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James Axley and Peter V. Nielsen
shortcomings and a deeper appreciation of its strengths. Furthermore, the theory will be presented so that simpler applications of it may readily be implemented using any one of a number of commercially available mathematical processing programs [e.g. MATLABŽ, MathematicaŠ or MathCad (MathWorks, 2000; MathSoft, 2004; Wolfram_Research, 2004)]. Building idealization and analytic approach In conventional single- or multi-zone airflow analysis, building systems are idealized as collections of zones and duct junctions linked by discrete, limiting-resistance airflow paths; external wind pressure boundary conditions acting on the building are defined in terms of an approach reference wind velocity; temperatures within the zones and duct junctions are specified (typically but not necessarily as uniform); and specific flow relations are assigned to each of the discrete flow paths or flow elements of the building idealization (Figure 4.39 on the left). Then, equations governing the behaviour of the system as a whole are formed by demanding that zone mass airflow rates be conserved. Finally, these equations are then complemented by assuming hydrostatic conditions exist in each of the modeled zones to achieve closure. The resulting nonlinear algebraic system equations, defined in terms of zone and duct junction node pressures, are then solved and the solution is back-substituted into the flow element equations to determine airflow rates within the system. This most common and thus conventional approach will be identified as the nodal approach to multi-zone airflow analysis. Alternatively, building systems may be idealized as shown to the right in Figure 4.39 – here both flow paths and zones are treated as finite-size control volumes separated by distinct port planes. In this more general approach, airflow variables associated with each port plane include, as Zone + flow element model
Control volume + port plane model
Fan control volume
Duct Fan node element
Duct control volume
Duct element
Inlet element
Building + HVAC system
Zone node
Inlet control volume
Port planes
Zone control volume
Figure 4.39 The conventional zones + flow element model (left) of a representative integrated building + HVAC system (centre) and an alternative model of control volumes and separating port planes with associated port plane airflows (right).