Air Change Effectiveness Theory and Calculation Methods PDF
Air Change Effectiveness Theory and Calculation Methods PDF
Air Change Effectiveness Theory and Calculation Methods PDF
Senior Member of the Technical Staff, Controls Group Research and Development, Johnson Controls, In c. , 507 East Michigan Street, Milwaukee,
WI 53202, USA, Tel: +1414274 5071, Fax: +1414274 5810, E-mail: clifford.cfederspiel@jci.com
.·
Federspiel
-
ant system parameters and variables to be displayed
graphically, which provides important intuitive
return �
knowledge for analyzing multi-zone systems. Theor
etical results for perfect-mixing and plug-flow sys
tems are derived. Relations between ventilation per
f,R artificial bypass \
formance measures described in this paper and those f., f. fs s
)
�
described in other papers are derived. In the section · · · · · · · · ·
\_-ouWoo'
'
entitled Multi-Zone Systems, general calculation
+
o
methods for multi-zone buildings are described. This
supply z ne
is followed by a discussion of the implication of the
theoretical results on previously published findings.
Data from a previously published paper are used to
illustrate the results. Fig. 1 Schematic diagram of a single-zone building
48
Air-Change Effectiveness: Theory and Calculation Methods
When f0 and R are constant, the PFND system is a lin where a:R=o is the mean age of air that would exist if
ear, time-invariant transport delay. The zone delay is R=O.
the time that it takes a particle to cross the zone from
the supply to the return. It is equal to the local nominal Air-Change Effectiveness
turnover time of the zone, denoted as T. Sandberg and Sjoberg (1983) defined the air diffusion
efficiency as the ratio of the nominal turnover time to
T=M (3) the volumetric mean age of air.
fs
t,,
It can be shmyn (see Appendix A) that, for a PFND g =-- (6)
system, the ret'ation between R, T, and a. is as follows: a a
"
.!:! 0.2
.,; If there were no recirculation, then the air-exchange
e0 �
0.1 - efficiency would provide a measure of the airflow
c
0.0 +----r--,---..-+---.---r---.==i-..-,,.--�-. pattern in the room. Therefore, another ventilation
0.00 0.25 0.50 0.75 1.00 l.25 1.50 l.75 2.00 2.25 2.50 2.75 3.00
49
Federspiel
zero. 0.9
0.8
T
g = (11) 0.7
r
--
2aR=O �
"E
0
0.6
·;;;
For a single-zone system, it can be shown (see Appen c: 0.5
"
E
dix B) that: 'ii 0.4
t,,J;
0.3
(12)
0.2
0.1
where as is the age of the supply air. Equation (12) dem 0.0
onstrates the similarity between i;, and the relative ven 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1. 0
and the contaminant removal effectiveness defined by Fig. 3 Relation between Ea, E,, and R
r
=
The air-exchange efficiency is a measure of how well
outdoor air is utilized. In Rask et al. (1988), a venti
----
T lation performance measure called ventilation ef
gr = (14)
2(c'i-t,.+n ficiency is defined as:
50
Air-Change Effectiveness: Theory and Calculation Methods
leaving a set chambers in series is equal to the sum of L fek<Xek L F;k<Xik (22)
k=1
-
k=1
the age of air had the chambers not been arranged in
series. These mathematical results and others are de
scribed in detail by Nauman and Buffham (1983).
The relation between the incoming age and the out For a chamber with just one input and one output,
going age for a chamber with m inputs and n outputs
Equation (22) becomes the following:
is as follows:
II ae-ai
Er = (23)
� F�1/X1:1; 2 (a-a;)
k=l (19)
F The calculation methods for multi-zone systems which
n m are analogous to Equations (13) and (14) are the fol
F = L Fek = L F;k (20) lowing:
k=1 k=l
T
The subscripts e and i refer to exit and inlet, respec
tively. M refers to the mass of air. Equation (19) states (24)
that the flow-weighted average of the outgoing age is
F ao . ..... /,F
: : r
,
plenum
zoneN-1 zoneN
F
Fig. 4 Schematic diagram of a multi-zone ven .
.. . . . .. . . . . .
.
51
Federspiel
T
(25)
zone 1 zone 2
(26)
1.0
where ae1 is the age of air leaving zone 1 to the plenum, 0.9
<t>,=o.5
ae1 is the age of air entering zone 1 from the terminal 0.8
0.3
(27)
0.2 <j>1=0.05 or 0.95
0.1
where:
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
(28) R, dimensionless
Fig. 6 Relation between &0, R, and <j>1 for the system shown in
Figure 5
and where aN is the volumetric mean age of air in zone
N, and CXeN is the age of air leaving zone N. This
method may be more appropriate for zone N because
it would probably be difficult to measure a;N, but rela short-circuiting may be arbitrarily high (i.e., E, arbi
tively easy to measure F No· trarily close to zero), and yet the value of Ea may be
arbitrarily close to 1/2 simply by choosing a suffi
ciently high recirculation fraction.
Discussion For multi-zone systems, nothing can be said about
Many published experiments on air-change effective the "within-zone" airflow patterns from Ea· Therefore,
ness involve tests on systems that recirculate air. Typic conclusions from tracer-gas tests such as "it is ob
ally the air diffusion efficiency or the air-exchange ef served that the AEE values are usually close to one
ficiency is reported, and the tests are often carried out implying no serious problems of short circuiting of
with large recirculation fractions (e.g., minimum out ventilation air" (Sekhar, 1997) may be incorrect. A
door air conditions). The theory presented above pre value of Ea close to 1/2 may be achieved even if there
dicts that under these conditions the air-exchange ef is arbitrarily large amounts of short circuiting or per
ficiency will be close to 1/2 (i.e., air diffusion efficiency fect plug flow in one or more zones simply by recircu
will be close to 1). This prediction is consistent with lating sufficiently large quantities of air. Furthermore,
many published findings such as Fisk et al. (1988), Per 'a value of Ea lower than 1/2 may be due solely to the
sily and Dols (1991), Persily et al. (1994), and Sekhar way that the supply air is distributed to the zones. In
et al. (1997), although some experiments such as those other words, the effects of airflow patterns on Ea are
described by Offermann (1988) have shown that the confounded by differing supply air fractions and recir
air-exchange efficiency may be significantly less than culation.
1/2 even with recirculation. For example, consider the two-zone system in Figure
The results of the section on air-change effectiveness 5. Assume that the zones are of equal size and that
illustrate that it is not possible draw quantitative con the airflow pattern in each zone is plug flow with no
clusions about the airflow pattern in single-zone sys diffusion. Under these conditions, it can be shown that
tems from Ea if air is recirculated. Only qualitative con the relation between Ea, R, and the fraction of the sup
clusions can be drawn. For example, the amount of ply air delivered to zone 1 (denoted as <l>i) is as follows:
52
Air-Change Effectiveness: Theory and Calculation Methods
53
l
l
Federspiel
original analysis indicates that the configuration de tween the rooms such as open doorways, closed door
signed to induce short-circuiting had the lowest air ways, and vents could be tested. Another good experi
exchange efficiency. However, by calculating E17 one ment would be to conduct a tracer gas test on a single
can see that the data actually suggests that the system zone system with either displacement ventilation or ex
with ceiling supply and return induced more short-cir treme short-circuiting and determine if the predicted ef
cuiting than the system designed to induce it. This is fect of recirculating air is close to the actual effect.
probably because the supply air velocities were higher
with the system designed for short-circuiting, and the
higher velocities probably entrained surrounding air Conclusions
and induced more mixing. l. This paper extends the theory of ventilation per
Another implication of the theory described in pre formance measurement to any building that can be
vious sections pertains to the use of experimentally treated as a set of interconnected chambers. A venti
determined effectiveness parameters in controlling lation effectiveness parameter called relative air
ventilation systems. The results of the Section on change effectiveness is defined.
Single-Zone buildings and the example described 2. Three methods of calculating relative air-change
above illustrate that an experimentally-determined effectiveness are described. One method is based on
value of Ea should not be used to modulate the nominal age of air measurements at three locations, while the
amount of outdoor air required to satisfy a ventilation other two are based on two age of air measurements
requirement. In particular, the nominally required and a flow rate measurement. Relations between rela
amount of outdoor air should not be multiplied by an tive air-change effectiveness and ventilation par
experimentally-determined value of Ea to determine ameters proposed previously are derived.
the actual amount of outdoor air to be supplied be 3. The results of the theory illustrate that published
cause it varies as the supply and recirculation flow conclusions about airflow patterns in buildings that are
rates vary. If the goal of the ventilation system were to based on tracer gas tests may be incorrect because of
ensure that the mean age of air in a zone was main the effects of recirculated air or air moving between
tained at or below a specified level, then experimen zones.
tally-determined values of E, could be used as follows.
First, the age of the supply air would be determined.
If there is no secondary recirculation, then it is the References
product of the nominal turnover time for the entire Etheridge, D. and Sandberg, M. (1996) Building Ventilation:
building and the recirculation fraction. Then the mean Theory and Measurement, New York, Wiley.
Federspiel, C.C. (1996a) "The Effect of Recirculation on Air
age of air in each zone would be calculated by adding Change Effectiveness Calculations". In: Yoshizawa, S., Ki
the age accumulated in the zone to the age of the sup mura, K., Ikeda, K., Tanabe, S. and Iwata, T. (eds) Proceed
ply air as follows: ings of Indoor Air '96, Nagoya, 7th International Conference
on Indoor Air Quality and Climate, Vol. 3, pp. 971-976.
T Federspiel, C.C. (1996b) "The Effect of Recirculation on Air
i'i.; =as +___!_ (31) Change Effectiveness". In: Proc. 17th AIVC Conference: Opti
mum Ventilation and Air Flow Control in Buildings, Gothen
burg, Vol. 1, pp. 15-23.
where the subscript i refers to the zone number. The
Federspiel, C.C. (1997) "Control and Performance Analysis of
value of T; would be computed from a measured value Ventilation Systems". In: Woods, J. E., Grimsrud, 0.T. and
of the supply flow rate to zone i and the volume of Boschi, N. (eds) Proceedings of Healthy Buildings/IAQ '97,
Washington, Vol. 2, pp. 529-534.
zone i. If the calculated value were greater than the
Fisk, W.J., Faulkner, D., Sullivan, D. and Bauman, F. (1997)
requirement, then the amount of outdoor air would be "Air Change Effectiveness and Pollutant Removal Ef
increased. If the value in every zone were less than the ficiency During Adverse Mixing Conditions", Indoor Air, 7,
requirement and if there were no conflict with other 55-63.
Fisk, W.J. and Faulkner, D. (1992) "Air Exchange Effectiveness
control requirements, then the amount of outdoor air in Office Buildings: Measurement Techniques and Results".
would be decreased. In: Murakami, S., Kaizuka, M., Yoshimo, H. and Kato, S.
Although the assumption on which the theory in this (eds) Proceedings of Room Air Convection and Ventilation Ef
fectiveness, pp. 213-223.
paper is based on not very restrictive, it would still be
Fisk, W.J., Prill, R.J. and Seppanen, 0. (1988) "Commercial
useful to conduct a controlled experiment designed to Building Ventilation Measurement Using Multiple Tracer
validate or invalidate the theory. One useful experiment Gases". In: Proceedings of 9th AIVC Conference, Ghent, pp.
161-182.
would be to test the independence of the residence time
Fisk, W.J., Faulkner, D. and Hodgson, AT. (1993) "The Pol
distributions by conducting a tracer gas test on a set of lutant Control Index: A New Method of Characterizing
rooms arranged in series. Different types of passages be- Ventilation in Commercial Buildings", In: Jaakkola, J.J.K.,
54
Air-Change Effectiveness: Theory and Calculation Methods
Ilmarinen, R. and Seppanen, 0. (eds) Proceedings of Indoor simply be h/v. However, since only 1-R of the supply
Air '93, Helsinki, 6th International Conference on Indoor
Air Quality and Climate, Vol. 5, pp. 9-14. air is fresh while R of it is recirculated return air, the
Janssen, J.E. (1984) "Ventilation Stratification and Air Mix age of air at the point h is:
ing". In: Proceedings of 3rd lntemationnl Co11ference 011 I11door
Air Q11nlity nnd Climnte, Vol. 5, pp. 43-48.
Kim, LG. and Homma, H. (1992) "Possibility for Increasing a.(h) = (1-R) ; + R (1-R) (; +T) + R2 (1-R)
(; + 2T) + R3 (1-R) (; + 3T)
Ventilation Efficiency with Upward Ventilation", ASHRAE (A2)
Trn11snctio11s, 98(1 ), 723-729.
+ ...
Mantegna, M. (1993) "An Invariant of the Age of Air: Proof
and Applications", Air Infiltrntio11 Review, 14(2), 14-18.
Nauman, E.B., and Buffham, B.A. (1983) Mixing in Co11ti11!1011s which can be expressed as:
Flow Systenis, New York, Wiley.
Offermann, F.J. (1988) "Ventilation Effectiveness and ADP!
Measurements of a Forced Air Heating Sy stem", ASHRAE
Transactions, 94(1), 694-704.
a. (h) = (1-R) :i
n=O
R" (� )
v
+ nT (A3)
.---____._
I _____, - H
lowing:
TR
f, R a =-- (A9)
s 1-R
TR
a= O.R=O + (AlO)
1-R
--
55
d________
. I
Federspiel
due to the additivity property of age of air. Using the Equation (15)
same argument, the volumetric mean age of air in a Substituting the quantity 2a from Equation (12) into
system with an arbitrary airflow pattern is given by Equation (S) gives the following:
---- -
Equation (S).
't11Er
Ea=
-
't,1 Ct.s + 2Ct.sEr
(B6)
-
Relations 'tnEr
Ea = ------ (B7)
Equation (9) 'tn Rrn + 2Rrner
Substituting Equation (4) into Equation (S) yields the Canceling 'tn in Equation (B7) yields Equation (lS).
following:
Substituting Equation (A9) into Equation (BS) leads to Comparing the right hand side of Equation (Bll) with
Equation (12). (Equation 13) shows that TJ is twice Er
56