
do not change during the measurement campaign. This section describes ways
of interpreting the records of tracer gas injection rates and concentration in the
different zones to get the airflow rates between zones, as well as airflow to and
from outdoors. For more information on tracer gases and analysers, see
Chapter 7, ‘Tracer gas dilution techniques’.
Let us assume that there are N zones in the measured building, denoted by the
suffixes i and j, into which, in principle, N different tracers, denoted by the index
k, are injected. In principle, each zone receives only one tracer, but the equations
presented below allow the use of several gases in the same zone. No tracer is
injected in the outside air (zone 0), which is assumed to be of infinite volume.
However, the tracer concentration in that zone may differ from zero.
The multi -zone tracer gas theory is based on the conservation of the mass of
tracer gas and of air and on the following three assumptions:
1 In each zone, tracer concentrations are always homogeneous.
2 The atmospheric pressure is constant.
3 The injection of tracer gas does not chang e the density of air.
The first assumption is the weakest. In practice , homogeneous concentration
may only be achieved by the use of mixing fans, but these fans may affect
infiltration conditions.
The other two hypotheses are easily satis fied because the short-time relative
variations of atmospheric pressure are of the order of 0.01 per cent (daily
variations of the order of a per cent) and tracer gases are generally injected at
relatively low concentrations (10
4
or less).
Conservation of the masses of air and tracer gas k in zone i
In each zone, the ra te of change of the air mass m
i
equals the sum of the
incoming flows minus the sum of the outgoing flows:
dm
i
dt
¼
X
N
j ¼0
Q
ij
ð1
ij
Þ
X
N
j ¼0
Q
ji
ð1
ij
Þð1:23Þ
Change
in mass
Incoming
flow rates
Outgoing
flow rates
where
ij
is equal to one only when i ¼ j, and zero otherwise. The sum is then
over all terms for which i 6¼ j. Note that, in most cases, the left-hand side of
these equations is close to zero and can be neglected.
The conservation equation of the mass of tracer, k, in the zone, i, states that
the change of tracer mass within the zone is the sum of the mass of injected
tracer and the mass of tracer contained in the air entering the zone, minus
the mass of tracer contained in the outgoing air:
dm
ik
dt
¼ I
ik
þ
X
N
j ¼0
C
jk
Q
ij
ð1
ij
ÞC
ik
X
N
j ¼0
Q
ji
ð1
ij
Þð1:24Þ
Variation Injection Inflow Outflow
Airflow Rates in Buildings 7
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