Pressure flow regimes

Low-pressure plasma systems operate at 13 Pa to 133 Pa (0.1 Torr to 1 Torr) with a continuous gas flow into the reactor. Therefore, the vacuum system must be able to maintain this pressure/flow regime. However, the moderate vacuum level does not require sophisticated pumps. Two stage mechanical pumps are satisfactory. The pump package is usually sized to allow pumpdown in less than 1 minute and to maintain an inlet gas flow of 50 cc/min to 1000 cc/min, depending on the size of the reactor. The most expensive part of the vacuum system is the perfluorinated lubricant required if an oxygen plasma is to be used. 

Many industrial filtrations are performed under variable rather than constant pressure conditions and Chapter 4 describes how sequences of constant pressure experiments can be used to provide scale-up constants that are valid for other pressure/flow regimes. Figure E.3 shows some experimental data for constant rate calcite filtrations where the pressure changes and flow measurements for the filtration have been provided by a software controlled pressure regulator and an electronic balance, respectively. In accordance with theory, a near linear relation is shown between pressure and time. The theoretical predictions also shown on Figure E.3 were produced using... 

By controlling fluid pressures, flow regimes, fluid viscosities, wetting properties, channel dimensions, and inlerfacial properties (i.e., surfactant concentration), it is possible to induce and control periodic breakup of a liquid stream to produce nuCTofluidic-generated emulsion drops. 

The majority of polymer flow processes are characterized as low Reynolds number Stokes (i.e. creeping) flow regimes. Therefore in the formulation of finite element models for polymeric flow systems the inertia terms in the equation of motion are usually neglected. In addition, highly viscous polymer flow systems are, in general, dominated by stress and pressure variations and in comparison the body forces acting upon them are small and can be safely ignored. 

Nonintrusive Instrumentation. Essential to quantitatively enlarging fundamental descriptions of flow patterns and flow regimes are localized nonintmsive measurements. Early investigators used time-averaged pressure traverses for holdups, and pilot tubes for velocity measurements. In the 1990s investigators use laser-Doppler and hot film anemometers, conductivity probes, and optical fibers to capture time-averaged turbulent fluctuations (39). 

Total pressure drop for horizontal gas/solid flow includes acceleration effects at the entrance to the pipe and fric tional effects beyond the entrance region. A great number of correlations for pressure gradient are available, none of which is applicable to all flow regimes. Govier and Aziz review many of these and provide recommendations on when to use them. 

Pressure Drop Some models regard trickle bed flow as analogous to gas/liquia flow in pipe lines. Various flow regimes may exist like those typified in Fig. 23-25/ but in a vertical direction. The two-phase APcl is related to the pressure drops of the individual phases on the assumptions that they are flowing alone. The relation proposed by Larkin et al. (AJChE Journal, 7, 231 [1961]) is APaj 5.0784... 

In addition to flow regime, hold-up and pressure drop are two other important parameters in two-phase gas-liquid flows. Hold-up is defined as the relative portion of space occupied by a phase in the pipe. It can be expressed on a time or space average basis, with the actual method chosen depending on the intended use of the hold-up value, and the measurement method employed. There are numerous correlations in the literature for hold-up, but most are based upon a pressure drop-hold-up correlation. The following expression is a widely recognized empirical relationship between hold-up and pressure drop ... 

The first two eases represent the smallest and largest vent sizes required for a given rate at inereased pressure. Between these eases, there is a two-phase mixture of vapor and liquid. It is assumed that the mixture is homogeneous, that is, that no slip oeeurs between the vapor and liquid. Furthermore, the ratio of vapor to liquid determines whether the venting is eloser to the all vapor or all liquid ease. As most relief situations involve a liquid fraetion of over 80%, the idea of homogeneous venting is eloser to all liquid than all vapor. Table 12-3 shows the vent area for different flow regimes. 

Visi-osity High viscosity crudes may flow in the laminar flow regime which causes high pressure drops. This is especially true of emulsions of water in high-viscosity crudes where the effective velocity of the mi slur e could be as much as ten times that of the base crude (see Volume 11... 

There are two flow regimes corresponding to sonic (or choked) flow for liigher pressure drops and subsonic flow for lower pressure drops. The transition between the two flow regimes occurs at tlie dimensionless critical pressure ratio, Ter,I, which is related to tlie gas lieiit capacity ratio y via... 

Rheological Classification of Drilling Fluids 829. Flow Regimes 830. Principle of Additive Pressures 834. Friction Pressure Loss Calculations 836. Pressure Loss Through Bit Nozzles 839. 

Weekman and Myers (W2) examined the fluid-flow characteristics of cocurrent downward flow of gas and liquid. The pulsing effect first noted by Larkins et al. was also observed in this work. Pressure-drop data could be correlated satisfactorily by a relation similar to those used for two-phase flow in pipes. Surface-active agents were observed to have a pronounced influence upon flow regime transition and pressure drop. 

Consideration will now be given to the various flow regimes which may exist and how they may be represented on a Flow Pattern Map to the calculation and prediction of hold-up of the two phases during flow and to the calculation of pressure gradients for gas-liquid flow in pipes. In addition, when gas-liquid mixtures flow at high velocities serious erosion problems can arise and it is necessary for the designer to restrict flow velocities to avoid serious damage to equipment. 

The relation between c and / and X (defined by equation 5.1) is shown in Figure 5.4, where it is seen that separate curves are given according to the nature of the flow of the two phases. This relation was developed from studies on the flow in small tubes of up to 25 mm diameter with water, oils, and hydrocarbons using air at a pressure of up to 400 kN/m . For mass flowrates per unit area of U and G for the liquid and gas, respectively, Reynolds numbers Rei L d/fii ) and Rec(G d/fia) may be used as criteria for defining the flow regime values less than 1000 to 2000, however, do not necessarily imply that the fluid is in truly laminar flow. Later experimental work showed that the total pressure has an influence and data presented by Gr1H ITH(i9) may be consulted where... 

Chapter 9 is devoted to regimes of capillary flow with a distinct interface. The effect of certain dimensionless parameters on the velocity, temperature and pressure within the liquid and vapor domains are considered. The parameters corresponding to the steady flow regimes, as well as the domains of flow instability are defined. 

---