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• W2330288537 abstract "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. The characterization of the two-phase flow in a heterogeneous solid-propellant rocket chamber and nozzle is crucial in ballistic/performance predictions, aeroacoustic studies, erosion analyses, slag accumulation rate estimates, predictions of thermal loads, plume analyses etc. In particular, aluminum particles initially embedded within the binder and injected in the flow during the burning of the grain, undergo mechanical and chemical interactions with the flow itself, and constitute a principal component of the condensed phase. Among the numerous techniques used to model the solid phase a Lagrangian approach 2,3,7 - coupled to an Eulerian formalism for the continuous phase - is possibly the most widely accepted. In the latter, also known as a ’discrete element’ model, the kinematics of each particle is solved in parallel with the fluid flow by integrating a large system of ODE’s. Such formulation has the advantage of attempting a direct numerical simulation of the two-phase flow thereby avoiding the requirement of any additional constitutive laws for the dispersed phase. Typically in such context only larger particles are modeled via the Lagrangian setting, whereas the very small particles (aluminum oxide smoke) are modeled as a continuum . 3,7 The individual motion of the large particles is tracked by integrating their momentum equation which couples to the continuous phase through an aerodynamic drag term evaluated from the fluid field properties at the particle location. Similarly, the combustion of aluminum particles is modeled through burn rate relations which depend both on the particle and on the surrounding fluid field states. Complete two-way coupling between solid and gas phase is achieved by ad-hoc source terms in the gas phase equations supplying the continuous phase with mass and energy from the condensed phase. The combustion process also produces" @default.
• W2330288537 created "2016-06-24" @default.
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• W2330288537 date "2008-07-21" @default.
• W2330288537 modified "2023-09-23" @default.
• W2330288537 title "Two Approaches for Condensed-Phase Modeling in Solid Rocket Motor Flows" @default.
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• W2330288537 doi "https://doi.org/10.2514/6.2008-4789" @default.
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