Flow Transition

Bigwood R, Gruebele M, Leitner D M and Wolynes P G 1998 The vibrational energy flow transition in organic molecules theory meets experiment Proc. Nati Acad. Sc/. 95 5960... 

The transition to turbulent flow occurred at Re of about 1,500. The authors noted that for smaller micro-channels, the flow transition would occur at lower Re. The early transition phenomenon might be affected by surface roughness and other factors. 

Hwang and Kim (2006) investigated the pressure drop in circular stainless steel smooth micro-tubes ks/d <0.1%) with inner diameters of 244 pm, 430 pm and 792 pm. The measurements showed that the onset of flow transition from laminar to turbulent motion occurs at the Reynolds number of slightly less than 2,000. It... 

Zhao and Rezkallah (1993), Rezkallah (1996), and more recently Lowe and Rezkallah (1999) developed two-phase flow transition models for micro-gravity channel flows based on liquid and gas Weber numbers. Zhao and Rezkallah (1993) suggested Wees 1 as the upper boundary for the surface tension-dominated zone, and Wees 20 as the lower boundary for the inertia-dominated zone. 

Furthermore, when d is smaller than the right-hand side of the above equation, the flow transition criterion is, according to Barnea et al. (1983) ... 

Figure 5.16c indicates that as the channel size was reduced to Jh = 0.866 mm, the dispersed bubbly flow pattern vanished from the flow regime map. Figure 5.16a-c indicates that the slug-churn flow transition line shifted to the right, as the channel size was reduced. Similar trends were also found in small circular tubes by the... 

The maximum rate of polymerization has been confirmed to occur at the laminar-turbulent flow transition. The rate of polymerization was observed to be maximum at the transition for both straight reactors as well as for the helically-coiled reactor for which the transition is at a Reynolds number higher than that of the straight tube. The helically coiled tubular reactor is of industrial interest since it is much more compact and, consequently, the cost and the temperature control problems are more tractable. 

To meet the products functional needs the wall thickness of the part can be varied. However, to obtain optimum processing cycles and reduce the chance of sink- and flow-mark formation, wall thickness should be kept as uniform as possible. Where variation in wall thickness is unavoidable, gradual transitions in the wall thickness should be provided to ease the polymer melt flow transitions. Part design, mold design, and gate location should work together to allow the material from heavier section into thinner walls for best appearance and process latitude. 

The issues of selection of the spatial wavelength and the deterministic character of the fine scale features of the microstructure are closely related to similar questions in nonlinear transitions in a host of other physical systems, such as macroscopic models of immiscible displacement in porous media - - the Hele Shaw Problem (15) - and flow transitions in fluid mechanical systems (16). 

However, several flow transition regimes have been identified between laminar and fully turbulent flow. The cessation of laminar Couette flow is marked by the appearance of Taylor vortices in the gap between the two cylinders. For the case of stationary outer cylinder, the critical angular velocity, C0crit> of inner cylinder at which these flow instabilities first appear can be estimated by using the following equations [102] ... 

Jayanti, S., and G. F. Hewitt, 1992, On the Prediction of the Slug-to-Chum Flow Transition in Vertical Two-Phase Flows, Int. J. Multiphase Flow 75 847 860. (3)... 

The transition from laminar to turbulent flow on a rotating sphere occurs approximately at Re = 1.5 4.0 x 104. Experimental work by Kohama and Kobayashi [39] revealed that at a suitable rotational speed, the laminar, transitional, and turbulent flow conditions can simultaneously exist on the spherical surface. The regime near the pole of rotation is laminar whereas that near the equator is turbulent. Between the laminar and turbulent flow regimes is a transition regime, where spiral vortices stationary relative to the surface have been observed. The direction of these spiral vortices is about 4 14° from the negative direction of the azimuthal angle,. The phenomenon is similar to the flow transition on a rotating disk [19]. 

ANNULAR MIST FLOW TRANSITION REGION MIST FLOW... 

Good flow" transitions the viewer logically and smoothly from one idea or section to the next. 

Fig. 7.13 Flow transitions for bubbles and drops in liquids (schematic).

These flow transitions lead to a complex dependence of transfer rate on Re and system purity. Deliberate addition of surface-active material to a system with low to moderate k causes several different transitions. If Re < 200, addition of surfactant slows internal circulation and reduces transfer rates to those for rigid particles, generally a reduction by a factor of 2-4 (S6). If Re > 200 and the drop is not oscillating, addition of surfactant to a pure system decreases internal circulation and reduces transfer rates. Further additions reduce circulation to such an extent that shape oscillations occur and transfer rates are increased. Addition of yet more surfactant may reduce the amplitude of the oscillation and reduce the transfer rates again. Although these transitions have been observed (G7, S6, T5), additional data on the effect of surface active materials are needed. 

We consider now the experimental data obtained under high pressure, using Charpentier s diagram. Here the parameter, X, does not represent in a satisfactory manner the influence of the total pressure on the flow transition between the low-and high-interaction regime (Figure 5.2-5). At elevated pressure, the transition zone shifts to higher G/X values [18]. 

Steady-state flow transitions in the radiative Rayleigh-Bdnard problem Visualizing a bifurcation diagram (with A.G. Salinger and J.J. Derby). Vid. J. Eng. Res. 3, 97-109 (1993). 

Convection in Melt Growth. Convection in the melt is pervasive in all terrestrial melt growth systems. Sources for flows include buoyancy-driven convection caused by the solute and temperature dependence of the density surface tension gradients along melt-fluid menisci forced convection introduced by the motion of solid surfaces, such as crucible and crystal rotation in the CZ and FZ systems and the motion of the melt induced by the solidification of material. These flows are important causes of the convection of heat and species and can have a dominant influence on the temperature field in the system and on solute incorporation into the crystal. Moreover, flow transitions from steady laminar, to time-periodic, chaotic, and turbulent motions cause temporal nonuniformities at the growth interface. These fluctuations in temperature and concentration can cause the melt-crystal interface to melt and resolidify and can lead to solute striations (25) and to the formation of microdefects, which will be described later. 

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