Eventos Anais de eventos
ENCIT 2022
19th Brazilian Congress of Thermal Sciences and Engineering
MATHEMATICAL MODEL FOR PROPELLANT GRAIN GEOMETRY REGRESSION
Submission Author:
Leib Neubarth , RJ
Co-Authors:
Leib Neubarth, Rachel Manhães de Lucena, Norberto Mangiavacchi, Daniel Chalhub, GIL ROBERTO VIEIRA. PINHEIRO, José da Rocha Miranda Pontes, Maurício Ferrapontoff Lemos, LAURILIO SILVA JUNIOR
Presenter: Leib Neubarth
doi://10.26678/ABCM.ENCIT2022.CIT22-0635
Abstract
Both in solid rocket engines and in gas generators (base bleed systems), the burning of a solid propellant - the grain - is the principle for gas generation. In these devices, the mass flow rate of gas generation is directly proportional to the surface area, on which the combustion chemical reactions are taking place, depending on the surface of exposed propellant in the combustion chamber. Therefore, the geometry adopted by these grains is an important element of their performance, which is measured through the mass flow rate vs time curve. In this work, a mathematical model and the correspondent computational method will be presented, to describe and predict how the geometry, and the exposed surface of a grain deflagrates over time. The devised method consists in describing the grain surface, during the deflagration, as an unstructured mesh. Each time step, unitary vectors normal to the surface are calculated. These vectors are used to compute the directions taken by the moving points. The amount of displacement is given by the regression rate, an experimental data. Despite being capable of predict the mesh evolution in a straightforward manner, two issues may appear during the simulation. First: two non-planar surfaces with normal pointing each other can cause point/surface overlapping. And second, the distance between the points can become so small that numerical errors arise. The first problem is addressed through the elimination of some some points, which smooths the surface. The criterion for deletion is based on the normals of the point’s adjacent surfaces. When the internal product between such vectors is negative, it means that the angle between the surfaces is smaller than 90 degree. So, the point at the intersection is deleted. The second problem is solved using a contour parameterization. This allows the surface to be interpolated in order to achieve a more homogeneous distance between each point. This combined approach is able to simulate consistently the surface area vs time evolution, which reflects the measured mass flow rate vs time curve.
Keywords
base bleed, solid fuel regression, burn rate, Geometrical Modeling, Numerical simulation
