Numerically evaluating energetic composite flame propagation with thermally conductive, high aspect ratio fillers
Graphical abstract
Introduction
Advanced energetic and propellent systems are increasingly being viewed as good candidates for additive manufacturing. This is particularly so when considering the use of nanomaterials which make traditional casting difficult. These systems rely on high volume loadings of a sub-micron metal fuel and an oxidizer either in the form of a polymer binder or sub-micron source of condensed oxygen (e.g. metal oxides, ammonium perchlorate). For full utility, these materials must not only have high energy density, but must release its chemically stored energy in a rapid, stable manner and must be mechanically durable. One significant aspect of the operational characteristics of self-sustained combustion in these materials is heat feedback to maintain flame front propagation, which implies that thermal transport properties play an important role. These materials fall into a much broader class of polymer composites.
Characterizing the tunability of thermal and mechanical properties of multi-phase (Cheng and Vachon, 1969) polymer systems has been difficult to explore both experimentally (Maiti and Ghosh, 1994, Kargar et al., 2018, Yuan et al., 2017, Smith et al., 2017) and theoretically (Pal, 2008, Pietrak and Wiśniewski, 2015, Nielsen, 1974) despite its importance in a variety of applications which include energy storage for electronics (Yuan et al., 2017, Dang et al., 2013), electrical shielding (Maiti and Ghosh, 1994, Wanasinghe et al., 2020), and heat exchange technologies (Maiti and Ghosh, 1994, Yuan et al., 2017, Du et al., 2018). Commonly used epoxies, acrylates, and fluoropolymers are poor conductors of heat and are generally treated as thermal insulators (Lawless et al., 2020). Thermally conductive fillers like carbides (Yuan et al., 2017), metals (Maiti and Ghosh, 1994, Meeks et al., 2017), and carbon structures (Kargar et al., 2018, Du et al., 2018, Agarwal et al., 2008, Zheng et al., 2012) with various morphologies (i.e. fibers, spheres, flakes) are oftentimes utilized to modulate the composite’s effective thermal conductivity. General candidate materials span a wide range of thermal conductivities as can be seen in Fig. 1. Improvements to thermal conductivity in composites has been primarily observed with the addition of thermally conductive fillers such as silver particles (Maiti and Ghosh, 1994), graphite (Zheng et al., 2012), carbon fibers (Agarwal et al., 2008), and carbon nanotubes (Smith et al., 2017, Du et al., 2018) (CNTs).
Despite the widespread experimental and theoretical work studying the effects of thermally conductive materials on the effective thermal conductivity of two-phase polymer systems, little modeling work has investigated the extent to which the inclusion of such materials effects flame propagation performance in self-propagating high temperature synthesis (SHS) (Mukasyan and Shuck, 2017, Rogachev and Baras, 2007, Song et al., 2011) and propellant systems (Cheng and Vachon, 1969, Smith et al., 2017, Meeks et al., 2017, Isert et al., 2017). Systems of primary interest are those which imbed condensed phase energetic constituents in the form of micron to nanoscale metal fuels, oxidizers, and/or other applicational additives of various morphologies within a polymer matrix binder (Rehwoldt et al., 2020, Kline et al., 2020, Yan et al., 2012, Chen et al., 2012, Mcclain et al., 2019, Wang et al., 2018, An et al., 2019, Shen et al., 2020, Huang et al., 2014, Muravyev et al., 2019).
In this paper, we explore the inclusion of materials with high thermal conductivity as a means to augment the energy release rate in a dense composite (Goroshin et al., 1998). In the absence of convective heat transfer, flame propagation behavior is dependent on how fast energy can be generated (chemistry) and how fast that released energy can be transferred to unreacted areas (thermal diffusivity). Thus, for a composite material with constituents having roughly the same order of magnitude of the specific thermal mass (~106 J m−3 K−1), , the local flame behavior is explicitly a function of the local thermal conductivity (Turns, 2012). The role of filler material parameters (e.g. volume percentage, material type, and geometric morphology) on composite properties have been explored with experimental studies which reference effective composite thermal conductivity theories, such as the Lewis-Nielson, Maxwell, and Percolation models (Maiti and Ghosh, 1994, Kargar et al., 2018, Pal, 2008, Pietrak and Wiśniewski, 2015, Nielsen, 1974). Experiments and Lewis-Nielson models have shown that the use of rods or fibers results in superior effective composite thermal conductivity over sphere-like morphologies at similar volume fractions since high aspect ratio additives tend to easily form a connective network along directions of interest (Smith et al., 2017, Nielsen, 1974, Du et al., 2018, Agarwal et al., 2008).
Here, a 2D implicit finite difference numerical model of the heat equation is used to analyze flame propagation behavior of energetic systems with low thermal conductivity (e.g. Al/PVDF) which incorporate thermally conductive fillers of varied volume percentages (vol%), aspect ratios (AR), and thermal conductivity. More specifically, we focus on a cross sectional area parallel to flame propagation in which rods of random azimuthal orientation lay in the plane. Results illuminate how thermal properties and materials distribution within the energetic composite correlates to flame front morphology, permeability of heat, rate of material consumption, and changes to overall energy release.
Section snippets
Thermal transport and chemistry
Self-sustaining combustion of a dense reactive material involves heat transfer initiating rapid chemistry, which in turn drives more heat transfer (Turns, 2012). The energy that is liberated during an exothermic reaction is converted to heat and observed as regions of temperature accumulation. Thermal gradients drive conductive energy transport from regions of high temperature to regions of low temperature through conductive pathways. For global flame propagation of a heterogenous reactive
Role of rod aspect ratio in combustion performance
Flame propagation modeling was carried out over a 500 µs time period. Energetic composites are incorporated with randomly oriented rods at varied volume percentages (vol% = 0%, 5%, 10%, 20%, 30%, 40%) and aspect ratios (AR = 1, 5, 15, 25, 35, 45, 55). Modeling of each parameter set was repeated 5 times. Temperature mappings in Fig. S3 illustrate overall flame morphology with hot spots designating zones undergoing transient exothermic chemistry. Analysis of flame propagation focuses on how the
Conclusion
In this study, a 2D finite element model is employed to evaluate the role of thermally conductive, high aspect ratio additives on propagation behavior in condensed phase energetic composites. Increases in the the total area burned and energy released was observed when the connectivity of thermally conductive rods throughout the composites is optimized at minimal volume percentages (AR > 25, vol% <20). In cases where the aspect ratio was too low (AR < 25) or additive vol% was too high
CRediT authorship contribution statement
Miles Rehwoldt: Conceptualization, Investigation, Methodology, Data Curation, Formal Analysis, Software, Visualization, Writing-original draft, Writing-review and editing. Dylan Kline: Conceptualization, Data Curation, Investigation, Formal Analysis, Software, Visualization, Writing-review and editing. Michael Zachariah: Conceptualization, Methodology, Project administration, Supervision, Funding aquisition, Validation, Writing-review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was partially supported by the AFOSR.
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