2D D
4D
Inside bottom head or shell
D
D D /2
Reproduced with permission from Process Industry Practices (PIP)
4D
Reprinted with permission from Oil & Gas Journal
FIGURE 3. Shown here are two alternate vortex breaker designs from Patterson [1], for tanks with bottom drainage (left) and verticalsuction discharge (right)
FIGURE 2.
This vortex breaker (PIP [ 2]) consists of a baffle arrangement that suspended or �ush with the tank bottom
D /2
D
D /2 (1 in. mininum)
2D
2D
2D Maximum one third of vessel diameter
to, but larger than the PIP design with a height ranging from 5 in. to 1.25 D, D D 4D and a width of 3.5 D to 5 D. Kister [6] references Patterson [1] and Waliullah [5] but provides no new data. McGuire [7 ] repeats the circular 4D Grating 2D plate suspended D /2 above the tank 2D bottom, like Patterson [1], but also D /2 D D D shows a 4-bladed, cross-pattern on top of a nozzle, extended above the tank bottom. However, this reference pro vides no recommended dimensions. McKetta [8] shows a 4-bladed design (4 D dimension, suspended D /2 above No top plate Top plate the tank bottom) that is within the Flat and cross plate baffles Grating baffle Waliullah [5] range. The vortex breaker design provided Reproduced with permission from Elsevier D = Diameter of pipe by Voss [9] shows a circular plate FIGURE 4. The vortex breaker design from Arnold [ 10] combines a 2- and 4-bladed suspended above the tank bottom of cross pattern pattern with a top plate that is either solid or made from porous grating similar size as before, plus an “X-bar” shape that is used to form the 4-bladed line reference manual provided in The discussion that follows on the cross-pattern. The author says the Ref. [13] from Goulds Pumps covers subsequent references will be treated blades should be “several inches high,” designs seen before, but also shows a without regard to whether non-swirlrather than related to the drain pipe’s critical submergence trend for vortex- ing or swirling flows were studied. diameter. In Figure 4, Arnold [ 10] sug- ing to appear for different flowrates. Using Perry’s “Chemical Engineergests both the 2- and 4-bladed crossLastly, Lastly, Rotonics Manufacturing [14] ing Handbook” [15] as a starting pattern (2 D diameter, suspended D off shows an “anti-siphon” device online point, the Kalinske [ 16] work from the the tank bottom, as with PIP [ 2]), plus that’s also listed as an “anti-vortex” de- early 1940s covered vertical drains nozzles. It is designed and overflow pipes. Perry next points the grating (4 D x 4 D x D /2, as with the vice for side-exit nozzles. design by Waliullah [5]). Arnold also by cutting off half of an extended pipe to a 1977 paper from McDuffie [ 17 ], ], suggests a combined design shown in end, to form a single curved baffle of as well as the 1968 work by Simpson Figure 4 (labeled “top plate”) of both sorts. One could imagine this “half- [18]. Simpson [18] consolidated the the 4-bladed cross-pattern and the pipe” being extended off the bottom of Kalinske [16] data with the 1938 work horizontal top plate. Arnold shows the a tank from a bottom-exit nozzle, but by Souders [19] on the limits of selftop plate being made solid as well as offering no construction advantage venting, weir-like flow down a drain, from porous grating, as shown. Note over the designs reviewed above. and the 1959 theoretical evaluation that Arnold’s blades protrude a short of critical submergence by Harleman Gas-entrainment potential distance down into the drain pipe. [20]. The Simpson [18] graphical comBorghei [11] provides a detailed Many of the following references (from parison used linear-scale axes but analysis of different configurations of designs discussed in the literature) plotted non-dimensional parameters the cross-baffle plate design, varying discuss “irrotational” or “vortex-less” of the Froude Number versus the ratio the design from 8 to 16 baffles, the di- draining scenarios. It is not clear how of submergence-to-pipe-diameter submergence-to-pipe-diameter.. mensions of each blade, the distance the experimental work maintained a By comparison, McDuffie [ 17 ] from the exit pipe, and the height non-swirling drain flow (without the changed the design chart to log-log off the bottom. Silla [12] references addition of of baffles or guides) and it scales, which allowed for better resoPatterson [1], showing the familiar is expected that industrial situations lution at low ranges, and converted 4-bladed design, with the option of a would have enough disruptions to the exponential equations to straight solid plate or grating on top. The on- make non-swirling flows unrealistic. lines. McDuffie [17 ] fitted an equation 38
CHEMICAL ENGINEERING
WWW.CHE.COM NOVEMBER 2010 2010
Gravity drain entrainment plot 10,000
Engineering Practice 1,000
to the Kalinske [16] data (Simpson [18] did not) and noted that the 1971 work of Anderson [ 21] closely followed Souders’ equation [19]. Simpson [ 22, 23] continued the reviews in 1969 and 1978, but included no new entrainment information. Equation (1) from Souders [19] predicts when a drain pipe would be running full with no gas entrainment versus the ability of a lower vessel being able to self-vent gas back to the original draining tank. In plotting Equation (1), Fr values (Froude Number, defined below) above the equation would imply self-venting occurring, while smaller Fr values would suggest flow with no gas entrainment, a condition referred to as running full. Note that this equation is only for H/D values (liquid height over exit-pipe diameter) less than 0.25. This equation is plotted in Figure 5 (left side). (1) where Fr is the Froude Number (the dimensionless ratio of inertia to gravity forces), defined as: (2)
100
Vapor entrainment Self-venting
r e b 10 m u n e d 1 u o r F
0.1
No entrainment, runs full
0.01 0.001 0.01
0.1
1 H/D
Souders
Simpson
McDuffie
Harlemen
10 Self-venting/ entrainment line
FIGURE 5.
A plot of Equations (1, 4, 5 and 6) distinguishes the locations of the three �ow conditions: self-venting, vapor-entrainment, and no-entrainment/runs full. Plotting the conditions of a draining tank helps to predict which regime the �ow is in and suggest when a vortex breaker is needed to help prevent vapor entrainment Expanded entrainment plot 10,000 1,000 100 r e b 10 m u n e d 1 u o r F
0.1
0.01
(3) 0.001 0.01
0.1
1
10
where: H/D H = the height (or depth) of the liqPalgrave-min Souders Gould (low rate, high D) Labour (low D) uid’s free surface over an exit Lang (high D) Palgrave-max Simpson Gould (high rate, low D) pipe’s entrance, ft Lang (low ) D Harleman Self vent Kocabas D = the exit pipe diameter, ft Labour (high D) McDuffie V = the average velocity in drain FIGURE 6. Shown here is the expanded master chart with additional rules of thumb pipe, ft/s g = gravity’s acceleration constant, added from data gathered from the literature. Disagreement among data sets can be undertood with closer inspection of the original test methods (this is shown in ft/s2 Figures 7–10) g' = approximates g for gas/liquid flows flow of the lower liquid. Some use S tion [ 20] is Equation (5), both related ρ = the gas-phase and liquid-phase instead of H to represent the “sub- to determining the transition between densities, lb/ft3 mergence” distance of the outlet pipe vapor entrainment versus running The non-dimensional Fr is the ratio below the free surface. Users should full. McDuffie [17 ] also showed new of the downward drag force of en- keep all units consistent. data that followed Equation (6). Note trained bubbles versus the upward McDuffie [17 ] states that when H/D the similar exponents. McDuffie [ 17 ] buoyancy force. If the downward drag is above 0.25, and when Fr is greater also reviewed Anderson’s 1971 selfis not great enough, the bubbles could than about 0.3–0.55, gas will become venting equation [ 21] with its leading float upward against the draining pipe entrained in the draining liquid flow, a coefficient of 2.31 being only slightly flow, and not be caught in the down- condition to be avoided, while for lower different from Souders’ 2.36 value ward flow. The definition is based on Fr values the flow will have no vapor [19], but with identical exponents. the possible case of another liquid entrainment (running full). McDuffie’s resting on top of the draining liquid regression [17 ] of Kalinske’s data [16] (4) and being entrained in the drainage is Equation (4) and Harleman’s derivaCHEMICAL ENGINEERING
WWW.CHE.COM NOVEMBER 2010
39
Gravity drain entrainment plot 10,000 Entrains gas 1,000
a n m e r l H a f f i e D u c M
100 Self-vent
Engineering Practice
tions (4, 5 and 6) may differ by the leading coefficient or exponent, they n o s still cover a similar part of the log-log m p S i plot of Figure 5 (Part of this variation could reflect differences in the experimental setup). Users of Figure 5 must 0.1 decide whether the upper part of the r s disputed area (formed by the over e 0.01 Runs full u d S o lapping of Equations (4) and (5), or the lower part via Equation (6), represent 0.001 a “conservative” design. If the desire is 0.01 0.1 1 10 H/D to avoid gas entrainment at all costs, Palgrave-min Souders Gould (low rate, high D) Labour (low D) then the lower-bound should be used, Lang (high D) Palgrave-max Simpson Gould (high rate, low D) as it is a more-conservative scenario. Lang (low D) Harleman Self vent Kocabas It should also be pointed out that in all the design equations, the tank’s diLabour (high D) McDuffie ameter does not appear in the design FIGURE 7. This is a repeat of the gravity-drain scenario in Figure 5, but includes all relationships using the Fr and the of the additional information, shown as dashed lines to de-emphasize them H/D notation. The assumption is that this diameter is much larger than the Lift pipe entrainment plot exit pipe’s diameter D and thus does 10,000 not affect the predictions (the actual experiments may have violated this 1,000 expectation). Entrains gas As noted earlier, to avoid opera100 tional problems associated with vapor i n m r e entrainment, operation in the regimes (No self-vent exists) v e b 10 r a g m l labeled “Self-venting” or “No entrain u P a n ment, runs full” is recommended. This e d 1 is especially true when vortex break u o r ers cannot be used due to cost consid F 0.1 a x erations or constraints such as a high - m v e a risk of fouling or plugging. r l g 0.01 Runs full P a In an attempt to update the information shown in Figure 5, additional 0.001 literature searches were conducted 0.01 0.1 1 10 but revealed only two new topic areas H/D that were not included previously. Palgrave-min Souders Gould (low rate, high D) Labour (low D) The recent publications tend to center Lang (high ) D Palgrave-max Simpson Gould (high rate, low D) around the use of computational fluid Lang (low D) Harleman Self vent Kocabas dynamics (CFD) modeling to analyze Labour (high D) McDuffie the shape of the “bathtub vortexes” that would lead to gas entrainment FIGURE 8. This new master chart shows two curves from Palgrave [28] and represents tanks that rely on suction-lift discharge pipes. The chart no longer has a S elfin draining tanks. These papers are vent region because rising bubbles that disengage from the liquid will �oat up the lift mostly interested in accurately modelpipe ing the shape of the vortex’s free sur values). Figure 5 shows Equations (1, face and predicting when the vertex of 4, 5 and 6) using log-log scales with the vortex dips down to the entrance (5) the newly added vertical line at H/D level of the drain pipe. = 0.25 to mark all three possible flow When comparing the references in (6) conditions. To the left of H/D = 0.25, the CFD papers, all tend to refer to only the self-venting and running-full other vortex-shape modeling work In plotting the design equations, conditions can occur. To the right of (for instance, see Stepanyants [ 24]). neither McDuffie [17 ] nor Simpson H/D = 0.25, the upper region switches In these papers, the main concern is [18, 22 and 23] nor even Perry [ 15] to the gas-entrainment condition the reduced flow-carrying capability labeled all of the three different flow (hence the need of the vertical divider of the drainage pipe when the vortex conditions that could exist depend- at H/D = 0.25), while the lower region is occupying a percentage of the open cross-sectional area in that pipe — the ing on the tank’s operating scenario remains running full. (found by plotting the Fr and H/D Note that while the design Equa- issue of gas entrainment seems to be r e b 10 m u n e d 1 u o r F
40
CHEMICAL ENGINEERING
WWW.CHE.COM NOVEMBER 2010
