Title: Kinetic Experiments and Data-Driven Modeling for Energetic Material Combustion
Description: Energetic materials (i.e., explosives, propellants, and pyrotechnics) have been used for centuries in a wide variety of applications that include celebratory firework displays, the demolition of ‘immovable’ structures, mining resources from the earth’s crust, launching humans into outer space, and propelling munitions across the battlefield. Many different scientific and engineering domains have found unique value in their characteristic release of significant heat and pressure. While the rate at which energetic materials react is often dependent on the source of initiation, surrounding thermodynamic conditions, and formulation sensitivity, many applications aim for a controlled combustion process to produce large amounts of work output – solid and liquid rocket motors and gun-launched projectiles are a few key examples. Other energetic material systems are often inadvertently exposed to thermal insults, which can result in similar combustion behavior. To accurately model these systems, it is important to have a fundamental understanding of the chemical kinetics that control various aspects of the combustion process (e.g., changes in temperature (T), pressure (P), and species mole fractions (X)).

Detailed chemical kinetic models are often used to understand and subsequently predict such behavior. Understanding the gas-phase reaction kinetics of energetic materials is essential when trying to predict critical performance parameters such as flame speeds, temperature and pressure profiles, and heat flux between material phases. These parameters can have significant impact on predictions of system-level performance (e.g., the specific impulse of solid rocket motors, propellant burn rates in projectile systems, and munition responses to thermal insult and extended temperature cycling). While the gas-phase reaction kinetics of energetic material combustion were heavily studied from the late 1970’s to the early 2000’s, research efforts beyond this time frame have primarily focused on condensed-phase chemistry as it is thought to be less understood. Over the past two decades, however, there have been significant advances in our understanding of small molecule reactions that have not yet been accounted for in many energetic material models.

One such example are chemically termolecular reactions – a new class of phenomenological reactions that have not yet been considered for inclusion in any energetic material kinetic models. Recent studies have indicated that chemically termolecular reactions, mediated through ephemeral collision complexes, have significant impact on the global kinetics of certain combustion systems. This discovery has since prompted the question of which systems are significantly influenced by chemically termolecular reactions and should therefore account for their presence in gas-phase phenomenological models. Although a select number of systems have already been investigated, such as flame speed and ignition delay predictions in common hydrocarbon combustion scenarios, the influence of chemically termolecular reactions on the kinetics of energetic materials has not yet been explored. As an initial investigation into energetic materials, a case study for RDX was performed, for which abundant computational and experimental data are available.

To aid in assessing the impact of chemically termolecular reactions, for which almost no data are available, this study leveraged an automated procedure to identify and estimate rate constants for potential chemically termolecular reactions based exclusively on data available for related reactions. Four detailed kinetics models for RDX were independently screened for potential chemically termolecular reactions. Model predictions including these chemically termolecular reactions revealed that they have significant potential impact on profiles of major species, radicals, and temperatures. T he analysis pinpointed ∼20-40 chemically termolecular reactions, out of the thousands of possibilities, estimated to have the largest impact. These reactions, including many mediated by ephemeral HNO** and NNH** complexes, are therefore worthwhile candidates for more accurate quantification via master equation calculations. More generally, just as the importance of including chemically termolecular reactions in hydrocarbon combustion models is becoming recognized, the present results show compelling evidence for the need for their inclusion in energetic material models as well.

The investigation into chemically termolecular reactions yielded a secondary conclusion based on the observed influence of the small molecule C/H/N/O chemistry on overall predictions of energetic material combustion – updating the small molecule chemistry in RDX models produced significant changes to predictions of major species and temperature, suggesting that the development of a comprehensive gas-phase energetic material combustion model would be of great value and have broad utility as a foundational model for a great variety of C/H/N/O energetic materials. To begin developing such a model, all small molecule chemistry in current kinetic models was reviewed with the intent of identifying a sub-model in need of revisions and subsequently addressing its uncertainties using targeted experiments to improve overall predictions. The ammonia sub-model was selected as it is both highly uncertain and highly influential in many energetic material models. Ammonia (NH₃) has garnered substantial attention in recent years due to its importance across many scientific domains – including its potential use as a carbon-free fuel and long-term energy storage option, its use in reducing combustion-generated nitrogen oxide emissions, its role as a decomposition fragment of many energetic materials, and its presence as an important impurity during biofuel and biomass combustion that can affect overall system kinetics, among others.

Yet, it is generally recognized that there are still significant gaps in the present understanding of ammonia kinetics -– in both experimental data sets and sub-models within the overall ammonia kinetic mechanism. For example, most experimental studies of ammonia oxidation have used molecular oxygen as the primary or sole oxidizer. While large mole fractions of molecular oxygen are encountered in many combustion scenarios, there are select systems where ammonia is more likely to be oxidized via nitrogen-containing species (e.g. N₂O and NO₂) and, more generally, there are relatively untested reaction sets that would be accentuated in such conditions. To address these gaps in available experimental data needed for the validation of ammonia kinetics models, jet-stirred reactor experiments were performed for mixtures of NH₃/N₂O/N₂ over an intermediate temperature range (850-1180 K). In these experiments, the mole fractions of NH₃, N₂O, and NO were measured using a combination of gas chromatography, chemiluminescence, electrochemical detection, and infrared absorption – where agreement among the different diagnostics (within 3% for N₂O and 7% for NO) ensured high confidence in the experimental measurements.

Comparison of the experimental results and model predictions suggested deficiencies in commonly used models for nitrogen kinetics. Various modeling analyses pointed to the central role of the N₂O + NH₂ = N₂H₂ + NO reaction, on which recent kinetic models all rely on the same rate constant estimate that appears to have not been tested in previous validation data sets for NH₃ kinetics. A second set of jet-stirred reactor experiments were performed for mixtures of NH₃/NO₂/O₂/N₂ over a slightly different temperature range (700–1100 K). Agreement among different diagnostics (≤7% for NO₂ and ≤4% for NH₃) and excellent experimental repeatability confirmed high confidence in all species measurements. Measured mole fractions were compared to predictions from five recently developed kinetic models using flux analysis and uncertainty-weighted kinetic sensitivity analysis, both of which pointed to the importance of reactions involving H₂NO that are both influential in this system and highly uncertain.

The measurements from the jet-stirred reactor experiments presented here were combined with comprehensive sets of experimental data and high-level theoretical kinetics calculations using the MultiScale Informatics (MSI) approach to unravel the large uncertainties present in current NH3 oxidation kinetic sub-models. Emphasis was placed on NH₃ oxidation via nitrogen-containing species as this chemistry has been shown to accentuate influential reactions (e.g., the NO₂+NH₂ and NH₂+NO reactions) that are known to be important during the combustion of many energetic materials (e.g., AN, ADN, and AP). The resulting MSI model accurately predicted nearly all of the experimental and theoretical target data within estimated or reported uncertainties. Additional predictions of two NH₃/NO₂ validation data sets, which were not included in the MSI framework, demonstrated its ability to accurately extrapolate predictions to untested T/P/X conditions, indicating that the converged MSI model demonstrates truly predictive behavior.

The MSI NH₃ oxidation model presented here should be considered for inclusion in many energetic material models as the NH₃/NOₓ kinetic system is known to be important to the combustion of various propellant and explosive formulations. This sub-model will help to form a foundational gas-phase kinetic model relevant to many different energetic materials, including those that contain inorganic additives for increased energy density and blast effects.