Finite Reaction Research Articles

Current-Voltage Relations for Electrochemical Thin Films

The dc response of an electrochemical thin film, such as the separator in a micro-battery, is analyzed by solving the Poisson-Nernst-Planck equations, subject to boundary conditions appropriate for an electrolytic/galvanic cell. The model system consists of a binary electrolyte between parallel-plate electrodes, each possessing a compact Stern layer, which mediates Faradaic reactions with nonlinear Butler-Volmer kinetics. Analytical results are obtained by matched asymptotic expansions in the limit of thin double layers and compared with full numerical solutions. The analysis shows that (i) decreasing the system size relative to the Debye screening length decreases the voltage of the cell and allows currents higher than the classical diffusion-limited current; (ii) finite reaction rates lead to the important possibility of a reaction-limited current; (iii) the Stern-layer capacitance is critical for allowing the cell to achieve currents above the reaction-limited current; and (iv) all polarographic (current-voltage) curves tend to the same limit as reaction kinetics become fast. Dimensional analysis, however, shows that ``fast'' reactions tend to become ``slow'' with decreasing system size, so the nonlinear effects of surface polarization may dominate the dc response of thin films.

MODELING GRAVITY EFFECT ON DIFFUSION FLAMES STABILIZED AROUND A CYLINDRICAL WICK SATURATED WITH LIQUID FUEL

The familiar flames from candles and oil lamps are representative examples of wick-stabilized diffusion flames. The shape and burning characteristics of these flames depend strongly on gravity-induced buoyant flows. To obtain a better understanding of the gravity effect, a diffusion flame model has been formulated and numerically solved. In the computation, gravity is treated as a parameter, spanning from zero to the high blowoff limit. The model includes realistic wick and candle geometry but assumes that the wick surface is coated with liquid fuel. The gas-phase formulation consists of the full Navier–Stokes equations with a one-step finite-rate overall chemical reaction. Gas-phase flame radiation, important in low gravity near the quenching limit, is included by solving the axisymmetric radiation transfer equation using the S N discrete ordinates method. The computed results include flame and flow structures, heat flux distributions, the energy budget, and the overall burning characteristics as a function of gravity and wick diameter.

Modeling the propagation of drying and decomposition fronts in wood

Decomposition of moist wood is modeled using the shrinking unreacted-core approximation for a finite rate of reaction and the assumption of a thermally controlled evaporation of moisture across an infinitely thin front at constant temperature. The one-dimensional, quasi-steady (along the char layer) equations also take into account convective, conductive, and radiative heat transfer and different physical properties for char, dry wood, and moist wood. The use of realistic values for all the input parameters results in acceptable agreement between predicted and measured weight losses for 0.04-m-thick beech wood particles (external radiative heat fluxes between 40 and 80 kW/m 2 and initial moisture contents between 0 and 47 wt% on a dry basis). A parametric analysis indicates that, apart from a linear dependence on the moisture content, the characteristic times are especially affected by water evaporation in the case of thick samples. It has also been found that assuming a coincident front for both wood decomposition and moisture evaporation, often done in gasification/combustion models, could be applied with sufficient accuracy only for thick samples with high moisture contents and subjected to severe thermal heating.

Lattice theory of trapping reactions with mobile species.

We present a stochastic lattice theory describing the kinetic behavior of trapping reactions A+B-->B, in which both the A and B particles perform an independent stochastic motion on a regular hypercubic lattice. Upon an encounter of an A particle with any of the B particles, A is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables--"gates," imposed on each B particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the A particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time t, the A particle survival probability is always larger in the case when A stays immobile, than in situations when it moves.

Computational fluid-dynamic model of laser-induced breakdown in air.

Temperature and pressure profiles are computed by the use of a two-dimensional, axially symmetric, time-accurate computational fluid-dynamic model for nominal 10-ns optical breakdown laser pulses. The computational model includes a kinetics mechanism that implements plasma equilibrium kinetics in ionized regions and nonequilibrium, multistep, finite-rate reactions in nonionized regions. Fluid-physics phenomena following laser-induced breakdown are recorded with high-speed shadowgraph techniques. The predicted fluid phenomena are shown by direct comparison with experimental records to agree with the flow patterns that are characteristic of laser spark decay.

Mean-field solution of the parity-conserving kinetic phase transition in one dimension

A two-offspring branching annihilating random walk model, with finite reaction rates, is studied in one-dimension. The model exhibits a transition from an active to an absorbing phase, expected to belong to the $DP2$ universality class embracing systems that possess two symmetric absorbing states, which in one-dimensional systems, is in many cases equivalent to parity conservation. The phase transition is studied analytically through a mean-field like modification of the so-called {\it parity interval method}. The original method of parity intervals allows for an exact analysis of the diffusion-controlled limit of infinite reaction rate, where there is no active phase and hence no phase transition. For finite rates, we obtain a surprisingly good description of the transition which compares favorably with the outcome of Monte Carlo simulations. This provides one of the first analytical attempts to deal with the broadly studied DP2 universality class.

A FINITE-VOLUME-BASED TIME-SPLITTING SCHEME FOR COMPUTATION OF ELECTRODEPOSITION

The LIGA process is emerging as a viable contender in the microfabrication of metallic high-aspect-ratio microstructures. The final step in the LIGA process is the electroplating of the metal part. In this step, metallic ions are transported to the cathode by the fluid and are deposited on it through chemical reactions. There are two kinds of chemical reactions: homogeneous dissociation reactions in the electrolyte bath, and finite-rate surface reactions on the electrode. In this article we develop a finite-volume method for computing electrodeposition in the LIGA process. We employ a time-splitting algorithm for coupling the bulk and surface reactions. First there is an instantaneous equilibration step in which the species existing in a cell are equilibrated to yield an intermediate concentration distribution. This serves as the initial condition to the transport step in which slow reactions and convective and diffusive transport are computed. As an alternative, the species concentration field is solved over the whole domain using a direct method. The two methods are compared to establish the validity and efficiency of the time-splitting algorithm.

Theoretical Performance of a Magnetohydrodynamic-Bypass Scramjet Engine with Nonequilibrium Ionization

The theoretical performance of a scramjet propulsion system in which a magnetohydrodynamic (MHD) energy bypass scheme is operated in a nonequilibrium ionization environment is evaluated. In the MHD generator, the incomingairflow at a temperature too low to produce the required ionization is seeded with cesium and ionized by the use of an unspecified external power source. The resulting nonequilibrium environment is described using a two-temperature model. The accelerator is operated with equilibrium ionization. The expansion through the nozzle is calculated with account taken of finite rate reactions, and the boundary layer is assumed to be fully turbulent. The results show that the required external power is of the same order of magnitude as that of the power generated in the MHD generator. An MHD energy bypass propulsion scheme looks to be more promising with the equilibrium ionization method than with the nonequilibrium ionization method.

Modeling of CO2 capture by aqueous monoethanolamine

AbstractThe process for CO2 removal from flue gases was modeled with RateFrac. It consists of an absorber, a stripper, and a cross heat exchanger. The solvent used in the model contains about 30 wt % monoethanolamine (MEA) in water. MEA reacts with CO2 in the packed absorber. The finite reaction rate requires a kinetic characterization. The RateFrac absorber model was integrated with a FORTRAN user kinetic subroutine to make the model consistent with the interface pseudo‐first‐order model and with a regressed Electrolyte‐NRTL equilibrium model. It was adjusted with laboratory wetted wall column data and field data from a commercial plant. Sensitivity analyses were performed on process variables to find operating conditions at low steam requirement. Many variables strongly affect the process performance, but an overall optimization shows that there are no economical ways to reduce the steam requirements by more than 10%. The reboiler duty can be reduced from that of a base case representing current industrial operating conditions, by 5% if acids are added to the solvent, by 10% if the absorber height is increased by 20%, and by 4% if the absorber is intercooled with a duty of one‐third of the reboiler duty. The power plant lost work is affected by varying stripper pressure, but not significantly, so any convenient pressure can be chosen to operate the stripper.

Effects of wind and oxygen concentration on a laminar diffusion flame established over a horizontal flat plate in micro-gravity environment

An experimental and numerical investigation of a laminar diffusion flame established over a horizontal flat plate in micro-gravity environment is described. Fuel is injected through the burner and the oxidiser (air) is provided by a forced flow parallel to the surface. The experiments were conducted in a range of oxygen concentration from 23% to 30% at two different wind velocities of 2.6 and 4 cm/s in a 5 s drop tower. The flame experiments make use of a pilot wire to ignite the sample in normal-gravity environment. It is observed that after the imposition of the micro-gravity, a pool-like flame is maintained momentarily due to the relaxation of the initial movement of the natural convection. The transition time is about 2.5 s for reducing an oscillated reacting flow to a forced boundary layer one. Two- and three-dimensional, time-dependent numerical solutions to the Navier–Stokes equations are used to simulate the experiments. Combustion process is described by a global one-step, finite-rate reaction given by the Arrhenius expression. Direct numerical simulation is used to provide a detailed description of the transition process of the flame in micro-gravity environment. The model results reflect the qualitative features of the experiments.

On the shock-induced explosion resulting from an impact by a planar detonation

We analyse the processes which occur when a planar detonation propagating from the fixed end of a donor explosive charge impacts on an acceptor homogeneous explosive. We propose a model for estimating the minimal length of the donor charge for which an explosion can be generated in the acceptor. We show that the self-similarity of the donor flow imposes a minimal length on the donor charge so its piston effect be capable of keeping the volumetric-expansion rate of the shocked acceptor to small-enough values and, thereby, of triggering explosion in a finite time. The donor detonation is represented as a Chapman-Jouguet discontinuity; the chemical decomposition in the acceptor is described by the Arrhenius global rate law. The model reproduces the experimental trend according to which the smaller minimal lengths are obtained with donor explosives that have larger heats of reaction and initial pressures. The minimal lengths predicted by the model agree well with those obtained by means of one-dimensional numerical simulations. Additional simulations show that the minimal length for generating an explosion is smaller than, but perhaps of the same order as, the minimal length for generating a transition to detonation. Further work is necessary to (i) analyse the case of donor explosives with finite reaction rates, and to (ii) account for the detonation cellular structure in the simulations of shock-to-detonation transitions.

Numerical Study of the Effect of Methane Combustion on Heat and Mass Transfer and Friction in the Boundary Layer

Calculation results are presented for laminar and turbulent boundary-layer flows on a porous plate with methane injection and combustion. The mathematical model is based on the boundary-layer approximation. Combustion was simulated by one global finite-rate reaction and the kinetic mechanism of hydrogen and carbon oxide afterburning. It is shown that injection and combustion in laminar and turbulent flows lead to more intense displacement of the flow away from the wall than in the case of injection into an isothermal flow, which decreases the friction drag and heat and diffusion fluxes. Combustion in a turbulent flow leads to flow laminarization and delay of the laminar–turbulent transition.

Numerical simulations on the stability of spherical flame structures

The paper presents investigations concerning the stability of spherical flames in a premixed lean hydrogen-air atmosphere and their evolution in case of instabilities. This is done by means of numerical simulations using the thermo-diffusive model with one-step finite rate chemical reaction and radiative heat loss under optically thin conditions. In the first part spherical symmetry is imposed leading to a one-dimensional problem. The results obtained in this way are compared with the asymptotic analysis and the numerical simulations from the literature. In the second part these solutions are employed as initial conditions for fully three-dimensional simulations using a high-resolution pseudo-spectral method. It allows the investigation of the nonlinear transient behavior of spherical flames with respect to three-dimensional perturbations. Different scenarios of their evolution are observed: extinction, spherical growth, and splitting. Also, for the first time, a steady flame ball is computed in a three-dimensional simulation. The different numerical and physical issues are discussed in detail and are related to available experimental observations as well as to theoretical analyses.

EFFECTS OF FINITE REACTION RATES ON THE KINETIC PHASE TRANSITIONS IN THE CATALYTIC OXIDATION OF CARBON MONOXIDE

Oxidation of carbon monoxide is one of the most extensively studied heterogeneous catalysis reactions, being important among other applications in automobile-emission control. Catalytic oxidation of carbon monoxide on platinum (111) surface was simulated by the Monte Carlo technique following an extended version of the model proposed by Ziff, Gulari and Barshad (ZGB). In the simulation, a simple square two-dimensional lattice of active sites replaces the surface of the catalyst. Finite reaction rates for (i) diffusion of the reactive species on the surface, (ii) reaction of a CO molecule with an oxygen atom in a nearest neighbor site, and (iii) desorption of unreacted CO molecules, have been taken into account. The produced CO 2 desorbs instantly. The average coverage of O, CO and the CO 2 production rate for a steady state configuration, as a function of the normalized CO partial pressure (P CO ), shows two kinetic phase transitions. In the ZGB model these transitions occur at P CO ≈ 0.39 and P CO ≈ 0.53. For 0.39 < P CO < 0.53 a reactive ( CO 2 production) steady state is found. Outside of the interval, the only steady state is a poisoned catalyst of pure CO or pure O. Our results show that finite reaction rates shift the values in which these phase transitions occur.

Sub-grid scale modeling of heterogeneous chemical reactions and transport in full-scale catalytic converters

This article presents a novel approach to treat heterogeneous catalytic reactions occurring in porous or honeycomb monoliths. The approach allows accurate modeling of full-scale catalytic converters with low computational cost. In this approach, the entire catalytic monolith is treated as an anisotropic porous medium, and sub-grid scale models are employed to represent the heterogeneous chemical reactions occurring at the solid-fluid interfaces within the monolith. Full coupling between fluid flow, heat transfer, species transport, and heterogeneous chemical reactions is achieved through flux balance of species and energy at the solid-fluid interfaces. The model allows for unlimited number of finite-rate reaction steps and species, including surface-adsorbed species and site coverage effects. The model was validated for hydrogen-assisted combustion of methane-air mixtures over platinum catalyst clusters in a full-scale catalytic converter. Validation against experimental data exhibits excellent match for ignition temperature for various methane and/or hydrogen inlet concentrations. Transient calculations show that the time constant for ignition matches well with previously reported results. Because the model is based on a sub-grid scale approach, it is orders of magnitude more efficient for modeling full-scale catalytic converters than conventional approaches where each channel within the catalytic monolith has to be represented by a computational grid.

Flame Stability Analysis of Turbulent Non-Premixed Reacting Flow in a Simulated Solid-Fuel Ramjet Combustor

ABSTRACTTo investigate the flame stability in a solid-fuel ramjet combustor, time-accurate calculations using a compressible flow solver with a modified Godunov flux-splitting scheme have been performed on high Reynolds number turbulent non-premixed reacting flows over a backward-facing step with mass bleed on one wall. The combustion process considered was a one-step, irreversible, and finite rate chemical reaction. The numerical results for reacting flows show that the two-dimensional (2-D) simulations can provide reasonable predictions on the dimensionless particle number decay rate and residence time in the flame holding recirculation zone, evolutions of both axial and transverse mean velocity profiles, and critical characteristic exhaust velocity separating the sustained combustion from the non-sustained combustion. In addition to the validation of 2-D reacting flow calculations, two- and three-dimensionally computed mean-velocity profiles are compared with existing experimental data for isothermal flows to check the suitability of 2-D simulations on capturing the large-scale mean flows.

논문 : 유한속도 화학반응을 고려한 초음속 로켓의 플룸 유동장 해석

케로신/액체산소 추진기관을 갖는 초음속 로켓의 플룸 유동장을 9 화학종 14 반응 모델과 연계된 레이놀즈 평균 Navier-Stokes 방정식을 이용하여 해석하였다. 유한속도 화학반응이 플룸 유동장에 미치는 영향을 고찰하기 위하여 그 결과를 화학적 동결유동 해석 결과와 비교하였다. 계산은 상용 CFD 소프트웨어인 FLUENT 5를 이용하여 수행하였다. 반응 유동 해석 결과는 노즐 내부에서의 화학반응에 따른 연소가스의 온도 증가로 인해 전체적으로 동결유동에 비해 더 높은 온도장을 나타내었다. 플룸에서의 모든 화학반응은 전단류와 배럴 충격파 반사지점 후방의 고온 영역에 국한되어 일어났으며 본 해석의 경우 플룸내에서의 유한속도 화학반응이 유동에 미치는 영향은 미약한 것으로 나타났다. 그러나 본 연구에서 이루어진 유한속도 화학반응을 고려한 플룸 해석을 통하여 플룸에서의 주된 화학 반응 및 이들의 반응 메커니즘을 확인할 수 있었다. A supersonic rocket plum flowfield of kerosene/liquid-oxygen based propulsion system has been analysed using the Reynolds-averaged Navier-Stokes equations coupled with a 9-species 14-reaction finite-chemistry model. The result were compared with chemically frozen flow solution to investigate the effect of finite-rate chemistry on the plume flowfield. The computations were performed using a commercial CFD software, FLUENT 5. The finite-rate chemistry solution exhibited higher temperature caused by the reactions within the nozzle. All the chemical reactions within the plum were dominated only in the shear layer and behind the barrel shock reflection region where the temperatures are high and the effect of finite-rate chemical reactions on the flowfield was found to be insignificant. However, the present plume computation including the finite-rate chemical reaction within the plume has revealed major reactions occurring in the plum and their reaction mechanisms.

Propagation and extinction mechanisms of opposed-flow flame spread over PMMA

To understand the propagation and the extinction mechanisms of spreading flame along a solid fuel, opposed-flow flame spread along a thick polymethyl methacrylate slab was experimentally investigated for several airflow rates from 0 to 0.67 m/s. The detailed temperature structure during flame spread near the flame leading edge was measured using holographic interferometry and IR thermography. The particletract laser sheet (PTLS) technique was employed to measure the local entrainment velocity to the flame front at the leading edge. This study found that the flame spread rate with a constant speed is proportional to the net total heat transfer rate. The heat transfer rate from the gas phase, Qy, is about 60% of the total heat transfer rate, QT, in the no imposed flow condition (u=0m/s). However, the heat transfer rate through the condensed phase, Qx, is over 80% of QT in the opposed flow near the extinction limit (u¯≈0.65m/s). The radiative heat loss from the surface, QR, increases with increasing opposed-flow rate and reaches at most 13% of QT at u¯≈0.65m/s. In spite of enough heat feedback to the condensed phase near the flame leading edge, the flame spread rate rapidly decreases close to the extinction limit. In order to interpret the extinction mechanism, we introduce the burning rate at the finite flame sheet with finite chemical reaction rate. The PTLS result shows that the local entrainment velocity at the flame leading edge increases with increasing opposed-flow rate. When the local entrainment velocity exceeds the burning rate at the leading edge, the flame may not be sustained. The flame retreats and finally it is extinguished.

Directed Energy Air Spike による空力加熱率減少の数値シミュレーション

This paper presents a computational parametric study showing how heat release affects aerodynamic characteristics, drag and heating rate, of a hypersonic flow over an axisymmetric blunt body. A chemical non-equilibrium viscous flow is assumed together with seven chemical species and finite-rate chemical reactions. Results show that heat release in the upstream of the body can reduce not only the aerodynamic drag but also the aerodynamic heating rate on the body. Three parameters which control heat release are introduced and their effects on the flow structure, especially on the drag and the heating rate, are presented. It is shown that the drag is reduced to 23% of the baseline value (the drag of the flow without heat release) and the aerodynamic heating rate to 76%.

Finite temperature amplitudes and reaction rates in thermofield dynamics

We propose a method for calculating the reaction rates and transition amplitudes of generic process taking place in a many body system in equilibrium. The relationship of the scattering and decay amplitudes as calculated in Thermo Field Dynamics the conventional techniques is established. It is shown that in many cases the calculations are relatively easy in TFD.