Eulerian thermo-mechanical simulations of heterogeneous solid propellants using an approximate projection method

Abstract

We present a mathematical model that describes thermo-mechanical deformations and thermal gradients on the unsteady burning of a heterogeneous solid propellant. A scaling study shows that the deformations in solid at combustion timescales can be treated as quasi-static. The resulting thermo-mechanical formulation is formulated on a Cartesian grid and makes use of a weak form of Chorin-type projection method to deal with large difference in shear modulus of constituent materials. A one-dimensional verification study is carried out by comparing numerical simulations with those of an analytical model. In addition, convergence studies for a two-dimensional propellant sandwich configuration are presented for the stress, velocity, and reference map components. Finally, simulations are carried out for a two-dimensional random propellant pack and the time-averaged burn rate and strains are reported.