Arrhenius Reaction Rate Research Articles

Solution of adiabatic and nonadiabatic combustion problems using step-function reaction models

We consider the use of step-functions to model Arrhenius reaction terms for traveling wave solutions to combustion problems. We develop a methodology by which the Arrhenius reaction rate term is replaced by a suitably normalized step-function. The resulting model introduces interior interfaces and allows the conservation equations for energy and species to be solved explicitly within the subdomains bounded by the interfaces. The problem can then be reduced to a small number of nonlinear algebraic equations governing appropriate interface conditions. We apply this methodology to a variety of single-reaction problems and show that the resulting solutions agree with those obtained by the well-known front δ-function) approximations for large Zeldovich numbers. We then consider multiple reaction problems, specifically problems involving two independent reactions and problems involving sequential reactions. For these problems we compare the results with simpler front models as well as with Arrhenius kinetics. We show that the step-function models are generally superior to the front models where available and agree, both qualitatively and with reasonable quantitative accuracy, with solutions obtained via full Arrhenius kinetics.

A thermodynamics-based homogeneous charge compression ignition engine model for adaptive nonlinear controller development

Low-temperature combustion modes, such as homogeneous charge compression ignition, represent a promising means to increase the efficiency and to reduce significantly the emissions of internal combustion engines. Implementation and control are difficult, however, owing to the dependence of the combustion event on the chemical kinetics rather than an external trigger. This work describes a nonlinear control-oriented model developed for a single-cylinder homogeneous charge compression ignition engine, which is physically based on a five-state thermodynamic cycle. This model is aimed at capturing the behavior of an engine which utilizes fully vaporized gasoline-type fuels, exhaust gas recirculation, and intake air heating in order to achieve homogeneous charge compression ignition operation. The onset of combustion, which is vital for control, is modeled using an Arrhenius reaction rate expression which relates the combustion timing to both the charge dilution and the temperature. Despite the fact that homogeneous charge compression ignition combustion is indeed fast, it is not perfectly instantaneous and therefore requires some finite amount of time to occur. To account for this phenomenon within the model, a Δθ term is added which shifts the point of instantaneous combustion from the start of combustion to a point of very-high-energy release based on experimental heat release data. The model is validated against experimental data from a single-cylinder compression ignition engine operating under homogeneous charge compression ignition conditions at two different fueling rates. Parameters relevant to control such as the combustion timing, peak in-cylinder pressure, and pressure rise rates from the simulation agree very well with the experiment in both operating conditions. The extension of the model to other fuels is also investigated via the octane index of several different gasoline-type fuels. Since this nonlinear model is developed from a controls perspective, both the output and the state update equations are formulated such that they are functions of only the control inputs and the state variables, therefore making them directly applicable to state-space methods for control. The result is a discrete-time nonlinear control model which provides a platform for developing and validating various nonlinear control strategies.

Thermochemical modeling of temperature controlled shock-induced chemical reactions in multifunctional energetic structural materials under shock compression

Multifunctional energetic structural materials (MESMs) are a new class of energetic materials which release energy due to exothermic chemical reactions initiated under shock loading conditions. In order to analyze shock-induced chemical reactions (SICR) for MESMs, theoretical models have been developed to calculate the Hugoniot data which include the heat released by shock temperature controlled reactions. The temperature rise of porous materials due to shock compression is first calculated using a constant volume and pressure adjustment. Then the Arrhenius reaction rate and Avrami-Erofeev kinetic models are used to calculate the extent of reaction of MESMs under shock compression. Thermochemical models for shock-induced reactions, in which the reaction efficiency is considered, are given by combining the shock temperature rise with the chemical reaction kinetics. The Hugoniot relations and temperatures are calculated by using the proposed method. The models developed have been validated against the experimental SICR data involving Fe2O3/Al, Al/Ni, and Ti/Ni mixtures. It has been shown that the theoretical calculations correlate reasonably well with the corresponding experimental and simulation results. The models presented can be used to predict the reaction results of MESMs over a wide range of pressure satisfactorily.

High-Temperature Oxidation Kinetics of Tungsten-Water Reaction with Hydrogen Inhibition

The high-temperature heterogeneous reaction rates of bulk tungsten (W) were studied using thermogravimetric analysis in steam (H2O) and hydrogen (H2) atmospheres. Reaction rates were determined at isothermal conditions for temperatures ranging from approximately 1100 to 1700 C. Constant system pressures of 1 atm were employed; however,H2O partial pressures ranged from 3.04 to 51.3 torr. Using Arrhenius reaction rate kinetics, the activation energy of the tungsten–H2O oxidation reactionwas calculated to be 51 kcal=mol, while theH2O pressure exponent, or reaction order, was determined to be 0.82. Increasing concentrations ofH2 were found to exponentially reduce the desorption rates of the tungsten oxides involved in the oxidation reaction. Addition of H2 slightly reduced the apparent activation energy of the reaction as well, indicating a stronger inhibiting effect at higher temperatures. Thederived oxidation rates indicate that, undermost rocketmotor conditions, corrosion of tungsten nozzles aremost likely limited by gas-phase diffusion of oxidizers to the nozzle surface and/or lack of available reaction sites (i.e., surface area limited or pressure independent).

The cumulative measure of a force: A unified kinetic theory for rigid-sphere and inverse-square force law interactions

By introducing a cutoff on the cumulative measure of a force, a unified kinetic theory is developed for both rigid-sphere and inverse-square force laws. The difference between the two kinds of interactions is characterized by a parameter, γ, which is 1 for rigid-sphere interactions and -3 for inverse-square force law interactions. The quantities governed by γ include the specific reaction rates, kernels, collision frequencies, arbitrarily high orders of transition moments, arbitrarily high orders of Fokker-Planck expansion (also called Kramers-Moyal expansion) coefficients, and arbitrarily high orders of energy exchange rates. The cutoff constants are shown to be incomplete gamma functions of different orders. The widely used cutoff constant in plasma physics (usually known as Coulomb logarithm) is found to be exactly the zeroth order of the incomplete gamma function. The well known Arrhenius reaction rate formula comes from the first order of the incomplete gamma functions, while the negative first order can be used for fitting the fusion reaction rate between deuterium and tritium.

Modeling detonation in liquid explosives: The effect of the inter-component transfer hypothesis on chemical lengths and critical diameters

This work discusses the two-component model of reactive fluid – reactants and products – widely implemented for simulating detonation dynamics in condensed explosives. This study analyzes the sensitivity of detonation characteristic lengths to the inter-component heat-transfer hypothesis required to obtain a closed set of governing equations. The slowest and the fastest transfers – isentropic reactants and thermal equilibrium, resp. – are investigated. Earlier studies were restricted to the thermodynamic phase plane and have found a weak effect of the transfer hypothesis on state variables. On the contrary, this analysis considers the chemical kinetic process. A state-sensitive Arrhenius reaction rate and two sets of constitutive parameters are used to generate three types of reaction profiles suited to most one-step energy releases in liquid explosives – specifically, long, balanced or short induction, relative to reaction. The chemical lengths and critical diameters of one- or two-dimensional detonations thus prove to be very sensitive to the transfer hypothesis – specifically much larger with the fastest – as well as to small variations of constitutive parameters. Importantly, the profile type is independent of transfer but not of parameters. Therefore, a pertinent response to a transfer change is to recalibrate the rate time-factor so as to keep constant some reference length, according to the profile type. For inductive or balanced profiles, any length can be used such as the CJ reaction length or the critical diameter. Asymptotic profiles require special attention because their length ratios depend on transfer. Constitutive parameters cannot be used with a transfer hypothesis different from that they were calibrated with. Too large experimental errors or numerically under-resolved calibrations may lead to skewed reaction profiles, and hence erroneous simulations of detonation dynamics. Thus, more accurate constitutive relations and information on steady reaction profiles in detonating liquid explosives are necessary.

Modified one-step reaction equation for modeling the oxidation of unburned hydrocarbons in engine conditions

The oxidation of unburned hydrocarbons from piston crevices was modeled using a modified one-step reaction equation. This new one-step oxidation model was developed by modifying the Arrhenius reaction rate coefficients of the conventional one-step reaction equation. The predictions of the new one-step oxidation model agree well with the results of the detailed chemical reaction mechanism in terms of the 90% oxidation time of the fuel. The effects of pressure and intermediate species in the burnt gas on the oxidation rate were also investigated and included as additional multiplying factors in the modification of the equation. To simulate the oxidation process of unburned hydrocarbons from a piston crevice, a two-dimensional computational mesh, based on the conventional engine geometry, was constructed with a fine mesh density at the regions of the piston crevice and cylinder wall. The number of cell layers in the cylinder was controlled according to the piston motion to model the out-flow of unburned hydrocarbons from the piston crevice during the expansion stroke. The effects of engine operational conditions on the oxidation rate were examined at several engine speeds and load conditions, and the sensitivity of the oxidation rate to the piston crevice volume was also evaluated. Finally, the new one-step oxidation model was applied to a three-dimensional computational mesh that modeled the three-dimensional engine geometry and piston-valve motions to simulate the oxidation of unburned hydrocarbons in a real engine condition.

Parametric study of shock-wave formation in a spatially inhomogeneous self-igniting medium for arrhenius combustion kinetics

An approach to describing the formation and propagation of small gas-dynamic perturbations in a spatially inhomogeneous self-igniting medium for arbitrary chemical reaction kinetics was developed in a previous paper. In the present paper, the proposed approach is illustrated by studying the problem for a simple reaction with an Arrhenius reaction rate. A comparison of calculation results with the solution of the complete system of gas dynamics equations shows that the approach provides good accuracy of quantitative estimates.

High-Temperature Heterogeneous Reaction Kinetics of Tungsten Oxidation by CO2, CO, and O2

The high-temperature heterogeneous reaction rates of bulk tungsten are studied using thermogravimetric analysis in oxygen (O 2 ), as well as carbon dioxide (CO 2 ) and carbon monoxide (CO) atmospheres. Isothermal reaction rates were determined at temperatures ranging from 1300 to 1700°C. Constant system pressures of 1 atm were employed; however, O 2 and CO 2 partial pressures ranged from 0.152 to 3.8 torr and 7.6 to 64.6 torr, respectively. Using Arrhenius reaction rate kinetics, activation energies of the W―O 2 and W―CO 2 reactions were found to be 23.5 and 64 kcal/mol, whereas pressure exponents were determined to be 0.89 and 0.6, respectively. Oxidation rates were higher for O 2 than CO 2 under constant partial pressure conditions. Increasing CO concentration in the presence of constant CO 2 partial pressure was found to reduce reaction rates significantly, emphasizing the impact gas mixtures may have on heterogeneous reaction rates. The results imply chemical erosion rates of nozzles may be altered significantly by small perturbations in propellant formulations, and O 2 may play a nonnegligible role, even in very small quantities present in rocket motors.

Numerical solutions of a model for the propagation of a surface-catalysed flame in a tube

Numerical simulations of a surface-catalysed flame in a tube are performed, corresponding to an experiment where a premixed fuel is fed into a tube whose inner surface is coated with a catalyst. In these experiments, subsequent to ignition, a reaction wave can be seen as a red-hot region which propagates back along the tube towards the inlet, and is due to low temperature combustion occurring only on the inner surface of the tube where the catalyst is present. The solutions of a mathematical model for this behaviour show that initial-value problems do indeed result in such steadily propagating waves. The numerically obtained wave speeds and steady solution are compared to a previous large Damkohler number (D a ) asymptotic analysis using a simple reaction rate model, and agreement is very good even for moderately large values of D a . However, for such Damkohler numbers, the wave speeds are found to be much larger than observed experimentally. Indeed, the simulations show that O(1) values of D a are required to obtain the lower experimental wave speeds. Nevertheless, the wave speeds as a function of flow rate through the tube do not agree well with the preliminary experimental results for any choice of the parameters. A more realistic, Arrhenius reaction rate model is then considered. The Arrhenius model predicts a rapid change in temperature at the wave front, in much better agreement with the experiments than for the simpler reaction model.

Hydrolysis of cyanides in aqueous solutions

The hydrolytic destruction of cyanides in aqueous solutions is studied. The reaction can be described by a first-order equation with respect to cyanide, and its rate depends on pH. An analysis of the parameters of the Arrhenius equation and reaction rate coefficients implies that molecular prussic acid is predominantly involved in the hydrolysis. A mathematical model is created for predicting the development of cyanide removal over time at different pHs and temperatures

Detonation waves in PBX 9501

For a planar detonation wave propagating in the plastic-bonded explosive PBX 9501, measurements of the reaction zone display a classical ZND profile. Moreover, the reaction-zone width is substantially less than the average size of an explosive grain. We show that the reaction zone is compatible with realistic constitutive properties and an Arrhenius reaction rate based on the bulk temperature. Thus, contrary to conventional wisdom, hot spots are not needed to propagate a detonation wave. Conventional wisdom is based, in part, on shock desensitization experiments; the observation that precompressing a PBX with a weak shock – which eliminates voids as nucleation sites for hot spots – can quench a propagating detonation wave. By analysing the temperature behind two shocks compared to a single shock and the corresponding change of the induction time, we show that a detonation wave sustained by the bulk reaction rate from shock heating is compatible with shock desensitization. Shock desensitization depends on having a temperature sensitive rate, which usually is associated with detonation wave instability. However, for PBX 9501 the temperature variation in the reaction zone is small, and one-dimensional simulations show that this results in a stable detonation wave. Furthermore, we show that two additional phenomena are compatible with the perspective that bulk burn can sustain a planar detonation wave: failure diameter, which does depend on the heterogeneous structure of a PBX; and PBXs with a lower HE content which display an irregular detonation front.

Systematics of corn stover pyrolysis yields and comparisons of analytical and kinetic representations

This paper focuses on the systematics of a large body of experimental corn stover pyrolysis yields measured with a Pyroprobe-FTIR system at Taiyuan University of Technology (TUT) using a wide range of heating rates, This large body of data is organized using an analytical semi-empirical model (ASEM) developed at the University of Florida that provides a reasonable account using only a small number of adjusted parameters. The data is also organized with a traditional kinetic model (Arrhenius reaction rates) and comparisons are made between the two models from the viewpoint of engineering applications of pyrolysis.

Polyurethane Foam Response To High Heat Fluxes

A Simple Polyurethane Foam (SPUF) mass loss and response model has been developed to predict the behavior of unconfined, rigid, closed-cell, polyurethane foam-filled systems exposed to fire-like heat fluxes. The model is based on simple two-step mass loss kinetics using distributed Arrhenius reaction rates. The initial reaction step assumes that the foam degrades into a primary gas and a reactive solid. The reactive solid subsequently degrades into a secondary gas. The SPUF decomposition model was implemented into the finite (FE) heat conduction codes COYOTE [l] and CALORE [2], which support chemical kinetics and dynamic enclosure radiation using element death. A discretization bias correction model was parameterized using elements with characteristic lengths ranging from l-mm to l-cm. Bias corrected solutions using the SPUF response model with large elements gave essentially the same results as grid independent solutions using 100-pm elements. The response model was used to simulate a 9cm diameter, 15-cm tall cylinder of foam that was heated with lamps. The predictions of the decomposition front locations were compared to the front locations determined from real-time X-rays. The predictions of the front locations were similar to the measured front locations using real time X-rays.

Soot inception temperature and the carbonization rate of precursor particles

The critical temperature for soot formation in diffusion flames has been the subject of prior measurements by various investigators. More recently, the presence of soot precursor particles in a variety of diffusion flames has been recognized, and the Arrhenius reaction rate constants for their conversion to carbonaceous soot have been reported. In this work the prediction of the soot inception temperature using the recent carbonization reaction rate data is investigated when temperature increases linearly with time. The temperature gradient and the detection sensitivity to the initial soot formation are two factors accommodated by the method of prediction. A good correlation is obtained between the predicted soot inception temperatures and the values previously measured by several investigators for eight hydrocarbon fuels of diverse molecular structures. Both the temperature gradient and the detection sensitivity of the experiments to the initial soot formation are significant differences among the several test protocols. The ability to predict the soot inception temperatures in diffusion flames for the wide range hydrocarbon fuels by means of the Arrhenius rate data are discussed.

Combustion Fronts in Porous Media

The equations governing combustion in situ in petroleum reservoirs are cast in a way that is appropriate to the study of the time asymptotic fundamental waves: rarefactions and shocks. The physical diffusion terms are maintained so that the internal structure of shocks can be analyzed. In this work, we determine the planar traveling wave solutions for the system of three evolution equations modeling combustion in two phase flow, obtained by neglecting heat losses and volume change effects. The chemical reaction rate is governed by Arrhenius' reaction rate law. Our analysis is intended to capture the main effect of combustion: the reduction of oil viscosity due to temperature increase and its practical result---the increase in oil recovery. It also is intended to resolve the difficulty introduced by the singularity in the Arrhenius reaction rate law. Our analysis shows that the combustion wave is represented by a heteroclinic connection in a nonhyperbolic system of three ordinary differential equations. It follows that numerical simulations need to resolve completely the small parabolic terms in the model to be reliable. The analysis also indicates that the phase diagram should be stable under perturbations of interest. Thus, the general structure of combustion waves in a more realistic model should be similar to the one we found here.

Glowing and flaming autoignition of wood

A study of the autoignition of wood by a radiant cone heater was conducted. Insulated redwood samples were exposed vertically to incident heat flux ranging from 10 to 70 kW/m2. IR thermography and normal video recording were used to view the sample surface. The surface temperature and mass loss were continuously recorded. Glowing and flaming autoignition were defined and examined. The times to glowing and flaming autoignition were measured and compared with the times to flaming piloted ignition. The study found that for incident heat fluxes less than 40 kW/m2, in some cases, the sample surface started to glow (glowing ignition) before a visible flame (flaming ignition) was eventually seen. However, for incident heat fluxes greater than 40 kW/m2, flaming ignition occurred very quickly (within 30 s). The measured ignition time, ignition temperature, and surface temperature history were compared with theoretical values. The mass flux (pyrolysis rate) was assumed to follow an Arrhenius reaction rate. The activation energy and the pre-exponential factor were determined from a best curve fit of the experimental data.

Collective effects and dynamics of non-adiabatic flame balls

The dynamics of a homogeneous, polydisperse collection of non-adiabatic flame balls (FBs) is investigated by analytical/numerical means. A strongly temperature-dependent Arrhenius reaction rate is assumed, along with a light enough reactant characterized by a markedly less than unity Lewis number (Le). Combining activation-energy asymptotics with a mean-field type of treatment, the analysis yields a nonlinear integro-differential evolution equation (EE) for the FB population. The EE accounts for heat losses inside each FB and unsteadiness around it, as well as for its interactions with the entire FB population, namely mutual heating and faster (Le < 1) consumption of the reactant pool. The initial FB number density and size distribution enter the EE explicitly. The latter is studied analytically at early times, then for small total FB number densities; it is subsequently solved numerically, yielding the whole population evolution and its lifetime. Generalizations and open questions relating to ‘spotty’ turbulent combustion are finally evoked.

Thermal degradation kinetics of thiamine in periwinkle based formulated low acidity foods

SummaryThe kinetics of the thermal degradation of thiamine in periwinkle‐in‐brine (PIB), periwinkle‐in‐sauce (PIS) and periwinkle‐in‐egusi soup (PES) were investigated in the temperature range 104–121.1 °C (5–40 min). Thiamine degradation could be modeled as a first order rate reaction with the rates being higher in the brine than the formulated food systems. The temperature dependence of the rates of destruction gave highly significant correlations when analyzed by the thermal resistance, Arrhenius and absolute reaction rate methods. Ea‐values ranged from 107.2 kJ mol–1 in PES to 111.5 KJ mol–1 in PIB. The ΔH# and ΔS# values ranged from 103.9 kJ mol–1 and 52.4 J deg–1 mol–1 respectively in PES to 108.3 kJ mol–1 and –40.5 J deg–1 mol–1 respectively in PIB while the z‐values were 26.3, 25.5 and 25.3 °C for PES, PIS and PIB respectively.

Turbulent transport in spatially developing reacting shear layers

Direct numerical simulation (DNS) of turbulent reacting shear layers with significant heat release and local Reynolds numbers up to 1000 based on the Favre-averaged vorticity thickness was performed. The combustion is simulated by a single-step, second-order reaction with an Arrhenius reaction rate. The transport equations are solved using a low Mach number approximation in which the effects of heat release are accounted for through variable density. Two-dimensional simulations illustrate how growth rate decreases with increasing heat release and how the shear layer is sensitive to reaction rate. A three-dimensional simulation is used to generate data to study in detail how the flame alters the turbulence using budgets of turbulent kinetic energy. The three-dimensional results reveal that turbulent transport and pressure transport have a unique role in the overall energy balance in that they tend to increase kinetic energy near the edges of the layer while decreasing it at the center. Opposite behavior is found for pressure dilatation. Dissiplation and convection everywhere act as sinks for turbulence. The DNS results are compared with the standard k-∈ model for production and turbulent transport. The Boussinnesq approximation with a typical eddy viscosity constant yields the proper profile for production but, in general, overpredicts the peak value. The evaluation also reveals that the dilatation dissipation is small compared with the solenoidal dissipation. The standard gradient-diffusion model for turbulent transport/molecular diffusion is satisfactory when the molecular diffusion is small. The similarity between pressuren transport and turbulent transport suggests that pressure transport could also be modeled using a gradient-diffusion expression.