Zonal Models

Zonal models are often used in analytical calculation of temperature, concentration, or humidity conditions in ventilated spaces. The space is divided in two or several zones, which typically have different target levels as described in Section 2.1 These typical zones can also be divided into additional subzones. 

Zonal models can be applied for each room air conditioning strategy (see Section 8.6), but they are mostly used in stratification and zoning strategies with different air distribution methods (see Section 8.7). 

E. Shilkrot and A. Zhivov, Zonal model for displacement ventilation design, in Roonwcnt 96 vol. 2. Yokohama, Japan, 1996. 

The terms zonal model and flow element are also used for the simplified characterization of the flow field in a single enclosure. 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 which is connected to other enclosures by air conductances (see The Airflow Network later). 

Itiacd C., Ikmta H., Dalicieux P. Prediction of air temperature distribution in buildings with a zonal model. Energy and Buildings, vol. 24, 1996. 

A zonal model for the carbon cycle in the atmosphere-ocean system... 

Nefedova E.I. and Tarko A.M. (1993). Investigation of the global carbon cycle within the framework of a zonal model in the atmosphere-ocean system. Proceedings of RAS, 333(5), 645-647 [in Russian],... 

In boundary-layer calculations, most workers simply use zonal models, with Eq. (9) in the inner region [which becomes Eq. (8) further from the wall] and something like Eq. (7) in the outer portion of the flow. Byrne and Hatton (B5) use a three-layer model as the basis for vt assumptions. Mellor and Herring (M2) have used concepts from the theory of matched asjTnptotic expansions to obtain composite representation for I valid across an entire turbulent boundary layer. A t j"pical distribution of 1 in a boundary layer is shown in Fig. 5. 

Zonal models are not new in relief valve development. They are prone to oversimplification, but have been used successfully to approximate fluid forces on a disk and approximate the lifting transient. " " ... 

Gutman, G. (1984). Numerical experiments on land surface alterations with a zonal model allowing for interaction between the geobotanic state and climate. /. Atmos. Sci. 41, 2679-2685. 

Step 3 Use the zonal model to determine the level of risk. Calibration can be based on the data from Steps 1 and 2, and the assumptions illustrated in Section 10.3 (Figure 10.6). Alternatively, these assumptions can be fine-tuned in the light of local information, much of which can be gathered from housing surveys and water consumption data. 

The models, which are described in more detail elsewhere (Van der Leer et al, 2002), enable the most relevant features of a water supply zone to be incorporated in the prediction of zonal compliance with lead standards, as a function of boA plumbosolvency (corrosivity of the water to lead) and the zone s physical characteristics. A zonal model simulates the emissions of lead at individual simulated houses, through time, across an entire water supply zone or area of supply. It uses a single pipe model to determine the lead emission profile at each simulated house, the characteristics of each simulated house being the outcome of the random ascription of variables, which follows the Monte Carlo method for establishing a probabilistic firame-work. 

The zonal model is set up by the random ascription of a series of zonal characteristics, as derived from sets of agreed statistical distributions, and by the use of agreed variables and constants. The statistical distributions that are shown in Figure 10.7 have been used successfully in many zonal modelling studies (e.g. Hayes et al, 2008). They have the following features ... 

Figure 10.7 Statistical distributions used to set up the zonal model (from Hayes, 2009)...

Table 10.2 Use of zonal model to predict RDT sampling compliance for a range of plumbosolvency reductions when 50% houses have a lead pipe...

From 1999 to 2002, 17.5% of random daytime samples had lead >10 pg/1 and 7.9% >25 pg/1. Laboratory plumbosolvency testing gave an average lead concentration after 30 minutes contact of around 50 pg/1 Zonal modelling indicated that an average ortho-phosphate dose in the range 0.6 to 0.9 mg/1 (P) should achieve >98% compliance with the fiiture lead standard of 10 pg/1. 

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