Frank and Ora Lee Marble Professor of Aeronautics and Mechanical Engineering

Hierarchical Theoretical Methods for Understanding and Predicting Anisotropic Thermal Transport and Enery release in rocket propellant formulations (University of Missouri/AFOSR)

Collaborating Institutions/PIs:

University of Missouri: T. Sewell (PI), D. Thompson (Co-PI)
California Institute of Technology: M. Ortiz
University of Illinois, Urbana-Champaign: D. Stewart, M. Matalon

A systematic hierarchical design approach that exploits intrinsic and engineered anisotropy We have longstanding interests in the fundamental physics, chemistry, and engineering required to realize the anisotropy- and hierarchical-design-based approach outlined above. Accordingly, we propose a focused, integrated program of fundamental theoretical and computational research designed to yield understanding and predictive capability regarding anisotropic thermal transport and energy release in advanced rocket propellants. The proposed research will contribute to a practical capability for the a priori design of smart, functional propellant materials based on intelligently designed polymer nanocomposite formulations augmented by non-traditional additives or passivation agents, possibly coupled to external fields.

We believe that the optimal approach is a hierarchical theoretical framework that combines, with as much rigor as possible:

  • Fundamental information from atomic-scale simulations
    • Nanoparticles and bulk
    • Interfaces
  • Detailed continuum-based mesoscopic models of interfaces and interphases, phase transformations, multi-phase transport, and chemistry
  • Explicit microstructure-resolved RVE scale and larger simulations that generate homogenized results induced by mesoscale constituents
  • Development of approaches that define engineering-scale models for propellant combustion uniquely defined by the hierarchical structures from the molecular, micro-, and mesoscopic models. These engineering-scale models are the ones that can be used to make system performance estimates.

Atomic-scale studies – molecular dynamics (MD) and electronic structure theory – will provide critical knowledge of the details of the physics and chemistry of materials that occur at and in the vicinity of interfaces in advanced propellant formulations. The proposed studies will result in consistent identification, characterization, and quantification of the unit processes of anisotropic mechanical response, transport phenomena, phase stability, and chemical transformation within well-defined (and computationally tractable) physical situations. We will study in detail the energy release, localization, and heat dissipation that occurs at or near nanostructured interfaces as a function of initial state and loading conditions. Dynamics at interfaces is a challenging problem due to their extended nature, which requires large simulations and long simulation times to establish steady-state conditions. Interfacial instabilities can significantly affect mixing, and therefore reactivity. Nevertheless, the study of interfaces is quite tractable and we propose simulations to address the critical behaviors of heterogeneous interfaces for conditions of practical relevance. Atomic-scale simulations will be carried out to predict the details of:

  • Thermo-mechanical and transport properties
  • Thermodynamic phase diagrams
  • Interfacial structure and processes
  • Ignition chemistry in multiple phases and mixing regimes.

The simulations will be done for conditions of temperature, stress-/strain-state, and tensoral strain rate relevant to propellant ignition and initiation. We will explore whether and to what extent hierarchical structural motifs (for instance, nanostructures engineered into microstructures) in the pre-reacted state can lead to spatially- and temporally-varying distributions of temperature, stress, strain, strain rate, material phase, mixing and transport, and ignition chemistry.

We will develop mesoscopic continuum-based models for chemically reactive materials. The general approach taken will follow standard methodologies used in the combustion community, but will include the complexities associated with anisotropy and heterogeneity that must be considered to describe nano- and microscale physical processes and their effects on chemistry. Those include consideration of phase changes including solid-state polymorphism and transitions among solid, liquid, and gas; and tracking of key species diagnostic of or critical to the overall reaction kinetics. Multiphase diffusion of species and diffusion of oxidizing and metal ions in oxide melt solutions (often thought to be involved in metal, intermetallic, and thermitic reactions) will be included. The mesoscopic models will predict:

  • Multiphase decomposition and reaction during chemical energy release at initially separate diffusive/reactive interfaces
  • Volumetric reaction and gaseous combustion
  • Formalism and constitutive theory used to describe reactants and their products that reflect the underlying material mechanics and physical chemistry of the constituents
  • Emission outputs (spectra) for “tagged” species in the continuum simulations that can be used to generate synthetic spectra for comparison to experiment.

Thus, we will generate highly constrained model simulations of multiphase decomposition and combustion events for which model spectra output can be compared directly to both experiments and MD simulations to develop temporally and spatially accurate reaction kinetics.

On the basis of the mesoscopic models we will develop RVE-scale methods for simulating experimentally relevant configurations such as:

  • 1-, 2- and 3-D laminates and plies
  • Spherical core/shell particles
  • Both periodic and stochastic microstructure with designated distributions of materials.

We will simulate a piece of material sufficiently large to yield, in a proper homogenization over the "microscopic" ensemble, statistical distributions of properties that can be used in macro-scale models.

The proposed research is primarily fundamental with the aim to provide guidance for practical applications. We will focus on establishing tight, direct coupling among the five main elements of the project (see Fig. 1). The PIs are committed to this aspect of the research. To the extent possible, we will study the same materials at each level of description so that information from one spatial scale can be used directly to inform or parameterize calculations at the other scales. For instance, the mesoscopic combustion models to be developed will use as much as possible bulk and interfacial thermo-physical properties calculated from atomic-scale simulations. Similarly, detailed specification of the plasticity models used in the RVE-scale models will use information about molecular crystal dislocation core structures, energetics, and mobilities predicted by atomic simulations and multiphase transport and chemistry obtained from the mesoscopic models. The fundamental methods and analysis tools we provide should be general, so we do not anticipate that they will be successful for one category of material but fail for another.

The research will establish new understanding of and capabilities for simulating the combustion (and non-detonative explosion) of high-energy-density materials on mesoscopic and macroscopic continuum scales, the atomic-scale details of physical and chemical interactions at dynamic interfaces, and improved methods for hierarchical upscaling and homogenization in multiphase reacting flows. The objective of the proposed research is to enhance progress toward a practical design capability for smart, functional propellant systems. Such materials might feature multiple, application-dependent ignition modalities; tunable initiation thresholds including fail-safe desensitization; and tailored spatio-temporal energy (temperature, pressure) and reaction product release properties.

Due to the need for validation against experiment to establish reliably accurate predictive methods that can be generally applied, we will focus initially on traditional formulation ingredients for which large databases exist – ammonium perchlorate (AP), aluminum (Al), hydroxy-terminated butadiene (HTPB) – for which extensive experimental databases already exist. We will consider RDX and HMX because of their use in propellants; they are beneficial in the initial stages of the work because of our considerable experience with them. Simultaneously, we will study hydrogen-bonded explosives – for example, FOX-7, FOX-12, and NTO – due to their highly anisotropic physical properties. Finally, because our goal is to understand and exploit anisotropy, with an eye toward future extensions to control system response using external fields, we will consider graphene and carbon nanotubes both with and without chemical decoration.

This set of constituent materials will allow us to establish the overall multiscale modeling methods with the detailed interscale connections required for subsequent applications to novel ingredients. We will focus special attention on proper treatment of anisotropy, physico-chemical transformation, and mixing at rapidly evolving interfaces and in reactive flow. We will explore and exploit stoichiometry on nanometer and micrometer scales by studying idealized microstructures that will yield control over both the molecular-scale and mesoscopic intimacy of mixing of chemical reactants. Specific ingredients for study on engineering scales (for instance, particle morphologies, size distributions, and formulation-compatible interfaces) will be chosen initially based on known propellants. Also, our team will collaborate with the FY12 AFOSR MURI Smart Functional Nanoenergetic Materials (Prof. Richard Yetter, PI). Professor Yetter has expressed willingness to interact closely with us and to provide experimental data for traditional materials as well as ones containing “exotic” ingredients (for example, boron, WO3, Ba2O3, intermetallics, and thermites) or promising structural motifs identified in that project. Planned MURI studies of propellants with incorporated metal particles and aggregates, and graphene-containing constituents assembled both traditionally and using self-assembly, will be of keen interest to our project. We think this interaction between teams will yield synergistic benefits to the overall AFOSR Space Power and Propulsion program.