ASHRAE Journal - February 2023 - 36

TECHNICAL FEATURE
With a further increase in the steam mass/velocity,
liquid condensate is pushed to the pipe boundaries
(annular flow). A further increase results in the liquid
condensate being lifted into the steam flow regime or
mist. The stratified flow regime is the most stable and
minimizes the probability of slug flow.
In the stratified regime, the gas/vapor is traveling at
a higher velocity, and liquid fills a portion of the pipe,
reducing the steam flow area. ASHRAE RP-1673 plotted
observed experimental data for the velocity ratio of
gas/vapor (Vg) to liquid velocity (VL) versus the steam
quality x% in Figure 2 (page 35). The difference between
the two velocities is described as the " slip velocity. "
ASHRAE RP-167 derived a curve fit equation for the
experimental data, which is expressed as a function of
the percent of flash steam (x). The following modified
version of the equation achieves a better curve fit for
the slip velocity ratio (S).
S = Vg /VL = exp [1.6677 - 0.0084 * ln(x)3]
where
x = decimal fraction of the flash steam quality
The slip velocity ratio (S) can then be used to calculate
the void fraction ag (percent of pipe area for vapor):5
S = Vg/VL = rf * x * (1-ag)/(rg * (1 - x) * ag)
where
Vg = velocity of vapor
VL = velocity of liquid
rf = density of liquid
rg = density of vapor
x = steam quality or percent steam
or ag = 1/(S * rg / rf * (1 - x)/x + 1)
Note that when S = 1 the void fraction is the same as
the volume fraction (Vc) in 2021 ASHRAE Handbook-
Fundamentals2 equation 26. The void fraction is always
smaller than the volume fraction when the slip ratio S is
greater than 1.
The pressure drop of both steam and liquid can be
estimated in the stratified flow regime using the pressure
drop of the liquid. The liquid pressure drop based
on gravity flow is equal to the liquid head pressure of the
36
ASHRAE JOURNAL ashrae.o rg
F E B R U A RY 2023
TABLE 1 Slope vs. pressure drop for gravity systems.
SLOPE
(in./10 ft)
0.090
0.120
0.181
0.25
0.5
0.723
1
1.445
1.5
2
2.89
SLOPE
0.08%
0.10%
0.15%
0.21%
0.42%
0.60%
0.83%
1.20%
1.25%
1.67%
2.41%
Dpsi/100 ft
1/32 (1/2 oz.)
1/24 (2/3 oz.)
1/16 (1 oz.)
0.09
0.17
1/4 (4 oz.)
0.35
1/2 (8 oz.)
0.52
0.69
1 (16 oz.)
upstream condensate and can be calculated by:
DPliquid (psi) = H*r/144 in.2/ft2
where
H = head pressure or liquid height (ft) or
pipe slope (s, %, in/ft·12 in./ft)
x total horizontal pipe length (ft)
r = liquid density at the receiver (lb/ft3) or 1/specific
volume (ft3/lb)
For I-P units using condensate density of 59.79
lb/ft3 (9.392 kPa/m) at 212°F (100°C) and 14.69 psia
(101.3 kPa) the equation can be shortened to:
Dpsi/100 ft = 0.346 * slope (in./10 ft) or
slope (in./10 ft) = 2.89 * psi/100 ft
Typical slopes for condensate systems are between
1/4 in. per 10 ft (6.4 mm per 3 m) (0.21%) and 1 in. per
10 ft (25 mm per 3 m) (0.83%). Table 1 shows how slope
(in./10 ft) relates to pressure drop rates psi/100 ft.
2021 ASHRAE Handbook-Fundamentals sizing charts
(green highlighted lines) are based on pressure drop
rates of 1/2 oz., 2/3 oz., 1 oz., 4 oz., 8 oz. and 16 oz.
per 100 ft. The rates of ounces per 100 ft in the 2021
ASHRAE Handbook-Fundamentals appear to be based on
rates used by early 20th century designers and have
carried through to today's tables.
The Pressure Cascade
Figure 3 is useful in describing pressure changes in the
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