On The Theory of burning of monopropellant droplets

Abstract

This thesis is concerned with theoretical investigations on some aspects of monopropellant droplet combustion. The burning characteristics have been obtained by solving the governing differential equations which are essentially nonlinear in character due to chemical kinetics. The problem of a monopropellant droplet, burning under adiabatic conditions has been studied, to examine the assumption of constant physical properties in the analysis. This study has revealed that the constant property assumption does not introduce any significant errors in the prediction of some gross characteristics like the mass burning rate, provided the constant properties are evaluated at an average temperature obtained from the study. A simple expression for the exponent (p) of the droplet radius (r?) in the burning rate (?) variation (? ? r??) has been obtained. The controversies prevalent in the literature over the limiting values of p have been completely resolved. The effects of inert non adiabatic conditions on the burning characteristics, in particular on the ignition and extinction characteristics, have been obtained. Increasing activation energies and decreasing ambient temperatures beyond some critical values led to multiple transition solutions which have been interpreted in terms of ignition–extinction characteristics. The effects of increasing activation energy and decreasing ambient temperature on the ignition and extinction states have been evaluated. The solutions indicate that a monopropellant droplet can be ignited if the size is increased beyond a critical value (by internal mass addition) without violating the quasi steady conditions. Further, the constant size droplet, burning in an inert atmosphere, has been investigated for its ignition and extinction characteristics brought about by varying the ambient temperature. The problem of a monopropellant droplet burning in a reactive environment has been studied using a two step reaction model. A numerical procedure has been developed for the solution of this two eigenvalue problem. The solutions indicate that the oxidant atmosphere greatly reduces the extinction droplet radius (roughly by 1/100 for oxygen atmosphere and by 1/6 for air, ambient temperature being 300°C) in comparison to that of the inert atmosphere. The solutions further show that the two flames - the decomposition flame and the diffusion flame - tend to separate with the former thinning at a faster rate than the latter as equilibrium is approached. The unsteady burning of a monopropellant droplet under supercritical conditions has been studied with the droplet being replaced by a gas pocket. This study is primarily motivated towards a critical examination of the utility of profile methods in such problems. The temperature profiles obtained by solving the partial differential equations exhibit similar characteristics (at various times) in the radial coordinate, with a quadratic profile describing the similar shape adequately. The solutions obtained by the profile method using these findings have good agreement with those of the partial differential equations. The basic results of the burning rate, obtained as above, have been used to study monopropellant rocket motor combustion under idealized conditions. The results of chamber lengths obtained, over a wide range of parameters, have been correlated in a simple form which is accurate to within five percent. The effect of pressure on the chamber length has also been discussed.