Canada
Bayesian Inference and Uncertainty Quantification for Hydrogen-Enriched and Lean-Premixed Combustion Systems
May 2021
Publication
Development of probabilistic modelling tools to perform Bayesian inference and uncertainty quantification (UQ) is a challenging task for practical hydrogen-enriched and low-emission combustion systems due to the need to take into account simultaneously simulated fluid dynamics and detailed combustion chemistry. A large number of evaluations is required to calibrate models and estimate parameters using experimental data within the framework of Bayesian inference. This task is computationally prohibitive in high-fidelity and deterministic approaches such as large eddy simulation (LES) to design and optimize combustion systems. Therefore there is a need to develop methods that: (a) are suitable for Bayesian inference studies and (b) characterize a range of solutions based on the uncertainty of modelling parameters and input conditions. This paper aims to develop a computationally-efficient toolchain to address these issues for probabilistic modelling of NOx emission in hydrogen-enriched and lean-premixed combustion systems. A novel method is implemented into the toolchain using a chemical reactor network (CRN) model non-intrusive polynomial chaos expansion based on the point collocation method (NIPCE-PCM) and the Markov Chain Monte Carlo (MCMC) method. First a CRN model is generated for a combustion system burning hydrogen-enriched methane/air mixtures at high-pressure lean-premixed conditions to compute NOx emission. A set of metamodels is then developed using NIPCE-PCM as a computationally efficient alternative to the physics-based CRN model. These surrogate models and experimental data are then implemented in the MCMC method to perform a two-step Bayesian calibration to maximize the agreement between model predictions and measurements. The average standard deviations for the prediction of exit temperature and NOx emission are reduced by almost 90% using this method. The calibrated model then used with confidence for global sensitivity and reliability analysis studies which show that the volume of the main-flame zone is the most important parameter for NOx emission. The results show satisfactory performance for the developed toolchain to perform Bayesian inference and UQ studies enabling a robust and consistent process for designing and optimising low-emission combustion systems.
The ‘Green’ Ni-UGSO Catalyst for Hydrogen Production under Various Reforming Regimes
Jun 2021
Publication
A new spinelized Ni catalyst (Ni-UGSO) using Ni(NO3)2·6H2O as the Ni precursor was prepared according to a less material intensive protocol. The support of this catalyst is a negative-value mining residue UpGraded Slag Oxide (UGSO) produced from a TiO2 slag production unit. Applied to dry reforming of methane (DRM) at atmospheric pressure T = 810 °C space velocity of 3400 mL/(h·g) and molar CO2/CH4 = 1.2 Ni-UGSO gives a stable over 168 h time-on-stream methane conversion of 92%. In this DRM reaction optimization study: (1) the best performance is obtained with the 10–13 wt% Ni load; (2) the Ni-UGSO catalysts obtained from two different batches of UGSO demonstrated equivalent performances despite their slight differences in composition; (3) the sulfur-poisoning resistance study shows that at up to 5.5 ppm no Ni-UGSO deactivation is observed. In steam reforming of methane (SRM) Ni-UGSO was tested at 900 °C and a molar ratio of H2O/CH4 = 1.7. In this experimental range CH4 conversion rapidly reached 98% and remained stable over 168 h time-on-stream (TOS). The same stability is observed for H2 and CO yields at around 92% and 91% respectively while H2/CO was close to 3. In mixed (dry and steam) methane reforming using a ratio of H2O/CH4 = 0.15 and CO2/CH4 = 0.97 for 74 h and three reaction temperature levels (828 °C 847 °C and 896 °C) CH4 conversion remains stable; 80% at 828 °C (26 h) 85% at 847 °C (24 h) and 95% at 896 °C (24 h). All gaseous streams have been analyzed by gas chromatography. Both fresh and used catalysts are analyzed by scanning electron microscopy-electron dispersive X-ray spectroscopy (SEM-EDXS) X-ray diffraction (XRD) and thermogravimetric analysis (TGA) coupled with mass spectroscopy (MS) and BET Specific surface. In the reducing environment of reforming such catalytic activity is mainly attributed to (a) alloys such as FeNi FeNi3 and Fe3Ni2 (reduction of NiFe2O4 FeNiAlO4) and (b) to the solid solution NiO-MgO. The latter is characterized by a molecular distribution of the catalytically active Ni phase while offering an environment that prevents C deposition due to its alkalinity.
A Model for Hydrogen Detonation Diffraction or Transmission to a Non-confined Layer
Sep 2021
Publication
One strategy for arresting propagating detonation waves in pipes is by imposing a sudden area enlargement which provides a rapid lateral divergence of the gases in the reaction zone and attenuates the leading shock. For sufficiently small tube diameter the detonation decays to a deflagration and the shock decays to negligible strengths. This is known as the critical tube diameter problem. In the present study we provide a closed form model to predict the detonation quenching for 2D channels. This problem also applies to the transmission of a detonation wave from a confined layer to a weakly-confined layer. Whitham’s geometric shock dynamics coupled with a shock evolution law based on shocks sustained by a constant source obtained by the shock change equations of Radulescu is shown to capture the lateral shock dynamics response to the failure wave originating at the expansion corner. A criterion for successful detonation transmission to open space is that the lateral strain rate provided by the failure wave not exceed the critical strain rate of steady curved detonations. Using the critical lateral strain rate obtained by He and Clavin a closed form solution is obtained for the critical channel opening permitting detonation transmission. The predicted critical channel width is found in excellent agreement with our recent experiments and simulations of diffracting H2/O2/Ar detonations. Model comparison with available data for H2/air detonation diffraction into open space at ambient conditions or for transmission into a weakly confined layer by air is also found in good agreement within a factor never exceeding 2 for the critical opening or layer dimension.
Nickel-Based Electrocatalysts for Water Electrolysis
Feb 2022
Publication
Currently hydrogen production is based on the reforming process leading to the emission of pollutants; therefore a substitute production method is imminently required. Water electrolysis is an ideal alternative for large-scale hydrogen production as it does not produce any carbon-based pollutant byproducts. The production of green hydrogen from water electrolysis using intermittent sources (e.g. solar and eolic sources) would facilitate clean energy storage. However the electrocatalysts currently required for water electrolysis are noble metals making this potential option expensive and inaccessible for industrial applications. Therefore there is a need to develop electrocatalysts based on earth-abundant and low-cost metals. Nickel-based electrocatalysts are a fitting alternative because they are economically accessible. Extensive research has focused on developing nickel-based electrocatalysts for hydrogen and oxygen evolution. Theoretical and experimental work have addressed the elucidation of these electrochemical processes and the role of heteroatoms structure and morphology. Even though some works tend to be contradictory they have lit up the path for the development of efficient nickel-based electrocatalysts. For these reasons a review of recent progress is presented herein.
Techno-economic Assessment of Hydrogen Production from Seawater
Nov 2022
Publication
Population growth and the expansion of industries have increased energy demand and the use of fossil fuels as an energy source resulting in release of greenhouse gases (GHG) and increased air pollution. Countries are therefore looking for alternatives to fossil fuels for energy generation. Using hydrogen as an energy carrier is one of the most promising alternatives to replace fossil fuels in electricity generation. It is therefore essential to know how hydrogen is produced. Hydrogen can be produced by splitting the water molecules in an electrolyser using the abondand water resources which are covering around ⅔ of the Earth's surface. Electrolysers however require high-quality water with conductivity in the range of 0.1–1 μS/cm. In January 2018 there were 184 offshore oil and gas rigs in the North Sea which may be excellent sites for hydrogen production from seawater. The hydrogen production process reported in this paper is based on a proton exchange membrane (PEM) electrolyser with an input flow rate of 300 L/h. A financially optimal system for producing demineralized water from seawater with conductivity in the range of 0.1–1 μS/cm as the input for electrolyser by WAVE (Water Application Value Engine) design software was studied. The costs of producing hydrogen using the optimised system was calculated to be US$3.51/kg H2. The best option for low-cost power generation using renewable resources such as photovoltaic (PV) devices wind turbines as well as electricity from the grid was assessed considering the location of the case considered. All calculations were based on assumption of existing cable from the grid to the offshore meaning that the cost of cables and distribution infrastructure were not considered. Models were created using HOMER Pro (Hybrid Optimisation of Multiple Energy Resources) software to optimise the microgrids and the distributed energy resources under the assumption of a nominal discount rate inflation rate project lifetime and CO2 tax in Norway. Eight different scenarios were examined using HOMER Pro and the main findings being as follows:<br/>The cost of producing water with quality required by the electrolyser is low compared with the cost of electricity for operation of the electrolyser and therefore has little effect on the total cost of hydrogen production (less than 1%).<br/>The optimal solution was shown to be electricity from the grid which has the lowest levelised cost of energy (LCOE) of the options considered. The hydrogen production cost using electricity from the grid was about US$ 5/kg H2.<br/>Grid based electricity resulted in the lowest hydrogen production cost even when costs for CO2 emissions in Norway that will start to apply in 2025 was considered being approximately US$7.7/kg H2.<br/>From economical point of view wind energy was found to be a more economical than solar.
Boundary Layer Effects on the Critical Nozzle of Hydrogen Sonic Jet
Oct 2015
Publication
When hydrogen flows through a small finite length constant exit area nozzle the viscous effects create a fluid throat which acts as a converging-diverging nozzle and lead to Mach number greater than one at the exit if the jet is under-expanded. This phenomenon influences the mass flow rate and the dispersion cloud size. In this study the boundary layer effect on the unsteady hydrogen sonic jet flow through a 1 mm diameter pipe from a high pressure reservoir (up to 70 MPa) is studied using computational fluid dynamics with a large eddy simulation turbulence model. This viscous flow simulation is compared with a non-viscous simulation to demonstrate that the velocity is supersonic at the exit of a small exit nozzle and that the mass flow is reduced.
A Comparative Study of Detonability and Propensity to Sustain High-speed Turbulent Deflagrations in Hydrogen and Methane Mixtures
Sep 2013
Publication
We’ve studied the conditions enabling a detonation to be quenched when interacting with an obstruction and the propensity for establishing subsequent fast-flame. Oxy-hydrogen detonations were found quench more easily than oxy-methane detonations when comparing the ratio of gap size and the detonation cell size. High-speed turbulent deflagrations that re-accelerate back to a detonation were only observed in methane-oxygen mixtures. Separate hot-spot ignition calculations revealed that the higher detonability of methane correlates with its stronger propensity to develop localized hot-spots. The results suggest that fast-flames are more difficult to form in hydrogen than in methane mixtures.
Mesh-Independent Large-Eddy Simulation with Anisotropic Adaptive Mesh Refinement for Hydrogen Deflagration Prediction in Closed Vessels
Sep 2019
Publication
The use of high-fidelity simulation methods based on large-eddy simulation (LES) are proving useful for understanding and mitigating the safety hazards associated with hydrogen releases from nuclear power plants. However accurate modelling of turbulent premixed hydrogen flames via LES can require very high resolution to capture both the large-scale turbulence and its interaction with the flame fronts. Standard meshing strategies can result in impractically high computational costs especially for the thin fronts of hydrogen flames. For these reasons the use of a recently formulated integral length scale approximation (ILSA) subfilter-scale model in combination with an efficient anisotropic block-based adaptive mesh refinement (AMR) technique is proposed and examined herein for performing LES of turbulent premixed hydrogen flames. The anisotropic AMR method allows dynamic and solution-dependent resolution of flame fronts and the grid-independent properties of the ILSA model ensure that numerical errors associated with implicitly-filtered LES techniques in regions with varying resolution are avoided. The combined approach has the potential to allow formally converged LES solutions (direct numerical simulation results are typically reached in the limit of very fine meshes with standard subgrid models). The proposed LES methodology is applied to combustion simulations of lean premixed hydrogen-air mixtures within closed vessels: a problem relevant to hydrogen safety applications in nuclear facilities. A progress variable-based method with a multi-phenomena burning velocity model is used as the combustion model. The present simulation results are compared to the available experiment data for several previously studied THAI vessel cases and the capabilities of the proposed LES approach are assessed.
A Turbulent Combustion Model for Ignition of Rapidly Expanding Hydrogen Jets
Mar 2013
Publication
A turbulent combustion model based on the Linear Eddy Model for Large Eddy Simulation (LEM- LES) is currently proposed to study self-ignition events of rapidly expanding hydrogen jets. The model is a one-dimensional treatment of a diffusion-reaction system within each multi-dimensional LES cell. This reduces the expense of solving a complete multi-dimensional problem while preserving micro-scale hotspots and their effects on ignition. The current approach features a Lagrangian description of fluid particles on the sub-grid for increased accuracy. Also Adaptive Mesh Refinement (AMR) is implemented for increased computational efficiency. In this paper the model is validated for various inviscid laminar 1-D mixing and ignition problems shock tube problems flames and detonations.
Effects of Chemical Kinetics on Ignition of Hydrogen Jets
Sep 2013
Publication
During the early phase of the transient process following a hydrogen leak into the atmosphere a contact surface appears separating air heated by the leading shock from hydrogen cooled by expansion. Locally the interface is approximately planar. Diffusion leads to a temperature decrease on the air side and an increase in the hydrogen-filled region and mass diffusion of hydrogen into air and of air into hydrogen potentially resulting in ignition. This process was analyzed by Li ˜nan and Crespo [1] for unity Lewis number and Li ˜nan and Williams [2] for Lewis number less than unity. We included in the analysis the effect of a slow expansion [3 4] leading to a slow drop in temperature which occurs in transient jets. Chemistry being very temperature-sensitive the reaction rate peaks close to the hot side of the interface where only a small fuel concentration present close to the warm air-rich side which depends crucially upon the fuel Lewis number. For Lewis number unity the fuel concentration due to diffusion is comparable to the rate of consumption by chemistry. If the Lewis number is less than unity diffusion brings in more fuel than temperature-controlled chemistry consumes. For a Lewis number greater than unity diffusion is not strong enough to bring in as much fuel as chemistry would burn; combustion is controlled by fuel diffusion. If the temperature drop due to expansion associated with the multidimensional jet does not lower significantly the reaction rate up to that point analysis shows that ignition in the jet takes place. For fuel Lewis number greater than unity chemistry does not lead to a defined explosion so that eventually expansion will affect the process; ignition does not take place [3 4]. In the current paper these results are extended to consider multistep chemical kinetics but for otherwise similar assumptions. High activation energy is no longer applicable. Instead results are obtained in the short time limit still as a perturbation superimposed to the self-similar solution to the chemically frozen diffusion solution. In that approximation the initiation step which consumes fuel and oxidant is taken to be slow compared with steps that consume one of the reactants and an intermediate species. The formulation leads to a two point boundary value problem for set of coupled rate equations plus an energy equation for perturbations. These equations are linear with variable co-effcients. The coupled problem is solved numerically using a split algorithm in which chemical reaction is solved for frozen diffusion while diffusion is solved for frozen chemistry. At each time step the still coupled linear problem is solved exactly by projecting onto the eigenmodes of the stiff matrix so that the solution is unaffected by stiffness. Since in the short time limit temperature is only affected at the perturbation level the matrix depends only on the similarity variable x t but it is otherwise time-independent. As a result determination of the eigenvalues and eigenvectors is only done once (using Maple) for the entire range of discretized values of the similarity variable. The diffusion problem consists of a set of independent equations for each species. Each of these is solved using orthogonal decomposition onto Hermite polynomials for the homogeneous part plus a particular solution proportional to time for the non-homogeneous (source) terms. That approach can be implemented for different kinetic schemes.
Measurements of Flow Velocity and Scalar Concentration in Turbulent Multi-component Jets
Sep 2017
Publication
Buoyancy effects and nozzle geometry can have a significant impact on turbulent jet dispersion. This work was motivated by applications involving hydrogen. Using helium as an experimental proxy buoyant horizontal jets issuing from a round orifice on the side wall of a circular tube were analyzed experimentally using particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) techniques simultaneously to provide instantaneous and time-averaged flow fields of velocity and concentration. Effects of buoyancy and asymmetry on the resulting flow structure were studied over a range of Reynolds numbers and gas densities. Significant differences were found between the centreline trajectory spreading rate and velocity decay of conventional horizontal round axisymmetric jets issuing through flat plates and the pipeline leak-representative jets considered in the present study. The realistic pipeline jets were always asymmetric and found to deflect about the jet axis in the near field. In the far field it was found that the realistic pipeline leak geometry causes buoyancy effects to dominate much sooner than expected compared to horizontal round jets issuing through flat plates.
State-of-the-Art and Research Priorities in Hydrogen Safety
Sep 2013
Publication
On October 16-17 2012 the International Association for Hydrogen Safety (HySafe) in cooperation with the Institute for Energy and Transport of the Joint Research Centre of the European Commission (JRC IET Petten) held a two-day workshop dedicated to Hydrogen Safety Research Priorities. The workshop was hosted by Federal Institute for Materials Research and Testing (BAM) in Berlin Germany. The main idea of the Workshop was to bring together stakeholders who can address the existing knowledge gaps in the area of the hydrogen safety including identification and prioritization of such gaps from the standpoint of scientific knowledge both experimental and theoretical including numerical. The experience highlighting these gaps which was obtained during both practical applications (industry) and risk assessment should serve as reference point for further analysis. The program included two sections: knowledge gaps as they are addressed by industry and knowledge gaps and state-of-the-art by research. In the current work the main results of the workshop are summarized and analysed.
Numerical and Experimental Investigation of Buoyant Gas Release
Sep 2009
Publication
Buoyant round vertical jet had been investigated using Large Eddy Simulations at low Mach number. For the purpose of comparison with in-house experimental data in the present work helium has been used as a substitute for hydrogen. The influence of the transient concentration fields on the volume of gas with concentration within flammability limits has been investigated and their evolution and relation with average fields ad been characterized. Transient concentration fields created during initial jet development had been considered. Numerical results have been compared with in-house experiments and data published in the literature.
Heat Transfer Analysis for Fast Filling of On-board Hydrogen Tank
Mar 2019
Publication
The heat transfer analysis in the filling process of compressed on-board hydrogen storage tank has been the focus of hydrogen storage research. The initial conditions mass flow rate and heat transfer coefficient have certain influence on the hydrogen filling performance. In this paper the effects of mass flow rate and heat transfer coefficient on hydrogen filling performance are mainly studied. A thermodynamic model of the compressed hydrogen storage tank was established by Matlab/Simulink. This 0D model is utilized to predict the hydrogen temperature hydrogen pressure tank wall temperature and SOC (State of Charge) during filling process. Comparing the simulated results with the experimental data the practicability of the model can be verified. The simulated results have certain meaning for improving the hydrogenation parameters in real filling process. And the model has a great significance to the study of hydrogen filling and purification.
Experimental Investigation of Spherical-flame Acceleration in Lean Hydrogen-air Mixtures
Oct 2015
Publication
Large-scale experiments examining spherical-flame acceleration in lean hydrogen-air mixtures were performed in a 64 m3 constant-pressure enclosure. Equivalence ratios ranging from 0.33 to 0.57 were examined using detailed front tracking for flame diameters up to 1.2 m through the use of a Background Oriented Schlieren (BOS) technique. From these measurements the critical radii for onset of instability for these mixtures on the order of 2–3 cm were obtained. In addition the laminar burning velocity and rate of flame acceleration as a function of radius were also measured.
Flammability Profiles Associated with High-pressure Hydrogen Jets Released in Close Proximity to Surfaces
Oct 2015
Publication
This paper describes experimental and numerical modelling results from an investigation into the flammability profiles associated with high pressure hydrogen jets released in close proximity to surfaces. This work was performed under a Transnational Access Agreement activity funded by the European Research Infrastructure project H2FC.<br/>The experimental programme involved ignited and unignited releases of hydrogen at pressures of 150 and 425 barg through nozzles of 1.06 and 0.64 mm respectively. The proximity of the release to a ceiling or the ground was varied and the results compared with an equivalent free-jet test. During the unignited experiments concentration profiles were measured using hydrogen sensors. During the ignited releases thermal radiation was measured using radiometers and an infra-red camera. The results show that the flammable volume and flame length increase when the release is in close proximity to a surface. The increases are quantified and the safety implications discussed.<br/>Selected experiments were modelled using the CFD model FLACS for validation purposes and a comparison of the results is also included in this paper. Similarly to experiments the CFD results show an increase in flammable volume when the release is close to a surface. The unstable atmospheric conditions during the experiments are shown to have a significant impact on the results.
Modelling Of Hydrogen Explosion on a Pressure Swing Adsorption Facility
Sep 2011
Publication
Computational fluid dynamic simulations have been performed in order to study the consequences of a hydrogen release from a pressure swing adsorption installation operating at 30 barg. The simulations were performed using FLACS-Hydrogen software from GexCon. The impact of obstruction partial confinement leak orientation and wind on the explosive cloud formation (size and explosive mass) and on explosion consequences is investigated. Overpressures resulting from ignition are calculated as a function of the time to ignition.
Experimental Study of the Spontaneous Ignition of Partly Confined Hydrogen Jets
Sep 2011
Publication
The current study addresses the spontaneous ignition of hydrogen jets released into a confined oxidizer environment experimentally. The experiments are conducted in a shock tube where hydrogen gas is shock-accelerated into oxygen across a perforated plate. The operating conditions and hole dimension of the plate were varied in order to identify different flow field and ignition scenarios. Time resolved Schlieren visualization permitted to reconstruct the gasdynamic evolution of the release and different shock interactions. Time resolved self-luminosity records permitted us to record whether ignition was achieved and also to record the dimension of the turbulent mixing layer. The ignition limits determined experimentally in good agreement with the 1D diffusion ignition model proposed by Maxwell and Radulescu. Nevertheless the experiments demonstrated that the mixing layer is two to three orders of magnitude thicker than predicted by molecular diffusion which can be attributed to the observed mixing layer instabilities and shock-mixing layer interactions which provide a much more intense mixing rate than anticipated from previous and current numerical predictions. These observations further clarify why releases through partly confined geometries are more conducive to jet ignition of the jets.
The Crucial Role of the Lewis Number in Jet Ignition
Sep 2011
Publication
During the early phase of the transient process following a hydrogen leak into the atmosphere a contact surface appears separating hot air from cold hydrogen. Locally the interface is approximately planar. Diffusion occurs potentially leading to ignition. This process was analyzed by Lin˜a´n and Crespo (1976) for Lewis number unity and Lin˜a´n and Williams (1993) for Lewis number less than unity. In addition to conduction these processes are affected by expansion due to the flow which leads to a temperature drop. If chemistry is very temperature-sensitive then the reaction rate peaks close to the hot region where relatively little fuel is present. Indeed the Arrhenius rate drops rapidly as temperature drops much more so than fuel concentration. However the small fuel concentration present close to the airrich side depends crucially upon the balance between fuel diffusion and heat diffusion hence the fuel Lewis number. For Lewis number unity the fuel concentration present due to diffusion is comparable to the rate of consumption due to chemistry. If the Lewis number is less than unity fuel concentration brought in by diffusion is large compared with temperature-controlled chemistry. For a Lewis number greater than unity diffusion is not strong enough to bring in as much fuel as chemistry would be able to burn and combustion is controlled by fuel diffusion. In the former case combustion occurs faster leading to a localized ignition at a finite time determined by the analysis. As long as the temperature drop due to the expansion associated with the multidimensional nature of the jet does not lower significantly the reaction rate up to that point ignition in the jet takes place. For fuel Lewis number greater than unity first the reaction rate is much lower. Second chemistry does not lead to a defined ignition. Eventually expansion will affect the process and ignition does not take place. In summary it appears that the reason why hydrogen is the only fuel for which jet ignition has been observed is a Lewis number effect coupled with a high speed of sound hence a high initial temperature discontinuity.
Simulation of Shock-Initiated Ignition
Sep 2009
Publication
The scenario of detonative ignition in shocked mixture is significant because it is a contributor to deflagration to detonation transition for example following shock reflections. However even in one dimension simulation of ignition between a contact surface or a flame and a shock moving into a combustible mixture is difficult because of the singular nature of the initial conditions. Initially as the shock starts moving into reactive mixture the region filled with reactive mixture has zero thickness. On a fixed grid the number of grid points between the shock and the contact surface increases as the shock moves away from the latter. Due to initial lack of resolution in the region of interest staircasing may occur whereby the resulting plots consist of jumps between few values a few grid points and these numerical artifacts are amplified by the chemistry which is very sensitive to temperature leading to unreliable results. The formulation is transformed replacing time and space by time and space over time as the independent variables. This frame of reference corresponds to the self-similar formulation in which the non-reactive problem remains stationary and the initial conditions are well-resolved. Additionally a solution obtained from short time perturbation is used as initial condition at a time still short enough for the perturbation to be very accurate but long enough so that there is sufficient resolution. The numerical solution to the transformed problem is obtained using an essentially non-oscillatory algorithm which is adequate not only for the early part of the process but also for the latter part when chemistry leads to appearance of a shock and eventually a detonation wave is formed. A validation study was performed and the results were compared with the literature for single step Arrhenius chemistry. The method and its implementation were found to be effective. Results are presented for values of activation energy ranging from mild to stiff.
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