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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Electrochemically Stable High Energy Density Lithium-Sulfur Batteries

Lithium-Sulfur batteries (LSB) have emerged as one of the strong contenders for high energy density rechargeable batteries in the Li-ion battery domain. The LSB system is considered as the most promising to achieve the next milestone in energy density of 500 Wh/kg. However, the LSB system is plagued with problems of polysulfide formation which are soluble in the organic electrolyte leading to loss in capacity and eventual cell failure. The problem is further compounded by dendrite formation on the Li anode during electrochemical cycling leading to puncturing of the separator causing eventual short-circuiting of the cell and consequent heat generation resulting in major safety hazards of flammability of the organic liquid electrolyte and impending explosion. This chapter describes various approaches developed to combat both cathode and anode issues. These involve synthesis and characterization of complex framework materials (CFMs) for confining the polysulfides and sulfur in the LSB cathodes. The CFMs include a CFM host and a coating applied to the CFM host, which includes one or more form of an electronic conductor, a lithium-ion conductor and a functional electrocatalyst for electrocatalytically converting the soluble polysulfides to Li 2 S. Further, sulfur is infiltrated into the CFM host creating a sulfur-carbon linkage serving as effective anchors for trapping the ensuing polysulfides. The systems have been tested in coin cells and pouch cells with metallic Li anodes under lean electrolyte conditions of 3-4 μl/mg of electrolyte (E) to sulfur (S) ratios showing promise and feasibility. New emergent dendrite-free alloys have also been identified to test against pure Li and CFM cathodes in coin cell and pouch cell configurations under lean electrolyte conditions. Results of these studies are described and discussed with thoughts on future directions.

25 ENERGY STORAGE↗
DOE OSTI2021

Atomic Layer Deposition for Materials-Based H2 Storage: Opportunities and Limitations

The transportation demands in our growing hydrogen (H2) economy requires robust storage systems. The current commercially implemented technology in fuel cell cars relies on the well-established technology of hydrogen gas compressed to 350-700 bar, depending on the application. The compressed gas tanks in use today are bulky and cost intensive. To address this challenge, material-based storage is one of the long-term alternatives considered and constitutes the focus of this talk. Material-based storage is broadly defined as hydrogen bound to solid materials, with its binding strength varying from physisorption to porous materials, such as zeolites and metal organic frameworks, to chemisorption in (complex) metal hydrides. The ultimate targets set by the U.S. Department of Energy for this technology include a system gravimetric capacity of 6.5 wt% and volumetric capacity of 40 g/L at 100 bar, operating temperatures ranging between -40 C and +40 C and adsorption/desorption timescales of < 5 min. Storage in the form of physisorbed or chemisorbed hydrogen has guided the materials research, which metal- organic framework and (complex) metal hydrides being the most promising materials classes. A variety of these materials have met one or more of the targets, but it has remained elusive for a single material system to meet all these stringent requirements. Nano-encapsulation and low-concentration chemical additives have previously been employed separately to overcome such challenges. Functionalization via atomic layer deposition (ALD), however, offers unique characteristics that make it suitable for both, nano-encapsulation and "doping" with low-concentration additives. This deposition technique has sub-monolayer thickness control, is highly conformal in high-surface area materials and is self-limiting, i.e., once the gas-phase precursor reacts with the available surface sites, the surface reactions stop. In this presentation, we will showcase examples where ALD, more generally vapor-phase functionalization, on (complex) metal hydrides and organic frameworks has improved the material properties for H2 storage. In our first study, Al2O3 was deposited on magnesium borohydride, Mg(BH4)2, at room temperature using trimethylaluminum (TMA) and water. From our findings, encouraging initial results were obtained: the H2 desorption temperature was lowered by 60-120 degrees C, the desorbed gravimetric H2 capacity at temperatures < 250 degrees C was doubled, and the desorption kinetics increased by a factor of ~6 compared to uncoated Mg(BH4)2. However, hydrolysis reactions caused by residual surface -OH groups from the ALD water-pulse degraded the sample substantially. Through this study, the use of TMA was observed to be highly reactive with the Mg(BH4)2 surface species, leading to the strategy of exposing the sample only to TMA. The relative mole fraction of the vapor-phase additive can be precisely controlled with the number of TMA pulses and pulse duration. By tuning these parameters, we show in our second study that 10 pulses of TMA at ambient conditions were able to decrease the H2 desorption temperature by ~100 degrees C while retaining <95 % of its H2 capacity. We applied this approach with other additives such as BBr3, TiCl4 and tetrahydrofuran, and demonstrate that this unique approach opens the door to a new class of molecular additives and catalysts which cannot easily be introduced with conventional mechano-chemical or solvent-based techniques for (complex) metal-hydrides. In the case of metal organic frameworks, ALD is a promising technique to functionalize the pores with metal atoms or functional groups able to tune the gas selectivity and binding energy, for which ~15 kJ/mol has been established as the optimal value for H2 storage in sorbent materials. Vapor-phase techniques such as ALD have numerous benefits over other functionalization tools for H2 storage materials opening innumerable opportunities to the field. To exploit these opportunities, the current limitations on room temperature and water-less ALD processes needs to be overcome which will greatly expand the possibilities of encapsulation and incorporation of additives for organic frameworks and (complex) metal hydrides.

atomic layer deposition↗
DOE OSTI2022

Li-ion Battery Material phase prediction through Hierarchical Curriculum Learning

Li-ion Batteries (LIB), one of the most efficient energy storage devices, are widely adopted in many industrial applications. Imaging data of these battery electrodes obtained from X-ray tomography can explain the distribution of material constituents and allow reconstructions to study electron transport pathways. Therefore, it can eventually help quantify various associated properties of electrodes (e.g., volume-specific surface area, porosity) which determine the performance of batteries. However, these images often suffer from low image contrast between multiple material constituents , making it difficult for humans to distinguish and characterize these constituents through visualization. A minor error in detecting distributions among the material constituents can lead to a high error in the calculated parameters of material properties.We present a novel hierarchical curriculum learning framework to address the complex task of estimating material constituent distribution in battery electrodes. To provide spatially smooth prediction, our framework comprises three modules: (i) an uncertainty-aware model trained to yield inferences conditioned upon global knowledge of material distribution, (ii) a technique to capture relatively more fine-grained (local) distributional signals, (iii) an aggregator to appropriately fuse the local and global effects towards obtaining the final distribution.

Tabassum, Anika↗
DOE OSTI2025

Computational Analysis of the Energetic Stability of High-Entropy Structures of a Prototypical Lanthanide-Based Metal–Organic Framework

High-entropy materials are characterized by their complex compositions, typically comprising five or more elements in near-equiatomic proportions. Applying this concept to metal ions in metal−organic frameworks (MOFs) has paved the way for exploring a new class of high-entropy MOFs. While the compositional strategy of high-entropy materials leverages configurational entropy to aid thermodynamic stability, it also poses significant analytical challenges due to the vast compositional landscape and diverse phases that these materials can adopt. We present a computational study of several complexities associated with selecting potential high-entropy versions of a prototype lanthanidebased MOF. We compute the energetics of metal mixing of these heterometallic MOFs using density functional theory (DFT) and machine learning interatomic potential (MLIP) methods. The use of MLIP methods allows a systematic exploration of the convex hull of thermodynamically stable MOF structures containing up to 5 distinct metals.

Chemical structure↗
DOE OSTI2023

EXPERIMENTAL AND MODELING STUDY OF MOLECULAR TRANSPORT PHENOMENA IN COMPLEX LIQUID MIXTURES USING COVALENT ORGANIC FRAMEWORK MEMBRANES

Currently, 10-15% of the world’s energy is consumed by chemical separations, and more than 80% of that is used to purify organic liquids and recover rare earth elements and critical minerals. Membrane nanofiltration presents an energy-efficient, cost-effective, and eco-friendly alternative to current separation technologies. These complex liquid environments require high- performance, chemically-resistant membrane materials. Recently discovered Covalent Organic Frameworks (COFs) possess desirable properties as membrane materials for complex liquid separations. COFs are highly crystalline, chemically and thermally stable, with tunable size and charge. COFs, especially two-dimensional highly crystalline COFs, possess narrow pore-size distribution and controlled porous structures. Two-dimensional COFs are also resistant to swelling, another feature beneficial in complex liquid separations. Molecular interactions in complex liquid systems often dictate final membrane performance, resulting in a discrepancy between designed and apparent COF properties. Understanding and resolving this discrepancy is critical in utilizing COF membranes as a viable alternative to energy-intensive separations. The primary objective of this thesis was to use a commercially available COF TpPa-1 as a platform to investigate how mixed solvent environment affects COF membrane performance via experimental and molecular modeling studies. Specifically, the effects of solution pH, solvent- solvent-solute interactions in mixed solvents, and COF chemistry were carefully examined on apparent TpPa-1 pore size and permeability and targeted solute rejection of COF membranes for neat and mixed solvents. Experimental COF filtration performance was compared and corroborated with modeling predication. Findings from this study will provide guidance for future COF design, synthesis, and desired functional COF membrane performance.

Barnes, Anastasia↗
DOE OSTI2026

Deep Gaussian process-based cost-aware batch Bayesian optimization for complex materials design campaigns

The accelerating pace and expanding scope of materials discovery demand optimization frameworks that efficiently navigate vast design spaces with complex response surfaces while judiciously allocating limited evaluation resources. We present a cost-aware, batch Bayesian optimization scheme powered by deep Gaussian process (DGP) surrogates and a heterotopic querying strategy. Our DGP surrogate, formed by stacking GP layers, models complex hierarchical relationships among high-dimensional compositional features and captures correlations across multiple target properties, propagating uncertainty through successive layers. We integrate evaluation cost into an upper-confidence-bound acquisition extension, which, together with heterotopic querying, proposes small batches of candidates in parallel, balancing exploration of under-characterized regions with exploitation of high-mean, low-variance predictions across correlated properties. Applied to refractory high-entropy alloys for high-temperature applications, our framework converges to optimal formulations in fewer iterations with cost-aware queries than conventional GP-based BO, highlighting the value of deep, uncertainty-aware, cost-sensitive strategies in materials campaigns.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Targeted materials discovery using Bayesian algorithm execution

Rapid discovery and synthesis of future materials requires intelligent data acquisition strategies to navigate large design spaces. A popular strategy is Bayesian optimization, which aims to find candidates that maximize material properties; however, materials design often requires finding specific subsets of the design space which meet more complex or specialized goals. We present a framework that captures experimental goals through straightforward user-defined filtering algorithms. These algorithms are automatically translated into one of three intelligent, parameter-free, sequential data collection strategies (SwitchBAX, InfoBAX, and MeanBAX), bypassing the time-consuming and difficult process of task-specific acquisition function design. Our framework is tailored for typical discrete search spaces involving multiple measured physical properties and short time-horizon decision making. We demonstrate this approach on datasets for TiO 2 nanoparticle synthesis and magnetic materials characterization, and show that our methods are significantly more efficient than state-of-the-art approaches. Overall, our framework provides a practical solution for navigating the complexities of materials design, and helps lay groundwork for the accelerated development of advanced materials.

42 ENGINEERING↗
DOE OSTI2023

Robust deep learning framework for constitutive relations modeling

Modeling the full-range deformation behaviors of materials under complex loading and materials conditions is a significant challenge for constitutive relations (CRs) modeling. Here, we propose a general encoder-decoder deep learning framework that can model high-dimensional stress-strain data and complex loading histories with robustness and universal capability. The framework employs an encoder to project high-dimensional input information (e.g., loading history, loading conditions, and materials information) to a lower-dimensional hidden space and a decoder to map the hidden representation to the stress of interest. We evaluated various encoder architectures, including gated recurrent unit (GRU), GRU with attention, temporal convolutional network (TCN), and the Transformer encoder, on two complex stress-strain datasets that were designed to include a wide range of complex loading histories and loading conditions. All architectures achieved excellent test results with an root-mean-square error (RMSE) below 1 MPa. Additionally, we analyzed the capability of the different architectures to make predictions on out-of-domain applications, with an uncertainty estimation based on deep ensembles. The proposed approach provides a robust alternative to empirical/semi-empirical models for CRs modeling, offering the potential for more accurate and efficient materials design and optimization.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Systematic Improvement of Quantum Monte Carlo Calculations in Transition Metal Oxides: sCI-Driven Wavefunction Optimization for Reliable Band Gap Prediction

Accurate determination of the electronic properties of correlated oxides remains a significant challenge for computational theory. Traditional Hubbard-corrected density functional theory (DFT+U) frequently encounters limitations in precisely capturing electron correlation, particularly in predicting band gaps. We introduce a systematic methodology to enhance the accuracy of diffusion Monte Carlo (DMC) simulations for both ground and excited states, focusing on LiCoO 2 as a case study. By employing a selected configuration interaction (sCI) approach, we demonstrate the capability to optimize wavefunctions beyond the constraints of single-reference DFT+U trial wavefunctions. Here, we show that the sCI framework enables accurate prediction of band gaps in LiCoO 2 , closely aligning with experimental values and substantially improving traditional computational methods. The study uncovers a nuanced mixed state of t 2g and e g orbitals at the band edges that is not captured by conventional single-reference methods, further elucidating the limitations of PBE+U in describing d-d excitations. Our findings advocate for the adoption of beyond-DFT methodologies, such as sCI, to capture the essential physics of excited-state wavefunctions in strongly correlated materials. The improved accuracy in band gap predictions and the ability to generate more reliable trial wavefunctions for DMC calculations underscore the potential of this approach for broader applications in the study of correlated oxides. This work not only provides a pathway for more accurate simulations of electronic structures in complex materials but also suggests a framework for future investigations of the excited states of other challenging systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Rational design of stable functional metal–organic frameworks

Functional porous metal–organic frameworks (MOFs) have been explored for a number of potential applications in catalysis, chemical sensing, water capture, gas storage, and separation. MOFs are among the most promising candidates to address challenges facing our society related to energy and environment, but the successful implementation of functional porous MOF materials are contingent on their stability; therefore, the rational design of stable MOFs plays an important role towards the development of functional porous MOFs. In this Focus article, we summarize progress in the rational design and synthesis of stable MOFs with controllable pores and functionalities. The implementation of reticular chemistry allows for the rational top-down design of stable porous MOFs with targeted topological networks and pore structures from the pre-selected building blocks. We highlight the reticular synthesis and applications of stable MOFs: (1) MOFs based on high valent metal ions (e.g., Al 3+ , Cr 3+ , Fe 3+ , Ti 4+ and Zr 4+ ) and carboxylate ligands; (2) MOFs based on low valent metal ions (e.g., Ni 2+ , Cu 2+ , and Zn 2+ ) and azolate linkers. We envision that the synthetic strategies, including modulated synthesis and post-synthetic modification, can potentially be extended to other more complex systems like metal-phosphonate framework materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Breaking Rayleigh’s Law with Spatially Correlated Disorder to Control Phonon Transport

Controlling thermal transport in insulators and semiconductors is crucial for many technological fields such as thermoelectrics and thermal insulation, for which a low thermal conductivity (κ) is desirable. A major obstacle for realizing low κ materials is Rayleigh’s law, which implies that acoustic phonons, which carry most of the heat, are insensitive to scattering by point defects at low energy. We demonstrate, with large scale simulations on tens of millions of atoms, that isotropic long-range spatial correlations in the defect distribution can dramatically reduce phonon lifetimes of important low-frequency heat-carrying modes, leading to a large reduction of κ—potentially an order of magnitude at room temperature. We propose a general and quantitative framework for controlling thermal transport in complex functional materials through structural spatial correlations, and we establish the optimal functional form of spatial correlations that minimize κ. Finally, we end by briefly discussing experimental realizations of various correlated structures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Tritium Transport Modeling at the Pore Scale in Ceramic Breeder Materials Using TMAP8

Fusion reactors depend on the blanket material to breed and release tritium at the same rate or faster than it is consumed by the fusion reaction. Cellular ceramic breeders (CCBs) are dense materials that can maintain a high tritium breeding ratio while promoting tritium release because of highly connected pores. Assessing the tritium breeding capabilities of these materials requires a combination of extensive experimental and modeling efforts. In this work, we develop and calibrate a multiphysics model of tritium transport. This novel model accounts for ceramic and pore diffusion, trapping and detrapping, and several surface reactions at the pore surface. We perform a sensitivity analysis and calibrate the model by comparing its predictions against experimental measurements of deuterium absorption. The calibrated model is then used to model tritium absorption in samples with different pore microstructures to investigate the effect of pore interconnectivity on tritium absorption. The model is part of the development of the multiscale, multiphysics framework for tritium transport [i.e., the Tritium Migration Analysis Program (TMAP8)], which is itself built on top of the finite-element multiphysics framework multiphysics object-oriented simulation environment (MOOSE). This study demonstrates some of TMAP8’s capabilities and is the first step toward assessing the tritium breeding capabilities of ceramic breeder material designs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Integrated Neutronics Modeling for Inertial Fusion Energy Systems: Development and Application to LD-FIRST

Lawrence Livermore National Laboratory (LLNL) is proposing a new Laser Driven Fusion Integration Research and Science Test Facility (LD-FIRST) with the goal of providing an experimental testbed for future Inertial Fusion Energy (IFE) systems. However, IFE systems require detailed and accurate multiphysics modeling to quantify material damage, thermal loading, and tritium breeding within complex chamber environments. This article presents the first step in an integrated multiphysics framework that couples meshed CAD-based geometry within Monte Carlo neutronic simulations to enable high-fidelity analysis of IFE chamber concepts, with future coupling to external codes. The neutronics workflow utilizes OpenMC and its third-party capability to use CAD-based geometries through DAGMC and tally on unstructured meshes with Libmesh to evaluate neutron transport behavior, geometric fidelity, and material performance under reactor-relevant conditions. The use of tailored tallies on unstructured meshes in this framework allows direct transfer without interpolating to CFD simulation tools. Two IFE chambers were evaluated, both conceived by LLNL: HYLIFE-II and Laser IFE (LIFE). This work produced high-fidelity conformal surface and volumetric meshes of the HYLIFE-II and LIFE chambers with mapped spatial insight into material damage, thermal loading, and tritium breeding. The HYLIFE-II model was built utilizing available resources and used as a test case to verify that the neutronics framework can handle complex geometries. The LIFE chamber CAD was provided by LLNL and was the main focus of this work. This work analyzes multiple ternary alloy breeding materials for the LIFE chamber, across different 6 Li enrichments to produce data relevant to the LD-FIRST project. This work also investigates the level of model fidelity for the LIFE chamber, and results show that inclusion of detailed first wall and coolant structures increased the predicted tritium breeding ratio (TBR) by ~30%, highlighting the sensitivity of tritium breeding and the need for a high-fidelity simulation framework for IFE chambers. These developments provide a scalable toolset for the design and optimization of next-generation IFE chambers, forming a solid foundation for future coupled multiphysics analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A Bioinspired Multicomponent Catalytic System for Converting Carbon Dioxide into Methanol Autocatalytically

Nature utilizes multicomponent catalyst systems to convert simple, abundant starting materials to complex molecules that are essential for life. In contrast, synthetic chemical transformations rarely adopt this strategy because the sophisticated supramolecular assemblies used by biology for active site separation and substrate trafficking are difficult to replicate. Herein, a method is described for multicomponent catalyst separation that involves encapsulating transition metal complexes in nanoporous materials called metal-organic frameworks. The multicomponent catalyst system was highly active for converting hydrogen and carbon dioxide to methanol, and it could be formulated so that it is readily recyclable. Moreover, an autocatalytic feature was uncovered that was only made possible by utilizing the multicomponent catalyst strategy employed. Furthermore, these results open avenues for obtaining fuel from abundant and renewable resources.

08 HYDROGEN↗
DOE OSTI2023

Numerical Analysis of Regular Material Point Method and its Application to Multiphase Flows

The material point method (MPM) is gaining wide popularity in engineering research to model and simulate complex multiphase flow dynamics. The method relies on solving the governing equations of motion and transport in a Lagrangian framework using particles also known as material points. The fluid and kinematic properties are stored on the material points while the spatial gradient calculation and temporal integration are performed on a background grid. This Lagrangian framework allows for large deformations, easy integration of constitutive models, and direct import of complex geometries as particles. However, despite their increasing popularity, very few studies have addressed the issues of numerical resolution and stability of MPM techniques. The presence of additional factors such as the number of material points-per-cell, the location of the material points, the CFL-like condition used in time update, and the grid shape functions also increase the complexity of the error analysis when compared to other finite element methods. In this presentation, we analyze the various forms of error incurred in the application of MPM to continuum mechanics and multiphase flows. The effect of the previously mentioned factors on the error dynamics is studied. The application of these principles to canonical and industrial problems is also presented.

high pressure reverse osmosis↗
DOE OSTI2023

Hybrid interatomic potential for Sn

To design materials for extreme applications, it is important to understand and predict phase transitions and their influence on material properties under high pressures and temperatures. Atomistic modeling can be a useful tool to assess these behaviors. However, this can be difficult due to the lack of fidelity of the interatomic potentials in reproducing this high pressure and temperature extreme behavior. Here, in this work, a hybrid EAM-R—which is the combination of embedded atom method (EAM) and rapid artificial neural network potential—for Tin (Sn) is described which is capable of accurately modeling the complex sequence of phase transitions between different metallic polymorphs as a function of pressure. This hybrid approach ensures that a basic empirical potential like EAM is used as a lower energy bound. By using the final activation function, the neural network contribution to energy must be positive, assuring stability over the whole configuration space. This implementation has the capacity to reproduce density functional theory results at 6 orders of magnitude slower than a pair potential for molecular dynamics simulation, including elastic and plastic characteristics and relative energies of each phase. Using calculations of the Gibbs free energy, it is demonstrated that the potential precisely predicts the experimentally observed phase changes at temperatures and pressures across the whole phase diagram. At 10.2 GPa, the present potential predicts a first-order phase transition between body-centered tetragonal (BCT) β-Sn and another polymorph of BCT-Sn. This structure transforms into body-centered cubic near the experimentally reported value at 33 GPa. Thus, the Sn potential developed in this paper can be used to study complex deformation mechanisms under extreme conditions of high pressure and strain rates unlike existing potentials. Moreover, the framework developed in this paper can be extended for different material systems with complex phase diagrams.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Machine-learning-assisted deciphering of microstructural effects on ionic transport in composite materials: A case study of Li 7 La 3 Zr 2 O 12 -LiCoO 2

The effective diffusivity of ionic species in multiphase materials is critical for the design and function of composite materials for electrochemical energy storage. In practice, effective diffusivity depends sensitively not only on the intrinsic diffusivities of constituting materials but also on their topological arrangement; nevertheless, these coupled contributions are oversimplified in most analytical models. Here, we combine atomistically informed mesoscale modeling and machine learning (ML) analysis to unravel how such features affect effective diffusivity in two-phase composites. Using the Li 7 La 3 Zr 2 O 12 -LiCoO 2 composite solid-state battery cathode as a model system, we compute effective diffusivity for 600 distinct dense polycrystalline microstructures with different topological configurations of grains, grain boundaries, and heterointerfaces. We verify that in addition to atomic-scale variabilities, microstructural feature diversity can significantly impact effective transport properties. Across the ensemble of test microstructures, this often results in bimodal distributions of effective diffusivity that encompass two qualitatively distinct operating mechanisms, which we identify via flux analysis. An ML approach reveals that the most critical determining factors for effective diffusivity are the connectivity of bulk phases and their heterointerfaces. The role of ionic mobility at the heterointerfaces is also discussed. These insights highlight the combined importance of microstructure and interface engineering in tuning the transport properties of ionic species in composite materials. In conclusion, our framework can also be extended for understanding generic microstructure-property relationships in other complex multiphase materials.

25 ENERGY STORAGE↗
DOE OSTI2026

Mathematical modelling of the concave front in the adjacent high explosive detonation problem

This study presents an analysis of the transition-zone in adjacent high explosive (HE) detonation problems which uses a $D, 𝜅, \dot{D}$ relationship, where $D$ is the detonation front-normal velocity, 𝜅 is the detonation front curvature and $\dot{D}$ is the time derivative of detonation front-normal velocity. Our approach extends the traditional $(D, 𝜅)$ model to accurately predict the behaviour of both diverging and converging detonation shock fronts. Our findings affirm that a hyperbolic type of front evolution equation, enhanced with wave acceleration, provides a robust framework for modelling complex shock front dynamics in HE materials. This approach not only captures the natural effects of straightness and boundary slope jumps in the transition-zone but also bridges the gap between mathematical predictions and experimental observations, offering insights into the behaviour of both diverging and converging detonation propagations in a homogeneous HE.

acceleration↗