Transitional flow

In this case there is good agreement between the values calculated for total pressure drop. Since gas flow is predominant, the total empty pipe pressure drop calculated from the gas-only pressure drop using eq. (7-41b) should be used. It should be noted that this Lockhart-Martinelli correlation is considered to be conservative when used in vertical downward flow. The original work was all in horizontal flow. 

With Kx given as ranging from 100 to 200, the pressure drop is expected to be 0.33 to 0.66 bar, or in English units, 4.8 to 9.6 psi. This is less than the maximum 10 psi allowed, and the design is acceptable based on this preliminary calculation. The static mixer vendor should be consulted for more exact determination of pressure drop based on the specific SMV mixing element being used. 

There are other comments to be made about this type of application. The liquid spray nozzle should supply liquid to the face of the mixing elements without appreciably wetting the vessel wall. A 30° full cone nozzle is typically used. Ideally, the spray should consist of droplets in the range 1000 to 2000 p-m range. A quick review of spay nozzle literature indicates that the appropriate spray nozzle for 44 gal/min of alkaline water would operate at about 100 psi pressure drop. Multiple nozzles could be used if a lower liquid-side pressure drop is desired. Fine atomization spray nozzles should be avoided since fine spray drops are difficult to separate in downstream mist eliminator equipment. A Alter or strainer should be installed on the liquid feed to prevent plugging the feed nozzle, especially if the nozzle orifice size is small. 

The previous discussion was devoted to processes that were either laminar or turbulent. The transition between these flow regimes is set by the Reynolds 

The Kenics HEV mixer, which consists of tabs, shows a transition in mixing performance at a very high Reynolds number. This is believed due to the change in vortex structure off the tabs at a specific tab Reynolds number rather than a pipe Reynolds number. Since the tab/diameter ratio is kept constant, this occurs at a higher pipe Reynolds number. 

Another possible scenario in the pipeline transport of acid gas is a transition from single-phase to two-phase flow or vice versa. For such a situation, it is veiy difficult to perform a calculation. These calculations, which involve a combination of fluid flow and phase equilibrium, should be performed using available software. 

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

In laminar flow there are no disturbances, and therefore all flow particles move in the same direction. Transitional flow is the flow regime that takes place during the change from streamline to turbulent flow. In the case of turbulent flow the particles move in a given flow direction, but the flow is erratic and random. 

Transitional flow The nature of flow in the zone between laminar and turbulent flow. 

Figure 10-153B. Shell-side film coefficient for longitudinal fins, transition flow. See Figure 10-153A for applicable details. (Used by permission Brown Fintube Company, A Koch Engineering Company, Houston, Texas.)...

Kn = 0.1-10 Transition flow between slip flow and free molecular flow, treated statistically, e.g., by the Boltzmann equation... 

A summary of the nine batch reactor emulsion polymerizations and fifteen tubular reactor emulsion polymerizations are presented in Tables III IV. Also, many tubular reactor pressure drop measurements were performed at different Reynolds numbers using distilled water to determined the laminar-turbulent transitional flow regime. 

XlylmnkT/ird ), or h = [TT[i 2RTI2p), as long as substituting the gap-dependent viscosity rather than the bulk viscosity. Because the effective viscosity decreases as the Knudsen number enters the slip flow and transition flow ranges, and thus the mean free path becomes smaller as discussed by Morris [20] on the dependence of slip length on the Knudsen number. 

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 first two cases the Navier-Stokes equation can be applied, in the second case with modified boundary conditions. The computationally most difficult case is the transition flow regime, which, however, might be encountered in micro-reactor systems. Clearly, the defined ranges of Knudsen numbers are not rigid rather they vary from case to case. However, the numbers given above are guidelines applicable to many situations encoimtered in practice. 

ESDU 93018 (2001) Forced convection heat transfer in straight tubes. Part 2 laminar and transitional flow. ESDU 98003-98007 (1998) Design and performance evaluation of heat exchangers the effectiveness-NTU method. 

LX Yu, JR Crison, GL Amidon. Compartmental transit and dispersion model analysis of small intestinal transit flow in humans. Int J Pharm 140 111-118, 1996. 

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

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. 

Knudsen s result for free molecular flow in a tube is given by Eq. (73). With/ = 1, Knudsen s result and the second term in Eq. (84) differ only by a numerical factor. In Knudsen s result, the numerical factor is 2/3 in Eq. (84), the corresponding factor is n/8. Thus, except for a modest difference in the numerical factor, the slip term in Eq. (84) is the Knudsen free molecular flow term, and transition flow in a tube appears as a mixture of free molecular flow and viscous flow. That is, the total flow behaves approximately as a sum of two parallel flow mechanisms. 

As the pressure increases from low values, the pressure-dependent term in the denominator of Eq. (101) becomes significant, and the heat transfer is reduced from what is predicted from the free molecular flow heat transfer equation. Physically, this reduction in heat flow is a result of gas-gas collisions interfering with direct energy transfer between the gas molecules and the surfaces. If we use the heat conductivity parameters for water vapor and assume that the energy accommodation coefficient is unity, (aA0/X)dP — 150 I d cm- Thus, at a typical pressure for freeze drying of 0.1 torr, this term is unity at d 0.7 mm. Thus, gas-gas collisions reduce free molecular flow heat transfer by at least a factor of 2 for surfaces separated by less than 1 mm. Most heat transfer processes in freeze drying involve separation distances of at least a few tenths of a millimeter, so transition flow heat transfer is the most important mode of heat transfer through the gas. 

Kaiampokis, A., Argyrakis, P., Macheras, P., Heterogeneous tube model for the study of small intestinal transit flow, Pharm. Res. 1999, 16, 87-91. 

Knowlton has cautioned on the difference between small diameter and large diameter systems for pressure losses. The difference between these systems is especially apparent for dense phase flow where recirculation occurs and wall friction differs considerably. Li and Kwauk (1989, 1989) have also studied the dense phase vertical transport in their analysis and approach to recirculating fluid beds. Li and Kwauk s analysis included the dynamics of a vertical pneumatic moving bed upward transport using the basic solid mechanics formulation. Some noncircular geometries were treated including experimental verification. The flows have been characterized into packed and transition flows. Accurate prediction of the discharge rates from these systems has been obtained. 

Joseph, S., and Klinzing, G. E., Vertical gas-solid transition flow with electrostatics, Powder Technol., 36 79-97 (1983). 

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