Two approaches for condensed-phase modeling in solid rocket motor flows

Modeling of the condensed phase in a solid rocket motor engine is typically accomplished via a two-fluid Eulerian approach or a direct Lagrangian approach. Each approach has its advantages and intrinsic disadvantages in terms of describing a polydispersed population of aluminum particles while it burns and convects within the carrier flow. A more unconventional approach is the Population Balance Equation (PBE) approach which solves a convection equation for a number density field, representative of the particulate phase. In the most general case the PBE is an integro-differential equation and can account for aerodynamic drag on particles, their combustion, breakage and agglomeration, via representative constitutive models. Here we will describe the PBE approach and will adopt it to simulate the aluminum particulate phase in a solid rocket engine. The results will be compared to those yielded by a more conventional Lagrangian approach. While the Lagrangian approach is spatially 3-dimensional, the PBE approach will adopt a quasi 1-dimensional assumption, leaving the extra two dimensions available for "internal" particle coordinates such as particle radius and velocity.