness SH= (v/a>)ln diffusion timescale 8h/D), i.e., when v/D t> 1. Re needs to be sufficiently high for the calculation to converge but sufficiently low such that the flow does not become turbulent. Experiment shows that, for large diameter wires (radius, r, — 1 cm), the condition is Re 2000. The solution Sh = 0.746Re1/2 Sc1/3(a/r)1/6, where Sh (the Sherwood number) = kmr/D and km is the mass-transfer coefficient,... 

The examples presented in this chapter [308 320] are illustrations of the concepts presented in the previous chapters. They correspond to recent numerical analysis of burners which are typical of most modern high-power combustion chambers, especially of gas turbines the flame is stabilized by strongly swirled flows, the Reynolds numbers are large, the flow field sensitivity to boundary conditions is high, intense acoustic/combustion coupling can lead to self-sustained oscillations. Flames are stabilized by swirl. Swirl also creates specific flow patterns (a Central Toroidal Recirculation Zone called CTRZ) and instabilities (the Precessing Vortex Core called PVC). 

In Table I the high-vacuum (HV) range means a pressure of 10 to 10 Torr entries designated by Torr mean pressures between 0.1 and 10 Torr flow refers to an unspecified steady-state flow pattern. It is apparent from Table I that there is a great diversity in the different oscillation conditions and catalytic systems. The pressures under which oscillations have been observed vary from 10 Torr for the CO/NO reaction on Pt(lOO) 141, 142) to atmospheric pressure for a large number of systems. The reactors used in these studies include ultrahigh-vacuum (UHV) systems, continuous stirred tank reactors (CSTRs), flow reactors, and reactors designed as infrared (IR) cells, calorimeters, and ellipsometric systems. 

Churn flow If the velocity of a two-phase mixture in slug flow is increased, the large slugs of gas will tend to become unstable, with the possibility of breakup. The result is the destruction of the slug flow pattern, with an oscillating characteristic being established. 

Theoretical solution of the Navier-Stokes equation for prediction of the collision efficiency, E(Dp,dp), for the general raindrop-aerosol interaction case is a difficult undertaking. Complications arise because the aerosol size varies over orders of magnitude, and also because the large raindrop size results in complicated flow patterns (drop oscillations, wake creation, eddy shedding, etc.) Pruppacher and Klett (1997) present a critical overview of the theoretical attempts for the solution of the problem. A detailed discussion of these efforts is outside our scope. However, it is important to understand at least qualitatively the various processes involved. 

The time series shows a. stationary pattern until a homogeneously oscillating flow rate around a constant level. However, an additive outlier occurs at time index 128. To analyse the time dependency pattern of the Naphtha time series, the effect of the outlier has to be removed. Therefore, the outlier s effect (i.e. the raise beyond the mean level) is estimated by modelling a simple linear regression model and the corresponding value of the time series is corrected by this estimate. For the corrected Naphtha time series, ACF and PACF are calculated (Figure 2.13a and Figure 2.13b). 

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