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At least 181 records · Page 10

Heat Integration Optimization and Dynamic Modeling Investigation for Advancing the Coal-Direct Chemical Looping Process

The purpose of the project is to address the optimization and startup operation of a modular coal direct chemical looping (CDCL) combustion system integrated with a steam cycle for power generation to reduce the risks involved in further scale-up of the technology. The modular reactor design of the CDCL process provides flexibility in the fabrication of the reactor and in its operating capacity (i.e. turndown ratio) at the cost of a more complex heat exchange network (HEN) design and integration. To address the technology gaps and advance the efficiency and economic feasibility of the CDCL technology, the project will perform a detailed and comprehensive analysis of the integration of a modular CDCL reactor system and a steam cycle system under both static and transient conditions via HEN process performance simulations and system dynamic modeling, respectively. The scope of work consists of 1) Experimental and computational studies of the CDCL combustor reactor 2) Comprehensive static (i.e. steady-state) system HEN design analysis in CDCL 550 MWe commercial unit for power generation and 3) Dynamic modeling of site specific design of 10MWe CDCL large pilot plant. The project team has successfully developed and validated a kinetic model for the oxidation of oxygen carriers in the combustor using the unreacted shrinking core model (UCSM). The model is capable of capturing the oxidation kinetics of fully or partially reduced oxygen carrier particles. A computational fluid dynamics (CFD) model is developed to simulate the hydrodynamics, heat transfer, and chemical reaction occurring in the CDCL combustor. The model is developed in MFIX and ANSYS Fluent. Key aspects of CDCL combustor operation, including heat transfer, oxygen carrier oxidation, and the transport of oxygen carrier particles, are simulated using this CFD model. The HEN for a commercial scale 550 MWe CDCL power plant is simulated and optimized using ASPEN Plus. Practical design considerations are incorporated based on industrial experiences. The performance and cost for the commercial CDCL plant is updated based on these analyses. A dynamic model for the 10 MWe CDCL pilot plant is developed in ProTRAX simulation software. The model is based on the pilot plant design developed in project DE-FE0027654 “10 MWe CDCL Large Pilot Plang – Pre-FEED Study” and the steam cycle data obtained from Dover Light & Power plant. The transient behaviors during pilot plant load variation are simulated using the dynamic model.

01 COAL, LIGNITE, AND PEAT↗

Dynamics and structure of turbulent premixed flames

In earlier work (Mantel & Bilger, 1994) the structure of the turbulent premixed flame was investigated using statistics based on conditional averaging with the reaction progress variable as the conditioning variable. The DNS data base of Trouve and Poinsot (1994) was used in this investigation. Attention was focused on the conditional dissipation and conditional axial velocity in the flame with a view to modeling these quantities for use in the conditional moment closure (CMC) approach to analysis of kinetics in premixed flames (Bilger, 1993). Two remarkable findings were made: there was almost no acceleration of the axial velocity in the flame front itself; and the conditional scalar dissipation remained as high, or higher, than that found in laminar premixed flames. The first finding was surprising since in laminar flames all the fluid acceleration occurs through the flame front, and this could be expected also for turbulent premixed flames at the flamelet limit. The finding gave hope of inventing a new approach to the dynamics of turbulent premixed flames through use of rapid distortion theory or an unsteady Bernoulli equation. This could lead to a new second order closure for turbulent premixed flames. The second finding was contrary to our measurements with laser diagnostics in lean hydrocarbon flames where it is found that conditional scalar dissipation drops dramatically below that for laminar flamelets when the turbulence intensity becomes high. Such behavior was not explainable with a one-step kinetic model, even at non-unity Lewis number. It could be due to depletion of H2 from the reaction zone by preferential diffusion. The capacity of the flame to generate radicals is critically dependent on the levels of H2 present (Bilger, et al., 1991). It seemed that a DNS computation with a multistep reduced mechanism would be worthwhile if a way could be found to make this feasible. Truly innovative approaches to complex problems often come only when there is the opportunity to work close at hand with the (in this case numerical) experimental data. Not only can one spot patterns and relationships in the data which could be important, but one can also get to know the limitations of the technique being used, so that when the next experiment is being designed it will address resolvable questions. A three-year grant from the Australian Research Council has enabled us to develop a small capability at the University of Sydney to work on DNS of turbulent reacting flow, and to analyze data bases generated at CTR. Collaboration between the University of Sydney and CTR is essential to this project and finding a workable modus operandum for this collaboration, given the constraints involved, has been a major objective of the past year's effort. The overall objectives of the project are: (1) to obtain a quantitative understanding of the dynamics of turbulent premixed flames at high turbulence levels with a view to developing improved second order closure models; and (2) to carry out new DNS experiments on turbulent premixed flames using a carefully chosen multistep reduced mechanism for the chemical kinetics, with a view to elucidating the laser diagnostic findings that are contrary to the findings for DNS using one-step kinetics. In this first year the objectives have been to make the existing CTR data base more accessible to coworkers at the University of Sydney, to make progress on understanding the dynamics of the flame in this existing CTR data base, and to carefully construct a suitable multistep reduced mechanism for use in a new set of DNS experiments on turbulent premixed flames.

Bilger, R. W.↗

Chemistry and transport in a multi-dimensional model

The focus of our research program is the achievement of a quantitative understanding of the spatial distribution and temporal variation of chemical species in the terrestrial middle atmosphere, with emphasis on ozone. Although not directed at assessments of anthropogenic impacts, our activities contribute to a refinement of model descriptions of chemical and dynamical processes that are needed for assessment tasks. A unique feature of our research effort is a close interaction with the chemical kinetics group at JPL and the field measurement groups at JPL. The principal tools used in our investigations are l-D and 2-D photochemical models. The advective component of the meridional transport in these models is approximated by the diabatic circulation, which is derived diagnostically from the net radiative heating rates. We are developing accurate radiative transfer algorithms to find the net heating rates and the diabatic circulation for use in the 2-D model.

Yung, Yuk L.↗

Flame Flashback Investigations in Hydrogen-Enriched Low Swirl Burner using High-Speed Hydroxyl Planar Laser-Induced Fluorescence

Hydrogen/ Hydrogen-rich flame is a potential strategy to reduce carbon emissions for the development of next-generation lean premixed combustors. However, the higher flashback propensity with hydrogen-enrichment owing to faster chemical kinetics is one of the key challenges in existing natural gas turbine combustors. In this study, the fundamentals of stabilized flame dynamics and flashback events in a premixed low swirl burner (LSB) configuration are visualized experimentally using nanosecond (ns)-based high-speed hydroxyl radical planar laser-induced fluorescence (OH-PLIF). The LSB has an optically accessible pre-mixing tube allowing laser diagnostic investigation of flashback events. The inlet conditions are varied systematically with respect to pre-mixer velocities, flame equivalence ratio (ϕ), and hydrogen content and OH-PLIF characterization is performed in stable flame at 20 kHz repetition rate. An increase in flashback propensity is observed with increasing ϕ, hydrogen content, and decreasing V via detailed investigation of flame lift-off length (L) above the burner rim. Flashback ϕ investigations show an expected linearly increasing trend with decreasing hydrogen content and increasing V for each swirler studied and the results agree well with detailed L investigations in stable flame configuration. The propagating flame anchored likely on the back side of the perforated plate within 30-40 ms of the entrance forming the distorted conical flame front.

Parajuli, Pradeep↗

Predictive Modeling of Fast-Curing Thermosets in Nozzle-Based Extrusion

This work presents an approach to modeling the dynamic spreading and curing behavior of thermosets in nozzle-based extrusions. Thermosets cover a wide range of materials, some of which permit low-temperature processing with subsequent high-temperature and high-strength working properties. Extruding thermosets may overcome the limited working temperatures and strengths of conventional thermoplastic materials used in additive manufacturing. This project aims to produce technology for the fabrication of thermoset-based structures leveraging advances made in nozzle-based extrusion, such as fused deposition modeling (FDM), material jetting, and direct writing. Understanding the synergistic interactions between spreading and fast curing of extruded thermosetting materials will provide essential insights for applications that require accurate dimensional controls, such as additive manufacturing [1], [2] and centrifugal coating/forming [3]. Two types of thermally curing thermosets -- one being a soft silicone (Ecoflex 0050) and the other being a toughened epoxy (G/Flex) -- served as the test materials in this work to obtain models for cure kinetics and viscosity. The developed models align with extensive measurements made with differential scanning calorimetry (DSC) and rheology. DSC monitors the change in the heat of reaction, which reflects the rate and degree of cure at different crosslinking stages. Rheology measures the change in complex viscosity, shear moduli, yield stress, and other properties dictated by chemical composition. By combining DSC and rheological measurements, it is possible to establish a set of models profiling the cure kinetics and chemorheology without prior knowledge of chemical composition, which is usually necessary for sophisticated mechanistic modeling. In this work, we conducted both isothermal and dynamic measurements with both DSC and rheology. With the developed models, numerical simulations yielded predictions of diameter and height of droplets, along with width and height of extruded lines cured at varied temperatures. Experimental results carried out on a goniometric platform and a nozzle-based 3D printer showed agreement with the numerical simulations. Finally, this presentation will show how the models are adaptable to the planning of tool paths and designs in additive manufacturing.

Xie, Jingjin↗

Static and Dynamic Gradient Based Directional Transportation of Neutral Molecules in Swollen Polymer Films

Abstract Materials which selectively transport molecules offer powerful opportunities for concentrating and separating chemical agents. Here, utilizing static and dynamic chemical gradients, transport of molecules within swollen crosslinked polymers is demonstrated. Using an ≈200 μm static hydroxyl to hexyl gradient, the neutral ambipolar nerve agent surrogate diethyl (cyanomethyl)phosphonate (DECP) is directionally transported and concentrated 60‐fold within 4 hours. To accelerate transport kinetics, a dynamic gradient (a “travelling wave”) is utilized. Here, the non‐polar dye pyrene was transported. The dynamic gradient is generated by an ion exchange process triggered by the localized introduction of an aqueous NaCl solution, which converts the gel from hydrophobic to hydrophilic. As the hydrophilic region expands, associated water enters the gel, and pyrene is pushed ahead of the expansion front. The dynamic gradient provides about 10‐fold faster transport kinetics than the static gradient.

Ali, Mohammad A.↗

Stiff neural ordinary differential equations

Neural Ordinary Differential Equations (ODEs) are a promising approach to learn dynamical models from time-series data in science and engineering applications. This work aims at learning neural ODEs for stiff systems, which are usually raised from chemical kinetic modeling in chemical and biological systems. We first show the challenges of learning neural ODEs in the classical stiff ODE systems of Robertson’s problem and propose techniques to mitigate the challenges associated with scale separations in stiff systems. We then present successful demonstrations in stiff systems of Robertson’s problem and an air pollution problem. The demonstrations show that the usage of deep networks with rectified activations, proper scaling of the network outputs as well as loss functions, and stabilized gradient calculations are the key techniques enabling the learning of stiff neural ODEs. The success of learning stiff neural ODEs opens up possibilities of using neural ODEs in applications with widely varying time-scales, such as chemical dynamics in energy conversion, environmental engineering, and life sciences.

97 MATHEMATICS AND COMPUTING↗

Elucidation of the physical factors that control activated transport of penetrants in chemically complex glass-forming liquids

Understanding the activated transport of penetrant or tracer atoms and molecules in condensed phases is a challenging problem in chemistry, materials science, physics, and biophysics. Many angstrom- and nanometer-scale features enter due to the highly variable shape, size, interaction, and conformational flexibility of the penetrant and matrix species, leading to a dramatic diversity of penetrant dynamics. Based on a minimalist model of a spherical penetrant in equilibrated dense matrices of hard spheres, a recent microscopic theory that relates hopping transport to local structure has predicted a novel correlation between penetrant diffusivity and the matrix thermodynamic dimensionless compressibility, S 0 ( T ) (which also quantifies the amplitude of long wavelength density fluctuations), as a consequence of a fundamental statistical mechanical relationship between structure and thermodynamics. Moreover, the penetrant activation barrier is predicted to have a factorized/multiplicative form, scaling as the product of an inverse power law of S 0 ( T ) and a linear/logarithmic function of the penetrant-to-matrix size ratio. This implies an enormous reduction in chemical complexity that is verified based solely on experimental data for diverse classes of chemically complex penetrants dissolved in molecular and polymeric liquids over a wide range of temperatures down to the kinetic glass transition. The predicted corollary that the penetrant diffusion constant decreases exponentially with inverse temperature raised to an exponent determined solely by how S 0 ( T ) decreases with cooling is also verified experimentally. Our findings are relevant to fundamental questions in glassy dynamics, self-averaging of angstrom-scale chemical features, and applications such as membrane separations, barrier coatings, drug delivery, and self-healing.

Science & Technology - Other Topics↗

Investigating the Effects of Chemical Mechanism on Soot Formation Under High-Pressure Fuel Pyrolysis

We performed Computational Fluid Dynamics (CFD) simulations using a Reynolds-Averaged Navier-Stokes (RANS) turbulence model of high-pressure spray pyrolysis with a detailed chemical kinetic mechanism encompassing pyrolysis of n-dodecane and formation of polycyclic aromatic hydrocarbons. We compare the results using the detailed mechanism and those found using several different reduced chemical mechanisms to experiments carried out in an optically accessible, high-pressure, constant-volume combustion chamber. Three different soot models implemented in the CONVERGE CFD software are used: an empirical soot model, a method of moments, and a discrete sectional method. There is a large variation in the prediction of the soot between different combinations of chemical mechanisms and soot model. Furthermore, the amount of soot produced from all models is substantially less than experimental measurements. All of this indicates that there is still substantial work that needs to be done to arrive at simulations that can be relied on to accurately predict soot formation.

02 PETROLEUM↗

Characterization of a swept-strut hydrogen fuel-injector for scramjet applications

Results of an experimental investigation of a swept-strut hydrogen fuel-injector simulating the center strut of a three strut scramjet module at Mach 6 flight conditions are presented. Detailed wall pressure distributions from over 100 separate tests with overall fuel flow from 0.1 to 1.3 times stoichiometric and test gas stagnation temperature from 1100 to 2400 K were recorded. The distance for pressure rise from the point of injection was found to increase with increasing test stagnation temperature. This trend indicates that chemical kinetics in the immediate region of perpendicular injection are not likely to be the mechanism controlling the onset of pressure rise. A fluid dynamic mechanism is suggested involving separation of the boundary layer downstream of injection which is forced upstream from the trailing edge by pressure rise due to combustion occurring in the base region of the strut. The results obtained indicate that the swept-strut fuel-injector concept can be adapted to a wide range of flight conditions by varying the amount of perpendicular fuel injection.

Northam, G. B.↗

Premixed Gas Combustion: An Excitable System

Rotating spiral and target patterns have been observed experimentally on freely-propagating premixed gas flames in large diameter tubes at normal gravity (1-g). These modes of propagation occur in near-limit mixtures which have a Lewis number (Le, defined as the ratio of the thermal diffusivity of the cold mixture to the mass diffusivity of the scarce component into the mixture) sufficiently greater than one. However, at 1-g, buoyant flows strongly distort the flame curvature, hydrodynamics (thus stretch) and convective transport of species and heat. In turn, these alter the critical Le required for onset of instability. To isolate and better understand the mechanisms which drive the observed patterns and their dynamics, 1-g and microgravity (micro-g) experiments are being conducted to determine: (1) the structure and dynamics of the patterns, (2) a map of the critical Le and heat loss for their occurrence, (3) the relative significance of the chemical kinetics, and (4) the effect of curvature (local wave and global flame front) on wave propagation. With this in hand, we will be better prepared to discuss an additional mode, a state of 'chemical turbulence,' which seems to be the ultimate fate of many of these near-limit flames prior to extinction.

Pearlman, Howard↗

Large-Eddy Simulation Study of Flow and Combustion Dynamics in a Full-Scale Hydrogen–Air Rotating Detonation Combustor-Stator Integrated System

In the present work, a first-of-its-kind three-dimensional (3D) large-eddy simulation (LES) study is conducted to numerically investigate the combustion dynamics as well as aero-thermal phenomena in a full-scale nonpremixed hydrogen–air rotating detonation engine (RDE) (with a diverging-shaped lower-end wall), when integrated with nozzle guide vanes (NGV) acting as the turbine stator. The wall-modeled LES framework incorporates hydrogen–air detailed chemical kinetics and adaptive mesh refinement (AMR). A comparative analysis is carried out for two operating conditions with different fuel/air mass flow rates but global equivalence ratio of unity, and considering RDE configurations without and with stator. The LES model is validated against available experimental data for the low mass flux condition with respect to detonation wave speed/height, wave dynamics, and axial static pressure distribution. Numerical results indicate significant deflagrative combustion occurring in the fill region near the inner wall due to formation of recirculation zones in the injection near-field driven by the backward facing step. The leading detonation wave is found to be trailed by an azimuthal reflected-shock combustion (ARSC) wave, consistent with experimental observations, which consumes unburned vitiated reactants that leak through the main detonation wave. The main detonation wave characteristics, such as detonation wave speed/height and combustion efficiency, do not change appreciably with the presence of NGV. A novel combustion diagnostic technique based on chemical explosive mode analysis (CEMA) is employed to quantify the fraction of heat release occurring in the detonative mode versus deflagrative mode for the simulated conditions. The exit flow is found to be nearly fully subsonic and supersonic for the low and high mass flux conditions, respectively. Further analysis of the exit flow profiles shows that the presence of NGV renders the flow more axial and significantly impacts the exit Mach number and total pressure, while the total temperature shows negligible change. In addition, the low mass flux operating point, despite exhibiting more deflagrative losses within the combustor, yields overall lower pressure drop from plenum to exhaust, which is mainly attributed to lower pressure drop across the injectors. Lastly, the rotating detonation engine-nozzle guide vanes (RDE-NGV) configuration exhibits higher total pressure loss compared to rotating detonation engine (RDE) without stator across both the mass flux conditions. In conclusion, this study extends the state-of-the-art in numerical modeling of pressure gain combustion (PGC) systems by demonstrating high-fidelity 3D reacting LES of full-scale RDE-NGV systems relevant to RDE-turbine integration for stationary power generation.

Combustion↗

Why are Lead Iodide‐Based Perovskite Precursor Inks Yellow?

A challenge faced by metal halide perovskite (MHP) photovoltaics is scaling up solution deposition processes to realize rapid and inexpensive manufacturing. The challenge lies in completely understanding and controlling solution speciation, nucleation, and self-assembly of iodoplumbate complexes during solvent evaporation as the liquid transforms into gels and solids. An accurate description of solution species, at all points in the transformation, is a prerequisite to design robust and reliable processes. Here, in this study, the common assumption that initial monoplumbate solution species typically invoked (e.g., [PbI 6 ] 4− ) are certainly not the origin of optical absorbance at >400 nm wavelengths is disproved, as are many large particles of common “intermediate” iodoplumbate phases with face- or edge-sharing connectivity. Instead, a new perspective is offered, involving (partially) corner-sharing iodo(poly)plumbates (>1 Pb 2+ per complex) that experience highly dynamic chemical environments. It is outlined how the MHP field would benefit by elucidating these phenomena. Future work is required to determine the size and kinetic behavior of polyplumbate species, and contextualize these findings in relation to broader trends in materials chemistry beyond MHPs. Ultimately, a complete explanation for the solution speciation, optical absorbance signatures, and the color of MHP precursor inks remains an open challenge to the community.

14 SOLAR ENERGY↗

Characterization of a new ultra-high pressure shock tube facility for combustion and propulsion studies

A new shock tube facility has been designed, constructed, and characterized at the University of Central Florida. This facility is capable of withstanding pressures of up to 1000 atm, allowing for combustion diagnostics of extreme conditions, such as in rocket combustion chambers or in novel power conversion cycles. For studies with toxic gas impurities, the high initial pressures required the development of a gas delivery system to ensure the longevity of the facility and the safety of the personnel. Data acquisition and experimental propagation were implemented with remote access to ensure safety, paired with a LabVIEW- and Python-based user interface. Thus far, test pressures of 270 atm, blast pressures of 730 atm, and temperatures approaching 10 000 K have been achieved. The extreme limitations of this facility allow for emission spectroscopy to be performed during the oxidation of fuel mixtures, e.g., alkanes diluted in argon and carbon dioxide. Ignition delay times were determined and compared to simulations using chemical kinetic mechanisms. The design, experimental procedures, processes of analysis, and uncertainty determination are outlined, and typical pressure profiles are compared with a new gas dynamics solver and empirical correlations developed across multiple shock tube facilities. Preliminary reactive mixture analyses are included with further investigation of the mixtures outlined.

47 OTHER INSTRUMENTATION↗

Spontaneous Reorganization of DNA-Based Polymers in Higher Ordered Structures Fueled by RNA

We demonstrate a strategy that allows for the spontaneous reconfiguration of self-assembled DNA polymers exploiting RNA as chemical fuel. To do this, we have rationally designed orthogonally addressable DNA building blocks that can be transiently deactivated by RNA fuels and subtracted temporarily from participation in the self-assembly process. Through a fine modulation of the rate at which the building blocks are reactivated we can carefully control the final composition of the polymer and convert a disordered polymer in a higher order polymer, which is disfavored from a thermodynamic point of view. We measure the dynamic reconfiguration via fluorescent signals and confocal microscopy, and we derive a kinetic model that captures the experimental results. Our approach suggests a novel route toward the development of biomolecular materials in which engineered chemical reactions support the autonomous spatial reorganization of multiple components.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mechanistic study of chemical looping reactions between solid carbon fuels and CuO

Copper (Cu) based chemical-looping combustion (CLC) is a promising process that utilizes solid carbon fuel such as coal and biomass. Understanding the reaction kinetics in this process can facilitate the industrial design of CLC units. Here, in this work, molecular dynamics (MD) simulations were performed to investigate the reaction kinetics of n-butane and two simplified solid carbon fuels (lignite and anthracite) with/without copper oxide (CuO) nanoparticle. In addition, experiments were conducted on the thermal characteristics, flammability, and flame speeds of CuO and solid carbon mixtures. For n-butane, oxidation on the CuO surface is the primary reaction since the activation energy of the surface reaction is much lower than that of oxygen (O 2 ) combustion (9.2 vs. 53.3 kcal/mol). On the other hand, for lignite, there is a smaller difference in the activation energy of O 2 combustion and surface reaction (23.04 vs. 6.34 kcal/mol). We hypothesize that some solid carbon fuels can have different reaction kinetics dependent upon temperature. This is proven by the case of a simplified anthracite coal: an Arrhenius plot shows that this solid carbon fuel has two different reaction kinetic regimes and the critical temperature for the change in kinetics is related to the oxygen uncoupling of the CuO nanoparticle. Like the modeling simulations, a change in activation energy is observed in the experimental results, where desorption of molecular oxygen from CuO becomes important.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Elucidating the Interfacial Barriers in Lanthanide Back-Extraction: From Water to Oil and Back Again

Recovery of critical rare earth elements from complex mixtures has long been realized via solvent extraction, where ions in an aqueous phase are separated into an organic phase using amphiphilic ligands. While a great deal of effort has been placed on understanding this forward reaction, substantial knowledge gaps in the back-extraction process remain. This includes the mechanism of interfacial dissociation and transport back into a highly acidic aqueous phase for further processing. In this work, we connect back-extraction kinetics made in realistic solvent extraction systems to salient interfacial chemistry and structure that represent bottlenecks in the back-extraction of lanthanide ions. We show that the interface between the two liquid phases varies dramatically based on the composition of both phases. Water stretching signals are shown to report on the population of lingering interfacial complexes and are thus used as a reporter of competitive adsorption from excess free ligands in solution for limited interfacial vacancies. We show that excess free ligands, often used to improve forward extractions, set up interfacial blockades inhibiting back-extraction both kinetically and thermodynamically. In conclusion, this insight opens up avenues to tune interfacial properties to facilitate a more dynamic, exchangeable interface to speed up back-extractions while using less energy intensive chemical swings.

Interfaces↗

Liquid rocket combustor computer code development

The Advanced Rocket Injector/Combustor Code (ARICC) that has been developed to model the complete chemical/fluid/thermal processes occurring inside rocket combustion chambers are highlighted. The code, derived from the CONCHAS-SPRAY code originally developed at Los Alamos National Laboratory incorporates powerful features such as the ability to model complex injector combustion chamber geometries, Lagrangian tracking of droplets, full chemical equilibrium and kinetic reactions for multiple species, a fractional volume of fluid (VOF) description of liquid jet injection in addition to the gaseous phase fluid dynamics, and turbulent mass, energy, and momentum transport. Atomization and droplet dynamic models from earlier generation codes are transplated into the present code. Currently, ARICC is specialized for liquid oxygen/hydrogen propellants, although other fuel/oxidizer pairs can be easily substituted.

Liang, P. Y.↗