Investigation of [CO.sub.2] tracer gas-based calibration of multi-zone airflow models.
The modeling and simulation of airflow dynamics in buildings has many applications including analyzing indoor air quality (IAQ) and ventilation flows, predicting contaminant dispersion dynamics, and calculating personal occupant exposure under extreme events. Traditionally, multi-zone airflow software programs have been used to study such effects during the design phase. Similar to detailed building energy use simulation programs, they can also be used to study the behavior and performance of existing buildings. Building-specific guidance from a calibrated multi-zone model provides greater confidence (as compared to a non-calibrated model) in analyzing IAQ issues during normal diurnal and seasonal operation, or in formulating response plans and analyzing the effectiveness of possible mitigation measures when the building is subject to either accidental or intentional air-borne contaminant releases. In such cases, the programs have to be calibrated, i.e., the numerous model parameters need to be tuned so that simulated output closely matches observed system performance under some baseline conditions. This paper proposes a calibration methodology intended to improve the prediction accuracy of multi-zone software programs.
Objectives and Scope
CONTAM (Walton and Dols 2008) is a multi-zone model software program for indoor air quality and ventilation analysis. The main applications of CONTAM include assessing adequacy of ventilation rates, design and analysis of smoke systems, assessing indoor air quality performance, predicting contaminant dispersion, and estimating personal exposure. The objective of this paper is to propose a new calibration methodology and to demonstrate it using CONTAM. Previous research efforts by Bahnfleth and colleagues (Firrantello et al. 2005, Firrantello 2007a, Firrantello et al. 2007b, Sae Kow 2010, Bahnfleth et al. 2012) have led to the development of a calibration methodology which is based on measured heating, ventilation, and air-conditioning (HVAC) airflow rates and inter-zonal airflow directions; this has been partially validated using collected field data. This paper builds upon, and subsequently improves, the previous work by developing a refined calibration methodology that explicitly utilizes measured tracer gas data to improve model prediction accuracy.
Previous Work on Multi-Zone Model Calibration
A specially developed version of CONTAM called the Project Creation Wizard (PCW) has been developed by Vandemusser (2007) which runs on the same simulation engine but differs from CONTAM in that it has a more "user friendly" graphical user interface and more built-in default model parameters that help reduce the time and effort needed to develop an airflow model. PCW was also designed to help with model calibration by integrating a "tuning" process which accepts actual measured data and updates the model based on those measurements to improve model accuracy. The calibration methodology integrated into PCW is based on the tuning algorithm developed by Firrantello et al. (2007b) which combines analytic and heuristic methods while utilizing building site measurements (e.g., HVAC airflow magnitudes and inter-zonal airflow directions) to improve model prediction accuracy. Two metrics were used to evaluate model quality throughout the tuning process: the percentage of correctly predicted airflow directions and the percentage of satisfactory statistical metrics presented in ASTM Standard D5157 (ASTM 2003).
The tuning algorithm (Firrantello et al., 2007b) was developed using two synthetic buildings and refined through testing on two real buildings. It includes the following recommendations: (1) measure all possible interior airflow directions and create a multi-zone model, (2) measure all bulk air handling unit (AHU) airflows, (3) identify all flow paths for which the simulation has incorrectly predicted flow direction, (4) identify the lowest unmeasured branch levels of HVAC flows associated with the incorrect airflow directions, (5) measure the associated HVAC airflows in those areas, (6) revise the model based on these measurements (this becomes the new "best guess" model), (7) evaluate model quality and repeat starting at step (2) if unsatisfactory, and (8) perform a regression analysis to estimate the difficult or impossible to measure factors (e.g., average interior and exterior leakage, shaft leakage, and terrain constant/coefficient). Firrantello et al. (2007b) found that the measurement of bulk HVAC airflows resulted in the greatest improvements in model quality metrics.
Sae Kow (2010) utilized the PCW program to implement, and further validate, the tuning algorithm developed by Firrantello et al. (2005) and Firrantello et al. (2007b) using additional measured data. The field tests were conducted on two buildings on a university campus. Sae Kow (2010) evaluated the improvement in model development efficiency with PCW as compared to CONTAM, the performance of the PCW model tuning process under different operating conditions, the suitability for a model calibrated under one condition in predicting different conditions (e.g., open vs. closed doors), and the repeatability of PCW calibration by developing and tuning a model for the same building used by Firrantello et al. (2007b) and comparing results.
In these previous research efforts, CO2 testing was only used to determine model adequacy as suggested by the ASTM D5157 metrics. Also, the results of these studies showed that even after implementing the tuning algorithm, the models were still incorrect in predicting certain airflow directions and certain ASTM D5157 metrics remained unsatisfactory. There-fore, further improvements in model calibration methodology were deemed necessary. Tracer gas data was not incorporated into the calibration effort in these studies; hence, one of the improvements suggested in this paper is to integrate the collected tracer gas data into the calibration methodology.
Important Research Assumptions
The calibration methodologies developed in this paper and in the previous work are not universally applicable and are subject to some significant research assumptions. Extrapolation of the developed methodology beyond these boundaries is not recommended.
1. Inherent in the use of multi-zone models is the assumption that all zones are under "well-mixed" conditions (i.e., a discrete set of state variables).
2. PCW assumes a simple AHU model for which the duct distribution systems are represented as a single volume of air. The details of the simple AHU model are discussed in the PCW user manual (Vandemusser 2007).
3. All zones use the PCW default air leakage relationships (i.e., all airflow path flow elements are one-way power law relationships with fixed coefficients and exponents). In a multi-zone model, airflow paths are building features which allow air travel between zones and the airflow element is the mathematical relationship between the magnitude of flow through an airflow path and the pressure difference across the path. One-way flow using power law models take the following form:
Q = k[([DELTA]P).sup.N] (1)
where Q is the volumetric airflow rate, [DELTA]P is the pressure difference across the flow path, k is the airflow coefficient and n is the airflow exponent, which are referred to as "leakage parameters". In PCW, leakage severity can be assigned automatically by the program as either "leaky", "normal", or "tight". These leakage parameter assignments are based on data surveyed from real buildings (Persily 1998).
4. All simulations are performed as transient contaminant dispersion and steady-state airflow simulations. This means that the building's pressure distribution and the resulting volumetric airflow rates through each flow path are calculated and remain fixed for one set of conditions (i.e., constant weather condition and constant air volume HVAC system operation) while contaminant concentrations are allowed to vary over time under these steady-state airflow conditions.
5. A constant air volume (CAV) condition is assumed for the HVAC system in all simulations.
6. All tracer gas releases are assumed to occur in an air handling unit.
The specific intent of the proposed methodology is to improve the previously developed tuning algorithm (Firrantello et al. 2005, Firrantello et al. 2007b) by explicitly using collected [CO.sub.2] tracer gas data during the process of calibrating multi-zone airflow models. The various steps of the proposed methodology are summarized below:
1. Preliminary Model Tuning: Develop a "somewhat" realistic multi-zone model of the building by calibrating based on the previously developed tuning algorithm (Firrantello et al. 2007b). This step is necessary for enhancing the robustness of the subsequent calibration steps.
2. Sensitivity Analysis: Evaluate whether the building airflow dynamics are climate or HVAC system dominated; if so, by how much. This sensitivity analysis is meant to identify the significant or important drivers of the system, and is needed to verify whether calibration performed under one set of operating and climatic factors still applies for other conditions.
3. Identify Macro-Zones for Model Reduction: Calibrating multi-zone airflow models is a highly over-parameterized problem. Model reduction is warranted and is achieved by grouping rooms into "macro-zones" or clusters of rooms with similar airflow and tracer gas dynamics under varying conditions. Macro-zone identification can be achieved by performing a tracer gas-based sensitivity analysis. A preliminary hypothesis is that the great effort of performing factorial sensitivity tests with tracer gas releases could be avoided by simply selecting the macro-zones based on room air change rates.
4. Tracer Gas Release Tests: Perform tracer gas release tests in the building being analyzed and place sensors in at least one room of each identified macro-zone. Some amount of replication is strongly advised.
5. Model Tuning and Calibration: Tune the flow parameters of the multi-zone models to improve the match between measured and predicted tracer gas concentration dynamics in each macro-zone. If flow parameter tuning is unsuccessful, investigate factors that significantly influence the room air change rates (i.e., HVAC airflow rates, room and system volumes, outside air percentage, etc.).
6. Evaluate Model Adequacy: Evaluate the adequacy of the updated model based on some metric. Since a robust metric for model adequacy has yet to be determined, and since previous research has questioned the confidence in conclusions from any one metric, the evaluation of the model can be based on several metrics such as (a) the percentage of correctly predicted airflow directions (which is arguable as a metric since the magnitude of the flow and not simply the flow direction influences indoor air contaminant dispersion), or (b) ASTM Standard D5157 statistical metrics or some modified form thereof which evaluates predicted vs. measured [CO.sub.2] concentrations.
We note that the previously developed tuning algorithm (Firrantello et al. 2007b) considered only one set of operating conditions (i.e., it did not account for varying ambient temperatures, wind speeds, wind directions, and assumed leakage parameters). Thus, a detailed calibrated model for only one set of typical conditions may provide a false sense of precision, and may not be accurate when extrapolated to different conditions. Our first intent, therefore, was to determine the sensitivity of the multi-zone model to varying ambient conditions and leakage assumptions. Next, the hypothesis was that model reduction, i.e. reducing the complexity of the model by grouping rooms into "macro-zones", would yield a more aggregated model that may provide greater accuracy under varying conditions. With macro-zones identified, tracer gas ([CO.sub.2]) concentration data could then be used to find aggregate (and realistic) leakage parameters for each of the airflow paths of each macro-zone. Such an updated model would then provide more accurate prediction of airflow behavior under the varying conditions.
DESCRIPTION OF SYNTHETIC AND REAL BUILDINGS ANALYZED
Initially, the methodology steps were developed and refined using a synthetic building (i.e., one whose dynamic behavior can be entirely simulated on a computer and does not need any real building data). This is similar to the procedure used by Firrantello et al. (2005) for the development of the tuning algorithm. The synthetic building used was a single story building that has 29 modeled zones (25 rooms, 4 corridor spaces) and three air handling units serving three HVAC zones (north perimeter, south perimeter, and core). Details of this building can be found in Snyder (2011).
An actual building, namely the MBNA building, was also selected for which measured [CO.sub.2] data, HVAC airflow rates, and airflow directions have been collected by Sae Kow (2010). The PCW model of this building that was tuned by Sae Kow (2010) using the previously developed tuning algorithm (Firrantello et al. 2007b) served as the starting point for our analysis. The MBNA building is a three story, 44,000 [ft.sup.2] [4090 [m.sup.2]] office and administration building which is served by three variable air volume (VAV) air handling units. Two of the units (AHU1 and AHU2) are located in an unconditioned basement and the third (AHU3) is located in a mechanical room on the third floor of the building. The evaluation of our methodology on the MBNA building focused exclusively on just the third floor since both Firrantello (2007a) and Sae Kow (2010) found that releases in AHU3 resulted in no cross contamination to the rest of the MBNA building. Similarly, releases in either AHU1 or AHU2 resulted in no cross contamination on the third floor. Therefore, for releases in AHU3, the third floor can be considered to be an isolated building. Also, the proposed methodology requires room-level [CO.sub.2] measurements and the data made available by Sae Kow (2010) only included room level measurements on the third floor of the MBNA building. It is important to note that there are a number of difficulties in measuring and interpreting the use of tracer gas tests in buildings as described in several publications (for example, Turk et al., 1989).
AIRFLOW-BASED SENSITIVITY ANALYSIS
The objectives of an airflow-based sensitivity analysis are: (1) to evaluate whether the airflow dynamics of the building are climate or HVAC dominated, (2) identify the significant or important drivers of the system, and (3) assist in reducing the model complexity by identifying macro-zones. Specifically, this analysis determines the sensitivity of the building's airflow dynamics to changing climate conditions and building leakage assumptions (i.e., ambient air temperature, wind direction, wind velocity, and building leakage severity). Since the other main influential driver is HVAC system airflow rates, low sensitivity to these climate and leakage factors would indicate HVAC system dominance of airflow dynamics.
The airflow-based sensitivity analysis involves several steps. First, possible influential drivers (wind speed, wind direction, ambient temperature, envelop leakage coefficients) of the airflow system are selected and representative nominal ranges are identified for each. Next, a full factorial experimental design is used to set up the simulation runs. A [2.sup.k] factorial analysis is used assuming that the relationships are linear. Then, a semi-quantitative airflow-based sensitivity analysis is performed based on the magnitude and direction of airflow through each airflow path. In the absence of a robust response metric and due to the deterministic nature of multi-zone models (which limits the ability to perform statistical significance tests), a formal sensitivity analysis where main and interaction effects are calculated has not been undertaken. Rather, graphical representations, especially scatter plots, are used to distinguish whether the building is HVAC dominated or climate dominated. Further, one can also determine whether the airflow-based sensitivity analysis is able to provide insights that would help to identify macro-zones.
The initial sensitivity analysis, as summarized in Table 1, performed on the synthetic building, included a [3.sup.3] full-factorial experimental design (27 PCW simulations) to determine the effects of varying ambient temperature, wind speed, and building leakage severity on the direction and magnitude of airflow through all airflow paths. Common temperature and wind conditions were used along with the default building leakage severity conditions in PCW. Four subsequent simulations, summarized in Table 2, were performed to analyze the impact of wind direction.
Table 1. Synthetic Building Sensitivity Analysis Summary Ambient Temperature ([degrees]F) [[degrees]C] Wind Speed (mph) [m/s] 0 [-18] 70  100  Leaky Leaky Leaky 0  Average Average Average Tight Tight Tight Leaky Leaky Leaky 5 [2.2] Average Average Average Tight Tight Tight Leaky Leaky Leaky 10 [4.5] Average Average Average Tight Tight Tight Table 2. Subsequent Simulations for Wind Effect Wind Direction Leakage Severity North West Leaky Tight West Leaky Tight Ambient temperature = 70[degrees]F [21[degrees]C] Wind Speed = 10 mph [4.5 m/s] Indoor Temperature = 72[degrees]F [22[degrees]C]
After analyzing several methods of plotting the simulation data, it was discovered that scatter plots provided the best visual representations of the dynamic airflow behavior. Each scatter plot compares the airflow magnitudes and directions of two different scenarios (one scenario per axis) with only one different condition. The unit on each axis is volumetric flow rate in cubic feet per minute (CFM). The direction of airflow is accounted for in the sign of the flow rate. Each point in the scatter plot represents flow through a single airflow path. These scatter plots allow for a simple visualization of how varying one condition impacts the magnitude and direction of the airflows. It was at this stage that it was determined a [2.sup.k] factorial analysis would suffice since the relationships between the factor levels and the effects appear to be linear.
Within these scatter plots, points which fall in the positive/positive and negative/negative quadrants imply that the altered condition did not result in a change in the airflow direction in that airflow path. On the other hand, points that fall within the positive/negative and negative/positive quad-rants show that the altered condition did change the airflow direction in that airflow path. Points that exhibit a "y = x" relationship indicate that the altered condition did not change the magnitude of airflow through that airflow path. Points that fall off of this line indicate that the altered condition did change the airflow magnitude. Therefore, scatter plots showing a "y = x" relationship signify HVAC dominance of airflow dynamics.
Figure 1(a) provides an example scatter plot of two simulations from Table 1 showing the effect of varying ambient air temperature. Figure 1(b) provides an example of the effect of varying wind direction. The effect of air temperature appears to be small with little airflow magnitude and direction changes. The change in wind direction, however, was found to alter the direction of flow through many airflow paths; this is concluded from the points in the negative/positive and positive/negative quadrants of Figure 1(b). After analyzing all scatter plots, it was found that wind speed and wind direction both had significant influences on airflow dynamics. This significance, however, is a function of building leakage severity (i.e., the effect is larger when the leakage severity is "leakier"). Most of the scatter plots for this analysis indicated HVAC dominance.
[FIGURE 1 OMITTED]
Since the synthetic building analysis revealed that a [2.sup.k] factorial is more appropriate and that wind direction is also an important factor, the analysis on the real building (MBNA) involved a [2.sup.4] full factorial experimental design (16 PCW simulations) to analyze the impacts of wind speed, wind direction, ambient air temperature, and leakage severity. A typical meteorological year (TMY) weather file was used to determine typical weather conditions near the building. Similar to the results of the synthetic building, it was found that these external drivers had negligible influence under "normal" and "tight" conditions (see Snyder 2011 for details on this real building analysis). Therefore, these conclusions reiterate the fact that buildings of this size which are mechanically ventilated are likely to have airflow dynamics dominated by the HVAC system.
IDENTIFY MACRO-ZONES FOR MODEL REDUCTION
A key concept of this paper was the recognition that calibrating a multi-zone airflow model such as CONTAM or PCW with numerous parameters specified by the user is a highly over-parameterized problem. This is a result of having only a few data points and many parameters to tune. When faced with such problems, the traditional approach is to reduce the order of the model and then perform system identification. In this case, the macro-zone approach offers such a reduction. We identify macro-zones, i.e. groups of rooms which have similar airflow dynamics under varying conditions, and then identify aggregate flow parameters of these macro-zone flow elements which can be used to update the model. The approach adopted was to identify macro-zones based on the results of a tracer gas-based sensitivity analysis (i.e., analyzing [CO.sub.2] decay curves, decay coefficients, and peak concentrations).
Macro-zone formation based on tracer-gas simulations can be conducted in several ways. First, [CO.sub.2] decay curves can be plotted for each room. Then, macro-zones can be identified by visually observing the decay rates and peak concentrations in each room under varying conditions. Visually identifying macro-zones, however, can be daunting if many rooms are to be considered at the same time. An alternative method is to use natural log transformation of the [CO.sub.2] concentration data thereby linearizing the exponential decay curves for each room and then perform linear regression to identify the decay coefficient (which is the slope of the transformed decay line) for each room. Macro-zones can then be found by identifying rooms with similar coefficients under varying conditions. The peak concentrations in each room should also be compared. Unfortunately, this approach was not found to be suitable because of higher order exponential decay dynamics (most likely due to return air reintroducing [CO.sub.2] into the supply air stream). Therefore, a natural log transformation did not result in linear transformation of the data from which a decay coefficient could be identified.
Macro-Zone Identification for Synthetic Building
Using PCW, simulations were performed where [CO.sub.2] was released in each AHU. The synthetic building has three air handling units, one serving the north perimeter zones, one serving the south perimeter zones, and one serving the core zones. For these simulations, [CO.sub.2] concentration decay data was obtained for each room. Table 3 provides a summary of all of the tracer gas releases simulated. The amount of tracer gas released corresponds to the same procedure used by Sae Kow (2010). This was specifically modeled in PCW by specifying an initial concentration of 2000 PPM in each room served by the AHU where the release occurred. Thus, the HVAC system volume is initially ignored, and the [CO.sub.2] curves show only the decay dynamics and not that during the uptake of [CO.sub.2].
Table 3. Synthetic Building Tracer 1 Summary Gas Simulation Release Location Leakage Severity Wind Direction North AHU Average North South AHU Average North Core AHU Average North 129 Exit Average North North AHU Leaky West South AHU Leaky West North AHU Leaky South South AHU Leaky South Ambient Temperature = 70[degrees]F [21 [degrees]C] Wind Speed = 5 mph [2.2 m/s]
Several methods of plotting the resulting tracer gas release data were explored. It was found that [CO.sub.2] concentration curves for individual rooms were the most promising for analyzing tracer gas dynamics and for identifying macro-zones. Since there were several AHU's where releases could occur, it became apparent that the release location has a significant impact on which rooms are affected by the contaminant. The tracer gas-based sensitivity analysis, summarized in Table 3, were consistent among themselves, i.e., similar room groupings were obtained for all the combinatorial experimental design runs under all conditions, indicating HVAC dominance of tracer gas behavior. This agrees with the results from the airflow-based sensitivity analysis. As discussed previously, wind speed and wind direction could have significant influence, especially under "leaky" conditions. However, only slight variations in decay rates and small amounts of cross contamination between zones were observed due to these changing conditions. Whether these slight variations are significant or not would depend on the circumstances under which calibration is being performed, the type of contaminant being analyzed, and the resulting difference in occupant expo-sure. Such factors are to be specified by the analyst at the onset of the calibration process depending on the circumstance and the criticality of the consequence.
By analyzing the tracer gas curves, the synthetic building was reduced from 29 model zones to 9 macro-zones consisting of rooms with similar behavior under varying conditions. The macro-zones identified did not change under the various conditions of both the airflow-based and tracer gas-based sensitivity analyses. This confirms that the airflow dynamics are HVAC dominated. Wind had the most impact resulting in slight variations in tracer gas behavior as well as cross contamination between zones. However, the significance of these slight variations in decay curves needs to be evaluated by the analyst under the specific circumstances. The particular assumptions used for simulating the release in the synthetic building did not account for system volume, and thus all rooms have the same peak concentrations. Therefore, only the decay rates are analyzed. Consequently, it was concluded that peak concentrations should also be considered for macro-zone identification by accounting for system volumes.
Macro-Zone Identification for Real Building
Using [CO.sub.2] tracer gas simulations to identify macro-zones was undertaken by simulating a release in AHU3 and plotting [CO.sub.2] concentration curves for each room on the third floor of the MBNA building. With three variables (wind speed, wind direction, and leakage severity) at two factor levels each, a [2.sup.3] factorial analysis was used to set up these [CO.sub.2] simulations as summarized in Table 4. Ambient temperature was ignored since it was determined to be insignificant from the airflow-based sensitivity analysis. Again, instead of performing a formal quantitative sensitivity analysis and calculating effects, the impact of changing conditions on apparent macro-zones were visually determined.
"Figure 2 shows the individual [CO.sub.2] concentration curves for each room on the third floor of the MBNA building for the first set of conditions described in Table 4 (i.e., 10 mph [4.5 m/ s] north wind and "Leaky"). Clearly, there is a wide range of responses to one release in the AHU. For the synthetic building, an initial [CO.sub.2] concentration was specified in each room ignoring the supply duct volume. Therefore, all rooms are initially at the same concentration and all that was observed was the concentration decay with time. Here, however, with a release more realistically simulated in the supply duct volume, the uptake and peak are seen along with the decay of [CO.sub.2].
[FIGURE 2 OMITTED]
The overall goal of these tracer gas simulations was to be able to identify macro-zones that do not change under varying conditions; however, the complexity of Figure 2 does not allow for such classification. With so many concentration curves on one plot it is too difficult to identify individual rooms or overlapping curves. Properly identifying macro-zones requires closer inspection of these graphs. Therefore, the tracer gas-based sensitivity analysis was performed by plotting concentration curves for each condition in Table 4 for individual rooms. Figure 3 shows an example of these tracer gas sensitivity plots for Room 1 of the MBNA 3rd floor. The slight variations observed lead us to conclude that wind direction and wind speed have little impacts on the concentration curves. However, leakage severity does have a large impact when there is wind. This is indicated by the faster decay in the rooms that are "leaky" when there is high wind. The concentration curves for "tight" leakage severity and high wind are almost identical to when there is no wind and for "leaky" or "tight" rooms. Even closer inspection of this graph revealed that wind in any condition increases the rate of decay of the tracer gas. This can be attributed to higher air change rates resulting from wind induced infiltration. Similar conclusions were drawn from the sensitivity plots of the other rooms.
[FIGURE 2 OMITTED]
Table 4. Real Building (MBNA) Tracer Gas Simulation Summary Wind Speed Wind Direction Leakage Severity (mph) [m/s] 10 [4.5] N Leaky 10 [4.5] NW Tight 10 [4.5] N Leaky 10 [4.5] NW Tight 0 N Leaky 0 NW Tight 0 N Leaky 0 NW Tight Indoor Air Temperature = 72[degrees]F [22[degrees]C] Ambient Air Temperature = 67[degrees]F [22[degrees]C]
"This tracer gas-based sensitivity analysis provided some useful insights into the building's airflow dynamics under various conditions. Wind speed and wind direction changes resulted in slight variations in the decay rate in rooms with exterior walls impacted by the wind and with "leaky" conditions. However, as noted with the synthetic building, changing climatic conditions mostly yielded insignificant differences in tracer gas behavior. The results also showed that the decay rates and peak concentrations for individual rooms were almost identical under all conditions. Therefore, macro-zones could be formed by visually comparing peak concentrations and decay rates for various graphs under one set of conditions.
The 33 rooms of the third floor of the MBNA building were reduced to 8 macro-zones by identifying rooms with similar tracer gas behavior. Figure 4 is an example of [CO.sub.2] concentration curves for each room in two of the identified macro-zones. Note that the tracer gas behavior is essentially identical for each room within each macro-zone. Since results from the real building and the synthetic building indicated that the building's airflow dynamics are largely HVAC dominated, these newly formed macro-zones were compared to the room air change rates calculated from the HVAC airflows measured by Sae Kow (2010). Table 5 shows that the macro-zones identified are directly related to the air changes per hour in each space. Consequently, from the definition of macro-zones, the tracer-gas behavior in these rooms is directly influenced by room air change rates. Despite the apparent HVAC dominance, climate conditions and leakage severity also have impacts. For each condition, the slight variations in peak concentrations and decay rates, as discussed previously, from wind changes and leakage severity changes, are not large enough to shift around macro-zones as identified by the air change rates. However, the significance of such variations may depend on the release scenario and the type of contaminant.
[FIGURE 4 OMITTED]
Table 5. Observed Macro-Zones for MBNA Building and Measured Room Air Changes Identified Macro-Zones 1 2 3 4 5 6 7 8 Air Changes (1/hr) 5.9 5.3 8.2 7.8 15.4 10.7 3.6 0.0 6.1 4.7 8.9 7.6 0.0 6.3 4.8 9.0 6.8 0.0 5.6 5.2 8.6 6.7 2.7 6.3 4.7 8.6 1.4 5.7 8.2 1.9 5.8 9.1 5.7
MODEL CALIBRATION USING [CO.sub.2] DATA
With macro-zones identified, the next step is to use actual measured [CO.sub.2] data to calibrate the model. To collect tracer gas data, [CO.sub.2] releases need to be performed in the building and [CO.sub.2] sensors need to be placed throughout the building to record [CO.sub.2] concentrations. The identification of macro-zones assists in determining where it would be advantageous to place [CO.sub.2] sensors. Ideally, there should be a [CO.sub.2] sensor in at least one room of each macro-zone. The procedures and equipment needed to perform such tracer gas tests are described by Firrantello (2007a) and Sae Kow (2010). Next, new "aggregate" flow parameters (flow coefficients and exponents), one set for exterior flow paths and one set for interior flow paths, are estimated for each of the identified macro-zones. Since all rooms in each macro-zone have similar airflow dynamics, one can tune the flow parameters for each flow path in a macro-zone by the same amount. These aggregated flow parameters simplify the calibration process, reduce the number of parameters that need to be calibrated, and hopefully provide aggregate leakage parameter values that are more representative of varying conditions. There are several ways by which this could be done. The method explored in this research was to set up a factorial sensitivity analysis where the response variable is the match between predicted and measured [CO.sub.2] concentration curves for each macro-zone. The quality of the match between the two curves can be evaluated visually or by some statistical measure, i.e. root mean square error. The factorial analysis will evaluate the effect of increasing and decreasing flow parameters in each macro-zone on how well the predicted [CO.sub.2] concentrations match the measured data. If significant differences between predicted and measured concentrations remain after tuning the flow parameters, then possible measurement errors and uncertainties for factors impacting room air changes (i.e., HVAC airflow rates, room volumes, and outside air percentages) should be investigated. Model calibration for the synthetic building was deemed too arbitrary and was there-fore only performed on the real building.
As mentioned above, this methodology identifies rooms where it would be advantageous to place [CO.sub.2] sensors during testing (i.e., at least one sensor per macro-zone). However, the macro-zones in this research were identified after the testing had been performed by Sae Kow (2010). Therefore, there was no guarantee that the sensor locations would match up with identified macro-zones. The seven [CO.sub.2] measurement location rooms used matched up with four of the macro-zones identified in this analysis. Thus, we were constrained to calibrating the rooms associated with these four macro-zones using the data collected by Sae Kow (2010). As a baseline, graphs of the measured [CO.sub.2] curves were plotted versus the predicted curves based on the final tuned model developed by Sae Kow (2010). Figure 5 (a) and (b) show example plots of measured vs. predicted [CO.sub.2] concentration curves for two rooms on the third floor of the MBNA building. The graphs indicate that even after using the previously developed tuning algorithm, there are still some discrepancies between the measured and predicted tracer gas behavior. Assuming the HVAC airflow rates were measured accurately, it was initially hypothesized that these differences must be attributed to airflow into and out of the room via the exterior envelop or inter-zonal airflow paths. Consequently, we attempted to adjust the flow parameters (coefficients and exponents) for these airflow paths. By first identifying macro-zones, the complexity of the model has been reduced and locations for [CO.sub.2] measurement have been identified. Reducing the complexity of the model also reduces the complexity of these flow parameter adjustments. The macro-zones identify groups of flow paths whose parameters can be changed by the same amount. Other sources of discrepancies between measured and predicted behavior could include uncertainties or errors in HVAC airflow rate and [CO.sub.2] concentration measurements, errors in the development of the PCW model, and the consequences of the well-mixed assumption. For the factorial analysis to tune leakage parameters, depending on the relationship between the predicted and measured curves, one can determine the direction in which to change these parameters to reduce the number of simulations. This method tunes one macro-zone at a time and does not provide a procedure for simultaneous calibration of all macro-zones. There-fore there is some ambiguity in how to tune the flow parameters for airflow paths which connect separate macro-zones.
[FIGURE 5 OMITTED]
Despite the lack of [CO.sub.2] data needed to calibrate the entire third floor of the MBNA building, one of the identified macro-zones was analyzed as an example of model calibration. The internal and external flow coefficients were varied [+ or -]15% and [+ or -]30%. After initial simulations, it became apparent that the leakage needed to be increased in order to reconcile measured and predicted behavior. Thus, simulations were performed with the flow coefficient changed by +50% and +75%. A flow coefficient increase beyond 75% would represent an unrealistic leakage coefficient based on the data gathered from real buildings (Persily 1998). The flow exponent was varied from the default of 0.65 to 0.5 and 0.7. This represents the range of typical flow exponents recommended by Walton and Dols (2008). Figure 6 below shows that despite all of these changes to the flow coefficient, there is no noticeable difference in the predicted concentrations for the measurement location of this macro-zone. The leakage exponent did have a more noticeable impact in shifting the entire curve. Changing to the flow exponent to 0.5 provides a better match for the decay part of the curve. However, the peak concentration is still far too high. These changes fail to adequately provide a better match between the predicted curve to the measured curve.
[FIGURE 6 OMITTED]
With the flow parameters having little impact, other possible sources of the discrepancies between measured and predicted tracer gas curves could include incorrect supply or return duct volume estimates, room volumes, HVAC flow rates, outside air percentages, the well-mixed assumptions, etc. Sae Kow (2010) discusses the impact of system volume estimates on the predicted tracer gas curves. An increase in the system volume results in a decrease in peak concentrations. However, not all measured locations have higher peak concentrations than predicted. Therefore, rather than adjusting the system volume, there may be errors in individual room volumes which were estimated from floor plans. Also, Sae Kow (2010) notes that uncertainties in the measurement of the outside air percentage for AHU3 were very large since the air temperature fraction method was used. It is therefore likely that the outside air percentage is incorrect. The well-mixed assumption of the multi-zone model may also be a significant source of error. Therefore, it is possible that the [CO.sub.2] sensor was placed in a location where it recorded concentrations that are not representative of the room average.
It was found that the tracer gas behavior in each room was much more sensitive to factors impacting air changes (i.e., room volume and outside air percentage) than to changes in flow parameters. Figure 7 shows the impact of changing room volume and Figure 8 shows the impact of changing outside air percentage on the match between the measured and predicted [CO.sub.2] curves for the measurement location in macro-zone 3. Increasing or decreasing room volume results in a decrease or increase, respectively, in the peak concentration with a negligible change in the concentration decay rate. In Figure 7, it is clear that changing the ceiling height from 8 ft -- 6 in [2.6 m] to 10 ft [3 m] provides a much better match between the predicted and measured peak concentrations. The room volumes in the model were taken from architectural plans. However, when creating a multi-zone model, each zone is a volume of air. Therefore, the ceiling height may not be the best value to use when defining the zone. If the room has an accessible ceiling with acoustic tile there may be significant air transfer to the plenum space above which may need to be accounted for in the model.
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
In the field testing performed on the MBNA building, Sae Kow (2010) noted difficulty in accurately measuring the outside air percentage for AHU3. Due to physical constraints, the only practical option for measuring the outside air percentage was to use the air temperature fraction method. The outdoor air, return air, and mixed air temperatures were measured using hot wire anemometers. However, the calculated outside air percentage based on these measurements had a very large uncertainty (approximately 70%). This was due to the small temperature difference between the outside air and the return air. Therefore, it is fair to assume that the outside air percentage of 20% initially used in the model is not accurate. Figure 8 shows that changing the outdoor air fraction to 40% provides a much better match in the decay rate (justified since the OA fraction measurement had a high measurement uncertainty). Therefore, accurate outside air measurement is significant. The outside air percentage, however, did not yield an improvement in matching the peak concentration. Although these changes are somewhat arbitrary, they help to illustrate that in rectifying differences between measured and predicted CO.sub.2] concentrations in buildings whose airflow dynamics are dominated by HVAC system airflow rates, one should focus on those factors which have significant impacts on room air change rates first and model flow parameters second.
SUMMARY AND CONCLUSIONS
The advantages and insights provided by the proposed methodology are listed below:
The concept of macro-zone identification provides a robust manner of calibrating a complex model consistent with experimental data. Macro-zones reduce the number of individual flow parameters that need to be tuned during calibration.
"This paper provided a scientific means of identifying sets of rooms or "macro-zones" which have similar airflow dynamics and tracer gas behavior. Therefore, occupants in these rooms are likely to be exposed in the same manner when a contaminant release occurs.
The identification of these "macro-zones" takes into account the effect of different climatic conditions and building flow characteristics (as against previous work which only considered one set of conditions).
The methodology proposed allows insights into experimental design; namely, suggests rooms where it would be advantageous to place [CO.sub.2] sensors and monitor concentration dynamics during testing.
It also allows calibrating flow parameters for different macro-zones based on measured [CO.sub.2] concentration data.
Finally, it facilitates understanding of building airflow behavior and tracer gas behavior under varying conditions via experimental design techniques.
This methodology was implemented on a synthetic building as well as a real building for which previous research efforts obtained measured tracer gas and airflow data. Various graphical methods of analyzing simulation data were explored (as described in Snyder 2011). [CO.sub.2] concentration curves and scatter plots proved to be the most useful in helping to understand building airflow dynamics and tracer gas behavior. Macro-zoning helps to simplify the model as well as identify locations where it would be advantageous to place tracer gas sensors during testing. Both of the buildings analyzed where found to have airflow dynamics dominated by HVAC system airflow rates. Similarly, the identified macro-zones were directly related to rooms with similar air change rates.
Altering the flow parameters in the airflow paths of macro-zones during calibration did not seem to significantly improve the match between measured and predicted tracer gas curves. It was hypothesized that after all of the HVAC flows had been measured and entered into the model, the remaining discrepancies between predicted and measured curves would be the result of incorrect flow parameters in the models describing the flow through the building envelope and between internal zones. The fact that altering the flow parameters did not appear to improve model prediction accuracy may indicate errors either in measurements or in model development. Due to the fact that airflow dynamics were found to be HVAC dominated and since the identified macro-zones are directly related to room air change rates, it is crucial that all factors impacting room air changes be measured accurately.
This research was funded by the Technical Support Working Group--Combating Terrorism Technical Support Office. The authors acknowledge invaluable assistance of J. Firran-tello and P. Sae Kow for sharing the relevant data and software files which were the starting point of this research. The technical support of A. Musser was also of great assistance during this work.
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Steven C. Snyder
Associate Member ASHRAE
T. Agami Reddy, PhD, PE
William P. Bahnfleth, PhD, PE
Steven Snyder is an energy services engineer for Johnson Controls Inc., Philadelphia, PA. T. Agami Reddy is a professor with faculty appointments in both the Design School and the School of Sustainable Engineering in the Built Environment at Arizona State University, Tempe, AZ. William Bahnfleth is a professor and Director of the Indoor Environment Center in the Department of Architectural Engineering of The Pennsylvania State University, University Park, PA.
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|Author:||Snyder, Steven C.; Reddy, T. Agami; Bahnfleth, William P.|
|Date:||Jul 1, 2012|
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