Computational Physics Group

Karel Matous










Chemo-thermal Model and Gaussian Process Emulator for Combustion Synthesis of Ni/Al Composites

M. Shabouei, W. Subber, C. Williams, K. Matous, and J. M. Powers

Center for Shock Wave-processing of Advanced Reactive Materials

Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame,
Indiana 46556, USA.


    We propose a chemo-thermal model that considers both diffusion and reaction phenomena, consumption and formation of species, and heat generation due to chemical reactions. We study the thermal and chemical processes in combustion of heterogeneous reactive materials at the microstructural level. The model is applied to the combustion of Nickel and Aluminum (Ni/Al) composites. We provide numerical results such as the reaction front speed, reaction time, and temperature evolution during reaction and compare those with the existing experimental data. Sensitivity analysis and Bayesian calibration of the diffusion and reaction parameters are performed. We show that both diffusion and reaction are strongly coupled in thin zones such that neither can be neglected. Moreover, a multi-fidelity and multi-scale Gaussian process emulator is developed to overcome the computational cost of the simulations at different length-scales.


    We have developed a two-way coupled chemo-thermal model and implemented it within a finite element framework to simulate combustion synthesis of NiAl composites. We show that the model satisfies the second law of thermodynamics. We consider both diffusion and reaction in the provided model and used non-linear Arrhenius type diffusion and reaction equations. Rigorous sensitivity analysis is performed to show the effect of the reaction and diffusion phenomena on the synthesis process. We observed that in the combustion zone both the reaction and diffusion play an important role. The influence of the microstructure on the behavior of the system was also investigated, and detailed simulation results, average chemical front speed, reaction time, and slope of temperature-time profile were provided. Additionally, we developed a multi-fidelity and multi-scale Gaussian process emulator to overcome the computational costs associated with simulations at different length-scales. The emulator is used within a Bayesian framework to estimate the parameters and the underlying length-scale of the microstructure from a synthesized measurement of the temperature profile.
    The emphasis of this work has been on the development of a mathematical and computational model for self-propagating material synthesis. We consider solid state reaction process and study micron-sized single particle systems with no voids. Numerical simulations of finer material systems (i.e., d0 ≤ 1.0 μm) or systems with more complex reaction mechanisms (i.e., intermediate phases) are important future topics.


This work was supported by the Department of Energy, National Nuclear Security Administration, under the Award No. DE-NA0002377 as part of the Predictive Science Academic Alliance Program II.

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