Entrainment region

Zhivaikin obtains a correlation for the film-thickness data of several workers for upward cocurrent fiow by plotting bVo againt r (with b in cm. and F in meters/sec.). Two lines result, one for the region showing no entrainment, and one for the entrainment region with Tor about 0.575 cm.Vsec. and affected only slightly by gas velocity. The two lines are ... 

It is interesting to consider the shapes of the subharmonic trajectories that lock on the torus in the various entrainment regions of order p/q. The subharmonic period 4 at the 4/3 resonance horn is, for example, a three-peaked oscillation in time [Fig. 7(a)] and has three closed loops in its phase-plane projection [Fig. 7(b)], while the subharmonic period 4 at the 4/ 1 resonance is a single-peaked, single-loop oscillation [Figs. 7(d) and 7(e)]. A subharmonic period 2 at the 2/3 resonance is also included in Figs. 7(g) and 7(h). Multipeaked oscillations observed in chemical systems (Scheintuch and Schmitz, 1977 Flytzani-Stephanopoulos et al., 1980) may thus result from the interaction of frequencies of local oscillators. Such trajectories are the nonlin-... 

In the 1/1 entrainment region each side of the resonance horn terminates at points C and D respectively. These points are codimension-two bifurcations and correspond to double +1 multipliers. As the saddle-node curve at the right horn boundary rises from zero amplitude towards point D, one multiplier remains at unity (the criterion for a saddle-node bifurcation) as the other free-multiplier of the saddle-node increases until it is also equal to unity upon arrival at point D. The same thing occurs for the left boundary of the resonance horn. The arc CD is also a saddle-node bifurcation curve but is different from those on the sides of the resonance horn. As arc CD is crossed from below, the period 1 saddle combines not with its companion stable node, but with the unstable node that was in the centre of the phase locked torus. As the pair collides, the invariant circle is lost and only the stable node remains. Exactly the same scenario is observed for the 1/2 resonance horn as well. 

Aronson, D., McGehee, R., Kevrekidis, I. Aris, R. 1986 Entrainment regions for periodically forced oscillators. Phys. Rev. A 33(3), 2190-2192. 

In the resonance region the system oscillates with the external frequency X and with an increased amplitude (entrainment region). Far away from resonance, the internal free oscillations are present. This behaviour is completely absent in systems, where no self-sustained oscillations can exist. A typical example of such a system is a nonlinear conservative system. The resonance diagram has been drawn in Figure 2 for both, the small and the large ampli tude oscillation. 

The coating thickness depends on six competing forces which operate in the fluid entrainment region (see also Ref. [59]) ... 

The distance between the spout jet inlet and the base of the draft tube is termed "entrainment region", since this corresponds to the area within the bed where there is... 

Extensive experimental work has been conducted to study the gas and particle flow characteristics in a 20 cm diameter, 1.2 m tall semi-cylindrical acrylic unit (Muir et al., 1990). Sand particles, having a mean diameter of 1 mm have been utilized to study the effects of spouting gas velocity, draft tube diameter and length of the entrainment region on the solids circulation rates achievable. Typical results obtained in this work are illustrated in Figure 19. 

Visual observation of the entrainment region, with the use of a high speed video camera, has allowed a careful interpretation of the trends in the results. In particular, the solids circulation rates have been correlated with the size and stability of the jet, forming over the entrainment region. Also, non-uniformities of the solids distribution within the spouting jet have been studied. 

In the FFA process, the droplets are injected at the central axis of the atomizer. To avoid the influence of entrainment, the droplet injection position is located below the entrainment region (Note In experiments the entrainment caused by secondary gas flow is eliminated by coupling primary gas flow). The mass median diameter (MMD, rfso.a) of the initial primary droplets is derived by the correlation in Rao and Mehrotra [24] ... 

Most of the AHoy 600 outer diameter tube corrosion has occurred in the region of the upper tubesheet near the open lane, ie, an untubed lane across the middle of the steam generator (16,17). The steam carries entrained droplets of water through the open lane to the upper tubesheet region where the droplets dry out and concentrate the chemicals. Long tube inserts have been used to sleeve tubes in this region where wall defects have been detected. 

Fig. 18. Separation of ethanol from an ethanol—water—benzene mixture using benzene as the entrainer. (a) Schematic representation of the azeo-column (b) material balance lines where I denotes the homogeneous and the heterogeneous azeotropes D, the end points of the Hquid tie-line and A, the overhead vapor leaving the top of the column. The distillate regions, I, II, and III, and the boundaries are marked. Other terms are defined in text.

Witze Am. In.st. Aeronaut. Astronaut. J., 12, 417-418 [1974]) gives equations for the centerline velocity decay of different types of subsonic and supersonic circular free jets. Entrainment of surrounding fluid in the region of flow establishment is lower than in the region of estabhshed flow (see Hill, J. Fluid Mech., 51, 773-779 [1972]). Data of Donald and Singer (T/V7/1.S. In.st. Chem. Eng. [London], 37, 255-267... 

Ripple flow has an upward-moving wavy layer of liquid on the pipe wall it may be thought of as a transition region to annular, annular mist, or film flow, in which gas flows in the core of the pipe while an anniilus of hquid flows up the pipe wall. Some of the liquid is entrained as droplets in the gas core. Mist flow occurs when all the liquid is carried as fine drops in the gas phase this pattern occurs at high gas velocities, typically 20 to 30 m/s (66 to 98 ft/s). 

Choosing an entrainer to give a residue cniwe map with specific-distillation regions and node temperatures. 

Exploitation of Homogeneous Azeotropes Homogeneous azeotropic distillation refers to a flowsheet structure in which azeotrope formation is exploited or avoided in order to accomplish the desired separation in one or more distillation columns. The azeotropes in the system either do not exhibit two-hquid-phase behavior or the hquid-phase behavior is not or cannot be exploited in the separation sequence. The structure of a particular sequence will depend on the geometry of the residue curve map or distillation region diagram for the feed mixture-entrainer system. Two approaches are possible ... 

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