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Article Excerpt
INTRODUCTION
Ventilation, and thus the transport of contaminants and clean air, is becoming an ever more important issue as we strive to both improve energy efficiency of buildings and the indoor air quality (IAQ) within buildings. Air motion is a complex interaction of naturally and mechanically induced pressures interacting with a wide variety of airflow paths between inside and outside and from zone to zone within the building.
Because geometric details of the pathways and the magnitude, direction, and space/time variability of driving pressures are difficult to determine precisely, it can be challenging to determine the quality and quantity of airflow in all but the simplest and most controlled building environments. If the entire building were very well mixed and acted like a simple single zone, extant techniques would make this determination straightforward. Buildings, however, are rarely so compliant. In fact, we often wish to measure, and even sometimes use departures from, the simple situation to examine impacts of ventilation efficiency, air distribution, contaminant removal effectiveness, and heat and mass exchange. When it is necessary to know how air and its constituents propagate, one must measure the air exchange using multizone tracer gas techniques that divide the building into a set of well-mixed zones.
The effectiveness of a given mechanical ventilation system will depend on airflows between each zone as well as flows to and from outside. Since it is the occupants' exposure to contaminants that we are ultimately interested in, it will also depend on the distribution of those contaminants and the activity pattern of the occupants in the building.
This paper will examine different air distribution paradigms, develop some prototype air distribution metrics, and apply the metrics to two case studies done with our multitracer measurement system (Sherman 1990b), which is now in its second generation (MTMS II).
BACKGROUND
It is, of course, well known that IAQ is impacted by the distribution of both sources and ventilation air. Many approaches have been used to attempt to account for this. One approach, for example, is to break a space up into a small number of well-mixed zones. Feustel (1990) investigated a zonal model similar to this.
But, it is often necessary to determine the air distribution within a zone. About 25 years ago, this was an active area of research where the concepts of ventilation efficiency and pollutant removal efficiency were developed. Sutcliff (1990) and Brouns and Water (1991) reviewed the work of that period and did a fine job of summarizing the key efforts. Persily et al. (1994) used such techniques to make measurements in commercial buildings.
A commonly used metric developed from that time is age of air. Maldonado and Woods (1983) described this metric and discussed how to measure it. ISO Standard 16000-8 (ISO 2007) describes how to determine the local mean age of air. While this metric is always a qualitative measure of ventilation, it can, as shown by Sherman (2008), be used to estimate IAQ only under certain pollutant generation assumptions. This will be discussed later.
Measuring age of air or other air-change-rate related metrics in buildings is normally done using a tracer gas. An ideal tracer gas is a substance that can be added to a volume of air (presumably in small amounts) and subsequently measured without impacting the properties of the air. No tracer is perfect, but a good tracer gas should be nontoxic, easy to measure in low concentrations, environmentally friendly, easily dispersed, and should not impact the thermo-physical properties of the air it is tracing. Grimsrud et al. (1980) did an intercomparison of different tracer gasses used for such measurements.
Harrje et al. (1985) reviewed many of the approaches that use tracer gasses to measure air-flow-related quantities. Their most common use in building science is to determine airflows under field conditions to support ventilation and pollutant transport work such as those described by Lagus and Persily (1985). McWilliams (2003) has more recently reviewed airflow measurement methods. The Air Infiltration and Ventilation Center (www.aivc.org) has a variety of technical publications that are related to tracer gas applications.
When using tracer gasses to quantitatively estimate airflows the concept of a well-mixed zone is important. Just as exposure to an air pollutant depends on knowing the concentration of that pollutant in the occupied zone, accurate estimation of airflow depends on knowing the concentration of tracer gas.
The theory and practice of using a tracer gas in a single zone has been well developed. In addition to the references above, Sherman (1990a and 1989a) reviewed the basic techniques and analyzed the associated errors of using those techniques. ASTM International (2000) developed a standard test method for making this measurement years ago.
More complex buildings or more complex airflow patterns require breaking the indoor space into multiple well-mixed zones. Multizone techniques analogous to the single-zone techniques have been developed including those discussed by Roulet and Compagnon (1989).
The most straight-forward generalization to the multizone situation requires that multiple, unique tracer gasses be used (i.e., one for each zone). These techniques allow the full range of analysis options and provide the most robust estimates of airflow. Sherman (1990b) describes such a system. Walker (1985) reviewed some issues of various approaches. Sherman (1989b) examined some of the analysis limitations based on inverse problem theory such as that presented by Tarantola (1987).
DISTRIBUTION METRIC DEVELOPMENT
In order to understand the value of air distribution in the control of indoor contaminants, we need to develop appropriate metrics. The metrics developed in this study are based on analyses using the following multizone continuity equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a matrix containing the volume of each zone ([m.sup.3]), [C.bar] is the vector of the rate of change of concentration of each pollutant (-), [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the matrix of volumetric airflow rates ([m.sup.3]/s), [C.bar] is the concentration (vector) in each zone (-), and [S.bar] is the source strength (vector) in each zone ([m.sup.3]/s).
From the point of view of ventilation standards (e.g., ASHRAE Standard 62.2 [ASHRAE 2007]), IAQ is usually defined in terms of the total dose of some generic pollutant over a long period of time. That is, ventilation rates are not set to protect against acute (or threshold) pollutants. Accordingly, only the steady-state part of the solution to the continuity equation is of interest. This implies that the concentration of the generic pollutant can be calculated for each zone using the following equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
If the building was treated as a single zone, it would lead to this similar scalar equation:
[C.sub.o] = [[S.sub.o]/[Q.sub.o]] (3)
where [C.sub.o] is the equivalent single zone concentration (-) and correspondingly, [S.sub.o] is the sum of all the entries in the source vector ([m.sup.3]/s), and [Q.sub.o] is the sum of all the entries in the airflow matrix for the whole building ([m.sup.3]/s).
These scalar quantities can also be used to normalize the matrix expression. This derivation can also be found in Sherman (2008).
The dose of contaminants that an occupant would be exposed to would be the concentration of the contaminants in the zone they were in times the number of hours they were in that zone. However, we are seeking to define metrics associated with the distribution system rather than the contaminant source or the total ventilation rate. Therefore, we will develop our metrics based on a relative dose that has taken out the total ventilation rate, the total exposure time, and the total contaminant emission, leaving the issues associated with air distribution.
Relative Exposure and Relative Dose
Our objective is to investigate the impact of ventilation (and source) patterns that are not uniform in space (or time) and compare them to the perfectly mixed, constant-ventilation case. We make that comparison based on the contaminant dose that an occupant would...
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