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At least 451 records · Page 25

Simulation of a rapid compression machine for evaluation of ignition chemistry and soot formation using gasoline/ethanol blends

Due to the projected decline of demand for gasoline in light duty engines and the advent of ethanol as a green fuel, the use of gasoline/ethanol blend fuels in heavy duty applications are being investigated as they are projected to have lower cost and lower lifecycle green house gas (GHG) emissions. In heavy duty engines, the primary mode of combustion is mixing controlled combustion where wide range of mixture conditions (equivalence ratio) exist. Soot emissions of these fuels in richer conditions are not well understood. The goal of this research is to evaluate some commercially available soot modeling codes for the particulate matter emissions from gasoline/ethanol fuel blends, especially at fuel rich conditions. A Rapid Compression Machine (RCM) is modeled in a three-dimensional numerical simulation using CONVERGE computational software using a reduced chemical kinetic mechanism with SAGE chemistry solver and a RANS k-ϵturbulence model with a sector model including the creviced piston. The creviced piston is used in the experimental setup to reduce boundary layer effects and to maintain a homogeneous core in the reaction cylinder. Computational fluid dynamics simulations are conducted for different gasoline-ethanol fuel blends from E10 (10% ethanol v/v) to E100. The fuel blend is modeled as a surrogate mixture of toluene, iso-octane, n-heptane for gasoline content, and ethanol. The computational results were validated against experimental results using pressure measurements and laser extinction diagnostics. Different soot models are investigated to evaluate their capability of predicting the sooting tendencies of fuel blends, especially in richer conditions experienced during mixing-controlled combustion. The experimental combustion characteristics such as the ignition delay of different blends of fuel are reasonably well predicted. The Particulate Size Mimic (PSM) model accurately predicts the soot generation characteristics of the different fuels, but the Hiroyasu-NSC model falls short in this regard. For accurate prediction of soot with the PSM model, the thermodynamic conditions during combustion must be accurately modeled. While the current computational modeling tools can produce accurate results for the prediction of particulate matter emissions, there is much work to be done in improving our understanding of the underlying fundamental processes.

Energy & Fuels↗

Experimental and fuel-surrogates modeling study of the high-pressure pyrolysis of specialty cetane number fuels: implications for fall-off in ethylene unimolecular dissociation

Single pulse shock tube experiments were conducted at 50 atm nominal pressure and 4 ms nominal reaction time over a temperature range of 900–1800 K, to study the pyrolysis speciation of a multi-component jet fuel, F-24, and six cetane number (CN) specialty fuels - CN30, CN35, CN40, CN45, CN50, and CN55. Gas chromatography (GC) was used to qualitatively and quantitatively analyze the post shock gases. The relationship between the formation of key pyrolysis species and the chemically controlled combustion propensity as reflected by the cetane number of each fuel was examined. A surrogate-based mechanism from the CRECK Modelling Group and chemical-functional group based optimized surrogates (CFGO) were used to simulate the pyrolysis speciation results. The model was able to capture the chemistry of most species except two important pyrolysis intermediates – ethylene and acetylene. Chemical kinetic analyses were performed to identify the important reactions which affect the chemistry of these species; however, the rate parameters of critical reactions were found to be unsuitable for simulating the present high-pressure studies. Here, to address this unsuitability, a theory-based fall-off analysis for three reactions representing the decomposition of ethylene and subsequent formation of acetylene was performed, and these are included in an updated version of the CRECK mechanism. This update resolves discrepancies between the experimental results and simulations for ethylene and acetylene. Reaction flux analyses using the updated surrogate model were also performed to identify the important reaction pathways responsible for the formation of crucial species and to provide an analysis of the chemistry of complex multi-component fuel systems. The fundamental reactions responsible for driving pyrolysis chemistry were greatly influenced by the chemical functional groups present in these fuels. In addition to updating the rate parameters of specific reactions to improve modeling, this study also emphasizes the effectiveness of the fuel-surrogate approach, where surrogates representing the chemical functional group composition of the parent fuel serve as a valuable tool for predicting the combustion chemistry of novel fuels.

Chemical Kinetics↗

Implementation of new mixture rules has a substantial impact on combustion predictions for H 2 and NH 3

Complex-forming reactions comprise a substantial fraction of all important combustion reactions and are central to combustion behavior. Despite being often called “pressure-dependent” reactions, their rate constants depend on not only the pressure but also the composition. While modern combustion codes allow arbitrarily high accuracy in treating pressure dependence, recent work has consistently demonstrated dramatic failures of essentially all available treatments of mixture dependence. In situations where mixture dependence is treated at all, it is inevitably treated through specification of pressure-dependent rate constants for a set of pure bath gases, which are then combined to estimate the rate constant in a mixture via a “mixture rule.” While there had been a generally unquestioning confidence in these mixture rules, they had, in reality, been scarcely tested until the last decade, when comparisons against master equation calculations revealed order-of-magnitude errors for important pressure-dependent reactions. New mixture rules, based on the reduced pressure, have recently been proposed and shown to reproduce master equation calculations for broad classes of complex-forming reactions very accurately. Here, in this work, we present an implementation of one such new mixture rule (“LMR-R”) in Cantera and then use it to enable simulations that use new high-accuracy ab initio data for individual bath gases (for the first time, since codes previously could not accommodate the complex bath gas dependence). Demonstrations focus on combustion of H 2 and NH 3 , where (1) high-accuracy ab initio data are available and (2) the impact is expected to be large due to the high fractions of efficient colliders (e.g., H 2 O and NH 3 ) in the burned and unburned gases. Indeed, we find the impact of this treatment to be substantial and may explain previous modeling difficulties for these important carbon-free fuels, particularly for NH 3 , whose extraordinarily high third-body efficiency (~20) is often omitted from kinetic models.

Ammonia↗

Development of Novel Combustion Codes for Supercritical CO2 Combustion: Cooperative Research and Development Final Report, CRADA Number CRD-20-17182

The Allam-Fetvedt Cycle, a novel supercritical CO2 (sCO2) power cycle developed by 8 Rivers Capital, LLC, generates low-cost power from fossil fuels while capturing combustion-CO2. This cycle employs high-temperature oxy-combustion using sCO2 as the working fluid, leading to a challenging environment for materials. The most critical component for reliable deployment of this technology is the combustor-turbine interface. In the proposed partnership between NREL and 8 Rivers, we will develop a simulation-based tool to provide key design inputs for defining the materials and geometries required in this critical area.

09 BIOMASS FUELS↗

Aviation Fuel Characterization at Operationally Relevant Conditions

To accelerate approval and potentially expand the allowable property range for aviation fuels, we are using high performance computing simulations to reveal fuel property effects on aviation combustor performance. These simulations are supported by fuel property measurements over temperatures and pressures that the fuel experiences in an aircraft engine and by validated chemical kinetics models for SAF combustion. Here we report density, viscosity, and surface tension results for conventional jet fuel and multiple synthetic fuels from -30 degrees Celsius to 200 degrees Celsius (-40 degrees Celsius for viscosity) and 1 atm to 70 atm including an assessment of method repeatability. Properties of surrogate mixtures are also investigated. Distillation, ICN, LHV, flashpoint, and Cp are also reported, and data are being used to develop models to predict fuel properties from composition (GCxGC).

33 ADVANCED PROPULSION SYSTEMS↗

Computational Risk Analysis of Propane Releases in Maintenance Facilities

Liquefied petroleum gas (LPG) is a viable, cleaner alternative to traditional diesel fuel used in busses and other heavy-duty vehicles and could play a role in helping the US meet its lower emission goals. While the LPG industry has focused efforts on developing vehicles and fueling infrastructure, we must also establish safe parameters for maintenance facilities which are servicing LPG fueled vehicles. Current safety standards aid in the design of maintenance facilities, but additional quantitative analysis is needed to prove safeguards are adequate and suggest improvements where needed. In this report we aim to quantify the amount of flammable mass associated with propane releases from vehicle mounted fuel vessels within enclosed garages. Furthermore, we seek to qualify harm mitigation with variable ventilations and facility layout. To accomplish this we leverage validated computational resources at Sandia National Laboratories to simulate various release scenarios representative of real world vehicles and maintenance facilities. Flow solvers are used to predict the dynamics of fuel systems as well as the evolution of propane during release events. From our simulated results we observe that both inflow and outflow ventilation locations play a critical role in reducing flammable cloud size and potential overpressure values during a possible combustion event.

03 NATURAL GAS↗

Experimental Insights into the Coupling of Methane Combustion and Steam Reforming in a Catalytic Plate Reactor in Transient Mode

The microstructured reactor concept is very promising technology to develop a compact reformer for distributed hydrogen generation. In this work, a catalytic plate reactor (CPR) is developed and investigated for the coupling of methane combustion (MC) and methane steam reforming (MSR) over Pt/Al 2 O 3 -coated microchannels in cocurrent and counter-current modes in transient experiments during start-up. A three-dimensional (3D) computational fluid dynamics (CFD) simulation shows uniform velocity and pressure distribution profiles in microchannels. For a channel velocity from 5.1 to 57.3 m/s in the combustor, the oxidation of methane is complete and self-sustainable without explosion, blow-off, or extinction; nevertheless, flashbacks are observed in counter-current mode. In the reformer, the maximum methane conversion is 84.9% in cocurrent mode, slightly higher than that of 80.2% in counter-current mode at a residence time of 33 ms, but at the cost of three times higher energy input in the combustor operating at ~1000 °C. Nitric oxide (NO) is not identified in combustion products, but nitrous oxide (N 2 O) is a function of coupling mode and forms significantly in cocurrent mode. Furthermore, this research would be helpful to establish the start-up strategy and environmental impact of compact reformers on a small scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Comparing Cetane Number Measurement Methods

Cetane number is one of the most important fuel performance metrics for mixing controlled compression-ignition “diesel” engines, quantifying a fuel’s propensity for autoignition when injected into end-of-compression-type temperature and pressure conditions. The historical default and referee method on a Cooperative Fuel Research (CFR) engine configured with indirect fuel injection and variable compression ratio is cetane number (CN) rating. A subject fuel is evaluated against primary reference fuel blends, with heptamethylnonane defining a low-reactivity endpoint of CN = 15 and hexadecane defining a high-reactivity endpoint of CN = 100. While the CN scale covers the range from zero (0) to 100, typical testing is in the range of 30 to 65 CN. Alternatively, several constant-volume combustion chamber (CVCC)-based cetane rating devices have been developed to rate fuels with an equivalent derived cetane number (DCN) or indicated cetane number (ICN). These devices measure ignition delay for fuel injected into a fixed volume of high-temperature and high-pressure air to simulate end-of-compression-type conditions. In this study, a range of novel fuel compounds are evaluated across three CVCC methods: the Ignition Quality Tester (IQT), Fuel Ignition Tester (FIT), and Advanced Fuel Ignition Delay Analyzer (AFIDA). Resulting DCNs and ICNs are compared for fuels within the normal diesel fuel range of reactivity, as well as very high (~100) and very low DCNs/ICNs (~5). Distinct differences between results from various devices are discussed. This is important to consider because some new, high-efficiency advanced compression-ignition (CI) engine combustion strategies operate with more kinetically controlled distributed combustion as opposed to mixing controlled diffusion flames. These advanced combustion strategies may benefit from new fuel chemistries, but current rating methods of CN, DCN, and ICN may not fully describe their performance. In addition, recent evidence suggests ignition delay in modern on-road diesel engines with high-pressure common rail fuel injection systems may no longer directly correlate to traditional CN fuel ratings. Simulated end-of-compression conditions are compared for CN, DCN, and ICN and discussed in the context of modern diesel engines to provide additional insight. Results highlight the potential need for revised and/or multiple fuel test conditions to measure fuel performance for advanced CI strategies.

47 OTHER INSTRUMENTATION↗

Impact of Detailed Parameter Modeling of Open-Cycle Gas Turbines on Production Cost Simulation: Preprint

Flexible resources are increasingly important as variable renewable energy deployment in the power system increases. Although many systems are transitioning away from fossil fuels, open-cycle gas turbines are likely to play an important balancing role for some time, thus requiring accurate modeling of their operational parameters. This paper explores the impact of detailed representation of three operational parameters - start- up costs, run-up rates, and forced outage rates - in the production cost model of a system as it adopts higher levels of wind and solar. Using PLEXOS simulations of the NREL-118 bus test system, the study examines how more detailed parameter modeling affects outcomes such as the number of start-ups and shutdowns, ramping and total generation costs for open-cycle gas turbines, as renewable energy levels increase. The results suggest the value of detailed parameter modeling and continued research on combustion turbines' ability to provide flexibility.

economic dispatch↗

CFD modeling of pre-spark heat release in a boosted direct-injection spark-ignition engine

Accurate predictions of low-temperature heat release (LTHR) are critical for modeling auto-ignition processes in internal combustion engines. While LTHR is typically obscured by deflagration, extremely late ignition phasing can lead to LTHR prior to the spark, a behavior known as pre-spark heat release (PSHR). In this research, PSHR in a boosted direct-injection spark-ignition engine was studied using 3-D computational fluid dynamics (CFD) and detailed chemical kinetics. The turbulent combustion was modeled via a hybrid approach that incorporates the G-equation model for tracking the turbulent flame front, and the well-stirred reactor model with detailed chemistry for assessing the low-temperature reactions in unburnt gas. Simulations were conducted using Co-Optima alkylate and E30 fuels at operating conditions characterized by different PSHR intensities. The predicted in-cylinder pressure and heat release rate were found to agree well with experiments. It was found the estimate of previous-cycle trapped residuals is of utmost importance for capturing PSHR correctly. A simulation best practice was developed which keeps the detailed chemistry solver active throughout the entire simulation, allowing to track the evolution of intermediate species from one cycle to the next. Following the validation, the dynamics of PSHR were analyzed in detail employing the pressure-temperature (P-T) trajectory framework. It was shown that PSHR correlated with the first-stage ignition delay of the fuel, hence showing close relation to the in-cylinder P-T trajectory and the chemical kinetics. Besides, it was indicated that LTHR is a self-limiting process that has the effect of attenuating the thermal stratification in the combustion chamber. Furthermore, it was observed the occurrence of PSHR caused the P-T trajectory of end-gas to overlap with the negative temperature coefficient region of the fuel’s ignition-delay maps. This effect was more significant in the fuel-rich regions where engine knock tendency would be generally higher, with potential implications on knock control and mitigation.

42 ENGINEERING↗

Evaluation of semi-empirical soot models for nonpremixed flames with increased stoichiometric mixture fraction and strain

Due to the size and complexity of industrial-scale systems and computing limitations, semi-empirical soot models are often employed in CFD simulations rather than computationally-expensive detailed models. Many of these models were developed for specific applications with unique characteristic timescales and/or validated only under fuel-air combustion conditions. Hence, their use in different contexts, such as oxy-combustion, could lead to inaccurate predictions. In this study, twelve semi-empirical models (1-step or 2-step) are evaluated on their ability to respond to changes in stoichiometric mixture fraction (Z st ) and strain in a series of ethylene counterflow flames which span the experimental sooting-to-non-sooting (yellow to blue) transition. A unique approach of plotting soot formation rate in normalized, local equivalence ratio space is introduced to aid in the analysis. Results show that no existing model is able to predict a blue flame when Z st is increased beyond the experimentally-measured sooting limit. Many models give the counter-intuitive result of increasing peak and/or integrated soot volume fraction (svf) as Z st increased, contrary to experimental observations. Two models are able to successfully predict a blue flame upon increase of strain to the sooting limit value. For two-step models, the strong dependence of growth rate on surface area results in high sensitivity of svf to changing flame boundary conditions, but with mixed accuracy. There is still a significant need for a robust semi-empirical model which can accurately predict soot fraction in systems with oxygen-enrichment or variable strain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling of the effects of non-equilibrium excitation and electrode geometry on H 2 /air ignition in a nanosecond plasma discharge

In this work, we present the results of two-dimensional modeling of the effects of non-equilibrium excitation and electrode geometry on H 2 /air ignition in a nanosecond plasma discharge. A multiscale adaptive reduced chemistry solver for plasma assisted combustion (MARCS-PAC) based on PASSKEy discharge modeling package and compressible multi-component reactive flow solver ASURF+ is developed and validated. This model is applied to simulate the impact of non-equilibrium plasma excitation and electrode geometry and heat loss on the dynamics of the discharge from streamer to spark and ignition kernel development in a H 2 /air mixture with a pair of cylindrical electrodes. The results show that the plasmagenerated species (N 2 (A), N 2 (B), N 2 (a'), N 2 (C), O( 1 D), O and H) in the spark and afterglow significantly accelerate the ignition kernel development. The increase of discharge voltage at the same total discharge energy promotes the non-equilibrium active species production. It is found that the production of electronically excited species at higher reduced electric field strength is more efficient in enhancing ignition in comparison to the vibrational excitation and heating. Moreover, the 2D simulation clearly reveals that the electric field and active species distribution are highly non-uniform. The streamers are initiated at the sharp outer edges of the negative and positive electrodes by a strong electric field while the electric field is much weaker at the centerline of the electrodes. Furthermore, the simulations reveal that the ignition enhancement is sensitive to the variation of electrode shape, diameter, and gap size due to the changes of electric field distribution and location of streamer formation. A cylindrical electrode produces a larger discharge volume and ignition kernel than the parabolic and spherical electrodes, when the discharge is localized near the axis of the gap. It is found that there is a non-monotonic dependence of ignition kernel size on the electrode diameter and inter-electrode distance. The increase of electrode diameter and gap size above the optimal conditions leads to the reduction of ignition kernel volume, due to the decrease of active species concentration and gas temperature. At a larger electrode surface area and electrode diameter as well as smaller electrode gap size, the heat loss to electrode plays a greater role in reducing the ignition kernel size and slowing ignition kernel development. This work provides insights and guidance to understand the kinetic enhancement of non-equilibrium plasma and the effects of electrode geometries on ignition for the optimization ignitors in advanced engines.

42 ENGINEERING↗

Real-fluid behavior in rapid compression machines: Does it matter?

Rapid compression machines (RCMs) have been extensively used to quantify fuel autoignition chemistry and validate chemical kinetic models at high-pressure conditions. Historically, the analyses of experimental and modeling RCM autoignition data have been conducted based on the adiabatic core hypothesis with ideal gas assumption, where real-fluid behavior has been completely overlooked, though this might be significant at common RCM test conditions. Here, this work presents a first-of-its-kind study that addresses two significant but overlooked questions for autoignition studies within RCMs in the fundamental combustion community: (i) experiment-wise, can unaccounted-for real-fluid behavior in RCMs affect the interpretation and analysis of RCM experimental data? and (ii) simulation-wise, can unaccounted-for real-fluid behavior in RCMs affect RCM autoignition modeling and the validation of chemical kinetic models? To this end, theories for real-fluid isentropic change are newly proposed and derived based on high-order Virial EoS, and are further incorporated into an effective-volume real-fluid autoignition modeling framework newly developed for RCMs. With detailed analyses, the strong real-fluid behavior in representative RCM tests is confirmed, which can greatly influence the interpretation of RCM autoignition experiments, particularly the determination of end-of-compression temperature and evolution of the adiabatic core in the reaction chamber. Furthermore, real-fluid RCM modeling results reveal that considerable error can be introduced into simulating RCM autoignition experiments when following the community-wide accepted effective-volume approach by assuming ideal-gas behavior, which can be as high as 64% in the simulated ignition delay time at compressed pressure of 125 bar and lead to contradictory validation results of chemical kinetic models. Therefore, we recommend the community to adopt frameworks with real-fluid behavior fully accounted for (e.g., the one developed in this study) to analyze and simulate past and future RCM experiments, so as to avoid misinterpretation of RCM autoignition experiments and eliminate the potential errors that can be introduced into the simulation results with the existing RCM modeling frameworks.

High-order Virial equation of state↗

Integration of a Microturbine Power Conversion Unit in MAGNET

The Microreactor Agile Non-nuclear Experimental Testbed (MAGNET) facility is being constructed at Idaho National Laboratory’s (INL’s) Energy Systems Laboratory to assist with the development, demonstration, and validation of microreactor components and systems. MAGNET will accommodate various types of test articles representative of different microreactor designs. A power conversion unit (PCU) simulator loop was proposed to use the rejected heat from the test article and mimic the thermal hydraulic conditions (e.g., temperature, pressure and flow rate) that would be experienced if an actual Brayton cycle PCU was attached. However, due to the high-estimated cost of the PCU simulator and the availability of a turbogenerator used for previous testing at Sandia National Laboratories, the PCU simulator design was abandoned in favor of integrating an actual PCU into MAGNET. A commercial Capstone C30 was modified by Sandia to use external electrical heating, rather than combustion heating, to provide a power output from 1 to ~30 kWe. The C30 has a single-stage centrifugal combustor, a static radial heat exchanger, and a radial inflow turbine arranged on a single shaft with a high-speed alternator. Since the operating temperature and energy transfer per unit working fluid mass are comparable, the MAGNET PCU will provide researchers with the ability to evaluate the test article heat transfer under representative operating conditions with the transient system behavior associated with a closed Brayton cycle PCU. This report examines the integration of a modified commercial Capstone C30 turbogenerator into MAGNET, outlines a proposed set of tests, and describes future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Droplet burning of n-butyl acetate/n-heptane mixtures in the standard atmosphere: experiments and numerical modeling

Blending petroleum fuels with oxygenates is a common approach to stem the depletion of crude oil while also mitigating the impact of their combustion on the environment. It has recently been considered that n-butyl acetate (BA, C6H12O2 , boiling point of 399K) could be a viable oxygenate additive to diesel fuel. In this application it is important to determine the influence of the fractional amount of BA on burning of the mixture. This presentation considers this problem from an experimental and computational approach using n-heptane (C7H14 , boiling point of 372K) as an essentially single component surrogate for diesel fuel. The burning configuration considered was ostensibly spherical symmetry as promoted by burning droplets under conditions where forced and natural convection effects were minimized. In this configuration the droplet and flame are concentric spheres and soot aggregates are trapped in a shell structure between the droplet and flame. Measurements were made of the droplet, flame and soot shell diameters through video imaging of the burning process. The experimental results were used to validate a detailed numerical model of the spherically symmetric droplet burning process that incorporated a consistent combustion kinetic mechanism for BA/heptane mixtures, comprised of 402 species and 16,872 reactions inclusive of soot chemistry. A model for soot formation was also included in the simulation to predict formation of the soot shell. The simulations agreed well with measured droplet and flame diameters. It was found both experimentally and computationally that adding BA to heptane had a minimal effect on the mixture burning rate, while the flame was positioned closer to the droplet surface and the simulated soot volume fraction decreased. The implications of these results are discussed for using BA as a potential additive to diesel fuel.

09 BIOMASS FUELS↗

Battery Electric Vehicle Eco-Cooperative Adaptive Cruise Control in the Vicinity of Signalized Intersections

This study develops a connected eco-driving controller for battery electric vehicles (BEVs), the BEV Eco-Cooperative Adaptive Cruise Control at Intersections (Eco-CACC-I). The developed controller can assist BEVs while traversing signalized intersections with minimal energy consumption. The calculation of the optimal vehicle trajectory is formulated as an optimization problem under the constraints of (1) vehicle acceleration/deceleration behavior, defined by a vehicle dynamics model; (2) vehicle energy consumption behavior, defined by a BEV energy consumption model; and (3) the relationship between vehicle speed, location, and signal timing, defined by vehicle characteristics and signal phase and timing (SPaT) data shared under a connected vehicle environment. The optimal speed trajectory is computed in real-time by the proposed BEV eco-CACC-I controller, so that a BEV can follow the optimal speed while negotiating a signalized intersection. The proposed BEV controller was tested in a case study to investigate its performance under various speed limits, roadway grades, and signal timings. In addition, a comparison of the optimal speed trajectories for BEVs and internal combustion engine vehicles (ICEVs) was conducted to investigate the impact of vehicle engine types on eco-driving solutions. Lastly, the proposed controller was implemented in microscopic traffic simulation software to test its networkwide performance. The test results from an arterial corridor with three signalized intersections demonstrate that the proposed controller can effectively reduce stop-and-go traffic in the vicinity of signalized intersections and that the BEV Eco-CACC-I controller produces average savings of 9.3% in energy consumption and 3.9% in vehicle delays.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Deep Learning Modeling Framework to Capture Mixing Patterns in Reactive-Transport Systems

Prediction and control of chemical mixing are vital for many scientific areas such as subsurface reactive transport, climate modeling, combustion, epidemiology, and pharmacology. Due to the complex nature of mixing in heterogeneous and anisotropic media, the mathematical models related to this phenomenon are not analytically tractable. Numerical simulations often provide a viable route to predict chemical mixing accurately. However, contemporary modeling approaches for mixing cannot utilize available spatial-temporal data to improve the accuracy of the future prediction and can be compute-intensive, especially when the spatial domain is large and for long-term temporal predictions. To address this knowledge gap, in this work we will present in this paper a deep learning (DL) modeling framework applied to predict the progress of chemical mixing under fast bimolecular reactions. This framework uses convolutional neural networks (CNN) for capturing spatial patterns and long short-term memory (LSTM) networks for forecasting temporal variations in mixing. By careful design of the framework—placement of non-negative constraint on the weights of the CNN and the selection of activation function, the framework ensures non-negativity of the chemical species at all spatial points and for all times. Our DL-based framework is fast, accurate, and requires minimal data for training. The time needed to obtain a forecast using the model is a fraction (≈ O(-6)) of the time needed to obtain the result using a high-fidelity simulation. To achieve an error of 10% (measured using the infinity norm) for capturing local-scale mixing features such as interfacial mixing, only 24% to 32% of the sequence data for model training is required. To achieve the same level of accuracy for capturing global-scale mixing features, the sequence data required for model training is 64% to 70% of the total spatial-temporal data. Hence, the proposed approach—a fast and accurate way to forecast long-time spatial-temporal mixing patterns in heterogeneous and anisotropic media—will be a valuable tool for modeling reactive-transport in a wide range of applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗