Chemical Engineering November 2010 - 55

Gravity drain entrainment plot
Engineering Practice
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)
(3)
where:
H = the height (or depth) of the liquid's
free surface over an exit
pipe's entrance, ft
D = the exit pipe diameter, ft
V = the average velocity in drain
pipe, ft/s
g = gravity's acceleration constant,
ft/s2
g' = approximates g for gas/liquid
flows
ρ = the gas-phase and liquid-phase
densities, lb/ft3
The non-dimensional Fr is the ratio
of the downward drag force of entrained
bubbles versus the upward
buoyancy force. If the downward drag
is not great enough, the bubbles could
float upward against the draining pipe
flow, and not be caught in the downward
flow. The definition is based on
the possible case of another liquid
resting on top of the draining liquid
and being entrained in the drainage
10,000
1,000
100
10
1
0.1
0.01
0.001
0.01
Souders
McDuffie
0.1
H/D
1
Simpson
Harlemen
10
Self-venting/
entrainment line
FIGURE 5. A plot of Equations (1, 4, 5 and 6) distinguishes the locations of the
three flow conditions: self-venting, vapor-entrainment, and no-entrainment/runs full.
Plotting the conditions of a draining tank helps to predict which regime the flow is in
and suggest when a vortex breaker is needed to help prevent vapor entrainment
Expanded entrainment plot
10,000
1,000
100
10
1
0.1
0.01
0.001
0.01
Souders
Simpson
Harleman
McDuffie
0.1
Palgrave-min
Palgrave-max
Kocabas
Labour (high D)
H/D
1
Labour (low D)
Lang (high D)
Lang (low D)
10
Gould (low rate, high D)
Gould (high rate, low D)
Self vent
FIGURE 6. Shown here is the expanded master chart with additional rules of thumb
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
Figures 7-10)
flow of the lower liquid. Some use S
instead of H to represent the " submergence "
distance of the outlet pipe
below the free surface. Users should
keep all units consistent.
McDuffie [17] states that when H/D
is above 0.25, and when Fr is greater
than about 0.3-0.55, gas will become
entrained in the draining liquid flow, a
condition to be avoided, while for lower
Fr values the flow will have no vapor
entrainment (running full). McDuffie's
regression [17] of Kalinske's data [16]
is Equation (4) and Harleman's derivation
[20] is Equation (5), both related
to determining the transition between
vapor entrainment versus running
full. McDuffie [17] also showed new
data that followed Equation (6). Note
the similar exponents. McDuffie [17]
also reviewed Anderson's 1971 selfventing
equation [21] with its leading
coefficient of 2.31 being only slightly
different from Souders' 2.36 value
[19], but with identical exponents.
(4)
ChemiCal engineering www.Che.Com november 2010 39
No entrainment,
runs full
Vapor
entrainment
Self-venting
Froude number
Froude number
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Chemical Engineering November 2010

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