Sharp JX-9400 Información técnica descargar pdf (Pagina 30)

C contains the diﬀerences in mass concentrations C

 C

of gas k in zone i.

I is the matrix containing the mass ﬂow rates I

of the tracer, k , in zone i.In

usual measurements, this matrix is diagonal.

Q is the so-called ﬂow matri x containing, the oﬀ-diagonal elements ( j 6¼ i)

being Q

, where Q

represents the mass ﬂow rates from zone j to zone

i. The diagonal elements with j ¼ i contain the sum of the ﬂows leaving

the zone i, as deﬁned in Equation 1.25.

In Equation 1.26, i and j run from 1 to N and this system results in N

equations for the inter-zonal ﬂows. The mass ﬂows to and from outside are

given by Equation 1.23.

When steady state is reached for tracer gas concentration, Equation 1.27

becomes:

Q  C ¼ I hence Q ¼ I  C

1

ð1:28Þ

This method looks very attractive, but has several disadvantages. First, the

number of tracer gases is limited, and it is therefore often impossible or at

least very impractical to have tracer gases injected in each zone. In this case,

the C-matrix is not square and cannot be inverted. In addition, this method

may give non-zero values to non-existent airﬂow rates, or even provide negative

airﬂow rates. For this reason, the node-by-node method, which allows writing

equations containing only signiﬁcant airﬂow rates, was developed.

Zone by zone systems of equations

Another presentation of the same model is found in Roulet and Compagnon

(1989). It is obtained as follows.

Combining Equations 1.23 and 1.24, then taking into account that

¼ m

 C

, and using:

¼ m

þ C

ð1:29Þ

we ﬁnally get:

¼ I

j ¼0

ðC

 C

ÞQ

ð1  

Þð1:30Þ

For each zone i, these N equations give the N ﬂows, Q

( j ¼ 0; ...;

i  1; i þ 1 ; ...; N). The ﬂows, Q

, are obtained from the same equations

applied to zone j and the remaining ﬂows, Q

, are given by Equations 1.23.

Further interpretation of the ﬂow matrix

The ﬁnal result of the measurements is the ﬂow matrix Q deﬁned above.

Further information can be deduced from this ﬂow matrix, as shown in the

following discussion (Sandberg, 1984).

Airﬂow Rates in Buildings 9

1 2 ... 25 26 27 28 29 30 31 32 33 34 35 ... 210 211

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