Technical report | Review of Solid Propellant Ignition Models Relative to the Interior Ballistic Modelling of Gun Systems

Abstract

The modelling of solid propellant ignition is investigated with the aim of implementation into the numerical code Casbar. The current state of the art in solid propellant ignition and combustion modelling is reviewed, with a simplified condensed phase ignition model chosen as the suitable candidate. A number of methods of solving the mathematical models are analysed, with results compared. Based on these results, the solution by integral methods to he condensed phase model was chosen for implementation into Casbar.

Executive Summary

Solid propellant ignition (and the evolution to self-sustained combustion) is a highly complex physicochemical process, involving the transition of a stable solid propellant state through to a luminous burning resulting from the application of heat energy [1]. For solid rocket and gun applications, ignition stimulus is usually in the form of a pyrotechnic igniter emitting heat energy and hot particles into the propellant bed. The action of simultaneous energy sources from convection of the hot gases, conduction from impingement of hot particles, radiation from both the hot igniter gases and particles, and even heat from atom recombination and vapour condensation, all act to ignite the propellant [2].

Interior ballistic modelling is used in a wide range of defence applications, and forms a key analytical tool for the assessment of gun and rocket propulsion systems. A range of phenomena occurring during the interior ballistics cycle are related to solid propellant ignition processes, therefore the accurate reproduction of ignition phenomena is important. Australia's Defence Science and Technology Organisation has capability in performing gun interior ballistics modelling through its numerical code, Casbar. Casbar solves the governing equations for the transient flow of chemically reacting gas and particulates within a Finite volume discretisation of the computational domain.

Currently in Casbar propellant ignition is modelled using a simple go/no-go condition, whereby if the gas surrounding the propellant is above the defined propellant ignition temperature, the grain will combust. This ignition criterion does not account for Finite-rate grain heating and the experimentally observed ignition delay of solid propellant grains,

and thus generally predicts an unrealistically fast propellant ignition.

This report describes the solid propellant ignition and combustion phenomena, and investigates a number of ignition models suitable for implementation into the Casbar code. The three main areas of ignition models (solid-phase, heterogeneous and gas-phase reactions models) encompass a broad range of complexity and numerical effiency. It is desirable to choose a model that is accurate, while being flexible. Ultimately, the solid-phase

ignition model was chosen for implementation in Casbar.

A number of numerical techniques for solution of the solid-phase ignition model were reviewed. In numerical modelling it is required that the solution of the model be adequately robust, while reducing the impact on the simulation time. In all of the investigated heat Flux scenarios, the integral method was able to adequately approximate the final ignition time to within an acceptable level of accuracy (in comparison to the finite difference approximation). Situations involving highly variable heat fluxes were employed to test the applicability of the integral method. These scenarios were constructed to accentuate the variability of the heat flux, and situations like this are not expected in typical interior ballistic simulations. The integral method is therefore considered an appropriate candidate for implementation in Casbar.