CONVECTIVE DROPLET VAPORIZATION WITH TRANSIENT LIQUID-PHASE HEATING IN THE ABSENCE OF LIQUID-PHASE MOTION

Abstract

The burning of a liquid fuel droplet in a combustor occurs essentially in a convective gaseous stream. An understanding of a single droplet vaporization in a hot convective environment is, therefore,_ essential to any' understanding of spray combustion. The process of droplet vaporization and combustion in a combustor is extremely rapid. The droplet is initially cold and heats-up in time and decreases in radius due to vaporization. All this makes the problem of droplet vaporization in a spray essentially unsteady. The effect of gas-phase convection on mass-vaporiza-tion rate under quasi-steady conditions has been express-ed, in the past, by semi-emperical correlations proposed by many investigators. The general approach has been to modify the spherico-symmetric results of droplet vaporiza-tion to take into account the effect of gas-phase convect-ion. These correlations are not satisfactory, especially during the transient period of heating. Recently, the problem of convective droplet vaporization of single-component droplet was analysed by Prakash and Sirignano[311. They considered the shear stress at the gas-liquid interface, due to relative motion, to cause the liquid-phase motion. The liquid-phase motion is expected to enhance the internal heat and mass transfer (for multicomponent iii fuel droplet)(24A,30, thereby modifying the droplet temperature and concentration fields and consequently the transient mass vaporization rate. The liquid-phase motion considered by Prakash and Sirignano DI] may be possible only in extremely purified systems. However, in the presence of surface active contaminants, the liquid-phase motion may be significantly damped [4]. However, the physical processes which lead to the damping and the complete inhibition of motion in small droplets have not been clearly understood[4]. Further, it is particularly difficult to conclude about the internal motion in situations like droplet vaporiza-tion in a hot convective environment. In the present investigation combustion behaviour of a non-circulating single component fuel droplet in a convective environment has been carried out and the results have been compared with Prakash and Sirignano[1].This study shoul( also provide a limit for larger droplets having non-negligible internal motion because the heating of these droplets would lie in between the two extreme cases viz. one with vigorous internal motion and the one without motion undertaken in the present study. The liquid-phase heating in the present study has been taken as an axis-symmetric two-dimensional transient iv problem in r-e• geometry and is solved by using an Alternate Direction Implicit (ADI) scheme. This ADI scheme for a spherical droplet was developed following the approach of Evans and GaneC53 for the cylindrical problem. This ADI scheme has been shown to work very well when applied to the sphere problem. The transient temperature field within the droplet is calculated using the proper initial and the boundary conditions. The liquid-phase heating has been coupled with the gas-phase boundary layer at the gas-liquid interface.