ASHRAE Journal - May 2020 - 33

TECHNICAL FEATURE

Inches

accumulate in puddles, then overFIGURE 1 Stack height with and without flow blockers with flow through floor.
ﬂow as the airplane changes attitude
Stack Height Without a Flow Blocker
Stack Height for a Sealed Envelope
during climb, for example.
120
Insulation
Occupants are the source of water
110
Crown
100
vapor and most contaminants in
90
Crown Height
Stack
80
ﬂight. The same air that brings water
Height 70
60
vapor into the insulation envelope also
R=78 in.
50
R=78 in.
Stack
40
brings cabin air contaminants with it.
Height
30
Hypothetical Airtight
20
If the air is drawn from cleaner areas
Flow
Blocker
10
Floor
0
of the cabin, some outdoor (fresh)
Open
to
air is lost. If the air comes from more
Flow
humid (and more contaminated)
areas of the cabin, the cabin air quality
improves, but the condensation rate
is 32.1740 lb)
increases.
ρ2 = air density behind the insulation (slug/ft3; one
There have been a few approaches and proposals to
slug is 32.1740 lb)
prevent dripping, such as how insulation is arranged,
h = height above the neutral plane (ft)
or ways to prevent or reduce the condensation itself, all
P1 = cabin air pressure (lb/ft2) (psia × 144)
with limited success.2 Very little, if any, attention has
been given to the effect of envelope ﬂow on cabin air
T1 = temperature in room (°R) (°F + 459.67)
T2 = temperature behind the insulation (°R) (°F +
quality. These will be discussed after an introduction to
459.67)
stack pressure.
R = individual gas constant for dry air =
Stack Pressure
1,716 ft2/(s2·°R)
Stack or buoyancy pressure differentials across perimg = acceleration due to gravity (32.2 ft/s2)
eter insulated envelopes are created by temperature dif∆P = stack pressure (lb/ft2) or customarily in units of
Pa (47.88 Pa/lb·ft2)
ferences between indoors and outdoors. These pressure
The stack pressure at the crown (the top of the cabin
differentials increase with increased temperature difstructure) of the aircraft wall when sealed at the cabin
ferential. Some airplane designs use ﬂow blockers (ﬁre
ﬂoor will draw conditioned cabin air behind the insustops) to reduce envelope ﬂow. Even with an airtight
lation between mid-height and the crown and expel it
ﬂow blocker in the envelope, the stack effect will draw
between mid-height and the cabin ﬂoor. If the cabin
air through cracks in the upper sections of the cabin
liner wall and ceiling and expel air through cracks in the air temperature is assumed to be 72°F (22°C) at a
lower sections of the cabin liner. The stack pressure itself pressure of 11.02 psia (75.98 kPa), the stack pressures
is then roughly half that of an envelope without the ﬂow can be calculated to determine the effect of the ﬂow
blocker.
blocker (Figure 1).
3,4
Using Equation 3, the stack pressure at the crown of
Stack pressures are predicted by
the cabin with an airtight ﬂow blocker near the ﬂoor
∆P = (ρ2 − ρ1) × g × h
(1) (Figure 2a) and without a ﬂow blocker (Figure 2b) are given
for a range of crown heights and temperatures behind
Substituting
the insulation.
ρ = P/RT
(2)
Gives

∆P = P1 (1/T1 - 1/T2) × g × h/R
(3)
where
ρ1 = air density in the living space (slug/ft3; one slug

Airﬂows Behind the Insulation

The airﬂow rate through the insulation envelope, Q, is
governed by the following equation
Q = ( ELA) Cd 2∆Pr / ρ
M AY 2020

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ASHRAE Journal - May 2020

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