On the Nonlinear Dynamics of Interfaces

Indiana University, Bloomington IN

Investigators

Abstract

DMS Award Abstract Award #: 0207308 PI: Frankel, Michael Institution: Indiana University Program: Applied Mathematics Program Manager: Catherine Mavriplis Title: On the Nonlinear Dynamics of Interfaces The main objective of the research project is the study of the nonlinear dynamics of flames. One of the major directions is the study of free-interface problems related to combustion and exothermal phase transitions. Free interface problems correspond to sharp changes in physical characteristics describing the problem; they arise naturally in many models in physics. An important example of free-interface problem to be studied is the model of SHS (Self-propagating High-temperature Synthesis a.k.a. solid combustion) which exhibits a remarkable variety of dynamics scenarios. SHS is a potentially new method of manufacturing composite materials with qualities superior to those obtained through traditional methods. Frankel will show the compactness and finite dimensionality of the attractor for SHS model. Frankel will also study the free-interface model of premixed gas combustion. The second major direction of the project is the study of surface evolution equations modeling certain basic flame instabilities and spatio-temporal patterns associated with them. These equations are expressed in terms of instantaneous geometrical characteristics and normal velocity of the surface which allows a more natural representation of the basic nonlinearities that are of a purely geometric origin. Solutions of these equations exhibit wrinkling and self-fractalization similar to those observed in experiments. They are also capable of generating the so-called fingering of the surface that occurs in many processes in fluid dynamics. The proposed work will include rigorous study as well as asymptotic methods and direct numerical simulation. This project addresses mathematical modeling of the complex dynamics of flames. The investigator will study two major themes to enhance the modeling of flame dynamics: 1) free-interface problems, i.e. ones in which there are sharp changes in physical characteristics and 2) surface evolution problems, i.e. where the equation is associated with the flame front deformation and motion. These methods could extend our understanding of flame instabilities, wrinkling, fingering as well as a form of solid combustion which could have new applications in manufacturing of composite materials. Date: May 8th, 2002