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Performance evaluation of network airflow models for natural ventilation.

The potential for natural ventilation in building design to reduce associated building cooling and fan energy consumption makes it an area of great interest. However, its increased use is dependent on the availability of accurate modeling tools to predict its impact on a given building design. Network airflow models have been developed to predict airflows within buildings and between indoor and outdoor, which usually require user-supplied thermal conditions in a space. Because of the dependency between airflow and space temperature in naturally ventilated buildings, network airflow models need to be incorporated into whole building energy simulation models. This study reviews existing network models that may be used for natural ventilation design and investigates the capability and accuracy of four prevalent network airflow models to simulate a wide range of natural ventilation scenarios, with varying combinations of geometry and natural ventilation driving forces. Comparison of predictions with measurements obtained from literature shows that the tools are generally able to predict natural ventilation rates within 35% except for the wind-driven single-sided ventilation case. The article indicates some significant needs for improvement of the network airflow model for natural ventilation applications.

Introduction

Natural ventilation is one of the most fundamental techniques to reduce energy usage in buildings. If the cooling capacity of ambient air can be harnessed to increase indoor thermal comfort, then the necessity for mechanical space conditioning lessens. Natural ventilation relies on natural forces: wind from the surrounding environment as well as buoyancy forces that develop due to temperature gradients within the building. Buildings can be designed to take advantage of either driving force or a combination of both. Though natural ventilation is an old technology, it has experienced a recent resurgence of interest, particularly in Europe where several major research initiatives have been carried out (Heiselberg 2002; Ghiaus et al. 2004; Op't Veld 2008).

Using natural ventilation in buildings offers additional benefits besides energy usage reductions. Research has shown that the acceptable thermal comfort range for naturally ventilated buildings is signficantly larger than for buildings with standard mechanical HVAC systems (De Dear and Brager 2002). To this end, ASHRAE Standard 55 has been revised to include an adaptive thermal comfort standard specifically for naturally ventilated buildings, which allows for increasing indoor temperatures as outdoor temperature increases. The generally high level of occupant control associated with naturally ventilated buildings is also thought to contribute to the acceptance of warmer indoor temperature. Additionally, natural ventilation systems have been shown to consistently outperform mechanical systems with respect to complaints of Sick Building Syndrome (SBS) and its associated symptoms. Seppannen and Fisk (2002), in a review of 18 different studies on SBS and ventilation systems, found that the prevalence of SBS symptoms was 30 to 200% higher in air conditioned buildings as compared to naturally ventilated ones. In general, when building occupants are more satistied with their working environment, their productivity and job satisfaction also increase. Thus, the advantages of using natural ventilation are significant even beyond the energy benefit.

To promote the use of natural ventilation in practice, building designers must have accurate and straightforward simulation tools available to ensure the acceptable thermal performance of their buildings. These tools must be able to accurately predict naturally driven ventilation rates as well as the associated effects on building space temperatures. Computational fluid dyanmics (CFD) tools can provide a robust model for prediction of natural ventilation. They have been widely used to predict various natural ventilation conditions, including purely wind- and buoyancy-driven flows as well as those with combined forces (for example, Jiang and Chen 2003; Yang et al. 2006; Ji et al. 2007; Horan and Fire1 2008; Allocca et al. 2003; Cook et al. 2005). Due to the computing complexity and cost, CFD is usually used to perform simulations on portions of a building under steady state conditions (Lomas et al. 2007), particularly where spatial temperature variations exist. Performing an annual CFD simulation of an entire building, as is required during building design stages, is impractical.

Network (or called zonal) airflow models have been developed to more quickly solve airflows throughout a building. The network/zonal model is based on numerical description of flowpaths between zones, and all zones are treated as well-mixed with uniform environment properties (such as air velocity, temperature, contaminant concentration, relative humidity, turbulence intensity, etc.). Megri and Haghighat (2007) and Axley (2007) provided very thorough reviews on multizone network airflow modeling in buildings. A variety of different multizone network models have been developed, for example, MIX (Li et al. 2000) and AIOLOS (Allard and Santamouris 1998), many of which are used internally by the developers. Several studies comparing these models to each other have been published, including Dascalaki et al. (1995) (AIRNET, BREEZE, COMIS, ESP, NORMA, PASSPORTAIR), Furbringer et al. (1996) (ASCOS, BREEZE, CBSAIR, COMIS, CONTAM, ESP-R, MZAP, PASSPORT-AIR, AND VENCON), and Haghighat and Li (2004) (COMIS, CONTAM, and ESP-r). The general conclusion of these studies is that the models are generally similar, with minor functional differences separating the tools. Literature review shows that the most commonly used multizone network models for natural ventilation are COMIS (Feustel 1999) and CONTAM (Walton and Dols 2006).

The multizone network model COMIS was originally developed at Lawrence Berkeley National Laboratory (LBNL) and was further developed under IEA Annex 2. Currently, COMIS v3.2 (Feustel et al., 2005) with user interface is available from the Centre Scientifique et Technique du Batiment. COMIS has been coupled with thermal models for natural ventilation modeling (for example, Breesch 2006). The CONTAM family of software was developed at the US National Institute of Standards and Technology (NIST). Originally developed for modeling contaminant flow in buildings, CONTAM is now a general-purpose multizone indoor air quality and ventilation analysis program, used to analyze building airflows, pressure differences, and contaminant transport rates. A version with a coupled thermal model (CONTAM97R), not currently available to the public, was used to model naturally ventilated Enschede Tax Building (Axley et al. 2002).

In naturally ventilated buildings, airflows and space temperatures are not independent. The variation of zone temperatures affects the buoyancy driving force, and the amount of ventilation affects zone temperatures. Thus, it is desirable to couple airflow simulation with thenmal models to fully model natural ventilation. Study on the possibility of solving all the governing equations for both airflow and thermal models simultaneously has determined that significant non-linearities that prevent solutions develop, except under the simplest of circumstances (Sahlin 2003). Thus, several different methods of coupling the two models while allowing each to solve independently have been investigated. This coupling has been achieved in a few different ways, such as the "onion" method, where both models are solved at each time step, and the "ping-pong" method, where the results of one model is fed as input to the other model at the next time step. Study has shown that the onion method can require increased computing time at small time steps, while the ping-pong method can generate substantial errors with large time steps (Hensen 1995). Generally, the ping-pong method has seen more use, though care should be exercised in the selection of time step.

Two most notable coupling efforts of network airflow models with thermal models were observed on ESP-r and EnergyPlus, two prevalent and fully capable building energy simulation tools. ESP-r, developed and maintained by the Energy Systems Research Unit at the University of Strathclyde (ESRU), is a public domain building energy simulation tool commonly used in Europe and worldwide. Its network airflow module, mfs, is based on AIRNET, a predecessor of CONTAM (Hensen 1991). In the United States, the DOE's latest energy simulation tool, EnergyPlus, is being developed as the successor to the popular DOE-2 simulation tool. EnergyPlus also includes a network airflow option (Gu 2007). The most recent module, "Airflow Network," is also based on AIRNET but incorporates some features of COMIS. In both programs, the network model has been incorporated using a form of pingpong coupling (Hensen 1995).

The aim of this research is to advance the use of natural ventilation concepts in building design by assessing the accuracy and usability of current building thermal-ventilation models for natural ventilation application. Published experimental data for a wide array of natural ventilation scenarios are used to evaluate the performance of the four commonly used multizone network airflow models (CONTAM, COMIS, EnergyPlus, and ESP-r). This article focuses on single-zone, steady-state scenarios where the space temperatures were fixed as part of the experiment. While the geometry involved in each scenario is relatively simple, the intent of the study is to further develop understanding of the performance of the models which can be later applied to more complex, real-world scenarios. An additional publication will show similar studies on naturally ventilated buildings which are considerably more complex in geometry, to fully investigate the coupling between the thermal and ventilation models.

Common principles of network models for natural ventilation

The general principle behind network airflow modeling is that pressure drops across various flow paths (e.g., openings and connections) drive the airflows in a building. The model constructs and solves a matrix of equations representing such pressure-drive airflow paths in a building. A "node" is used to describe each zone connected by one or more airflow paths, and external nodes characterize the external conditions on each facade of the structure (Figure 1). Each path in the network (window, crack, and so on) is described mathematically using the Bernoulli's equation:

+ pg([z.sub.1] -- [z.sub.2]), (1)

[FIGURE 1 OMITTED]

where the "1" and "2" subscripts represent properties of the nodes on either side of the component. Please note that [delta]P includes all imbalanced terms from the Bernoulli's equation (such as mechnical loss). If it is the pure Bernoulli's equation, then [delta]P = 0. The resulting matrix is then solved numerically, typically by the Newton-Raphson method (Conte and De Boor 1972). Convergence is reached when the sum of all mass flow rates through all components approaches zero within the tolerance band specified.

The treatment of large openings, such as doors and windows, is of obvious importance to natural ventilation modeling. In CONTAM, ESP-r, and EnergyPlus, the air density on either side of a large opening is assumed to be constant. COMIS offers the added capability to treat air density as a linear function varying with height through the opening:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

where [[rho].sub.0i] is the air density at the bottom of the opening. In order to use this capability, the user must specify temperature gradients in the space, from which the "b" factor is calculated. Applying the Bernoulli's equation with this density gradient leads to a relationship for pressure difference across the opening as a function of height:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

The velocity at any level z of the opening is then defined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

Assuming the existence of some neutral planes at which there is no pressure difference, the equation above can be set to zero, which can lead to zero, one, or two real solutions. Each solution represents neutral plane location. The "zero solution" case means there is no neutral plan within the opening, so only one-way flow occurs through the opening. The "one solution" and "two solution" cases represent bi-directional flow. In the instance of oneway flow, the mass flow rate is calculated via:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

where W is the opening width, H is the opening height, and [C.sub.d] is the coefficient of opening discharge. In the instance of bi-directional flow, the two mass flow rates are:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7)

This treatment of airflow in buildings includes two major assumptions. First, momentum of air entering a zone is assumed to be negligible. These means airflows in network modelling are treated as if air momentum is dissipated quickly on the entrance of each zone. This assumption is likely valid in most naturally ventilated scenarios except where large openings are coupled with strong wind driving forces. Second, since a single node is considered for each zone in the building, each room is assumed to have uniform air proproties, and temperature variation within a zone can not be investigated (unless with some special treatments). While this assumption is likely acceptable for many building spaces, zones with very high ceilings, such as atriums, often have a large temperature gradient and thereby increase the buoyancy driving forces of natural ventilation. In instances such as atrium, the well-mixing assumption may have a significant impact on the accuracy of simulation results.

Evaluation of network models with laboratory experiments

In order to fully evaluate the network model's accuracy and capability to predict natural ventilation, a selected body of experimental data encompassing a wide variety of configurations was gathered. Table 1 summarizes each data set chosen for modeling, as well as the missing parameters for which assumptions must be made. Network models were constructed for each of these cases using the four modeling tools. The study compared the simulation results against the experimental data as well as between the tools. Based on the results from each scenario, recommendations can then be made for which areas of the network model need the most improvement for accurate natural ventilation modeling.

TEST 1: Wind-driven cross ventilation (Jiang 2002)

This experiment was conducted in a wind tunnel with no buoyancy sources. A clear Plexiglas box was used to represent a small-scale "zone" with an opening on each side (Figure 2). The experiment was conducted with a constant wind speed, and measurements of the air velocity in and around the zone were taken with a laser doppler anemometer (LDA). Measurements of the wind profile in the tunnel and the static pressure around the box were also taken. The windward and leeward pressure coefficients were measured as 0.6 and -0.1, respectively. There was no study on the discharge coefficient of the openings, but the author recommends a value of 0.78 for sharp openings as taken from Santamouris et al. (1995), so this value was used for modeling. No total airflow rates were measured, though Jiang used the air velocity measurements to create and validate a CFD model, from which airflow rates were calculated. The flow prediction from the calibrated CFD simulation was used in comparison with the network modeling results. Table 2 presents the results of modeling the simple case of wind-driven cross ventilation as studied experimentally by Jiang (2002).

[FIGURE 2 OMITTED]

The simulation results show that with proper handling of variables between the four programs, these models perform nearly identically for this scenario. This indicates that each of the four programs is forming and solving the equation matrix in the same manner for natural ventilation with no buoyancy sources. However, the models' underprediction of the wind driven air volume flow rate by approximately 25% is less than desirable. The cause for the discrepancy may be due in part to the model's assumption that zone air is still and momentum effects are negligible. With identically sized openings directly across from each other and relatively close together, as in the experimental case, the momentum of the air entering the zone is likely not dissipated and momentum may play a more important role in this geometry.

The discharge coefficient used in the original network model, 0.78, is a source of uncertainty, because no discharge coefficient were given for the specific openings used in the experiment. To investigate the effect of this uncertainty, a sensitivity study was conducted. Results in Figure 3 show the predicted airflow rate is linearly related to the discharge coefficient. While increasing it from the original value would improve the results, this value is already higher than the range of discharge coefficients typically used in published literature, 0.6 to 0.65.

[FIGURE 3 OMITTED]

Another uncertainty in the input values is the windward side pressure coefficient. While the experimenter did measurethe pressure and calculate the pressure coefficient, the value varies over the height of the zone. The value used in the original modeling, 0.6, was chosen as a representative average of the measured values. The sensitivity study shows the model's dependence on this parameter. However, over the range of reasonable values, 0.5 to 0.7, the model's sensitivity to the windward pressure eoefficient is not signficant enough to correct the model's underprediction of airflow.

TEST 2: Wind-driven single-sided ventilation (Jiang 2002)

This experimental setup is similar to the previous cross ventilation case, except that only one opening was used. All four network airflow models break down in the case of single-sided purely wind-driven ventilation. COMIS reports that it cannot converge at a solution. CONTAM and ESP-r calculate zero airflow. EnergyPlus reports a severe error because at least two links are required for the airflow network. This behavior is not unexpected given the nature of the large opening model used in each program. Bidirectional flow is only considered in cases where a temperature difference exists across the opening, so in a isothermal scenario, the model only considers flow in one direction through the opening. Since there is only one opening in the zone and the fluid is treated as incompressible, the flow is calculated as zero, while Jiang obtained 0.0026 [m.sup.3]/s (5.5 cfm) for this case.

TEST 3: Buoyancy-driven cross ventilation (Li 2007)

This experiment was conducted on a full-size zone within an environmental chamber. The zone had both a low-level vertical opening and a ceilinglevel horizontal opening. The temperature difference between the zone and the ambient environment was held constant through each run of the experiment. Several different runs of the experiment were conducted, varying the sizes of the two openings as well as the temperature difference between the zone and ambient, as shown in Table 3.

For both the horizontal and vertical openings, a discharge coefficient of 0.65 was used as recommended by the author, based on Andersen (2003). A tracer gas technique was used for volume flow rate measurements. Temperature and air velocity measurements were also taken in several places within the zone. Some smoke visualization studies were also performed, in which Li noted three different flow regimes: uni-directional flow in both openings, bi-directional flow in the vertical opening with flow out of the horizontal opening, and bi-directional flow in the horizontal opening with flow into the vertical opening.

In EnergyPlus, this experiment was modeled using the "Purchased Air" option to hold the zone temperature constant for comparison with airflow models CONTAM and COMIS. In ESP-r, two different opening types were used: Type 130, which is the large-opening model allowing for bi-directional flow, and Type 40, which is a simple orifice-type relationship. Figure 4 shows the simulation results for CONTAM, EnergyPlus, and ESP-r. ESP-r predicts a slightly different result from EnergyPlus and CONTAM, which are very similar to each other. Cases A, B, and C each have the same horizontal opening while the vertical opening is increased. Cases D, E, and F have the same vertical opening, but the horizontal opening is varied. The network model predictions for all cases were very accurate except Case E In this case, a large horizontal opening was used, and bi-directional flow was noted in the opening. While these network models have relationships for bi-directional flow in vertical openings, all four revert to a simple orifice flow relationship for horizontal openings. Thus the network models are not able to accurately model the airflow behavior of Case F, and the models all underpredict the airflow rate.

TEST 4: Buoyancy-driven single-sided ventilation (Jiang 2002)

This experiment was conducted on a full-size zone constructed in a laboratory setting, as shown in Figure 5. The zone had one opening to the ambient environment. A 1500 W (5118 Btu/h) heater was used to generate the buoyancy. Three different runs of the experiment were conducted using a large doorway-type opening. Though the heat source in the room was held constant through each run of this experiment, different ambient conditions resulted in different steady-state zone temperatures. One additional run was conducted replacing the large opening with a smaller window-type opening. Table 4 gives a description of the four experimental runs conducted. Since there was no wind in the experiment, pressure coefficients are irrelevant. The author recommended that 0.61 be used as the opening discharge coefficient. This value is typical for sharpedged orifices, and no measurements were taken to validate its use for this scenario. Several arrays of hot sphere anemometers were used to measure temperature and air velocity throughout the zone and in the laboratory at different heights. Temperature measurements in the zone were averaged to determine the zone temperature used in the network models. SF6 tracer gas was also used to measure volume flow rate.

[FIGURE 4 OMITTED]

Modeling results for the case of bouyancy-driven single-sided ventilation are shown in Figure 6. The "Purchased Air" option was also used in the EnergyPlus model of this experiment, in order to simulate a constant node temperature. EnergyPlus and CONTAM provide nearly identical rcsults, while COMIS results are signficantly higher. For all three models, the percent error with respect to the measured values is much less in the "Window" case than in the other three cases using the larger "Door" sized opening.

[FIGURE 5 OMITTED]

Further numerical testing revealed that the cause of the discrepancy between COMIS and CONTAM/EnergyPlus was related to the ambient humidity, modeled as 10g/kg in all cases. However, COMIS results were found to match the other two programs by changing the relative humidity to zero. Changing the ambient humidity in CONTAM and EnergyPlus produced no change in results (humidity was treated as a trace contaminant). Thus, the COMIS model obviously treats humidity differently than the other two, but the results are not improved.

As earlier described, the COMIS model can apply a linear density gradient on either side of a large opening, based on user-defined temperature gradients in the adjacent zones. In the simulations described above, no temperature gradients were input in order to keep inputs the same across the three programs. However, the effect of adding the temperature gradient data to the COMIS model was also explored. The experimental data for temperature distribution within the zone is shown in Figure 7 for Case 1. Also shown are the temperature gradients as input into COMIS, first with a simple l-gradient case, and then with a more realistic 2-gradient case.

[FIGURE 6 OMITTED]

Using these temperature gradients does improve the COMIS results to some extent, as shown in Figure 8, but the results are still not within the error bars of the experimental data for the three "door" cases. For the window case, the model results are similar to experiment values, and adding temperature gradient layers makes little effect. While this functionality of COMIS is not currently used in EnergyPlus or ESP-r, its addition to a building simulation program would be difficult for modelers to use, as the expected temperature gradients within a building are not typically known in the design phase.

Because this case involves only bouyancy without wind driving forces, the only ambiguous paranaeter required for input to the network airflow modcls is the discharge coefficient. A sensitivity study, shown in Figure 9, reveals that the predicted air flow rate is simply linear with the discharge coefficient. Reducing the discharge coefficient also reduces the predicted airflow by the same proportion.

TEST 5: Combined-driven cross ventilation (Larsen 2006)

This experiment was conducted on a full-size zone in a wind-tunnel. Identical openings were used on opposite sides of the zone (Figure 10). Heaters were controlled to maintain a constant temperature difference between the zone and the ambient environment. Both temperature difference (0[degrees]C/32[degrees]F, 5[degrees]C/41[degrees]F, and 10[degrees]C/50[degrees]F) and wind speed (1 m/s/197 fpm, 3 m/s/591 fpm, and 5 m/s/984 fpm) were varied in the experiment, with tracer gas measurements of volume flow rate at steady state taken in each case. Anemometers and thermocouples were also used in the experiment. It should be noted that the opening sizes used in the experiment were at the same level and relatively narrow, so bouyancy forces are likely to be small. Larsen lists a discharge coefficient of 0.65 to be appropriate for the openings used in the experiment. Pressure coefficient were also provided (windward side: 0.6; leeward side: -0.2). The wind profile of the tunnel was stated to be uniform, so the wind profile inputs in the network models were manipulated so the stated wind speed for each case occurs at the level of the window opening.

[FIGURE 7 OMITTED]

Figure 11 shows the modeling results for the case of cross ventilation with both wind and buoyancy driving forces. Results from ESP-r, EnergyPlus, CONTAM, and COMIS were so nearly identical that the differences were less than the resolution of the graph. Thus, only one line has been printed to represent all four model results.

[FIGURE 8 OMITTED]

For increasing wind speed, the model predictions, while not numerically accurate, at least displays a somewhat accurate trend. The discrepancy in the predicted value could be due to inaccuracy in the discharge coefficient, which was an estimated value. As in the case of single-sided buoyancy driven ventilation, the airflow rate was found to be linearly proportional to the discharge coefficient.

For increasing temperature difference, the model underpredicts the effect of buoyancy. In the experiments, changing the temperature difference significantly affects the air flow rate. In the model, the temperature difference changes the airflow results only negligibly. Thus, due to the shape and location of the openings, the network models basically predict only wind-driven flow.

Because the experimenter did not take detailed measurements of the wind profile of the tunnel, a sensitivity study was conducted on the wind speed uncertainty to determine its effect on air volume flow rate. As seen in Figure 12, the ventilation flow rate was found to vary linearly with wind speed change. With an increase of 20%, the overall error between the predicted and measured results is reduced. Conducting a similar sensitivity on the discharge coefficient produced similar results, as this parameter also has a linear relationship with predicted flow rate.

[FIGURE 9 OMITTED]

TEST 6: Combined-driven single-sided ventilation (Larsen 2006)

A similar experiment was also conducted by Larsen on single-sided ventilation. The same full-size zone and wind tunnel were used, with a larger opening on only one side of the structure (Figure 13). The same series of experiments were performed, varying the temperature difference (0[degrees]C/32[degrees]F, 5[degrees]C/41[degrees]F, and 10[degrees]C/50[degrees]F) and wind speed (1 m/s/197 fpm, 3 m/s/591 fpm, and 5 m/s/984 fpm). The same wind parameters and discharge coefficient were used. Figure 14 shows the simulation results from the four network models, which are nearly identical and superimposed on each other.

[FIGURE 10 OMITTED]

For the case of no temperature difference, these experiments revert back to simply wind-driven single-sided ventilation. As discussed in the previous section, because of the model used for large openings, there must be at least two openings or some driving temperature difference for the airflow network model to find a non-zero flow rate. Similarly, with the addition of the temperature difference (5[degrees]C/41[degrees]F and 10[degrees]C/50[degrees]F), a flow rate is predicted but the value does not change as wind speed increases. This is caused by the same model limitation that prevents solutions for single-sided wind-driven conditions: the model treats each large opening as having constant wind pressure across the entire opening.

[FIGURE 11 OMITTED]

TEST 7: Buoyancy-driven atrium ventilation (Ji et al. 2007; Holford and Hunt 2003)

This experiment was conducted using smallscale geometry with water as the ambient fluid and salt-water injection to simulate a bouyancy source (Holford and Hunt 2003). Grashoff number similarity is difficult to achieve using small scale air models with bouyancy sources, so water was used as the working fluid in this experiment. The geometry consisted of a zone connected to an atrium, both of which were also connected to the environment (Figure 15). Different runs of the experiment were conducted varying the opening sizes. Once steadystate was reached in each run, density measurements were taken from which the equivalent temperature distribution in a full-size scenario could be calculated. Discharge coefficients of each opening were also estimated. Flow measurements of the small-scale experiment were not taken, but Ji et al (2007) created a CFD model for the full-size geometry and validated it using this data collected from the experiment. Flow measurements used for comparison with the network models were taken from the CFD model. For this case, modeling results from EnergyPlus and CONTAM fall within the measurement error of the experiment for the first three runs (Figure 16). For the final run with the largest effective opening area, the models do not predict the same increase in airflow that was noted in the experiment.

[FIGURE 12 OMITTED]

While these network airflow results seem very promising, the conditions of this experiment are not identical to those that would be experienced in a full-size building. Because only one perfectly steady buoyancy source was used, only two layers of fluid develop in the building: one at ambient temperature, and another at a higher temperature. The interface height between the two layers was all located within the zone for each of the four test cases. The entire atrium was filled with fluid at the higher temperature, and therefore the atrium, in this case, was well-mixed. In a full-sized atrium, uniform temperatures would not likely exist, and the use of the well-mixed assumption would introduce more error. Furthermore, the effective opening areas used were relatively small, approximately 0.13 [m.sup.2]/1.4 [ft.sup.2] in the largest case, which is 1% of the building floor area. Most naturally ventilated building utilize larger openings. Therefore, the extremely accurate results of this study are likely due to the simplistic nature of the bouyancy driving force and the resultant temperature distribution in the experiment.

[FIGURE 13 OMITTED]

[FIGURE 14 OMITTED]

[FIGURE 15 OMITTED]

TEST 8: Combined-driven atrium ventilation (Kotani et al. 2003)

Kotani et al. (2003) investigated natural ventilation with combined wind and buoyancy driving forces using a small-scale model of a high-rise apartment building with an atrium through the center of the structure (Figure 17). Grashof number similarity was not maintained in the experiment due to the extremely high heat generation required. In the experiments, nichrome wires in the bottom of the atrium served as a heat source. Airflow ventilation rates were measured using tracer gas, and temperatures were measured with an array of thermocouples. Different runs of the experiment were conducted varying both the heat generation rate and the wind speed. Kotani lists the discharge coefficients as 0.855 for the lower opening and 2.187 for the upper opening. However, the network models limit the discharge coefficient to a maximum value of 1.0. Instead, ca values of 0.6 and 1.0 were input to the network model for the lower and upper openings, respectively. The wind profile exponent was measured at 0.25, and the wind pressure coefficients were measured as 0.4 for the lower opening and -0.58 for the upper opening. All these values were used as inputs to the network models.

[FIGURE 16 OMITTED]

[FIGURE 17 OMITTED]

[FIGURE 18 OMITTED]

This experiment was modeled only in EnergyPlus due to the control of heat flux rather than temperature. The temperatures in the zone were not fixed as in the previous EnergyPlus models. Instead the heat gencration rate was fixed as was the case in the experiment. Generally the EnergyPlus results for these experiments are within 15% error. From the trends shown in Figure 18, the simulation tool underestimates the contribution of wind, as error increases with higher wind speeds. One other notable deficiency with respect to the experimental results is the cross-over that occurs between the Q = 30 w (102 Btu/h) and Q = 40 W (136 Btu/h) flow rates as wind speed increases. EnergyPlus does not duplicate this behavior in its results.

Discussion of results

Model comparison

All four tools tested in this study (EnergyPlus, COMIS, CONTAM, and ESP-r) exhibit variations in naming conventions and availability of some input parameters. For example, ESP-r offers additional wind profile options, while the other three tools offer only an exponential profile. COMIS's "building characteristic height" is the same as CONTAM's "roof or wall height." CONTAM does not allow the user to modify the wind speed reference height, which is the height at which wind speeds were measured, while the other tools do. However, these variations were found to be inconsequential when modeling the above described scenarios. With careful manipulation of input parameters, the four tools can be forced to model identical scenarios.

Results from modeling the scenarios can be compared to investigate the relationships between the tools. The four tools were found to predict identical volume flow rate values for the simplest case of wind-driven cross-ventilation. Nearly identical results were also obtained in the combined driven cross-ventilation case, which had only a very slight buoyancy driving force. While some care is required to ensure identical inputs regarding external wind conditions, the tools are obviously performing the same calculations to determine wind-driven ventilation rates.

However, in scenarios where buoyancy is a driver, the COMIS model was shown to behave somewhat differently than the other tools, due to a different treatment of humidity. The COMIS model was found to be in agreement with the other tools if all relative humidities in COMIS, zone and ambient, were zet to zero. In CONTAM and EnergyPlus, varying the relative humidity had no effect on the results. Thus, the COMIS tool is performing some additional calculations, likely related to its density calculations. However, COMIS's error with respect to measured results in that test was higher than the other tools, so there is no known benefit to its treatment of humidity.

COMIS's ability to apply a density gradient on each side of the opening is the only major functional difference between the four tools. The option's dependence on user-supplied zone temperature gradients makes its utilization difficult for modelers who do not know this information. Furthermore, as tested in the single-sided buoyancy-driven scenario, the associated improvement in results was not significant enough to merit its incorporation into EnergyPlus or other coupled thermal-ventilation tools.

Scenario comparison

Comparing the results of the tools across the eight different scenarios investigated as part of this work shows a broader view of the tools' ability to model natural ventilation. In two cases, wind-driven singlesided and combined-driven single sided, the models break down. In reality, wind turbulence is the driver in any single-sided ventilation case. None of the tools has any model for the turbulence component of wind, and wind pressure is treated as constant across each opening at the same height. A significant addition to the airflow network model would be required in order to model these scenarios.

Another significant shortcoming in the models was noted in the buoyancy-driven cross ventilation case, where a horizontal opening was used in the ceiling of the zone. In the experimental data, when a large horizotal opening was used, bi-directional flow was noted at this opening. While the network models can predict bi-directional flow in vertical openings, the relationship is based on the change in height across the vertical opening. Since there is no change in height in a horizontal opening, the network airflow model can not predict bi-directional flow in it.

Figure 19 shows the average error for each of the six workable tests. Values for this figure were taken from the CONTAM results. The only major discrepancy is with COMIS in the buoyancy-driven single-sided case, as expounded in the previous section.

[FIGURE 19 OMITTED]

On average the results for the bouyancy-driven cross ventilation case, as well as the two small-scale atrium cases, were excellent, with less than 10% error as compared to measured values. However, for the other three cases, the results were much worse with error in the 25-35% range. In the wind-and combined-driven cross ventilation cases, the error is an underprediction. In the buoyancy-driven single-sided ventilation case, the tools actually predict more flow than was measured.

The primary uncertain input parameter is the discharge coefficent, as it was not measured except in one case. Sensitivity study of this parameter showed that airflow predictions are linearly dependent on the value, and therefore modifying it can significantly improve results. However, within the range of typically used [c.sub.d] values, this parameter was not shown to effectively correct the model, and often modifying worsened the trend of predictions across the different runs of the experiment. For example, in the buoyancy-driven single-sided ventilation case, decreasing the discharge coefficient improves the results for the large opening case, but hurts the results for the small opening case.

Comparing the percent error within each scenario with the size of the opening, as shown in Figure 20, indicates that there may be some correlation between large error and large openings. Some support for this correlation may be observed within the buoyancy-driven single-sided and buoyancy-driven cross ventilation cases. In both cases the size of the openings was varied in the experiment, and larger error was observed for the larger openings, while smaller error was observed for smaller openings.

However, more data using a wider variety of opening sizes is required to confirm this correlation. At this stage, based on the data used for this study, the trend could be coincidental. As an example, in the case of buoyancy-driven cross ventilation, a significantly larger error was observed when a very large (1 [m.sup.2] [10.764 [ft.sup.2]]) opening was used in the roof of the zone. However, this discrepancy is also explained by the model's inability to model bi-directional flow in horizontal openings, which was observed in the experiment.

[FIGURE 20 OMITTED]

Conclusions

The stand-alone airflow models COMIS and CONTAM along with the airflow models built-in to EnergyPlus, and ESP-r were tested to model a variety of natural ventilation scenarios. Flows driven by buoyancy, wind, and combinations of both were investigated for both single-sided and cross ventilation geometries. For each case, model predictions were compared with measurements obtained from prior experimental work found in literature.

Study of the governing principles behind all four models indicated that they are all fundamentally the same. Modeling results generally confirmed this finding. Naming conventions and other details vary among the programs, but with care taken to ensure identical inputs, the four tools can yield similar predictions for the scenarios modeled in this research. One exception is the simulation results from COMIS for buoyancy-driven cases. Because the COMIS model does offer the added ability to include zone density gradients, its treatment of cases with temperature differences is different from the other three tools. Specific testing of this capability of COMIS did not show significant improvement of results. Thus this study does not give any evidence that the COMIS density gradient functionality should be added to other network models.

The following additions to the network model are desirable:

* A relationship for bi-directional flow in horizontal openings. Naturally ventilated building often have vents in the roof, so this scenario is not uncommon. The same goes to indoor stairwells (or any large penetration of floors).

* A relationship for wind-driven single-sided ventilation. Without one, the network models break down even when a bouyancy source is also present.

With respect to measured wdues, the network airflow model was found to generally be able to yield predictions for the cases evaluated within 30% error. The configuration with the worst modeling results was buoyancy-driven single-sided ventilation. However, results are highly dependent on several coefficients, particularly the opening discharge coefficient, which is difficult to accurately determine without testing. Other important and somewhat ambiguous parameters include the wind pressure coefficient and the wind profile exponent. Some scenarios investigated in this study also indicate that the network airflow model may be less accurate for large openings. However, more experimental data from cases with large openings is needed to prove the relationship. Received March 16, 2011; accepted July 28, 2011

DOI: 10.1080/10789669.2011.617291

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Mary-Hall Johnson, Associate Member ASHRAE, was Graduate Student. Zhiqiang (John) Zhai, Member ASHRAE, is Associate Professor. Moncef Krarti, Member ASHRAE, is Professor.

Mary-Hall Johnson, Zhiqiang (John) Zhai, * and Moncef Krarti Department of Civil, Environmental and Architectural Engineering, University of Colorado at Boulder, Boulder, CO, USA

* Corresponding author e-mail: john.zhai@colorado.edu
Table 1. Experimental datasets chosen for modeling.

Experiment               NV mechanism        Controlled

Jiang (2002) (Test-1)    Wind-driven cross   Wind speed
Jiang (2002) (Test-2)    Wind-driven         Wind speed
                         single-sided
Li (2007) (Test-3)       Bouyancy-driven     Temperature
                         cross
Jiang (2002) (Test-4)    Bouyancy-driven     Heat flux
                         single-sided
Larsen (2006) (Test-5)   Combined-driven     Temperature,
                         cross               wind speed
Larsen (2006) (Test-6)   Combined-driven     Temperature,
                         single-sided        wind speed
Ji et al.                Buoyancy-driven     Heat flux
(2007)/Holford and
Hunt (2003) (Test-7)     atrium
Kotani et al. (2003)     Combined-driven     Wind speed,
(Test-8)                 atrium              heat flux

Experiment               Measured       Missing info

Jiang (2002) (Test-1)    Air velocity   Flowrate, [c.sub.d]
Jiang (2002) (Test-2)    Air velocity   Flowrate, [c.sub.d]

Li (2007) (Test-3)       Flowrate       [c.sub.d]

Jiang (2002) (Test-4)    Temperature,   [c.sub.d]
                         flowrate
Larsen (2006) (Test-5)   Flowrate       Wind profile, [c.sub.d]

Larsen (2006) (Test-6)   Flowrate       Wind profile, [c.sub.d]

Ji et al.                Temperature    Flowrate
(2007)/Holford and
Hunt (2003) (Test-7)
Kotani et al. (2003)     Temperature,
(Test-8)                 flowrate

Table 2. Modeling results for wind-driven cross ventilation.

                            Airflow,
                        [m.sup.3] (s/cfm)   % Error

Measured (Jiang 2002)     0.0465 (98.5)
EnergyPlus               0.034976 (74.1)     24.8
CONTAM                   0.034978 (74.1)     24.8
GOMIS                    0.035094 (74.4)     24.5
ESP-r                    0.035022 (74.2)     24.7

Table 3. Experimental cases for buoyancy-driven cross ventilation
[from Li (2007)].

          Horizontal opening           Vertical          [T.sub.amb,
                 area,                  opening           [degrees]C
         [m.sup.2]([ft.sup.2])           area,           ([degrees]F)
                                 [m.sup.2]([ft.sup.2])

Case A        0.04 (0.43)             0.04 (0.43)        11.5 (52.7)
Case B        0.04 (0.43)             0.16(l.72)         13.5 (56.3)
Case C       0.(14 (0.43)             0.36 (3.88)        12.9 (55.2)
Case D        0.16 (1.72)             0.04 (0.43)        10.5 (50.9)
Case E        0.36 (3.88)             0.04 (0.43)        10.2 (50.4)
Case F       1.00 (10.76)             0.04 (0.43)        10.5 (50.9)

         [T.sub.zone],
          [degrees]C
         ([degrees]F)

Case A    18.5 (65.3)
Case B     19 (66.2)
Case C    18.2 (64.8)
Case D     17 (62.6)
Case E     18 (64.4)
Case F    16.5(61.7)

Table 4. Experimental cases for buoyancy-driven single-sided
ventilation.

Case          [T.sub.amb],             [T.sub.zone],
         [degrees]C ([degrees]F)   [degrees]C ([degrees]F)

Door 1        24.228 (75.6)             27.40 (81.3)
Door 2        22.558 (72.6)             25.33 (77.6)
Door 3        25.722 (78.3)             29.01 (84.2)
Window        25.556 (78.0)             29.40 (84.9)
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