# Two-Zone Model Calculation

The calculation of the two-zone model is based on the balance equations for air mass flow, contaminant mass flow, water vapor mass flow, and heat flow of both zones. T / ( V 5 ^ J ^ □ " r G U i
 FIGURE 8.5 The height of the lower zone boundary in the zoning strategy.

 T. °C The air, contaminant, and water vapor mass flow elements in outer boundaries and between the zones are created by

1. Supply air

2. Extract air

3. Heat and contaminant sources

4. Local ventilation

5. Plumes of the buoyancy sources through the zone boundary

6. Possible return air from the upper zone into the lower zone

7. Flows along wall surfaces due to temperature differences

8. Infiltration and exfiltration

9. Mixing between zones due to turbulence and disturbances The heat flow elements are created by

3. Heat transport through surface boundary layers

A general steady-state balance calculation of a two-zone model is pre­sented in Figs. 8.6-8.7 and Eqs. (8.10)—(8.17).  Air mass flow balance for the lower zone:

 (8,10) Psltfsi ~ ^Pexl’оexl ^ Pbtf b ~H. Pwb<1wb~ Pоtffol + Polfn ~ ^LPcbmQcbm ~ 0.

Air mass flow balance for the upper zone:

 (8.11 ) Psltfs2 YPex2Й ex2 ~ Pbtfb ^-Pwbtfwb ~ Pltffo2 + PolfH + РсЬтйсЬт = 0- Heat flow balance for the lower zone air:

 (8. Ф*1 — 1Фех1 + фь — — Ф/о 1 + Ф/П — 1ФСЬп,

+ + ХФ™л + ^bt = 0-

Heat flow balance for the upper zone air:

 (8.13) — 2Фех2 — Фь + 2Фwb — Ф/о2 + Ф^’2 +

+ ХФс2 + ХФс1„2-Ф^= 0.

Heat flow balance for the lower zone walls:

-2Ф,«.1 + £Фг*1 + 2Фг«,2]-ХФ«11 = 0 ■ (8-14)

Heat flow balance for the upper zone walls:

-I^»2 + 1Фги/2-21Фги-21-1Фс<12 = ^ • (8.15)

Contaminant mass flow balance for the lower zone:

 (8.16) Gsi — XGexl + Gb-YGwb-Gfol + Gfn + ZGci + Ght = 0.

Contaminant mass flow balance for the upper zone:

 (8.17) GS2 — L(t<iX2 — G/, + ^Gwi, — Gfol + G{,2 + + YGc2 — Gbt = 0.

SHAPE \* MERGEFORMAT The balance equations for water vapor flows are similar to balance equa­tions for contaminant flows, but in addition possible condensation and evapo­ration must be calculated. Also they must be considered in heat flow equations.

The air and wall temperatures and the concentrations in both zones are solved by iteration toward a steady-state situation or by simulating the time- dependent development. In the time-dependent calculation the heat capacity of the walls should be included.

In wall heat balance Eqs. (8.14) and (8.15), the radiation heat flows y ®rwi and V <5>nvl from the heat sources and V ®nt,2i from upper zone wall surfaces to lower zone wall surfaces are assumed to increase the temperature of the walls. In practical cases it is quite complicated to determine how much of the radiation flow rate will be distributed to outer walls and to other surfaces.

Vertical buoyant flows on the wall boundaries X qwb, Ј ®wb ? ar|d Y. Gwb are the sum of several upward and downward flows through the zone bound­ary, which can be calculated using plume and jet theories.

The convection flows from the heat sources Y <I>cl and X <J:2 as well as contaminant flows from contaminant sources are flows loading the room. In the sources additional heat and pollutant flows may be generated, which are exhausted directly out by local ventilation and are not included in the balance calculation.

The pollutant sources IGcl and T Gc2 may be without any buoyancy forces or they may be sinks, in other words negative sources or filters.

The flow rate of the plume through the zone boundary depends on the plume strength and vertical temperature gradient.6 In the case of a zoning strategy, the plume flow rate may also depend on the air distribution method and device because of the interaction between the plume and the supply air.2

The turbulent mixing between the zones depends on the air distribution method and device.7,8