Air change effectiveness and age of air

In deriving the concentration equation (2.16) and its simplified versions, it has been assumed that a perfect mixing of the supply air with room air occurs, i.e. perfect dilu-tion of the indoor contaminants. In reality this is very rarely the case and, invariably, the supply air does not mix perfectly with the air in the occupied zone, which can lead to outdoor air being exhausted before picking up its full share of indoor contaminants, i.e. short circuiting. As a result, different concentration rates will exist in the occupied zone and to achieve the threshold limit value a larger air supply rate will be required.

The effectiveness of an air distribution system in supplying outdoor air to a room is expressed by the term ‘air change effectiveness’ or sometimes called ‘air exchange efficiency’. Another useful concept in determining the length of time the outdoor air supplied by a system remains in a ventilated space is the ‘age of air’. On the other hand, the ability of the air distribution system of removing internally produced pollutants is referred to as the ‘ventilation effectiveness’ or sometimes called the ‘ventilation effi-ciency’. These and related concepts which have become standard terms in ventilation research and applications will be briefly considered here but the interested reader may refer to the book by Etheridge and Sandberg for further details [41].

2.4.1 Age of air

Etheridge and Sandberg [41] considered the movement of particles in the air (e.g. air, contaminants, tracer particles, etc.) of a room by defining for a particle:

• the time that has elapsed since the particle has entered the room, i.e. the internal age,τi

• the remaining time for the particle in the room, i.e. the residual life time, τrl

• the total time the particle remains in the room from the time it enters until it leaves, i.e. the residence time,τr.

Hence,

τr= τi+ τrl (2.25)

The residence time is an indicator of how long a particle remains in the room. In particular, for a particle entering the room at the air supply point, its age is zero and for one leaving the room through the exhaust opening its age is the same as the residence time, as the residual life time is zero at the exhaust. Similarly, a mean age and a mean residence time may be defined for a particular group of particles, such as a particular pollutant or a tracer gas. However, these parameters do not provide information on how effective the air distribution system is in removing the internally produced pollutants.

In practice the age of air and residence time can be evaluated experimentally using tracer gas techniques (step-up or step-down methods) or by solving the age equation in a computational fluid dynamic code (see Chapters 3 and 8 respectively). The local mean age of air at a particular point, p, in a room, ¯τp, can be calculated by integrat-ing the local tracer concentration, Cp(t), with time and dividing this by the initial concentration at t= 0, C(0), namely:

¯τp=

_∞

0 Cp(t) dt

C(0) (2.26)

Equation (2.26) can be applied to calculate the local mean age of air at certain points of interest in the room, such as the breathing zone. Sometimes it is useful to know the mean age of air in the room as whole,  ¯τ . This can be quantified by measuring the tracer concentration at the exhaust air point and integrating this with time, namely:

 ¯τ =

_∞

0 tCe(t) dt

_∞

0 Ce(t) dt (2.27)

where Ce(t) = concentration at the exhaust at time t.

If the mean age is required for a certain zone in the room, e.g. the occupied zone, the measurement of tracer concentration is required at a number of points within the zone and the local mean age at each point is calculated using equation (2.26). The mean value for the whole zone can then be calculated by taking an arithmetic or geometric mean of all the values. The interested reader may refer to reference [42].

2.4.2 Air change effectiveness

The ‘local air change effectiveness’ (LACE), sometimes called ‘local air exchange index’, is the effectiveness of the air distribution system of delivering the supply air to a particular point in the room. On the other hand, the ‘mean air change effectiveness’

(MACE), or the mean air exchange index, is a measure of effectiveness of ventilation air delivery to the room. LACE is defined by:

Ep= τn

2¯τp (2.28)

whereτnis the nominal time constant for the room in seconds which is found from a knowledge of the air supply rate and the room volume using:

τn= V/ ˙V (2.29)

the air change rate, N, is the reciprocal of the nominal time constant, i.e.:

N= 1/τn= ˙V/V s⁻¹ or

N= 1/τn= 3600 ˙V/V h⁻¹ (2.30)

The room mean air change effectiveness is represented by:

¯E = τ2 ¯τ ⁿ (2.31)

2.4.3 Ventilation effectiveness

This is the effectiveness of an air distribution system in removing internally generated pollutants or heat from the ventilated space. There are two values: one refers to the distribution of pollutants which is defined in terms of the concentration of the pollutant in the room [43] and the other refers to the temperature distribution which is defined in terms of the temperature in the room [44]. The local ventilation effectiveness expresses how the system’s ventilation ability varies between different parts of a room. It can be expressed either as a local relative effectiveness or as an average or overall relative effectiveness for the whole occupied zone.

The local ventilation effectiveness for the removal of pollutants,εc, is expressed as:

εc= (ce− c_∞)/(cp− c_∞) (2.32)

and the overall ventilation effectiveness for the removal of pollutants, ¯εc, is expressed as:

¯εc= (ce− c_∞)/(¯c − c_∞) (2.33)

where c= contaminant concentration at a point (p.p.m.); ¯c = mean concentration in the occupied zone (p.p.m.); c_∞ = contaminant concentration in the outdoor supply air (p.p.m.) and ce = contaminant concentration in the exhaust air (p.p.m.). For steady-state situations, the concentration in the exhaust, ce, is obtained using:

ce= ˙mc/ ˙ma

where ˙mcis the rate of discharge from the pollution source (kg s⁻¹or m³s⁻¹) and ˙ma

is the rate of supply of outside air (kg s⁻¹or m³s⁻¹).

The definition for pollutant removal effectiveness given by equation (2.32) is a relative value, i.e. represents a ratio of the value at one point relative to another point. If one, however, is interested in the ability of the ventilation system in reducing the pollution concentration at a point with time, then another definition referred to as the absolute ventilation efficiency,εa, is used which is expressed by [43]:

εa= (co− ct)/(co− c_∞) (2.34)

where cois the initial concentration at a point and ctis concentration at the same point after time, t, seconds.

The relative ventilation effectiveness for pollutant removal is a measure of pollutant dispersion and does not take into account either the absolute concentration levels or changes in concentration from initial values. The value of εc is always positive and can be less than, equal to or greater than one depending on the position in the room and the method of air distribution used. However, the absolute ventilation efficiency, εa, represents the change in concentration as a result of change in the ventilation rate and it is always less than one.

To overcome the effect of imperfect dilution of indoor pollution by the outdoor air, an air supply rate greater than that given in the concentration equations (2.16)–(2.24) will be required. This is expressed quantitatively by replacing ˙V in these equations by

¯εc˙V. The value of ¯εcis clearly dependent on the type of air distribution system which is used to supply and extract the air to the room (see Section 2.5). The ventilation effectiveness for heat distribution or removal is dealt with in Section 2.6.

2.4.4 Purging flow

Although the concept of mean age of air is useful and the parameters involved are relatively easy to measure and calculate, it does not express the contaminant removal capability of a ventilation system. Therefore, the concept of the ‘local purging flow rate’ is used to describe the nature of the contaminant purging process at a point or a region within a ventilated enclosure. This concept originates from the study of chemical reactors involving concentration of chemical or biological species but was first introduced to ventilation applications by Sandberg and Sjöberg [45]. When applied to ventilated enclosures it can characterize the local pollutant-purging capability of ventilation air. A small purging flow rate at a point or a region suggests that that point or region is weakly connected with the ventilation process whereas a large value would suggest the reverse. Although it was originally introduced to quantify the net flow rate at which a pollutant present at a point is removed by the local air flow, it can also be used to characterize the distribution of ventilation air in an enclosure. The ‘local purging flow rate’ is sometimes defined as the net flow rate at which air is supplied from the inlet to a point or region within the enclosure. In other words, this concept can be used to quantify the rate at which a passive pollutant (one that moves with the air particles) is ‘flushed’ out from a point or a homogeneously mixed region, or the rate at which ventilation air is supplied to the point or region.

It can be seen from the above definition that the purging flow rate refers to local properties and is therefore usually referred to as the ‘local’ purging flow rate, Up. To define Up, a small control volume that conforms to mass continuity is considered such that, within this control volume, a source of pollutant emitting a mass flow rate of mp

will result in a pollutant concentration of cpleaving the control volume, i.e.

Up= mp/cp (2.35)

In principle the local purging flow rate may be determined by releasing a short burst of a known mass, M, of a tracer gas at the point of interest and measuring the local concentration of the tracer with time as given by the following equation:

Up= M

_∞

0 c(t) dt (2.36)

However, in practice it may be possible to measure Up at one or two points or small regions but it would be a difficult task to do in a large enclosure where multiple zones are involved. In a single zone, it would be possible to inject a tracer gas at a known rate, m, measure the spatial average concentrationc and apply the expression below to obtain the mean purging flow rate,Up , corresponding to that zone:

Up = m/c (2.37)

The accuracy in the value ofUp depends on how uniform the pollution is dispersed in the zone and on the accuracy of measuring the mean concentration,c , in the zone.

For the purpose of finding the mean purging flow rate for the zone, it would be pos-sible to achieve a uniform tracer concentration within a particular zone, e.g. a room, by artificial mixing of the tracer using a fan. However, care must be exercised in this case because such a mixing process could interfere with the natural air movement in the zone.

If a complete mixing of the tracer gas with air is achievable in each zone of a multi-zone building, then the principle of local purging flow may be extended to determine interzonal flow rates. The mass conservation equations (air or tracer flow) will, in this case, result into a flow matrix that contains terms for the interzonal flows and the flows between the zones and outdoor. For a building of n zones, e.g. n separate rooms, there will be(n²− n) internal zonal flow terms and 2n flow terms between the zones and outside, i.e. n(n + 1) flow terms and the same number of equations. Hence, for a small house consisting of five rooms there will a total of 30 equations to solve to give the same number of flow rates for air or tracer gas. This will require repeating the measurement n, or in this case 30, times or using n different tracer gases simultaneously. Using a large number of tracer gases requires a large capital expenditure on tracer measuring equipment whereas using a single tracer is a very time consuming task and therefore, in practice, interzonal flows is limited to a few number of zones. The methods used in the measurement are explained in Chapter 3 and the interested reader may also refer to other publications on the subject, such as the AIVC TN 34 [46].

Purging flows and interzonal flow rates can also be calculated using computational fluid dynamics and applying statistical methods, such as a Markov chain model. How-ever, the calculation tasks involved for three-dimensional geometry with a number of zones are huge and these are currently restricted to simple cases of two-dimensional enclosures, see e.g. [47–49].