Method

! 1.4.2.1 Summary

Multizone airflow models are used to calculate airflows between zones and the outside, driven by pressure forces induced by wind action, stack ef­fects, and fans.

Multizone airflow models are based on a network approach. The building is subdivided into zones or nodes, representing spaces of perfectly mixed air. Each zone is characterized by its zone node temperature and pressure and pos­sibly its contaminant concentrations. The zone nodes are linked by conduc­tances (airflow elements), modeling the airflow paths (cracks, openings, ducts, etc.). Pressure coefficients, relating local wind pressure at the building faзade to the reference wind pressure, can be attributed to external nodes. Not only wind effects but also buoyancy effects resulting from air density differences are taken into account. In addition, pressure and flows induced by compo­nents of a mechanical ventilation system (tans, ducts) are also considered. Us­ing air mass conservation, a system of nonlinear equations is built and iteratively solved for the zone pressures, providing airflow rates through all conductances. From these, zone-related flows are determined.

With given contaminant source and sink schedules and outdoor concentra­tions, concentration evolutions over time can be determined for the individual zones on the basis of the calculated airflow rate values per time step. Further postprocessing allows the determination of accumulated values such as air change rate or concentration histograms (see the later example) or inhaled dose values.

Basic Equations

Considered are mass conservation of air and species (contaminants and humidity). Momentum equations are not considered on a global scale but have been used in some cases for the definition of the airflow-pressure relation of the individual links. Heat fluxes and thus energy conservation equations are not considered.

Multizone Models vs. Zonal Models

The terms Zonal model and Flow element are also used for the simplified characterization of the flow field in a single enclosure.1 There, a zone repre­sents a partial volume of air in the enclosure, whereas in the multizone models described here, a zone represents a specific enclosure w’hich is connected to other enclosures by air conductances (see “The Airflow Network” later).

11.4.2.2 Driving Mechanisms

Infiltration and ventilation are driven by pressure differences across the building envelope, which are caused by

• Wind-induced pressures. The pressure at a location on the envelope depends on the shape of the building, the shielding of the building, the wind direction, and the wind speed. Air-exchange due to wind turbulence effects is normally not considered.

• Pressure differences due to the different densities of the air inside and outside the building (stack effect).

In certain computer models, a user-defined temperature, humidity, or con­taminant concentration gradient can be considered. Nevertheless, this gradient is preset in the input and is not recalculated by the program on the basis of the results of the previous time step.

Airflow Conductances

Airflow conductances can be

• Leaks in the building envelope, due to cracks in walls or joints, gaps in window and door frames

• Purposely provided openings such as ventilators or passive stacks

• Large openings (windows and doors)

• Ducts, T-junctions, inlet and outlet grills

• Fans

• Flow controllers

Leak and opening-type airflow conductances normally are characterized by a power-law relation between the pressure difference across the conduc­tance AP and the resulting mass airflow Qm through the conductance (C, flow coefficient; N, flow exponent):

Q„, — C(Ap)" (11.18)

For large openings, the vertical pressure profiles on both sides of the opening are considered, and the air exchange is determined by calculating the velocity profile in the opening. This is determined using Bernoulli equations for the individual horizontal stream lines. From this, two airflow rate values, one for each flow direction, are calculated for a given situation (Fig. 11.42).

For pure convectional flow (no net flow through the opening) and homoge­

Neous temperature distribution in the two zones, the air exchange volume flow through a rectangular opening (<?„) can be described by

= (11.19)

FIGURE 11.42 Vertical velocity profile in a large opening (warmer air inside, colder air outside, no influence of wind or other openings in the building).

Where Cd is the discharge coefficient, A is the net cross-sectional area of open­ing, AT is the temperature difference between inside and outside [Kj, T Is the mean temperature [K], G is gravity acceleration, and H is the height of open —

Ing … . .

The airflow rates depend on the selected discharge coefficient cj, which is

Introduced to account for both friction and contraction effects.3 Flow’ through large openings has been the subject of quite a number of recent research projects. Van der Maas4 deals with flow through internal as well as external openings, Weber5 gives discharge coefficient values for horizontally pivoted hinge window openings, and Dascalaki et al.6 cover the relative influence of gravitational and inertia forces on the discharge coefficient in single-sided ven­tilation situations. For the interrelation between flow rates and thermal behav­ior of the room, see Section 11.5.

External Nodes

An external node represents a boundary node, i. e., a fixed pressure value or a location on the building faзade which is linked to a specific set of wind pressure coefficients Cp e for this location (a set of values for different wind di­rections ®w). The pressure Pe at such a location E is then given by wind velocity at reference level; p, air density):

Pa = Cp>e(®w) ■ I — P ■ yr2ef 0 1-20)

11.4.2.5 Solution Process for Airflows

Airflows are determined basically by a steady-state calculation for each time step. At each time step, first, pressures at external nodes are calculated on the basis of the wind pressure coefficients and the actual wind speed and di­rection. Then, for all conductances, the local pressures at each side of the link are calculated. At internal links, this pressure is dependent on the (unknown) zone pressure Pi and the aerostatic pressure variation due to the height of the link with respect to the zone reference height. At external links, this pressure is dependent on the external node pressure and the aerostatic pressure variation due to the height of the link with respect to the stack reference height. For the aerostatic pressure, the air density is determined considering the temperature, the humidity, and (if relevant) the contaminant concentrations in the zone or in the outside air, respectively. From this, the pressure differences across each conductance can be calculated, and from this the mass airflow Qc • for each conductance /.

The mass flow total Ft for each zone I is set up (qc -, flows through the indi­vidual conductances connected with zone; Nj, number of conductances con­nected with zone /), and the requirement of mass flow balance for each zone I Leads to the iterative solution for the unknown zone pressures p = {px, pT,… ,

Pi)- ‘

Nj

Fl(p)=Yqc, i = 0 (11.21)

/= i

Usually, modified Newton-Raphson methods with relaxation are ap­plied.7 Additional iteration loops are necessary for the determination of the dynamic pressure losses in ducts and duct fittings.

At the start of the iteration, an initial guess for the zone pressures can be found by using linearized pressure-airflow relations for the links, zero pres­sure values, or values from the previous time step.

11.4.2.6 Humidity and Contaminant Transport

The humidity and contaminant transport calculation is based on the pre­viously calculated airflows, applying again the principle of mass conservation for the species under consideration. For each time step, the concentrations are calculated on the basis of the airflows, the source and sink strengths in the zones, and the concentration values at the previous time step. In contrast to the airflow calculation, which is a steady-state calculation at each time step, the contaminant transport calculation is dynamic. Therefore, the accuracy of the concentration results depends on the selected time-step interval.

11.4.2.7 Limitations

As previously outlined, perfect mixing is assumed in the individual zones. The spatial distribution of air velocities, contaminant concentrations, and air temperatures in a zone cannot be determined. Air exchange due to wind tur­bulence effects is not considered.

Many natural ventilation problems are related to the thermally driven air exchange in a building. Such cases must be most often treated using com­bined thermal and ventilation models or thermal models with an integrated natural ventilation model (see Section 11.5). For example, in COMIS,8 a simple, single-zone thermal model is included for transient single-sided ven­tilation calculations.

In COMIS, source or sink strength can be defined as time dependent but not dependent on actual concentrations or temperatures. COMTAM969 in­cludes more sophisticated models such as chemical reactions, adsorption and desorption to building materials, filtration, and deposition to surfaces.

Also, in the tools presented, possibilities for control functions, e. g., temperature-dependent window opening or demand-controlled fan opera­tion, are very limited.

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