Sharp JX-9400 Informazioni Techniche Scaricare il pdf (Pagina 29)

where:

is the mass of tracer gas k in zone i;

is the injection rate of tracer gas k in (or just upwind of ) zone i;

is the concentration of tracer k in zone j;

is the concentration of tracer gas k in zone i;

is the airﬂow rate from node j to node i.

An extension of assumption 1 above is implicit in this equation, that is:

4 The airﬂow entering a zone does not modify the homogeneity of the concen-

tration of tracer gases in that zone, i.e., an immediate and perfect mixing is

assumed.

If there are N tracers or N diﬀerent sets of measurements using a single tracer

injected at various rates in the various zones, Equations 1.23 and 1.24 above

give a full set of N(N þ 1) equations. Therefore, this allows the N(N þ 1) ﬂows

between all the zones, including the outdoor air as the zone zero to be determined.

There are two methods to transform this set of equations before solving. Since they

each have various advantages and disadvantages, they are both described below.

Global system of equations

The most common technique to be found in the literature (Sinden, 1978;

Sherman et al., 1980; Perera, 1982; Sandberg, 1984) is the following.

Let us express by Q

the sum of all the ﬂows entering the zone i:

j ¼0

ð1  

Þð1:25Þ

Using the above notation and taking apart the ﬂows coming from outside,

Equation 1.24 becomes:

¼ I

j ¼1

ð1  

ÞþC

 C

ð1:26Þ

Since any change in the outdoor level of tracer gas concentrations, C

, will be

negligible, these leve ls are the base levels of tracer gas concentrations anywhere

else. In this case the tracer mass balances expressed in Equation 1.26 can be

written in a matrix form:

½M  CþQ  C ¼ I ð1:27Þ

where each row of the N  N matrices M  C, Q  C and I corresponds to a zone

and each column to a given tracer gas. More speciﬁcally:

M is a diagonal matrix whose elements are the masses of air contained in each

zone:

¼ 

or M ¼ V

where  is the diagonal matrix of the air densities in the zones, 

, and V the

diagonal matrix of the volumes of the zones, V

8 Ventilation and Airﬂow in Buildings

1 2 ... 24 25 26 27 28 29 30 31 32 33 34 ... 210 211

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