Transitional flow region

Figure 19 Velocity distribution and slip flow in a gas in the transition flow region.

For the transition flow region BCD which extends up to ReM - 10000, the parameters C and x in equation 5.20 vary continuously. 

In the transitional flow region of the flow switches between laminar and nirbulent randomly. 

All previous models for drop coalescences assume the existence of a turbulent field. Stamatoudis (S32), on the other hand, derived models for drop coalescences for the case of laminar and transition flow regions. The same models given by Eqs. (67) and (68) were used with the following modifications for F and t ... 

The flow region between laminar and turbulent flow is called transitional flow. It is three dimensional and varies with time. 

However, on die basis of the relation between pressure drop and die minimum fluidisation velocity of particles, the point of transition between a packed bed and a fluidised bed has been correlated by Ergun41 using (17.7.2.3). This is obtained by summing the pressure drop terms for laminar and turbulent flow regions. 

NPei and NRtt are based on the equivalent sphere diameters and on the nominal velocities ug and which in turn are based on the holdup of gas and liquid. The Schmidt number is included in the correlation partly because the range of variables covers part of the laminar-flow region (NRei < 1) and the transition region (1 < NRtl < 100) where molecular diffusion may contribute to axial mixing, and partly because the kinematic viscosity (changes of which were found to have no effect on axial mixing) is thereby eliminated from the correlation. 

Between the laminar and turbulent zones, there exists a transition region in which the viscous arid inertial forces are of comparable magnitudes. No simple mathematical relationship exists between Np and Re in this flow region and, at a given value of Re, N p must be obtained from the appropriate power curve. 

For most medium- and large-scale micromanifold structures, where one passage feeds multiple parallel channels, flow traverses through turbulent and transition flows in the micromanifold region. This fluid in turbulent to transition flow also turns in the micromanifold region as it drops flow into parallel microchannels, which are primarily in the laminar flow regime. 

In the flow region between laminar and fully developed turbulent flow heat-transfer coefficients cannot be predicted with certainty, as the flow in this region is unstable, and the transition region should be avoided in exchanger design. If this is not practicable the coefficient should be evaluated using both equations 12.11 and 12.13 and the least value taken. 

As the pressure is lowered, slip occurs, and the flow mechanism is referred to as transition flow. At pressures so low that collisions between gas molecules are rare compared to the collisions between the gas and the tube wall, the flow is said to be Knudsen flow or free molecular flow. Free molecular flow prevails when Lla > 1. For air at 25°C, this condition means that we have free molecular flow when aPm on < 5. We now consider an intuitive derivation of the result for Fc in the free molecular flow region. 

If Re is of the order of 105, the drag on the sphere may be reduced if the fluid stream is turbulent. The flow in the boundary layer changes from streamline to turbulent and the size of the eddies in the wake of the particle is reduced. The higher the turbulence of the fluid, the lower is the value of Re at which the transition from region (c) to region (d) occurs. The value of Re at which R /pu2 is 0.15 is known as the turbulence number and is taken as an indication of the degree of turbulence in the fluid. 

Clearly, the solution of this equation at forced-convection electrodes will depend on whether the fluid flow is laminar, in the transition regime, or turbulent. Since virtually all kinetic investigations have been performed in the laminar flow region, no further mention will be made of turbulent flow. The reader interested in mass transport under turbulent flow is recommended to consult refs. 14 and 15. 

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