Transient Processes in a Rigid Slurry Droplet During Liquid Vaporization and Combustion

Abstract

The transient internal processes of heat conduction and liquid surface regression are investigated theoretically. The volume fraction of solid particles is considered large enough so that the overall droplet diameter is constant. Vaporization occurs at the regressing surface of an inner sphere of solid particles and liquid, which is surrounded by an outer porous shell of solid particles that grows in thickness because of the surface regression. Singular perturbation expansions are used to obtain approximate solutions for the temperature profiles of the inner sphere and the regression velocity of its surface. The expansion parameter is the ratio of energy required to raise the inner sphere to the liquid vaporization temperature, to that required for liquid vaporization. For small values of the parameter: (i) The inner sphere is heated by the inward diffusion of energy from the regressing surface, (ii) the decrease in the cube of the diameter of the inner sphere is approximately linear with time, (iii) an approximate expression for the vaporization time is linearly proportional to both the liquid volume fraction and the square of the overall droplet diameter. For large values of the parameter: (i) The inner sphere is heated by the inward propagation of a thermal wave front located at the regressing surface, (ii) an approximate expression for the vaporization time is proportional to the liquid volume fraction raised to an exponent less than unity and the square of the overall droplet diameter