Overview

Multizone models find the airflows and pollutant dispersion in a building. This page describes general aspects of multizone models, their uses, and background:

• Introduction to multizone models.
• Sample results from a multizone calculation.
• Airflow details on how multizone models find the airflows.
• Flow through cracks, and uncertainty in the airflow system.
• Pollutant transport details on the multizone view of pollutant dispersion.
• Limitations of multizone models.
• References to important literature.

Other pages contain information specific to the COMIS multizone model:

• Capabilities and development of the COMIS program.
• Integrated simulation tools that combine COMIS with other software, in order to solve whole-building airflows as part of a larger problem.
• User information for help running COMIS, including supporting programs.
• Version information on obtaining the various distributions of COMIS.
• Original COMIS web pages at LBNL.

Introduction to Multizone Models

Multizone models find the airflows and pollutant dispersion in a building. They represent a building as a network of well-mixed spaces, or zones, connected by discrete flow paths such as doors, windows, wall cracks, fans, ducts, and so on.

Multizone models represent a building as a network of well-mixed spaces, or zones, connected by flow elements, or links. The links represent discrete airflow paths, such as doors, windows, wall cracks, fans, ducts, and so on.

Within a multizone program, the user describes a building by assembling various component models, each representing a zone, a point outside the building, or one of a number of types of flow paths. The program then predicts the system's behavior based on the interaction of the assembled components.

For example, the plan below shows the first floor of a three-story commercial building. A multizone model of this building would link the zones (including the hallway and stairwell) using models of the doors, windows, and ventilation system components. It might also include leakage elements, for example to represent cracks in the walls, floors, and ceilings.

First floor of a three-story building. Ventilation system not shown.

Multizone models have two primary uses:

1. Finding the airflows. A typical multizone model finds the steady-state airflows between the zones of the building. Three main forces drive the flow: (a) pressure due to wind on the building facades; (b) pressure differences related to thermal buoyancy, known as the stack effect; and (c) mechanical devices, such exhaust fans and ducted air conditioning systems.
    
2. Finding the pollutant distribution. The zone-to-zone airflows give rise to dynamic pollutant transport through the building. Pollutants include both gases and aerosolized particles. The model tracks the movement of these contaminants as a function of time. Some multizone models include transport mechanisms other than airflow, for example deposition of particles and reaction kinetics of chemicals.

Two popular multizone models, COMIS and CONTAM, take this approach. COMIS was developed during a workshop at the Lawrence Berkeley National Laboratory. The Airflow and Pollutant Transport Group continues to develop and use this model. CONTAM is a product of the National Institute of Standards and Technology. Both programs have similar capabilties and similar shortcomings.

Sample Results

The figure below shows the concentration for several rooms in the sample three-story building depicted above. The simulation ran under the following assumptions:

• Zone 101 has a pollutant source of 10^-6 kg/s. The source runs for 10 minutes.
• The ventilation system provides 2.8 air changes per hour to each room. That is, it supplies enough air to completely fill each room 2.8 times every hour.
• The ventilation system removes 97% of the air it supplies, taking the air out of the hallways. The remaining 3% of the supply air escapes to the outside through doors and windows.
• Of the air taken out of the hallways, 70% gets mixed with fresh air and recirculated back to the supply side of the ventilation system. The remaining 30% gets dumped outside.
• Wind comes from the North at 3 m/s.

Concentration predictions for the three-story building.

The pollutant source in zone 101 (blue line) fills the room for the ten minutes it is active. After ten minutes, the source shuts off and the concentration in the release zone begins to decay. This fall-off in concentration happens as the polluted room air mixes with relatively clean air from the ventilation system, plus outside air infiltrating due to wind pressure on the North facade.

Air exits the release zone into the hallway, carrying pollutant with it. However, the hallway concentration (red line) does not reach the same level as in the release zone, because clean air from the other zones flows into the hallway, diluting the pollutant there. Air enters the hallway from all zones on the floor, because the ventilation system takes air out of the hallway, keeping it at a negative pressure with respect to the other zones on the floor.

Because the ventilation system takes air out of the hallway, the air supply eventually becomes polluted, too. Thus it distributes pollutant to every room in the building, including those on the third floor (green line). However, the concentration on the third floor stays well below that of the first-floor hallway. Again, the lower concentration results from dilution. In this case, the dirty air from the first-floor ventilation return gets diluted not only by relatively clean air from the second- and third-floor returns, but also by the clean outside air that the ventilation system takes in.

As time passes, the zone concentrations show two main trends. First, they all fall towards zero, as the ventilation system flushes the building with clean outside air. Second, they all converge to the same concentration, even though their concentrations at the ten-minute mark were quite different. This tendency to reach identical concentrations is typical of zones that have strong mixing between them. In this case, the mixing comes entirely from the ventilation system, which recirculates air among all the zones of the building.

Airflow Details for Multizone Models

As noted above, multizone models idealize a building as a network of zones, connected by discrete flow paths. Zone models tend to be fairly simple. They do not, in general, predict flow details within each zone. Rather, a zone has a hydrostatic pressure distribution, in which the pressure decreases with increasing height, based on the temperature (and hence the density) of the air in the zone. Outside zones (or external nodes) also let the pressure vary due to wind on the building facade. The zone temperatures are assumed known-- either prescribed by the modeler, or found by an iterative procedure that couples the multizone model to an energy analysis program.

Two broad approaches exist for predicting airflows within a room: (1) introduce fluid-dynamic models, and solve the discretized governing equations (the Computational Fluid Dynamics approach); or (2) rely on the analyst to divide the room into appropriate regions, each defined by an engineering approximation of that region's behavior (the zonal or sub-zonal approach). The Airflow and Pollutant Transport Group's comparisons of these approaches indicate that the sub-zonal methods rely strongly on prior knowledge of the expected flow patterns, and still produce generally inferior predictions compared to CFD.

The flow paths permit more modeling variety than do the zones. Each flow element finds the airflow as a function of the pressure drop across it. The exact relation depends on the type of flow element-- whether a fan, a window, a crack, or so on. Simple flow elements, such as cracks, allow flow in one direction at a time, but more complicated element models, such as for doors and windows, may calculate simultaneous flows in both directions.

The net flow through most element models increases with the pressure drop. However, multizone models typically allow paths with fixed flows, for example to simulate a ventilation system with a known delivery rate.

To solve the airflow system, a typical multizone program chooses a set of zone pressures, then calculates the pressure drops across the flow elements, finds the flows in the paths, and sums the flows entering and exiting each zone. Mass balance requires a zero net flow out of each zone. The solver iterates, choosing new sets of zone pressures, until it finds a consistent solution to all the zone and flow element equations.

Crack Flow and Multizone Model Uncertainty

While multizone models provide a number of types of flow elements, the canonical crack model exemplifies the approach.

The crack model follows from analogy to the engineering equation for orifices, in which the flow varies with the square root of the pressure drop. The figure below shows the basic crack flow equation, with an exponent of 0.65 replacing the square root. The exponent 0.65 has become a standard choice in multizone models, based on observational data (in terms of mechanical energy loss, an exponent 0.5 corresponds to fully-turbulent flow, while an exponent 1.0 corresponds to laminar flow).

Pressure-flow relation for a simple crack model.

The figure shows that the airflow through a crack increases with increasing pressure drop across the crack. In addition, comparing different cracks, the leakage increases with a crack's Effective Leakage Area (ELA). In practice, one does not measure the leakage area directly. Instead, one may impose a known pressure drop across a flow path of interest, and measure the resulting airflow. The ELA gives the nominal crack area that would give that experimentally-observed flow at the reference pressure drop (here, 4Pa) and an assumed orifice discharge coefficient, C_d (here, 1.0).

The three values of ELA in the figure all correspond to experimental measurements of the leakage characteristics of exterior masonry walls. For more on leakage characteristics of flow paths, see the report by Persily, or the ASHRAE Handbook, cited in the References below.

For exterior masonry walls, an ELA of 0.6 cm² (blue line) gives a lower bound on the expected leakage per square meter of wall surface area. An ELA of 4.2 cm² (green line) is an expected mean value for the leakage per square meter of wall. Finally, an ELA of 11.4 cm² (red line) represents the maximum expected leakage per square meter.

The wide range of variation in the ELA, and the wide range of resulting airflows, suggest how difficult it is to build a multizone model with complete confidence. In particular, after performing a tracer-gas study of a building, it may be possible to choose many different sets of leakage characteristics that all explain the experimental data equally well. The Airflow and Pollutant Transport Group studies how uncertainty in the model causes uncertainty in the model predictions. Uncertainty includes both parametric questions, such as the correct value of ELA for a particular wall, and modeling questions, such as whether the multizone idealization is even appropriate for a particular study.

Pollutant Transport Details for Multizone Models

For the most part, multizone models use the well-mixed assumption to account for pollutant mass in zones. That is, they assume a uniform concentration of pollutant at every point in a zone. The multizone approach does support ad hoc models of non-uniform pollutant distribution-- for example, some versions of COMIS allow the user to specify a vertical distribution of pollutant in each zone, in order to account for e.g. smoke rising. However, moving beyond such approximations requires the use of Computational Fluid Dynamics (CFD) models.

Multizone models normally do not account for pollutant mass in the flow paths. Thus, they implicitly assume that flow paths move contaminants from one zone to another instantaneously.

Airflow is the main means of transporting contaminants through a building, and between the building and outdoors. However, transport does not depend only on airflow. Therefore, multizone models typically allow other transport processes than just advection. Other important transport processes in buildings include:

• Filtration. Airborne particles can get trapped in flow paths. This occurs not only on filters in ventilation ducts, but also in adventitious openings, such as the cracks around a window, or holes in ductwork. The loss rate of particles depends strongly on the particle size. For example, particles of about 0.3 µm in diameter penetrate cracks more effectively than do larger or smaller particles.
   
• Deposition. Particles deposit out of the air onto room surfaces, including ceilings and walls as well as floors. As with filtration, deposition depends on particle size.
   
• Tracking and resuspension. Human activity can move particles around a building. In addition to tracking particles from one room to another, e.g. on shoes or clothing, people can disturb particles that have previously deposited. This may account for the "personal cloud" effect, in which an individual's exposure to particulate matter typically is higher than background room concentrations. Again, these processes depend on particle size.
   
• Sorption. Semivolatile organic compounds can sorb onto walls and other porous surfaces. This can reduce the peak exposure of the room occupants, but prolong their overall exposure as the compounds desorb back into the room air. Sorption can depend strongly on humidity and temperature. For example, the daily thermal cycling of a ventilation system can cause particles trapped on filters to adsorb, and then later release, large quantities of semivolatile pollutants. Buildings have a higher ratio of surface area to volume than outdoors, so sorption is relatively more important than in the atmospheric sciences.
   
• Identity change. Pollutants can change forms. Reaction kinetics, particle coagulation, and particle disaggregation affect the concentration of pollutants. Furthermore, because coagulation and disaggregation affect the particle size, they can affect the dynamics of the other transport processes.

The Airflow and Pollutant Transport Group studies some of these processes, including models of particle transport and sorption processes.

At present, COMIS does not provide models for all the processes listed above. For advanced particle models, the Airflow and Pollutant Transport Group currently uses the MIAQ4 particle transport model, with airflows calculated by COMIS.

Limitations of Multizone Models

Limitations in multizone models arise mainly for programming reasons. In order to improve the computational efficiency of the code, the current generation of programs, including COMIS, enforce a number of requirements:

• Each flow element has exactly two connections.
• Each flow element calculates the airflow as a function of the pressure difference between its terminals.
• The flow between two zones never decreases, and ideally always increases, as the pressure difference between them increases.
• Every zone in the network connects, either directly or through a series of paths, to a zone of known pressure.
• The state of each zone (that is, the pressure and density at each point in the zone) depends on a single reference pressure, plus a known temperature distribution through the height of the zone.
• The conversion of mechanical to thermal energy within a flow path is, to some degree, calculated at a global level, rather than on an element-by-element basis.

Many modeling elements for whole-building simulation satisfy these criteria. However, due to these restrictions, COMIS and other multizone programs cannot directly simulate the following:

• Detailed zone airflows. Finding the flows within a zone requires more variables than a single reference pressure. For example, to model jets from a ventilation system inlet, wind-driven flows, or recirculation due to thermal currents in a room, requires using the Navier-Stokes equations to relate flow velocities, pressures, and temperatures throughout the zone.
   
• Poorly-mixed zones. Lacking details of the airflow in a zone, the multizone model must determine the pollutant distribution by other means. The well-mixed assumption, which asserts that all pollutants in a zone instantly mix uniformly throughout the zone, is the most common. This assumption: (1) over- or under-estimates the exposure of occupants in the zone, depending on their location; (2) over-estimates the rate at which pollutants propagate through the room to other rooms, and hence over-estimates the rate of propagation through the building; and (3) over- or under-estimates the amount of pollutant that leaves the zone by each flow path, depending on where the flow path connects to the room.
   
• Bidirectional floor-to-floor flows. The airflows across a horizontal partition sometimes result from opposed driving forces. Thermal buoyancy due to temperature differences between floors may favor flow in one direction, while pressure differences imposed from other parts of the building may favor the opposite flow. In a real building, bidirectional flow between floors may result. The pollutant transport due to these flows may be significant, especially in stairwells or elevator shafts, due to their large cross-sectional area. If the airflow program imposes its own, global, assumptions about the energy balance through the flow element, the stairwell flow model cannot control this aspect of the calculation.
   
• Duct junctions. Duct junctions, as three-port flow elements, cannot be defined solely in terms of the pressure differences between two zones. The alternate approach, modeling the junction as a zone, does not capture the fluid mechanics, because the mechanical energy dissipated in each branch of a junction depends on the flow in the other branches. For example, changing the flow in one branch of a junction can produce suction on another branch that previously faced a retarding pressure.

A final important limitation in multizone models does not result from any intrinsic modeling restriction, but merely from a lack of implementation:

• Transport delays. As noted above, multizone models assume that flow paths move contaminants from one zone to another instantaneously. Thus, the models over-estimate the speed at which pollutants propagate through the building, especially where long duct runs connect physically remote zones. The failure to account for transport delays affects the accuracy of the programs' transient pollutant calculations, but need not affect their accuracy in finding steady-state concentrations (for example, as the result of running a constant pollutant source for a long time).

The figure showing sample results from a multizone calculation, above, demonstrates the combined effect of the well-mixed assumption, plus the failure to account for transport delays in flow paths. In that simulation, the peak pollutant concentration in the hallway occurs at the same time as the peak in Zone 101, where the pollutant was released. This results from the assumed instantaneous spread of pollutant through the release zone, and, to a lesser degree, from the assumed instantaneous transport into the hallway. In practice, modeling the time it takes to move pollutant through the doorway would not much affect this result. However, adding transport delays in the long ventilation system ducts would slow the predicted uptake of pollutant by the rest of the building.

References for Multizone Models

For more information on the topics on this page, please see the following references. Sources denoted with an LBNL number may be found among the publications of the Airflow and Pollutant Transport Group, or on the Indoor Environment Department publications page.

• Multizone modeling overview. Lorenzetti. Predicting Indoor Pollutant Concentrations, and Applications to Air Quality Management. Lawrence Berkeley National Laboratory, 2002. LBNL-51582.
   
• Effective Leakage Areas for building models. Persily and Ivy. Input Data for Multizone Airflow and IAQ Analysis. National Institute of Standards and Technology, 2001. NISTIR-6585.
   
• Building infiltration and ventilation data. ASHRAE Fundamentals Handbook. American Society of Heating, Refrigerating and Air-Conditioning Engineers, 1997.
   
• Multizone model critique. Lorenzetti. Assessing Multizone Airflow Simulation Software. Proceedings of the 9th International Conference on Indoor Air Quality and Climate, 2002, v.1, pp.267-271. LBNL-49578.
   
• Multizone airflow formulation. Lorenzetti. Computational Aspects of Nodal Multizone Airflow Systems. Building and Environment, 2002, v.37, n.2, pp.1083-1090. LBNL-46949.
   
• Pollutant transport formulation. Axley. Multi-zone Dispersal Analysis by Element Assembly. Building and Environment, 1989, v.24, pp.113-130.
   
• Particles. Thatcher et al. Factors Affecting the Concentration of Outdoor Particles Indoors (COPI): Identification of Data Needs and Existing Data. Lawrence Berkeley National Laboratory, 2001. LBNL-49321.
   
• COMIS model. Feustel. COMIS-- an International Multizone Air-flow and Contaminant Transport Model. Energy and Buildings, 1999, v.30, n.1, pp.3-18. LBNL-42182.
   
• CONTAM model. Dols. A Tool for Modeling Airflow and Contaminant Transport. ASHRAE Journal, 2001, v.43, n.3, pp.35-42.
   
• MIAQ4 model. Nazaroff and Cass. Mathematical Modeling of Indoor Aerosol Dynamics. Environmental Science and Technology, 1989, v.23 pp.157-165.

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