Pipe flow regimes

The boundary constraints used in pipe flow regimes are inlet velocity profile, zero velocity on solid non-slip walls, and stress free (or for long pipes developed flow) exit conditions. In shell and tube systems with solid and porous walls, used in thickening of suspensions by cross-flow filtration, a different set of boundary conditions must be given. These are the inlet velocity profile, zero velocity on outer shell s solid walls, stress-free conditions at the exit, and the following Darcy flow conditions on porous wall ... 

The gaseous tracer method yields the equivalent piston flow linear velocity of the gas flow in the pipe without any constraints regarding flow regime under the conditions prevailing for flare gas flow. 

Fig. 11. Flow regimes for air—water in a 2.5-cm horizontal pipe where is superficial Hquid velocity and is superficial gas velocity.

In inclined or vertical pipes, the flow regimes are similar to those described for horizontal pipes when both gas- and Hquid-flow rates are high. At lower flow rates, the effects of gravity are important and the regimes of flow are quite different. For Hquid velocities near 30 cm/s and gas velocities near... 

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... 

HEM for Two-Phase Pipe Discharge With a pipe present, the backpressure experienced by the orifice is no longer qg, but rather an intermediate pressure ratio qi. Thus qi replaces T o iri ihe orifice solution for mass flux G. ri Eq. (26-95). Correspondingly, the momentum balance is integrated between qi and T o lo give the pipe flow solution for G,p. The solutions for orifice and pipe now must be solved simultaneously to make G. ri = G,p and to find qi and T o- This can be done explicitly for the simple case of incompressible single-phase (hquid) inclined or horizontal pipe flow The solution is implicit for compressible regimes. 

Lockhart and Martinelli used pipes of one inch or less in diameter in their test work, achieving an accuracy of about -l-/-50%. Predictions are on the high side for certain two-phase flow regimes and low for others. The same -l-/-50% accuracy will hold up to about four inches in diameter. Other investigators have studied pipes to ten inches in diameter and specific systems however, no better, generalized correlation has been found.The way... 

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 ... 

Example calculations are included, and Figure 2-52 illustrates the effect of pipe size on the placement of the flow regime. 

Figure 2-52. Flow regime diagram for solid-water flow in 1 -in. PVC pipe. By permission, Turian, R. M. and Yuan, T. F., Fiow of Slurries in Pipelines, A.I.Ch.E. Journal, vol. 23,1977, p. 232-243.

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. 

To analyze their data, they assumed that the flow in the conical top was characterized as a perfectly-mixed regime (the conical volume was agitated separately by a fan) and that a plug flow regime characterized the flow through the piping system. 

In order to predict Lhe transition point from stable streamline to stable turbulent flow, it is necessary to define a modified Reynolds number, though it is not clear that the same sharp transition in flow regime always occurs. Particular attention will be paid to flow in pipes of circular cross-section, but the methods are applicable to other geometries (annuli, between flat plates, and so on) as in the case of Newtonian fluids, and the methods described earlier for flow between plates, through an annulus or down a surface can be adapted to take account of non-Newtonian characteristics of the fluid. 

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. 

Therefore, to study the flow regimes at higher superficial gas velocities the pipe diameter was decreased. 

Fig. 5.35a-h Flow regimes in the pipe of 25 mm at f/os = 36 m/s (a) Uis = 0.016 m/s, disturbance waves with motionless droplets (b) Uis = 0.027 m/s, disturbance waves with moving droplets (c) U s = 0.045 m/s, disturbance waves and liquid film on the upper tube part (d) Uis = 0.17 m/s, disturbance air-water waves and liquid film on the upper tube part (e) Uis = 0.016 m/s, small air-water clusters (f) Ui = 0.027 m/s, air water clusters fe) Uis = 0.045 m/s, huge air-water clusters (h) Uis = 0.17 m/s, huge air-water clusters that block the tube cross-section. Reprinted from Hetsroni et al. (2003b) with permission... 

Experiments in annular and slug flow were carried out also by Ghajar et al. (2004). The test section was a 25.4 mm stainless steel pipe with a length-to-diameter ratio of 100. The authors showed that heat transfer coefficient increases with increase in liquid superficial velocity not only in annular, but also in slug flow regimes. 

For conventional size pipes the flow regimes depend on orientation. Two-phase air-water flow and heat transfer in a 25 mm internal diameter horizontal pipe were investigated experimentally by Zimmerman et al. (2006). Figure 5.38 shows the flow... 

In Fig. 5.39a-d the local heat transfer coefficients derived in the horizontal tube are compared to those obtained in the 8° upward inclined pipe and presented by Hetsroni et al. (2006). The results show a clear improvement of the heat transfer coefficient with the pipe inclination. Taitel and Dukler (1976) showed that the flow regimes are very sensitive to the pipe inclination angle. In the flow regime maps presented in their work, the transition from stratified to annular flow in the inclined tube occurs for a smaller air superficial velocity than for the case of the horizontal tube. 

The last two factors are used primarily for the translation from mostly air-water data to other gas-oil systems. This empirical mapping, like many others since then, such as those of Butterworth (1972) and Wallis and Dobson (1973), suffers from a lack of basis for the mechanisms that are responsible for the transition of flow regimes. An accurate analysis of regime transitions with flows in horizontal pipes... 

Figure 3.9 compares the separated-to-intermittent flow regime boundaries for both 8-in.- and 4-in.-pipe experiments. The conditions are presented in terms of nondimensional superficial velocities J = Jk[pk/(pL - pc)gZ)]1/2 (or the density-modified Froude numbers). For 4-in.-pipe experiments, data have been obtained only for 3 MPa, while for the 8-in.-pipe experiments, data have been obtained for pressures of 3.0, 5.0, and 7.3 MPa. Note the value of J at the flow regime transition increased with pressure for the 8-in.-pipe experiments. 

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