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The paper presents a hybrid Finite Volume Method (FVM) for the laminar combustion of a double-base (homogeneous) solid propellant burning inside a two-dimensional narrowed pipe. The approach for the hydrodynamics in the gas phase is based on an Implicit-Continuous Eulerian method, implemented with the Arbitrary Lagrangian-Eulerian FVM, while the condensed phase is modelled with an Implicit Eulerian FVM approach. The hypothesis of pre-mixed laminar flame, and homogeneous solid phase are assumed. The formulation is based on the conservation equations of mass, species, momentum and energy. The processes of degradation and pyrolysis are both taken into account in the solid phase by means of two finite chemical reactions. The complete chemical model is implemented with 7 unidirectional global finite rate chemical reactions and 12 reactive species. The outcomes of the model are pressure, temperature, density, heat release, species concentration in gas and solid phase, gas speed and bulk burning rate. The numerical model is time dependent, and it is able to describe the main production of the flame structure, including the induction (dark) zone. The numerical results obtained for the burning rate are in good agreement with the empirically based Saint-Roberts law which relates the burning rate withe the bulk pressure by means of an exponential law. The method has also been proved suitable for solving time dependent two dimensional chemically reactive flows problems presenting sub-sonic and super-sonic regimes in the same integration domain.

ICE-ALE modelling for the combustion of homogeneous solid propellant