Zone modeling

Fig. 4. (a) The crack tip plastic zone and (b) the Dugdale plastic zone model. Terms are defined in text. 

R. F. Carsel and co-workers. Users Manual for the Pesticide Toot Zone Model (PRZM), Release I, USEPA 600/3-84-109, Washiagton, D.C., 1984. 

Spouted bed Well-mixed Two-zone model Liu and Litster, Powder Tech, 74, 259(1993) Litster, et al. [Proc. 6th Int. Symp. Agglom., Soc. Powder Tech., Japan, 123 (1993). 

The zone model has the following basic limitations 1) complex enclosure geometries cannot be addres.sed, 2) forced ventilation cannot be realistically modeled using simple unit models, 7 ) burning other combustibles remote from the initiating source are not modeled, and 4) siipprcssion activities are not included. 

Two-zone models are especially useful for stratification and zoning strategies because of the typical vertical accumulation of heat, contaminants, or water vapor within these strategies. The level of the boundary between the lower and the upper zone is usually determined on the level of the highest temperature or/and concentration gradient. 

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. 

A genera steady-state balance calculation of a two-zone model is presented in Figs. 8.6-8.7 and Eqs. (8.10H8.17). 

Specified solutions of the general two-zone model have been presented previ-ously.i " ... 

Bach et al., Pozin, and Shilkrot and Zhivov - present two-zone models for mixing, zoning, and stratification strategies with different air distribution methods. 

Mundt presents a two-zone model for the calculation of temperature gradient within a stratification strategy. 

Sandberg et al. present a two-zone model for a zoning strategy and active displacement air distribution method. 

When the zoning strategy is applied, the two-zone model is a useful and simple tool for the determination of the thermal, contaminant, and humidity accumulations. Principles of two-zone modeling are presented in Section 8.4. 

Figures 8.33 and 8.34 describe a two-zone model application of the zoning strategy where all the main variable parameters are presented. Figure 8.33 (temperature model describes the accumulation of heat and Fig. 8.34 (concentration model) the accumulation of contaminants. After solving for the temperatures, heat flow s, and airflows, contaminant concentrations can lie calculated. The models are here determined for stationary loads, airflow rates, and indoor/outdoor conditions, but they can be developed also for dynamic simulations.

Choice of program and input should be in accordance with the problem and the answers sought. For simple problems, adequate results may also be obtained with an adapted simple model. Many cases can be solved using a single-zone model various models are available.A single-zone model is also described in a CEN standard. 

Fig. 5.1. The electrostatic configurations of the Neilson-Benedick three-zone model describe a piezoelectric solid subject to elastic-inelastic shock deformation which divides the crystal into three distinct zones. Zone 1, ahead of the elastic wave, is unstressed. Zone 2 is elastically stressed at the Hugoniot elastic limit. Zone 3 is isotropically pressurized to the input pressure value (after Graham [74G01]).

High pressure explosive loading was carried out on both z- and y-cut crystals at pressures between about 25 and 60 GPa ([83S01, 77S01]). The z-cut crystals responded in the plus-x orientation with current pulse wave shapes as predicted by the three-zone model. Nevertheless, limited experiments in the minus-z orientation of lithium niobate do not show the positive currents expected from the three-zone model. 

Good agreement is reported to exist between the Dugdale plastic zone model and optical interference experiments, performed at the tip of a crack. Morgan and Ward [79], Fraser and Ward [80] and more recently and extensively Doll and... 

Konczol [81] looked at PMMA, PC, PVC and other thermoplastic polymers. Their results support the plastic zone model. 

Carsel RF, Mulkey LA, Lorber MN, et al. 1985. The pesticide root zone model (PRZM) A procedure for evaluating pesticide leaching threats to groundwater. Ecological Modeling 30 49-69. 

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