An approach formulated in terms of conserved variables for the characterisation of propellant combustion in internal ballistics

Abstract

Summary A model formulated in terms of conserved variables is proposed for its use in the study of internal ballistic problems of pyrotechnical mixtures and propellants. It is a transient two‐phase flow model adapted from the non‐conservative Gough model. This conversion is mathematically attractive because of the wide range of numerical methods for this kind of systems that may be applied. We propose the use of the AUSM+, AUSM + up and Rusanov schemes as an efficient alternative for this type of two‐phase problem. A splitting technique is applied, which solves the system of equations in several steps. A second‐order approach based on Monotonic Upstream‐Centred Scheme for Conservation Laws (MUSCL) is also used. Some tests are used to validate the code, namely a shock wave test, a contact discontinuity problem and an internal ballistics problem. In this last case, one‐dimensional numerical results are compared with experimental data of 155‐mm gunshots. Copyright © 2015 John Wiley & Sons, Ltd.

An Energetic Model for Detonation of Granulated Solid Propellants

“…That allows the use of numerical schemes for conservative fluxes with a finite-volume approach. This way, updated numerical methods for compressible flow can be applied for the numerical resolution [7]. Moreover, an extension of approximated Riemann solvers to the solid phase was considered for the numerical integration of the problem.…”

“…Simulations were carried out using Rusanov and MacCormack-TVD numerical schemes and their results are compared in the following pages. Figure 2 shows a comparison of the present model with flame front solution provided by Hoffman and Krier [11] for two cases: the case of the model that includes a modification of the momentum equation (i.e., model formed by the Equations (1)-(4), (6), (7), and (9), Figure 2a) and the case of the model that includes a porosity limiter (Figure 2b). In addition, Figure 3 shows a comparison of the time evolution of porosity distributions with the spatial domain for momentum equation modification.…”

“…The system to be considered is formed by the Equations (1)-(4), (6), (7), and (9) and the solutions are plotted in Figure 5. The results obtained with Rusanov and MacCormack agree well at 40 µs and present slight but not relevant differences at 60 µs for porosity, pressure, and gas temperature.…”

“…Another type of approach is that developed by Gough [6] and adopted by Oton-Martinez et al [7] among others, which is based on the formal averaging of the solid propellant and the surrounding gas in the spatial domain considered. This approach relies on the conservation equations of the solid and gas phases where the phases are considered to be a homogeneous continuum.…”

Modelado de la combustión de propulsantes sólidos

“…Another type of approach is that developed by Gough [16] and adopted by Oton-Martinez et al [17] among many others which is based on the formal averaging of the solid propellant and the surrounding gas in the spatial domain considered. This approach relies on the conservation equations of the solid and gas phases.…”