Turbulent upper phase

Turbulent upper phase Laminar upper phase... 

From the physical point of view, the destabilizing dynamic term, J, stems from the interfacial dynamic interactions of a turbulent (upper) gas phase with the perturbed free interface. Therefore, Equation 25 for > 0 embodies, in fact, two criteria for instability, according to the flow regime of the upper phase ... 

Consider Figure 7a for relatively large diameter tube, D = 9.5cm. For demonstration, maintaining the liquid flow rate at = 0.4cm/s, while increasing the gas rate, the latter becomes turbulent at point 1 (Re > 2,100). However Equation 33.1 is not yet fulfilled, and, therefore, at point 1, the smooth interface is still stable with turbulent flow in the upper phase. With further increase of the air flow rate. Equation 33.1 is met at point T , which represents a transitional point from stratified-smooth to stratified-wavy. The locus of all transitional points as obtained by Equation 33.1 (represented by the solid line) constitutes the predicted stratified-smooth boundary. Note that Equation 33.2 as represented by a dashed line is irrelevant in this case since it assumes laminar conditions. 

O stratified-smooth/slug, stratified-smooth/wavy, A stratified wavy/annular, turbulent/laminar transition of upper phase. 

Thus, due to limitations on the available computer memory, DNS of homogeneous turbulent reacting flows has been limited to Sc 1 (i.e., gas-phase reactions). Moreover, because explicit ODE solvers (e.g., Runge-Kutta) are usually employed for time stepping, numerical stability puts an upper limit on reaction rate k. Although more complex... 

Fuvpi, %uvP2/ and Vuvp3 are the average liquid velocities for transducers 1, 2, and 3, respectively, from channel 0 to the channel where the gas-liquid interface is located. The constant 0.7 is obtained in the region 0single-phase turbulent flow the assumption made here is that the gas phase is located in the upper part of the pipe and the liquid velocity, not disturbed by the gas phase, develops in the lower part of the pipe as it does in single-phase turbulent flow. 

Telionis DP (1981) Unsteady Viscous Flows. Springer-Verlag, New York Thomas NH, Auton TR, Sene K, Hunt JCR (1983) Entrapment and transport of bubbles by transient large eddies in multiphase turbulent shear flows. In Stephens HS, Stapleton CA (eds) International Conference on Physical Modelling of Multi-Phase Flows, BHRA Fluid Engineering, pp. 169-184, Cranfield Thomson WJ (2000) Introduction to transport phenomena. Prentice Hall, Upper Saddle River... 

In the turbulent bed the upper surface becomes more diffuse. Individual particles and small clusters are entrained into the lean phase at the freeboard while the large clusters move downward giving rise to back mixing in the bed. If the freeboard height is kept sufficiently high, the entrainment can be reduced to a small amount. Thus, a turbulent bed operates in the captive region. 

The existence of two branches points out the multiplicity of solutions, which become even more complicated along the ZNS, ZNS boundaries, also due to the discontinuities which evolve from laminar-turbulent flow regime transitions in either of the two phases (and the associated change in the shear stresses). Note, that for low gas holdup (H/D > 0.5), the destabilizing effect of may be dampened even when the gas flow is turbulent due to the strong effect of the upper wall on the turbulent structures. Therefore, the ZNS line in Figure 8 is extended (beyond gas phase L-T transitional boundary) up to the H/D = 0.5 line. 

Dense phase fluidization Gas fluidized beds are considered dense phase fluidized beds as long as there is a clearly defined upper limit or surface to the dense bed. The dense-phase fluidization regimes include the smooth fluidization, bubbling fluidization, slugging fluidization, and turbulent fluidization regimes. In a dense-phase fluidized bed the particle entrainment rate is low but increases with increasing gas velocity. 

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