Droplet heating effects

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 Heating of Droplets When a cold liquid fuel droplet is injected into a hot stream or ignited by some other source, it must be heated to its steady-state temperature Ts derived in the last section. Since the heat-up time can influence the V/2 law, particularly for high-boiling-point fuels, it is of interest to examine the effect of the droplet heating mode on the main bulk combustion characteristic—the burning time. 

To study the effects due to droplet heating, one must determine the temperature distribution T(r, t) within the droplet. In the absence of any internal motion, the unsteady heat transfer process within the droplet is simply described by the heat conduction equation and its boundary conditions... 

The soot temperature was found to exceed the gas temperature as measured by thermocouples in the absence of droplet injection but decayed at a similar rate. This is attributed to bulk heating effects associated with the localized burning of vaporized material. A detailed diffusion flame calculation for a cylindrical source of reactants and relative velocity on the same order as these experimental data, indicate that this bulk heating effect is reasonable. 

The d -law assumes a constant Tg. However, in many practical situations the temperature of the droplet when introduced into the evaporator is far below this final, equilibrium value. Hence an initial transient heating period exists during which y, and Tf all increase whereas H decreases. Furthermore it can be estimated also that the sensible heat required to heat the droplet is of the same order as the latent heat of vaporization. Hence droplet transient heating effects on the bulk vaporization characteristics are expected to be significant. Two such models, representing extreme rates of internal heating, will be discussed. 

For the subcritical pressure range of interest, gas-phase heat and mass diffusion rates are of the order of 10 -1 cm /sec while the liquid-phase heat transfer rate is of the order of 10" cm /sec, and the liquid surface area regression rate is approximately 10" -10" ctn /sec. Inasmuch as the gas-phase transfer rates are much faster than all of the liquid-phase transfer rates, gas-phase heat and mass transfer can be represented as quasi-steady processes. The validity of this quasi-steady approximation has been substantiated by the numerical study of Hubbard et al. (10). Furthermore, Law and Sirignano (6) have demonstrated that effects caused by the hquid surface regression during the droplet heating period are negligible relative to the liquid-phase heat conduction rate. 

The previously mentioned droplet evaporation effect and inner flame development are caused by the presence of heat and oxygen in the gas phase of a spray stream. 

The simplest model for droplet evaporation is based on an equilibrium uniform-state model for an isolated droplet [28-30]. Miller et al. [31] investigated different models for evaporation accounting for nonequilibrium effects. Advanced models considering internal circulation, temperature variations inside the droplet, and effects of neighboring droplets [30] may alter the heating rate (Nusselt number) and the vaporization rates (Sherwood number). For the uniform-state model, the Lagrangian equations governing droplet temperature and mass become [28-30]... 

Suspension polymerization is a polymerization process in which dispersed monomer droplets are stabilized by surfactant and mechanical agitation in a liquid phase such as water. As in emulsion polymerization, the monomers used for suspension polymerization are usually insoluble in water. Advantages of suspension polymerization compared with other polymerization methods include easy removal of reaction heat, effective temperature control, low viscosity of the reaetion system, simple polymerization mechanism, high purity of the produet, easy separation and purifieation of the produet and shaped product in particle form. Polymers prepared by suspension polymerization inelude... 

A third screening smoke-type is white phosphoms [7723-14-0] (WP), P (see Phosphorus and THE phosphides), which reacts spontaneously with air and water vapor to produce a dense cloud of phosphoms pentoxide [1314-56-3]. An effective screen is obtained as the P2O5 hydrolyzes to form droplets of dilute phosphoric acid aerosol. WP produces smoke in great quantity, but it has certain disadvantages. Because WP has such a high heat of combustion, the smoke it produces from bulk-filled munitions has a tendency to rise in pillarlike mass. This behavior too often nullifies the screening effect, particularly in stiU air. Also, WP is very brittle, and the exploding munitions in which it is used break it into very small particles that bum rapidly. 

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. 

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