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.

A variational formulation of thermomechanical constitutive update for hyperbolic conservation laws

“…Remark 6. A ratio of updated and previous values of the temperature appears here through the expression of the Lagrange multiplier (41), which is reminiscent of the one already appearing in the discrete integration factor of the discrete incremental potential introduced in [82,70]. However, this ratio serves different purposes in this work and in that of these authors.…”

“…Especially, thermomechanically coupled constitutive models are written for dissipative media in solid mechanics using Helmholtz's free energy [44,83], which is a function of the temperature, while their constitutive updates are driven with some strain measure and also the temperature [67,68,52], obtained from the solution of balance equations. Generally, the latter consist of the heat equation and the linear momentum balance [68], whose weak forms are solved using any discretization method for the spatial part like finite elements [6,8] or particle methods [47], following either Lagrangian [17,50,3], Arbitrary-Lagrangian-Eulerian [7,23,26,15] or Eulerian [41] descriptions, plus some explicit time discretization scheme. In very fast processes, heat conduction effects can be neglected, then the heat equation can be solved locally on the temperature increment.…”

A diffuse interface method for solid-phase modeling of regression behavior in solid composite propellants

“…The second is to use the level-set (LS) method, which relies on the evolution of a surrogate field, the isocontours of which are regarded as a sharp surface. This was originally applied by Wang et al [35] and others [36,37] to modeling surface regression in SCPs. Here, surface regression is effected by local calculation of regression rate, which is used to update the surrogate field at the interface.…”