Comparisons between thermodynamic and one-dimensional combustion models of spark-ignition engines

A one-dimensional combustion model, employing a constant eddy diffusivity and a one-step chemical reaction, has been developed and applied to study the flame propagation in a spark-ignition engine. Calculations have been made at 1600 and 4200 rev min⁻¹ under fuel rich conditions and compared with available engine pressure data. One- and two-zone thermodynamic models have also been developed and applied to study the combustion process in the engine. The thermodynamic models have been compared with the one-dimensional model results and comparisons include the average mixture temperature, the temperatures of the burned and unburned gases and the flame surface area. These comparisons indicate that the one-dimensional model predictions are very sensitive to the eddy diffusivity and reaction rate data. The two-zone thermodynamic model predicts, first, a monotonically increasing flame surface area with time and, then, a monotonically decreasing surface area, whereas the one-dimensional model always predicts a monotonically increasing flame surface area. The average mixture temperature predicted by the one-zone thermodynamic model is higher than those of the two-zone and one-dimensional models during the compression stroke, while that of the one-dimensional model is higher than the temperatures predicted by the one- and two-zone models during the expansion stroke. The one-dmensional model predicts an accelerating flame even when the front approaches the cold cylinder wall. This yields a faster fuel consumption rate than those predicted by the one- and two-zone thermodynamic models which predict smoother burned fuel mass profiles.     

Trace element concentrations in an urban area and source identification

Summary A winter sampling programme of measurements of 10 trace elements (SO ₄ ⁼ , Fe, Pb, Zn, K, Ca, Mg, Cd, Cr and Ni) was performed at four different locations (two samples points were located in the city centre, another one in a suburban area and the other one in the outskirts) in the city of Valladolid (Spain), with the purpose of identifying the main sources that contribute to their presence in the environment. In order to identify the specific sources of the trace elements analysed,R andQ clustering techniques have been applied to the concentrations of these trace elements. The comparison of the results obtained through these techniques, their ability for getting information as well as their advantages and disadvantages are discussed.

---

Riassunto è stato eseguito un programma di campionamento invernale di misurazioni di 10 elementi in tracce (SO ₄ ⁼ , Fe, Pb, Zn, K, Ca, Mg, Cd, Cr e Ni) in quattro diverse località (due punti dei campionatori si trovavano nel centro della città, uno nell'area suburbana ed un altro in periferia) della città di Valladolid (Spagna), allo scopo d'identificare le principali fonti che contribuiscono alla loro presenza nell'ambiente. Per identificare le fonti specifiche degli elementi in tracce analizzati, sono state applicate le tecniche di accumulazione alle concentrazioni di questi elementi in tracce. Si discute il confronto tra i risultati ottenuti con queste tecniche, la loro capacità di ottenere informazioni, nonchè i loro vantaggi e svantaggi.

---

Резюме Приводятся результаты измерений по зимней программе контроля концентрации 10 элементов (SO ₄ ⁼ , Fe, Pb, Zn, K, Ca, Mg, Cd, Cr, и Ni) в 4 различных точках города Валладолида (Испания) (2 точки расположены в центре города, одна в городской зоне и одна на окраине). Цель программы—идентификация главных источников, которые дают вклад в загрязнение окружающей среды. Чтобы идентифицировать источники проанализированных элементов, используется техникаR иQ кластеризации для определения концентраций этих элементов. Проводится сравнение полученных результатов. Обсуждаются возможности этих методик для получения информации, а также их преимущества и недостатки.

     

Study of low concentrations of dicumyl peroxide on the molecular structure modification of LLDPE by reactive extrusion

The effect of low concentrations of dicumyl peroxide (DCP) on the molecular weight of a linear low density polyethylene (LLDPE) during a reactive extrusion process was studied. The experiments were arranged in a two level factorial design in order to evaluate the effect of peroxide concentration (X₂), temperature zones (X₁) and screw rpm (X₃) on the crosslinking of LLDPE. The melt flow index (MFI) was used as a response variable. It was verified that the thermal properties, crystalline melting temperature (T_m), the heat of fusion (ΔH_melt) and the degree of crystallinity (X%) tend to decrease with increase of the peroxide concentration. The crystallization temperature (T_c) increased up to 0.5% w/w peroxide, whereafter the level stays almost constant. In this study, it was also verified through the dynamic rheological data that there was an increase of the complex viscosity and the complex modulus (G′ and G″). These results can be an indication that there was an increase of the polymer average molecular weight (M_w) and polydispersity (MWD). The gel content of the samples, however, indicated that a three-dimensional network was negligible in the experimental conditions used.     

Nucleophilic Addition to C,C-Double Bonds. Part VIII. The standard enthalpies of formation of anti9,10-10endo-hydroxytricyclo [4.2.1.12,5]deca-3,7-dien-9-one and 9-Oxatetracyclo [5.4.0.03,10.04,8]undec-5-en-2-one and kinetic data for the cyclization of the olefinic alcohol to the ether

In view of the significance of steric compression in the base-catalyzed intramolecular cyclization of polycyclic olefinic alcohols, the standard enthalpies of formation of anti^9,10-10 endo-hydroxytricyclo [4.2.1.1^2,5]deca-3,7-dien-9-one (1) and 9-oxatetracyclo [5.4.0.0^3,10.0^4,8]undec-5-en-2-one (2) as well as the kinetics of the ether formation 1 → 2 were determined.     

Thermal conductivity of superconducting tunneling junctions

We present the first measurements of thermal conductivity of superconducting tunneling junctions. Point contact junctions were established between a GaAs (Zn) point and a superconducting Nb base. We also used a dielectric tip made of GaAs (Cr).We conclude that electrons carry the heat across these type of junctions, in the same way they do in a bulk superconductor, and that the acoustical mismatch at the interface is not affected by the superconducting transition of the base metal.     

Tricritical lines and spin reorientations in S = 1 ferromagnets

We have studied in the molecular-field approximation the statistical mechanical properties of various generalized Blume—Capel Hamiltonians, which describe singlet—doublet and three-singlet magnetic systems. Phase diagrams exhibit tricritical lines and spin reorientations.     

Adaptive methods of lines for one-dimensional reaction-diffusion equations

Adaptive and non-adaptive finite difference methods are used to study one-dimensional reaction-diffusion equations whose solutions are characterized by the presence of steep, fast-moving flame fronts. Three non-adaptive techniques based on the methods of lines are described. The first technique uses a finite volume method and yields a system of non-linear, first-order, ordinary differential equations in time. The second technique uses time linearization, discretizes the time derivatives and yields a linear, second-order, ordinary differential equation in space, which is solved by means of three-point, fourth-order accurate, compact differences. The third technique takes advantage of the disparity in the time scales of the reaction and diffusion processes, splits the reaction--diffusion operator into a sequence of reaction and diffusion operators and solves the diffusion operator by means of either a finite volume method or a three-point, fourth-order accurate compact difference expression. The non-adaptive methods of lines presented in this paper may use equaliy or non-equally spaced fixed grids and require a large number of grid points to solve accurately one-dimensional problems characterized by the presence of steep, fast-moving fronts. Three adaptive methods for the solution of reaction-diffusion equations are considered. The first adaptive technique is static and uses a subequidistribution principle to determine the grid points, avoid mesh tangling and node overtaking and obtain smooth grids. The second adaptive technique is dynamic, uses an equidistribution principle with spatial and temporal smoothing and yields a system of first-order, non-linear, ordinary differential equations for the grid point motion. The third adaptive technique is hybrid, combines some features of static and dynamic methods, and uses a predictor-corrector strategy to predict the grid and solve for the dependent variables, respectively. The three adaptive techniques presented in this paper use physical co-ordinates and may employ finite volume or three-point, compact methods. The adaptive and non-adaptive finite difference methods presented in the paper are used to study a decomposition chemical reaction characterized by a scalar, one-dimensional reaction-diffusion equation, the propagation of a one-dimensional, confined, laminar flame in Cartesian co-ordinates and the Dwyer-Sanders model of one-dimensional flame propagation. It is shown that the adaptive moving method presented in this paper requires a smaller number of grid points than adaptive static, adaptive hybrid and non-adaptive methods. The adaptive hybrid method requires a smaller time step than adaptive static techniques, due to the lag between the grid prediction and the solution of the dependent variables. Non-adaptive methods of lines may yield temperature oscillations in front of and behind the flame front if Crank-Nicolson techniques are used to evaluate the time derivatives. Fourth-order accurate methods of lines in space yield larger temperature oscillations than second-order accurate methods of lines, and the magnitude of these oscillations decreases as the time step is decreased. It is also shown that three-point, fourth-order accurate discretizations of the spatial derivatives require the same number of grid points as second-order accurate, finite volume methods, in order to resolve accurately the structure of steep, fast-moving flame fronts.     

Oscillating annular liquid membranes

Summary The response of annular liquid membranes to sinusoidal mass flow rate fluctuations at the nozzle exit is analyzed as a function of the amplitude and frequency of the axial velocity fluctuations at the nozzle exit and thermodynamic compression of the gas enclosed by the membrane. It is shown that both the pressure of the gases enclosed by the annular membrane and the axial distance at which the annular membrane merges on the symmetry axis are periodic functions of time which have the same period as that of the mass flow rate fluctuations at the nozzle exit. They are also nearly sinusoidal functions of time for small amplitudes of the mass flow rate fluctuations at the nozzle exit, and exhibit delay and lag times with respect to the sinusoidal axial velocity fluctuations at the nozzle exit. Both the delay and the lag times are functions of the amplitude and frequency of the mass flow rate fluctuations at the nozzle exit and the polytropic exponent. The amplitudes of both the pressure of the gases enclosed by the annular liquid membrane and the convergence length increase and decrease, resp., as the amplitude and frequency of the mass flow rate fluctuations at the nozzle exit, resp., are increased. They also increase as the polytropic exponent is increased.

---

Oszilierende rotationsschalenförmige Flüssigkeitsmembranen

Übersicht Untersucht wird das Verhalten rotationsschalenförmiger Flüssigkeitsmembranen in Abhängigkeit von der Amplitude und Frequenz der axialen Geschwindigkeitsschwankungen an der Düsenmündung und der thermodynamischen Verdichtung des eingeschlossenen Gases, wenn sich der Massestrom an der Düsenmündung sinusförmig ändert. Es wird gezeigt, daß der Druck des eingeschlossenen Gases und der axiale Mündungsabstand des Scheitels der geschlossenen Membran periodische Zeitfunktionen mit der Frequenz der Masseflußschwankung am Düsenaustritt sind. Für kleine Amplituden des Massestroms ist ihr Zeitverhalten ebenfalls fast-sinusförmig, wobei sie bezüglich der sinusförmigen axialen Geschwindigkeitsschwankungen an der Düsenmündung eine Ansprechzeit und Phasenverschiebung aufweisen. Ansprechzeit und Phasenverschiebung sind Funktionen von Amplitude und Frequenz der Massestromschwankung sowie des polytropen Exponenten. Die Amplitude von Gasdruck und Abstand des Membranscheitels von der Düse wächst bzw. fällt mit wachsender Amplitude und Frequenz des Massestroms. Beide nehmen außerdem mit dem polytropen Exponenten zu.

     

An analysis of laminar boundary layers on liquid curtains

A simplified analysis of the laminar boundary layer along an isothermal liquid curtain falling under gravity is presented. The analysis uses a von Kármán-Pohlhausen integral method and includes the effects of gravity, pressure differences, surface tension and nozzle exit geometry on the convergence length of liquid curtains which have applications as chemical reactors and as protection systems in laser fusion reactors. It is shown that the effects of the surrounding gases on the curtain shape and convergence length are small, and that good approximations to the liquid curtain shape can be obtained by using inviscid flow analyses.     

Mathematical modelling of spark-ignition engines

The flow field, scavenging efficiency, power output, heat transfer losses, and unburned hydrocarbon emissions have been numerically studied by means of a two-equation model of turbulence in a four-stroke, homogeneous-charge, spark-ignition engine. The engine is equipped with an intake valve, an exhaust valve, and a constant rate heat source which simulates the spark plug. Combustion has been modelled by means of a one-step irreversible chemical reaction whose rate is controlled by an Arrhenius-type expression. The numerical results indicate that the intake stroke is characterized by the formation of two eddies which persist in the compression stroke. Turbulence is generated at the shear layers of the air jet drawn into the cylinder, but its level decreases in the compression stroke. Due to the heat released by the spark plug and the chemical reaction, a spherical flame kernel is formed. This kernel evolves into a cylindrical flame when the flame front reaches the piston. Fuel remains unburnt at the corner between the cylinder head and the cylinder wall due to heat transfer losses. The numerical results also indicate that despite uncertainties about the turbulence and heat transfer models, an engine model such as the one studied here can be used to understand the flow field, heat transfer losses, scavenging efficiency, and power output in conventional spark-ignition engines. Such capabilities are very helpful in the development and optimization stages of engines. For example, here the engine model thermal and scavenging efficiencies are 15.69% and 94%, respectively. The peak pressure is 33 atm and occurs at 6° ATDC. The unburnt hydrocarbon emissions are 7.41% of the total fuel admitted into the cylinder.