Abstract:
Solid propellant is the highly energetic fuel burnt in the combustion chamber
of ballistic weapons. It is manufactured, for this purpose, in either granular
or stick form. Internal ballistics describes the behavior within the combustion
chamber throughout the ballistic cycle upto projectile exit from the muzzle of
the gun barrel. Over the last twenty years this has been achieved by modelling
the process using two-phase flow equations.
The solid granules or sticks constitute the first phase, which can be assumed
to be incompressible over typical pressure ranges within the chamber. The
gas-phase is composed of both the original ambient gas contained around the
propellant and additional gas produced by the propellant gasifying on heating.
Equations can be derived that describe the conservation of mass, momentum
and energy in terms of average flow variables. The equations are a highly
non-linear system of partial-differential- equations. High-speed flow features
are observed in internal ballistics and ordinary fini te- difference methods are
unsuitable numerical methods due to inaccurate prediction of discontinuous
flow features. Modern shock-capturing methods are employed, which solve the
system of equations in conservation form, with the ability to capture shocks
and contact discontinuities.
However, although the numerical solutions compare well with experiment
over the bulk of the combustion chamber, the ignition models used in internal
ballistics are unreliable. These are based on either gas or solid-surface temperature
achieving some empirically measured 'ignition temperature' after which
the propellant burns according to an empirical pressure dependent burning
law. Observations indicate that this is not an adequate representation of ignition.
Time differences between first solid gasification and ignition imply two
distinct processes occurring. ]Further, ignition occurring in gas-only regions
indicates that ignition is controlled by a gas-phase reaction.
This thesis develops simple ideas to describe possible mechanisms for these
physical observations. The aim is to provide an improved model of the ignition
of solid propellant. A two stage reaction process is described involving
endothermic gasification of the solid, to produce a source of reactant gas, followed
by a very exothermic gas-phase ignition reaction.
Firstly the gas-phase ignition is considered. A very simple reaction is suggested
which is assumed to control the combustion of reactant gas, produced
by solid gasification. Ignition is, by definition, the initiation of this exothermic
reaction. Chemical kinetics are included in the gas-phase flow equations to explore the evolution of the reactant gas that is subject to changes in temperature
and pressure. By assuming spatial uniformity, analytical solutions of the
problem are deduced. The physical interpretation of the solution is discussed,
in particular, the relationship between temperature, reactant concentration
and ignition is explored.
Numerical methods are required to solve the one-dimensional flow equations.
Development of suitable CFD methods provides a method of solution.
Finite-volume schemes, based on the original work by Godunov, are used to
solve the conservation form of the equations. A simple test problem is considered
whereby reactant gas is injected into a cylindrical combustion chamber.
By examining the resulting flow histories, valuable information is gathered
about the complicated coupling of chemistry and flow.
Chemistry is included into a system of two-phase flow equations. By using
standard averaging methods along with an equation for gas-phase species,
equations are derived that describe the rate of change of average flo%v variables
for both gas and particle phases. Numerical schemes are developed and
some of the difficulties involved in two-phase flow systems, that are not an
issue in single-phase flow, are presented. An internal ballistics application is
considered as a test case and the solution discussed.
The other important reaction involved in the combustion cycle, solid gasification,
is explored. The model is based on detailed description of interphase
mass and energy transfer at the solid-gas interface. This involves the solution
of the heat conduction equation with a moving boundary that divides the
solid and gas regions. Similar numerical schemes are constructed to solve the
equations. Finally, this model is coupled with the equations of gas-phase reaction.
This describes the complete cycle whereby increases in gas temperature
cause the solid to increase in temperature and gasify. Subsequent gas-phase
combustion of the reactant gases produces heat-transfer between the solid and
gas and continues to accelerate gasification. Eventually this results in selfsustained
combustion of the solid propellant.