Annular two-phase flow in pipe or duct

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temperature, pressure, and composition may all be needed. Other reasons for sampling may be to determine equipment performance, measure yield loss, or determine compliance with regulations.

Location of a sample probe in the process stream is critical especially when larger particles must be sampled. Mass loading in one portion of a duct may be severalfold greater than in another portion as affected by flow patterns. Therefore, the stream should be sampled at a number of points. The U.S. Environmental Protection Agency (R-1) has specified 8 points for ducts between 0.3 and 0.6 m (12 and 24 in) and 12 points for larger ducts, provided there are no flow disturbances for eight pipe diameters upstream and two downstream from the sampling point. When only particles smaller than 3 | m are to be sampled, location and number of sample points are less critical since such particles remain reasonably well dispersed by brownian motion. However, some gravity settling of such particles and even gases of high density have been observed in long horizontal breeching. Isokinetic sampling (velocity at the probe inlet is equal to local duct velocity) is required to get a representative sample of particles larger than 3 | m (error is small for 4- to 5-| m particles). Sampling methods and procedures for mass loading have been developed (R-1 through R-8).

Particle Size Analysis Many particle-size-analysis methods suitable for dry-dust measurement are unsuitable for liquids because of coalescence and drainage after collection. Measurement of particle sizes in the flowing aerosol stream by using a cascade impactor is one

of the better means. The impacting principle has been described by Ranz and Wong [Ind. Eng. Chem., 44,1371 (1952)] and Gillespie and Johnstone [Chem. Eng. Prog., 51, 75F (1955)]. The Andersen, Sierra, and University of Washington impactors may be used if the sampling period is kept short so as not to saturate the collection substrate. An impactor designed specifically for collecting liquids has been described by Brink, Kennedy, and Yu [Am. Inst. Chem. Eng. Symp. Ser., 70(137), 333 (1974)].

Collection Mechanisms Mechanisms which may be used for separating liquid particles from gases are (1) gravity settling, (2) iner-tial (including centrifugal) impaction, (3) flow-line interception, (4) diffusional (brownian) deposition, (5) electrostatic attraction, (6) thermal precipitation, (7) flux forces (thermophoresis, diffusiophoresis, Stefan flow), and (8) particle agglomeration (nucleation) techniques. Equations and parameters for these mechanisms are given in Table 17-2. Most collection devices rarely operate solely with a single mechanism, although one mechanism may so predominate that it may be referred to, for instance, as an inertial-impaction device.

After collection, liquid particles coalesce and must be drained from the unit, preferably without reentrainment. Calvert (R-12) has studied the mechanism of reentrainment in a number of liquid-particle collectors. Four types of reentrainment were typically observed: (1) transition from separated flow of gas and liquid to a two-phase region of separated-entrained flow, (2) rupture of bubbles, (3) liquid creep on the separator surface, and (4) shattering of liquid droplets and splashing. Generally, reentrainment increased with increasing gas velocity. Unfortunately, in devices collecting primarily by centrifugal and inertial impaction, primary collection efficiency increases with gas velocity; thus overall efficiency may go through a maximum as reentrainment overtakes the incremental increase in efficiency. Prediction of collection efficiency must consider both primary collection and reentrainment.

Procedures for Design and Selection of Collection Devices

Calvert and coworkers (R-9 to R-12 and R-19) have suggested useful design and selection procedures for particulate-collection devices in which direct impingement and inertial impaction are the most significant mechanisms. The concept is based on the premise that the mass median aerodynamic particle diameter dp50 is a significant measure of the difficulty of collection of the liquid particles and that the collection device cut size dpc (defined as the aerodynamic particle diameter collected with 50 percent efficiency) is a significant measure of the capability of the collection device. The aerodynamic diameter for a particle is the diameter of a spherical particle (with an arbitrarily assigned density of 1 g/cm3) which behaves in an air stream in the same fashion as the actual particle. For real spherical particles of diameter dp, the equivalent aerodynamic diameter dpa can be obtained from the equation dpa = dp(ppC")v2, where pp is the apparent particle density (mass/volume) and C is the Stokes-Cunningham correction factor for the particle size, all in consistent units. If particle diameters are expressed in micrometers, pp can be in grams per cubic centimeter and C can be approximated by C = 1 + Ac(2X/Dp), where Ac is a constant dependent upon gas composition, temperature, and pressure (Ac = 0.88 for atmospheric air at 20°C) and X is the mean free path of the gas molecules (X = 0.10 |m for 20°C atmospheric air). For other temperatures or pressures, or gases other than air, calculations using these more precise equations may be made: Ac = 1.257 + 0.4 exp [-1.1 (dp/2X)] and X = ||/0.499pg x im (where || is the gas viscosity, kg/mh; pg is gas density, g/cm3; and |m is the mean molecular speed, m/s. um = [8R„T/nM]°-5, where Ru is the universal gas constant, 8.315 kJ/kg mol K; T is the gas absolute temperature, K; and M is the molar mass or equivalent molecular weight of the gas. (n is the usual geometric constant.) For test purposes (air at 25°C and 1 atm), pg = 1.183 kg/m, |g = 0.0666 kg/m h, X = 0.067 |m, and um = 467 m/s. For airborne liquid particles, the assumption of spherical shape is reasonably accurate, and pp is approximately unity for dilute aqueous particles at ambient temperatures. C is approximately unity at ambient conditions for such particles larger than 1 to 5 |m, so that often the actual liquid particle diameter and the equivalent aerodynamic diameter are identical.

When a distribution of particle sizes which must be collected is present, the actual size distribution must be converted to a mass dis tribution by aerodynamic size. Frequently the distribution can be represented or approximated by a log-normal distribution (a straight line on a log-log plot of cumulative mass percent of particles versus diameter) which can be characterized by the mass median particle diameter dp50 and the standard statistical deviation of particles from the median Og. Og can be obtained from the log-log plot by Og = Dpa50/Dpe at 15.87 percent = Dpe at 84.13 percent/D^o

The grade efficiency n of most collectors can be expressed as a function of the aerodynamic particle size in the form of an exponential equation. It is simpler to write the equation in terms of the particle penetration Pt (those particles not collected), where the fractional penetration Pt = 1 — n, when n is the fractional efficiency. The typical collection equation is

where Aa and B are functions of the collection device. Calvert (R-12) has determined that for many devices in which the primary collection mechanism is direct interception and inertial impaction, such as packed beds, knitted-mesh collectors, zigzag baffles, target collectors such as tube banks, sieve-plate columns, and venturi scrubbers, the value of B is approximately 2.0. For cyclonic collectors, the value of B is approximately 0.67. The overall integrated penetration Pt for a device handling a distribution of particle sizes can be obtained by

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