Homogeneous Schemes Research Articles

Relaying phase synchrony in chaotic oscillator chains

We study the manner in which the effect of an external drive is transmitted through mutually coupled response systems by examining the phase synchrony between the drive and the response. Two different coupling schemes are used. Homogeneous couplings are via the same variables while heterogeneous couplings are through different variables. With the latter scenario, synchronization regimes are truncated with an increasing number of mutually coupled oscillators in contrast to homogeneous coupling schemes. Our results are illustrated for systems of coupled chaotic Rössler oscillators.

Microphysical simulations of new particle formation in the upper troposphere and lower stratosphere

Abstract. Using a three-dimensional general circulation model with sulfur chemistry and sectional aerosol microphysics (WACCM/CARMA), we studied aerosol formation and microphysics in the upper troposphere and lower stratosphere (UTLS) as well as the middle and upper stratosphere based on three nucleation schemes (two binary homogeneous schemes and an ion-mediated scheme related to one of the binary schemes). Simulations suggest that ion-mediated nucleation rates in the UTLS are 25 % higher than its related binary scheme, but that the rates predicted by the two binary schemes vary by two orders of magnitude. None of the nucleation schemes is superior at matching the limited observations available at the smallest sizes. However, it is found that coagulation, not nucleation, controls number concentration at sizes greater than approximately 10 nm. Therefore, based on this study, processes relevant to atmospheric chemistry and radiative forcing in the UTLS are not sensitive to the choice of nucleation schemes. The dominance of coagulation over other microphysical processes in the UTLS is consistent with other recent work using microphysical models. Simulations using all three nucleation schemes compare reasonably well to observations of size distributions, number concentration across latitude, and vertical profiles of particle mixing ratio in the UTLS. Interestingly, we find that we need to include Van der Waals forces in our coagulation scheme to match the UTLS aerosol concentrations. We conclude that this model can reasonably represent sulfate microphysical processes in the UTLS, and that the properties of particles at atmospherically relevant sizes appear to be insensitive to the details of the nucleation scheme. We also suggest that micrometeorites, which are not included in this model, dominate the aerosol properties in the upper stratosphere above about 30 km.

Performance analysis of UPQC with heterogeneous control during load power factor variation

SUMMARYThis paper deals with the analysis of a unified power quality conditioner (UPQC) with a new heterogeneous control applied to its active power filters (APF). This control, when applied to the APFs of UPQC, relieves completely the reactive power burden of the source and makes the input power factor unity. The proposed control, termed as heterogeneous control, utilizes sinusoidal pulse width modulation (SPWM) for series APF (SAPF) and hysteresis PWM for parallel APF (PAPF). No transformation is used in this control for generating the reference quantities for both voltage and current. The performance of UPQC with the proposed control is compared with other transformation less homogeneous control schemes which include hysteresis and SPWM for both APFs. The heterogeneous control performance is found superior in terms of complete reactive power support from the PAPF with reduced APF ratings. PSCAD/EMTDC simulation results are presented to show the effectiveness of the proposed control. Copyright © 2011 John Wiley & Sons, Ltd.

Problems of heat, mass and charge transfer with discontinuous solutions

Typical problems with solutions characterised by first-kind discontinuities occurring at interfaces of layered inhomogeneous media are considered with respect to second-order differential equations in partial derivatives. Direct, inverse and mixed types of solution discontinuities are considered. Presented are generalised formulations of problems under consideration, having discontinuous solutions and allowing a uniform description of the processes of heat, mass and charge transfer in multilayer media. Homogeneous difference schemes built on the basis of generalised solutions, which are illustrated by test problems with analytical solutions, are given.

Homogeneous combustion of fuel-lean H 2/O 2/N 2 mixtures over platinum at elevated pressures and preheats

The gas-phase combustion of H 2/O 2/N 2 mixtures over platinum was investigated experimentally and numerically at fuel-lean equivalence ratios up to 0.30, pressures up to 15 bar and preheats up to 790 K. In situ 1-D spontaneous Raman measurements of major species concentrations and 2-D laser induced fluorescence (LIF) of the OH radical were applied in an optically accessible channel-flow catalytic reactor, leading to the assessment of the underlying heterogeneous (catalytic) and homogeneous (gas-phase) combustion processes. Simulations were carried out with a 2-D elliptic code that included elementary hetero-/homogeneous chemical reaction schemes and detailed transport. Measurements and predictions have shown that as pressure increased above 10 bar the preheat requirements for significant gas-phase hydrogen conversion raised appreciably, and for p = 15 bar (a pressure relevant for gas turbines) even the highest investigated preheats were inadequate to initiate considerable gas-phase conversion. Simulations in channels with practical geometrical confinements of 1 mm indicated that gas-phase combustion was altogether suppressed at atmospheric pressure, wall temperatures as high as 1350 K and preheats up to 773 K. While homogeneous ignition chemistry controlled gaseous combustion at atmospheric pressure, flame propagation characteristics dictated the strength of homogeneous combustion at the highest investigated pressures. The decrease in laminar burning rates for p ⩾ 8 bar led to a push of the gaseous reaction zone close to the channel wall, to a subsequent leakage of hydrogen through the gaseous reaction zone, and finally to catalytic conversion of the escaped fuel at the channel walls. Parametric studies delineated the operating conditions and geometrical confinements under which gas-phase conversion of hydrogen could not be ignored in numerical modeling of catalytic combustion.

Experimental and numerical investigation of hetero-/homogeneous combustion of CO/H 2/O 2/N 2 mixtures over platinum at pressures up to 5 bar

The hetero-/homogeneous combustion of fuel-lean CO/H 2/O 2/N 2 mixtures over platinum is investigated at pressures up to 5 bar, inlet temperatures ( T IN) up to 874 K, and a constant CO:H 2 molar ratio of 2:1. Experiments are performed in an optically accessible channel-flow catalytic reactor and involve planar laser induced fluorescence (LIF) of the OH radical for the assessment of homogeneous (gas-phase) ignition and 1-D Raman measurements of major gas-phase species concentrations over the catalyst boundary layer for the evaluation of the heterogeneous (catalytic) processes. Simulations are carried out with an elliptic 2-D model that includes detailed heterogeneous and homogeneous chemical reaction schemes. The predictions reproduce the Raman-measured catalytic CO and H 2 consumption, and it is further shown that for wall temperatures in the range 975 ⩽ T w ⩽ 1165 K the heterogeneous pathways of CO and H 2 are largely decoupled. However, for wall temperatures below a limiting value of 710–720 K and for the range of pressures and mixture preheats investigated, CO(s) blockage of the surface inhibits the catalytic conversion of both fuel components. The homogeneous ignition distance is well-reproduced by the model for T IN > 426 K, but it is modestly overpredicted at lower T IN. Possible reasons for these modest differences can be the values of third body efficiencies in the gas-phase reaction mechanism. The sensitivity of homogeneous ignition distance on the catalytic reactions is weak, while the H 2/O 2 subset of the CO/H 2/O 2 gaseous reaction mechanism controls the onset of homogeneous ignition. Pure hydrogen hetero-/homogeneous combustion results in flames established very close to the catalytic walls. However, in the presence of CO the gaseous combustion of hydrogen extends well-inside the channel core, thus allowing homogeneous consumption of H 2 at considerably shorter reactor lengths. Finally, implications of the above findings for the design of syngas-based catalytic reactors for power generation systems are discussed.

Differential operators and automorphism schemes

The ring of global differential operators of a variety is in closed and deep relation with its automorphism scheme. This relation can be applied to the study of homogeneous schemes, giving some criteria of homogeneity, a generalization of Serre-Lang theorem, and some consequences about abelian varieties.

Flame dynamics in catalytic and non-catalytic mesoscale microreactors

The dynamics of fuel-lean (equivalence ratio φ = 0.5) premixed hydrogen/air flames are investigated numerically in a 2-mm-height planar channel with platinum-coated walls, as a function of the inlet velocity and catalytic reactivity. An elliptic 2-D transient code is used, with elementary heterogeneous (catalytic) and homogeneous (gas-phase) chemical reaction schemes and detailed transport. The channel wall temperature is prescribed and the inlet properties are uniform. The catalytic reactivity is controlled by varying the model parameter A s, which denotes the ratio of the catalytically active area to the geometrical channel surface area. It is shown that the rich flame dynamics of the non-catalytic case ( A s = 0), which include non-stationary repetitive ignition/extinction and oscillating flames, can be suppressed by suitable selection of the catalytic reactivity. The repetitive/ignition extinction flames are eliminated at A s = 0.003 and the oscillating ones for A s > 0.01, while for higher values of A s only stationary “closed symmetric” and “asymmetric” flames are obtained. The results suggest that the application of a predetermined catalyst loading on the channel walls is a feasible method to eliminate unsteady combustion modes in practical mesoscale reactors.

CFD Simulation of Catalytic Oxidation of Ethyl Acetate over Cr-HZSM-5 Catalyst

This paper reports the results of a study on a three-dimensional computational fluid dynamics (CFD) simulation for a study of gas catalytic oxidation of ethyl acetate over Cr-HZSM-5 catalyst. A gaseous stream, containing N2, O2 and ethyl acetate (in which ethyl acetate concentration in mixture was 2000 ppmV) with GHSV= 32000 h-1 as the feed, was inserted into a glass reactor, charged with a required amount of Cr-HZSM-5 catalyst under atmospheric pressure. The catalytic reactions were allowed to occur at atmospheric pressure and at different temperatures. Fluent 6.2 was used for the simulation of the catalytic process. The simulation was present for the model geometry of 20 solid spheres in a tube with a tube-to-particle diameter ratio equal to 2. Results of the simulation showed a good agreement with the experimental results. It was experimentally, and by simulation, observed that the increasing of the temperature and the decreasing of the inlet mass flow rate led to the increase of ethyl acetate conversion. Velocity vector profiles of the fluid were obtained with an emphasis on the catalytic region. Temperature and pressure contours of the fluid inside the reactor were predicted by simulation. Furthermore, the surface deposition rate of oxygen (during the step of catalyst oxidation) and species concentration along the reactor were obtained. This study revealed that CFD is the best tool to study detailed homogeneous and heterogeneous reaction schemes, even for complex catalyst geometries.

Suppression of combustion instabilities of premixed hydrogen/air flames in microchannels using heterogeneous reactions

The dynamics of fuel-lean ( φ = 0.5) premixed hydrogen/air atmospheric pressure flames are investigated numerically in a 1-mm-height planar channel with platinum-coated walls, as a function of the inlet velocity and the catalytic reactivity. Simulations are carried out with a fully elliptic 2D transient code that includes detailed heterogeneous (catalytic) and homogeneous (gas-phase) chemical reaction schemes. The channel wall temperature is prescribed and the inlet properties are uniform, while the catalytic reactivity is controlled by varying the parameter A s, which is the ratio of the catalytically-active area to the geometrical channel surface area. It is shown that the rich flame dynamics of the non-catalytic case ( A s = 0), which include oscillating and asymmetric flame modes, can be suppressed by appropriate selection of the catalytic reactivity. The oscillating flames disappear at A s = 6 × 10 −3 and the asymmetric ones at A s = 1.15 × 10 −2, while for higher values of A s only stationary and symmetric V-shaped flames are obtained. The suppression of the flame dynamics can be attributed to the theoretically-predicted diminishing sensitivity of the homogeneous ignition distance to small perturbations of the gaseous reactivity with increasing catalytic reactivity. The results indicate that a feasible way to eliminate undesirable unsteady combustion modes in practical microcombustors is to apply a pre-determined catalyst loading on the channel walls.

Experimental and numerical investigation of the hetero-/homogeneous combustion of lean propane/air mixtures over platinum

The pure heterogeneous and the coupled hetero-/homogeneous combustion of fuel-lean propane/air mixtures over platinum have been investigated at pressures 1 bar ⩽ p ⩽ 7 bar, fuel-to-air equivalence ratios 0.23 ⩽ φ ⩽ 0.43, and catalytic wall temperatures 723 K ⩽ T w ⩽ 1286 K. Experiments were performed in an optically accessible catalytic channel-flow reactor and involved 1-D Raman measurements of major gas-phase species concentrations across the reactor boundary layer for the assessment of catalytic fuel conversion and planar laser induced fluorescence (LIF) of the OH radical for the determination of homogeneous ignition. Numerical predictions were carried out with a 2-D elliptic CFD code that included a one-step catalytic reaction for the total oxidation of propane on Pt, an elementary C 3 gas-phase chemical reaction mechanism, and detailed transport. A global catalytic reaction step valid over the entire pressure–temperature-equivalence ratio parameter range has been established, which revealed a ∼ p 0.75 dependence of the catalytic reactivity on pressure. The aforementioned global catalytic step was further coupled to a detailed gas-phase reaction mechanism in order to simulate homogeneous ignition characteristics in the channel-flow reactor. The predictions reproduced within 10% the measured homogeneous ignition distances at pressures p ⩽ 5 bar, while at p = 7 bar the simulations overpredicted the measurements by 19%. The overall model performance suggests that the employed hetero-/homogeneous chemical reaction schemes are suitable for the design of propane-fueled catalytic microreactors.

Hetero-/homogeneous combustion of hydrogen/air mixtures over platinum at pressures up to 10 bar

The hetero-/homogeneous combustion of fuel-lean hydrogen/air premixtures over platinum was investigated experimentally and numerically in the pressure range 1 bar ⩽ p ⩽ 10 bar. Experiments were carried out in an optically accessible channel-flow catalytic reactor and included planar laser induced fluorescence (LIF) of the OH radical for the assessment of homogeneous (gas-phase) ignition, and 1-D Raman measurements of major gas-phase species concentrations for the evaluation of the heterogeneous (catalytic) processes. Simulations were performed with a full-elliptic 2-D model that included detailed heterogeneous and homogeneous chemical reaction schemes. The predictions reproduced the measured catalytic hydrogen consumption, the onset of homogeneous ignition at pressures of up to 3 bar and the diminishing gas-phase combustion at p ⩾ 4 bar. The suppression of gaseous combustion at elevated pressures bears the combined effects of the intrinsic homogeneous hydrogen kinetics and of the hetero/homogeneous chemistry coupling via the catalytically produced water over the gaseous induction zone. Transport effects, associated with the large diffusivity of hydrogen, have a smaller impact on the limiting pressure above which gaseous combustion is suppressed. It is shown that for practical reactor geometrical confinements, homogeneous combustion is still largely suppressed at p ⩾ 4 bar even for inlet and wall temperatures as high as 723 and 1250 K, respectively. The lack of appreciable gaseous combustion at elevated pressures is of concern for the reactor thermal management since homogeneous combustion moderates the superadiabatic surface temperatures attained during the heterogeneous combustion of hydrogen.

Convergence rate of vector subdivision scheme

In this paper, some characterizations on the convergence rate of both the homogeneous and nonhomogeneous subdivision schemes in Sobolev space are studied and given.

Experimental and numerical investigation of supported rhodium catalysts for partial oxidation of methane in exhaust gas diluted reaction mixtures

The partial oxidation of methane/oxygen mixtures with large exhaust gas dilution (46.3 vol% H 2 O and 23.1 vol% CO 2 ) has been investigated experimentally and numerically over Rh / CeO 2 – ZrO 2 , Rh / ZrO 2 and Rh / α - Al 2 O 3 catalysts. Experiments were carried out in a short-contact-time ( ∼ 8 ms ) reactor at 5 bar and included exhaust gas analysis, temperature measurements along the reactor, and catalyst characterization. Additional experiments were performed in an optically accessible channel-flow reactor and involved in situ Raman measurements of major gas-phase species concentrations over the catalyst boundary layer and laser-induced fluorescence (LIF) of formaldehyde. A full elliptic two-dimensional numerical code that included elementary hetero-/homogeneous chemical reaction schemes and relevant heat transfer mechanisms in the solid was used in the simulations. The employed heterogeneous reaction mechanism, including only active Rh sites, reproduced the experiments with good accuracy. The ratio of active to geometrical surface area, deduced from hydrogen chemisorption measurements, was the single model parameter needed to account for the effect of different supports. This indicated that water activation occurring on support sites, resulting in inverse OH spillover from the support to the noble metal sites, could be neglected under the present conditions with high water dilution. An evident relationship between noble metal dispersion and catalytic behavior, in terms of methane conversion and synthesis gas yields, could be established. Both measurements and predictions indicated that an increasing Rh dispersion (in the order Rh / α - Al 2 O 3 , Rh / ZrO 2 , and Rh / CeO 2 – ZrO 2 ) resulted in higher methane conversions, lower surface temperatures, and higher synthesis gas yields.

Applying the dual operator formalism to derive the zeroth-order boundary function of the plasma-sheath equation

The article constructs the asymptotic solution of the Tonks-Langmuir integro-differential equation with an Emmert kernel, which describes the potential both in the bulk plasma and in a narrow boundary layer. Equations of this type are singularly perturbed, because the highest order (second) derivative is multiplied by a small coefficient. The asymptotic solution is obtained by the boundary function method. The second-order differential equation describing the behavior of the zeroth-order boundary function is investigated using the dual operator formalism — an analog of the conjugate operator in the linear theory. The application of this formalism has produced an asymptotic solution and has also made it possible to propose a number of homogeneous discrete three-point schemes for solving the equation.

Laser induced fluorescence of formaldehyde and Raman measurements of major species during partial catalytic oxidation of methane with large H 2O and CO 2 dilution at pressures up to 10 bar

The catalytic partial oxidation (CPO) of CH 4/O 2 mixtures diluted with large amounts of H 2O and CO 2 (up to 43% and 21% vol., respectively) was investigated experimentally and numerically in the pressure range 4 bar ⩽ p ⩽ 10 bar. Experiments were carried out in an optically accessible channel-flow catalytic reactor coated with Rh/ZrO 2, and included planar laser induced fluorescence (LIF) of formaldehyde for the assessment of homogeneous (gas-phase) ignition and one-dimensional spontaneous Raman measurements of all major gas-phase species for the evaluation of the heterogeneous (catalytic) processes. Simulations were performed with a full elliptic model that included detailed heterogeneous and homogeneous chemical reaction schemes. Over the reactor length with negligible gas-phase chemistry contribution, the employed heterogeneous reaction scheme provided good agreement to the measured methane consumption and synthesis gas yields, overpredicting mildly the partial over the total oxidation route. It was shown that the added water provided a source of O(s) and OH(s) surface radicals that enhanced the methane conversion and H 2 yields and reduced the CO yields. Moreover, the addition of CO 2 had a negligible chemical effect on the aforementioned parameters. An increase in pressure from 4 to 10 bar had a minor impact on the methane conversion and hydrogen selectivity. The employed gaseous scheme reproduced the LIF-measured onset of homogeneous ignition, although it underpredicted the extent of the formaldehyde zone ahead of the flame and the flame propagation characteristics at the highest investigated pressure (10 bar).

Hetero-/homogeneous combustion and stability maps in methane-fueled catalytic microreactors

The hetero-/homogeneous steady combustion and the stability limits of methane-fueled catalytic microreactors (Pt-coated) have been investigated numerically in a 1-mm-gap channel at pressures of 1 and 5 bar. Computations were carried out with a full-elliptic two-dimensional model for the gas- and solid-phases that included elementary heterogeneous and homogeneous chemical reaction schemes, heat conduction in the solid wall, surface radiation heat transfer, and external heat losses. Gas-phase chemistry extended the low-velocity stability limits due to the establishment of strong flames and to an even greater degree the high-velocity blowout limits due to the heat release originating primarily from the incomplete homogeneous oxidation of methane. When considering the same mass throughput, the stable combustion envelope at 5 bar was substantially wider than its 1 bar counterpart due to the increased reactivity of both catalytic and gaseous pathways at elevated pressures. Stable combustion could be sustained with solid thermal conductivities at least as low as 0.1 W/mK, while the stability limits reached their larger extent between 20 and 50 W/mK, a range that covers many practical metallic compounds. The stability limits of catalytic microreactors were wider than those reported for non-catalytic systems. Surface radiation heat transfer greatly impacted the microreactor energy balance and combustion stability. At conditions well-below the stability limits, surface radiation provided an efficient heat loss mechanism that moderated the surface temperatures, whereas close to the limits it could stabilize combustion by transferring heat from the hotter rear of the channel to the colder front. Investigation of smaller confinements has shown that gas-phase combustion could be sustained in catalytic microreactors with gaps as low as 0.3 mm.

Modeling the high-temperature catalytic partial oxidation of methane over platinum gauze: Detailed gas-phase and surface chemistries coupled with 3D flow field simulations

The high-temperature catalytic partial oxidation (CPO) of methane over a platinum gauze reactor was modeled by three-dimensional numerical simulations of the flow field coupled with heat transport as well as detailed gas-phase and surface reaction mechanisms. Model results agree well with data of CPO experiments over Pt-gauzes in the literature, confirming the presence of strong mass and heat-transport limitations. The conversions of CH 4 and O 2 increase with an increased contact time and were practically constant in the temperature range of 1000–1200 K. The selectivity to CO linearly increases with temperature. H 2 was only observed above 1200 K, below this temperature H 2O was the only hydrogen-containing product. The contribution of heterogeneous steps in the overall process is prominent, but in the later stages of the reactor, gas-phase reactions become significant at certain conditions of temperature, pressure, and residence time. For example, simulations predicted some gas-phase production of ethane and ethylene via methane oxidative coupling at elevated pressure and residence time. The study shows that today's CFD tools allow the implementation of detailed homogeneous and heterogeneous reaction schemes even for complex catalyst geometries.

Experimental and numerical investigation of the catalytic partial oxidation of [formula omitted] mixtures diluted with [formula omitted] and [formula omitted] in a short contact time reactor

The catalytic partial oxidation (CPO) of fuel-rich CH 4 / O 2 mixtures, heavily diluted with H 2 O and CO 2 (46.3% and 23.1% volumetric feed composition, respectively), was investigated experimentally and numerically at 5 bar. Experiments were carried out in an ∼ 8 ms residence time prototype gas-turbine honeycomb reactor coated with a Rh/ ZrO 2 catalyst and included temperature measurements along the reactor and exhaust gas analysis. Simulations with detailed hetero-/homogeneous chemical reaction schemes were performed using a steady, full elliptic 2D code for both the gas and solid phases. The employed catalytic reaction scheme overpredicted mildly the impact of the total over the partial oxidation route and this effect was more pronounced at lower reactor inlet temperatures ( < 523 K ). The contribution of the various chemical pathways to the synthesis gas yields and selectivities has been elucidated. It was shown that the addition of water provided a source of surface oxygen and hydroxyl radicals, which in turn enhanced the CH 4 conversion and H 2 selectivity and reduced the CO selectivity. On the other hand, the addition of CO 2 had a minor impact on the aforementioned parameters. The increase in the H 2 / CO product ratio with water dilution is highly desirable in new power generation processes with large exhaust gas recycle, which utilize the “catalytic rich combustion” methodology (the partial oxidation products stabilize a post-catalyst flame). At steady operation the catalyst surface temperatures exceeded by 200 K the adiabatic equilibrium temperature and standard (passive) heat transfer mechanisms in the solid were shown to be ineffective in providing proper reactor thermal management. Catalytic ignition was achieved at 670 K, however, the strong ignition/extinction hysterisis allowed for sustained steady CPO at inlet temperatures as low as 473 K.

Characteristics of Co-combustion of Low-Rank Coal with Biomass

The fundamentals of ignition, NOx (NO and N2O) emissions, and ash formation characteristics for biomass and mixtures of coal with biomass are precisely elucidated in this study. In this study, biomass, coal, and a biomass−coal mixture are burned, using an electrically heated drop tube furnace. In the combustion test, the focus is on the ignition behavior, combustion efficiency, NOx emission behavior, and formation characteristics of particulate matter, based on the results of gas compositions along the furnace axis and a collection of particulate matter by a low-pressure impactor. As a result, the addition of biomass into low-rank coal affects combustion behavior, especially for ignition enhancement. The NO and N2O concentrations in co-combustion are almost the same as those in coal combustion, even if the quantity of input fuel nitrogen under the co-combustion condition is half of that under the coal combustion conditions. A kinetic simulation of the NO and N2O behavior results is conducted, using the homogeneous reaction schemes at constant temperature. The simulation result of NO concentration agrees with the experimental result obtained. However, the N2O concentration calculated is less than the experimental result, because the heterogeneous schemes that are related to N2O are not considered in this simulation. Fine particulates with a size of <2 μm during biomass combustion are produced. Burning the biomass with coal shifts the particle size distribution from fine particles to coarse particles, which can be captured by dust collection systems.