gas conservation equations can be rearranged so as to obtain one system of
equations per node, giving all airflow rates entering in this node. At steady
state
I
ik
¼
X
N
j ¼0
½C
jk
C
ik
Q
ji
ð2:6Þ
where:
I
ik
is the injection rate of tracer gas k in (or just upwind of ) node i,
C
jk
is the concentration of tracer gas k in (or just downwind of ) node j,
Q
ji
is the airflow rate from node j to node i.
‘Just upwind’ and ‘just downwind’ mean far enough from the node to ensure a
good mixing, but close enough to have no branching between the injection port
or sampling location and the node.
Each system can be rewritten in a matrix form:
~
II
i
¼ C
i
~
QQ
i
ð2:7Þ
where:
~
II
i
is the vector containing the tracer gas injection rate in the zone i,
C
i
is the matrix containing the concentrations differences, C
jk
C
ik
, of tracer
k between zones j and i,
~
QQ
i
is the vector of airflow rates entering into zone i from zones j.
Airflow rates leaving the zones are determined by mass conservation equations
Q
i0
¼
X
N
j ¼0
½1
ij
Q
ji
X
N
j ¼1
½1
ij
Q
ij
ð2:8Þ
An application to a typical air handling unit is presented below.
General method for ‘black box’ air handling unit
In most cases, it is not practical to inject tracer gases and to sample the air
within the air handling unit. It is often much easier to find (or to bore) small
holes in duct walls to insert the injection and sampling tubes. Therefore, a
method for assessing airflow rates in air handling units using injection and
sampling ports located only outside the units is presented below.
Building the system of equations
The ducts, leakage and shortcut network in the air handling system seen from
outside, like a black box, are represented schematically in Figure 2.8.
Recirculation may be on purpose, or could result from leakage such as
that sometimes found in heat excha ngers. It occurs anyway between nodes 6
and 2. Regarding indoor air quality, there is no difference whether the
24 Ventilation and Airflow in Buildings
Commenti su questo manuale