Single spherical droplet, symmetrical

COSILAB Combustion Simulation Software is a set of commercial software tools for simulating a variety of laminar flames including unstrained, premixed freely propagating flames, unstrained, premixed burner-stabilized flames, strained premixed flames, strained diffusion flames, strained partially premixed flames cylindrical and spherical symmetrical flames. The code can simulate transient spherically expanding and converging flames, droplets and streams of droplets in flames, sprays, tubular flames, combustion and/or evaporation of single spherical drops of liquid fuel, reactions in plug flow and perfectly stirred reactors, and problems of reactive boundary layers, such as open or enclosed jet flames, or flames in a wall boundary layer. The codes were developed from RUN-1DL, described below, and are now maintained and distributed by SoftPredict. Refer to the website http //www.softpredict.com/cms/ softpredict-home.html for more information. 

Hence a complete analysis of the phenomena of interest will involve the simultaneous descriptions of the chemical reactions in the gas phase, the phase change processes at the interface, the heat, mass, and momentum transport processes in both the gas and liquid phases, and the coupling between them at the interface. The processes are transient and can be one dimensional (spherically symmetric) or two dimensional (axisymmetric). Although extensive research on this problem has been performed, most of it emphasizes the spherical-symmetric, gas-phase transport processes for the vaporization of single-component droplets. Fuchs book (84) provides a good introduction to droplet vaporization whereas Wise and Agoston (21), and Williams (22), have reviewed the state of art to the mid-flfties and the early seventies, respectively. 

In the next section some of the important time scales are identified and transient droplet heating effects during the spherically symmetric, single-component droplet vaporization are reviewed. Spherically symmetric, multicomponent droplet vaporization and droplet vaporization with nonradial convection are discussed in later sections. 

Transient Droplet Heating during Spherically Symmetric Single-Component Droplet Vaporization... 

Oince the earliest theoretical models by Spalding (I) and Godsave (2) describing the quasi-steady, spherically symmetric combustion of individual fuel droplets in quiescent atmospheres, numerous more elaborate theories have been proposed to provide a better understanding of droplet spray combustion. These theories are based on the premise that the physical and chemical processes involved dmmg single-droplet combustion are fundamental to complex spray combustion processes. 

For a drop in a quiescent atmosphere, that is, a drop under non-forced convection, exact expressions for the Nusselt and Sherwood numbers can be derived tmder the assumption that the problem is spherically symmetric. The initial derivation for a single species drop is due to Spalding [26, 27]. An insightful presentation of this approach can be found in Kuo [15]. Essentially the same methodology can also be apphed to multi-species droplets and the resulting expressions for the Sherwood and Nusselt numbers are formally the same as for a single species drop. For more details see Gradinger [12]. 

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