Flame model, assumptions made

The theoretical approach to modelling frontal polymerization is based on the well developed theory of the combustion of condensed materials.255 "6 The main assumptions made in this approach are the following the temperature distribution is one-dimensional die development of the reaction front is described by the energy balance equation, including inherent heat sources, with appropriate boundary and initial conditions. Wave processes in stationary and cyclical phenomena which can be treated by this method, have been investigated in great detail. These include flame spreading, diffusion processes, and other physical systems with various inherent sources. 

Most theories of droplet combustion assume a spherical, symmetrical droplet surrounded by a spherical flame, for which the radii of the droplet and the flame are denoted by and respectively. The flame is supported by the fuel diffusing from the droplet surface and the oxidant from the outside. The heat produced in the combustion zone ensures evaporation of the droplet and consequently the fuel supply. Other assumptions that further restrict the model include (/) the rate of chemical reaction is much higher than the rate of diffusion and hence the reaction is completed in a flame front of infinitesimal thickness (2) the droplet is made up of pure Hquid fuel (J) the composition of the ambient atmosphere far away from the droplet is constant and does not depend on the combustion process (4) combustion occurs under steady-state conditions (5) the surface temperature of the droplet is close or equal to the boiling point of the Hquid and (6) the effects of radiation, thermodiffusion, and radial pressure changes are negligible. 

Blast effects can be represented by a number of blast models. Generally, blast effects from vapor cloud explosions are directional. Such effects, however, cannot be modeled without conducting detailed numerical simulations of phenomena. If simplifying assumptions are made, that is, the idealized, symmetrical representation of blast effects, the computational burden is eased. An idealized gas-explosion blast model was generated by computation results are represented in Figure 4.24. Steady flame-speed gas explosions were numerically simulated with the BLAST-code (Van den Berg 1980), and their blast effects were calculated. 

Heat Transfer by Conduction. In the theoretical analysis of steady state, heterogeneous combustion as encountered in the burning of a liquid droplet, a spherically symmetric model is employed with a finite cold boundary as a flame holder corresponding to the liquid vapor interface. To permit a detailed analysis of the combustion process the following assumptions are made in the definition of the mathematical model ... 

The API (1996) method was originally developed for flare analysis, but is now applied to jet fires arising from accidental releases. Flare models apply to gas releases from nozzles with vertical flames. For accidental releases, the release hole is typically not a nozzle, and the resulting flame is not always vertical. For the modeling approaches presented here, the assumption will be made that the release hole can be approximated as a nozzle. The asstomption of a vertical flame will provide a conservative result, since the vertical flame will provide the largest radiant heat flux at any receptor point. 

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