Multizone model approach 

Two multizone models are widely used, and are maintained by U.S. national laboratories: COMIS and CONTAM. While COMIS is used in this research and some of the references may refer to COMIS, none of the ensuing discussion is limited to this particular model. Feustel (1999) and Feustel and Rayner-Hooson (1990) describe the physical foundations of COMIS.

Multizone models require knowledge of the following boundary conditions: wind velocity and pressure fields around the building, internal and external temperatures, and fan characteristic operation curves that relate airflow to pressure differential. Using these conditions, the airflow between two zones is calculated using the pressure differential between the zones and a set of equations that relate the airflow rates to the pressure difference and flow resistance. The flow paths between two zones may include doors, windows, cracks, and ducts. I discuss the equations used to describe some flow components briefly. Additional details on flow components can be found in the Feustel references.

The crack component is commonly used to describe leakage between two zones. A power law equation is used to model airflow through a crack:

n

Q P

C

Q= (∆ ) (2.1)

properties, and n ranges from 0.5 and 1, depending on whether the airflow resistance is dominated by either inertial or viscous forces. When viscous forces dominate n Æ 1, and

n Æ 0.5 when inertial forces dominate (Liu and Nazaroff, 2001).

Rather than specifying sets of parameters for every possible flow pathway across a building envelope, a collection of pathways are often grouped into a single set of parameters (CQ and n) that represent the overall envelope leakage for a pair of zones. Fan

pressurization tests can be conducted to calculate a building’s leakage characteristics. In lieu of experimentation, leakage parameters may also be estimated using published estimates, such as from ASHRAE.

Most building systems, especially in commercial buildings, include networks of ducts; thus, the prediction of duct airflow is important. Airflow through a duct is modeled using this fluid flow equation:

2 2 D v L P=λ ρ ∆ (2.2)

where L is the duct length, D is the diameter, ρ is the air density, v is mean air speed, and

λ is a function of the flow regime and characteristic fluid properties. This equation can be rearranged to fit the power law function (equation 2.1) where the exact value of CQ

and n will depend on the airflow conditions (i.e., whether the flow regime is laminar, transition or turbulent). Because CQ and n depend on the airflow rate, the model must

calculate these values iteratively.

The energy or pressure loss through duct fittings, such as through elbows can also be calculated using basic fluid dynamic equations and correlations. While this presentation implies a simplicity at a fundamental level, the challenge in airflow prediction arises from

complex network. For example, while correlations are available to predict energy loss through individual fittings, the cumulative effect of closely connected fans, fittings, junctions, and elbows is not as easily quantifiable. These closely connected flow elements, especially when they are placed near fans, increase the overall pressure losses and is known as the system effect (Coward, 1990).

Modeling airflow through large openings such as open doors and windows is a challenging task. Airflow is influenced by a combination of steady-state buoyant flow, dynamic wind effects, and recirculating flows from thermal effects. Large openings may have zero or one neutral-pressure planes, which will result in one-way or two-way flows. Therefore, airflows through vertical openings are calculated in sections, using the pressure differential of each section. At any level, z, the velocity across the opening is related to the pressure differential using Bernoulli’s equation.

2 / 1 2 1( ) ( ) 2 ) ( _⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − = ρ z P z P z v (2.3)

COMIS combines these pressure difference relationships and solves for the airflows at each node by enforcing mass balance. To solve the governing equations, the computational solver iterates on values of the zones’ reference pressures, using a gradient based optimization routine, until mass balance is reached within each zone. Details of the computation can be found in Lorenzetti (2002b).

Contaminant transport is subsequently computed, for each time step, using the modeled airflows and applying the mass-balance relationship to the contaminant. In the situation where the contaminant is transported solely by advection, the mass-balance relationship for the contaminant in zone i is:

∑

∑

where Vi is the volume of zone i, Ci is the concentration of contaminant in zone i, Ei is the

emission source in zone i (which can vary with respect to time), Nin zones supply Qji

airflow to zone i, Cj is the concentration of contaminant in zone j, and zone i supplies Qij

airflow to Nout zones.

Equation 2.4 assumes that the contaminant behaves as an ideal tracer. As noted in Section 2.2.2, gaseous species and particles may not behave as passive tracer gases and species-specific characteristics can affect the rates at which different contaminants are transported among building zones. The multizone modeling framework can be extended to reflect cases where a contaminant is significantly impacted by processes such as sorption (for gaseous species) or deposition (for particles). For example, Sohn et al. (2007) linked the MIAQ4 particle model with the multizone model COMIS to model the fate and transport of environmental tobacco smoke. Since this dissertation uses tracer gas experiments as the basis for the data, it treats the contaminant as a tracer.