NUMERICAL SIMULATION OF BENARD CONVECTION IN A CLOSED RECTANGLE (Ⅱ)——THREE-DIMENSIONAL CASE

In the paper, numerical simulation is performed for Benard convection in a closed three-dimensional rectangle with non-slippery bound. Numerical results show that when Rayleigh number Ra<3.6×104, Benard convection is steady, and when Ra≥3.6×104 it is unsteady and irregular. The cross sections and correlation coefficients of various fields are studied, and it is found that the external correlation scales of flow decrease as Ra increases when Ra≥ 7.5×104. Moreover, statistical analyses show that the Taylor inner scales (λv,λθv and so on) also decrease as Ra increases, and that the changing rates of λv and λθv with height are very different to each other in the vicinity of upper and lower bounds. Furthermore, statistical analyses show that the computed Nusselt number Nu is close to the lower limit of many experimental values, and in the transient region of flow pattern d1gNu/d1gRa is relatively greater than that in other region. In addition, other statistical quantities of the fields of temperat     

CHARACTERISTICS OF NATURAL CONTENTS OF CHEMICAL ELEMENTS IN PROFILES OF SOME SOIL TYPES IN CHINA AND THEIR RELATIONSHIP

The natural contents of 23 elements in the main soil types in China, the degree of enrichment of those elements and the characteristics of regional differences of the element arrangement are discussed in this paper. Through comparison between the element contents of 10 soils in China and the soils of the world, we have found that it is necessary to consider the equilibrium of the compositions of the soil types, when we try to find out a soil background content of the world or large region. The paper also deals with the concept and model of the regional differential coefficients of the elements. In the end of the paper, we analyse the correlation between 23 elements. The results show that there is a correlation between some elements of different soils in different geographical zones.     

ACTIONS OF SUMMER MONSOON TROUGHS(RIDGES) AND TROPICAL CYCLONES OVER SOUTH ASIA AND THE MOVING CISK MODE

The analyzed wind field during MONEX shows that the monsoon troughs (or ridges) over South Asia have 30—50 day oscillation and slowly propagatu northward. Simultaneously, the tropical cyclones in South Asia could disperse energy to the east.Considering the feedback effect of the cumulus convection and the influence of the shearing basic flow, we introduce the vertical shearing basic flow into the conditional instability of the second kind (CISK) model and obtain a moving CISK mode. Under the Summer Monsoon in South Asia, the meridional propagation speed (northward) is about 0.6 latitude per day and the oscillation period is about 34 days for this CISK mode. And it has an easterly group velocity. The above-mentioned characteristics of this mode are similar to the analyzed results of the data during MONEX. Therefore, it can be initially concluded that the CISK mode caused by the shearing basic flow and the feedback effect of the cumulus convection seems to be an important mechanism driving the monsoon tr     

UNSTABLE SPIRAL INERTIAL-GRAVITY WAVES IN TYPHOONS

It is proposed in this paper that there are two cireular regions of a typhoon where unstable spiral waves can occur. Furthermore, the instability mechanism is different in each region. The locations of these regions coincide with the inner and outer spiral rain bands respectively. Analysis indicates that in the inner unstable region, some eigenwaves are reflected by the strong nonuniformity of the typhoon's basic flow and a"quantum condition" is established correspondingly, which gives the eigenfrequency and growth rate. The estimated growth rate, spiral arm number, wave length, polarization and thermal structure for the proferentially growing eigenwaves are comparable with the observations of inner spiral Cb cloud bands.     

MULTIPLE EQUILIBRIA IN BAROCLINIC ATMOSPHERE BY THERMAL FORCING RELATED TO SUBTROPICAL HIGH

By using Lorenz's moist general circulation model, a nonlinear and dissipative system describing atmospheric motion has been obtained in approximation of Low Order.The multiple equilibria and the transformation between the flow patterns of winter and summer, the latitudinal oscillation of subtropical high by thermal forcing and nonlinear interaction of general circulation are studied in this paper.The results show that the transformation of flow patterns is a discontinuous leaping, and is a process of resetting new flow pattern by rapid exchange inflow field.In the corresponding dry model, we cannot find the latitudinal oscillation of the center of subtropical high.In the moist model, after the thermal effect of water vapor is drawn into the model, nonlinear interaction appears between flow and heating fields.This effect helps to bring about the latitudinal oscillation of subtropical high.     

A MODEL OF CAPILLARY NETWORKS FOR THE EXCHANGE OF SUBSTANCES

A mathematical model of substantial exchange between three capillaries and the surrounding tissue is presented.We suppose that three capillaries, which are parallel to each other and have the same radius and circular section, are arranged in equilateral triangle.Fluid movement across the capillary walls is assumed to be governed by the generalized Starling's law.The motion of the interstitial fluid obeys Darcy's law.The calculated result obtained in this paper shows that in order to study the effect of capillary networks on the tissue space, as a whole, we have found a concept of equivalent pressure, concentration and source strength for the networks.     

KINETICS STUDIES OF MINERAL-WATER REACTIONS IN HYDROTHERMAL FLOW SYSTEMS AT ELEVATED TEMPERATURES AND PRESSURES

This paper describes new experimental results on mlneral-water reaction kinetics obtained in plug-flow systems at high temperatures and pressures. As an example, the rates of reaction between calcite, fluorite, albite and water in the continuous flowing system have been measured in three separate studies. All experiments are carried out by suspending a sample bag in the plug-flow vessel, by pumping water at carefully controlled rates through the vessel, and by collecting and analyzing the reacted solution. In addition, the reaction mechanisms of fluorite and albite in a packed bed reactor have been studied with the aid of an axial dispersion model. The main factors controlling the effective dissolution rate with respect to temperature, solvent flow rate, and chemistry of the input solutions have been evaluated. It is also found that a non-steady state process is, in some cases, still observed, even under conditions where steady state conditions should have been attained. These results provide informatio     

DIGITAL ANALYSIS TECHNOLOGY FOR MORPHOLOGY OF POLYMER CHAIN COILS IN FLOW FIELDS

Polymer chain coils with entanglement is a crucial scale of structures in polymer materials since their relaxation times are matching practical processing times. Based on the phenomenological model of polymer chain coils and a new finite element approach, we have designed a computer software including solver, pre- and post-processing modules, and developed a digital analysis technology for the morphology of polymer chain coils in flow fields (DAMPC). Using this technology we may simulate the morphology development of chain coils in various flow fields, such as simple shear flow, elongational flow,and any complex flow at transient or steady state. The appli cations made up to now show that the software predictions arecomparable with experimental results.     

THE CISK-OVERSTABILITY CONVECTION

A kind of the conditional instability of the second kind (CISK)--overstability convec-tion presented in the hurricane model is investigated in this paper. The structure of thisunstable mode and the basic conditions to excite it are also shown for discussion. In the tropical atmosphere, the cumulus convection could excite the CISK oscillatoryunstable mode through the CISK mechanism, and the cumulus friction (cumulus momentummixing) gives a fundamental effect to produce this overstability convection. Some meteorologists assumed that the waves in the lower stratosphere in the tropicalatmosphere may be caused by the forcing of the condensation heating. The present investi-gation shows from the dynamic angle that the CISK-overstability convection excited by thecumulus convection heating, especially by the cumulus momentum mixing, through the CISKmechanism is a fundamental factor to drive the waves in the equatorial stratosphere and theoscillatory phenomena in tropical atmosphere.     

MATHEMATICAL SIMULATION OF BUBBLING FLUIDIZED BED REACTORS——THE CLOUD PHASE FLOW MODEL

Based on the calculation equation of the bubble growth and the interphase gas exchange, which was suggested by the authors, the present paper further proposes the cloud phase flow model for predicting the gas unconverted fraction in the bubbling fluidized bed reactor. This model assumes that all the gas entering the fluidized bed passes through the bed as a cloud phase and that the bubble diameter can be represented by an average value of integration along the bed height.The calculation equation of the unconverted fraction is in good agreement with the data of bubbling fluidized beds and there is no unknown parameter. In addition, the additional consideration for the distributor region is unnecessary and the bed diameter has no effect on scale-up of bubbling fluidized bed reactors when the model proposed by the present paper is used to design.     

Coordination polyhedron growth mechanism model and growth habit of crystals

A new growth mechanism model, coordination polyhedron growth mechanism model, is introduced from the angle of the coordination of anion and cation to each other at the interface. It is pointed out that the force driving the growth unit to enter the crystal lattice is the electrostatic attraction force between ions, whose relative size can be approximately measured by the electrostatic bond strength (EBS) that reaches a nearest neighbor anion (or cation) in the parent phase from a cation (or anion) at the interface. The growth habits of NaCI, ZnS, CaF2 and Csl crystals are discussed, and a new growth habit rule is proposed as follows. When the growth rate of a crystal is determined by the step generation rate, the growth habit of this crystal is related to the coordination number of the ion with the smallest coordination rate at the interface of various crystal faces. The smaller the coordination number of the ion at the interface, the faster the growth rate of corresponding crystal face. When the growth     

A RHEOLOGICAL MODEL FOR POLYMER MELTS WITH INTERNAL STRUCTURE IN FLOW FIELDS*

Conceptually, an imagined conformation ellipsoid is supposed to represent the shape of a polymerchain for polymer melts in flow fields and to be equivalent to the volume element in a mathematical sense incontinuum mechanics. A power law dependence of shear modulus of polymer melts on detC, referred to asenvelope volume, is proposed. Based on those assumptions and the non-linear relation of shear modulus, aphenomenological viscoelastic model is derived. The model is tested in simple shear flow, simpleelongational flow, oscillatory shear flow, and relaxation process after flow suddenly stopped. The resultsshow that the model works well to predict the change of internal structure and viscoelastic performance ofpolymer melts in flow fields.     

Chemical Reactions and Kinetics of the Carbon Monoxide Coupling in the Presence of Hydrogen

The chemical reactions and kinetics of the catalytic coupling reaction of carbon monoxide to diethyl oxalate were studied in the presence of hydrogen over a supported palladium catalyst in the gaseous phase at the typical coupling reaction conditions. The experiments were performed in a continuous flow fixed-bed reactor. The results indicated that hydrogen only reacts with ethyl nitrite to form ethanol, and kinetic studies revealed that the rate-determining step is the surface reaction of adsorbed hydrogen and the ethoxy radical (EtO-). A kinetic model is proposed and a comparison of the observed and calculated conversions showed that the rate expressions are of rather high confidence.     

EFFECTS OF MOIST PROCESSES ON LOW-FREQUENCY OSCILLATIONS OF GENERAL CIRCULATION OVER NORTHERN HEMISPHERE DURING SUMMER TIME

In this paper the Lorenz's moist low-order spectral model~([1]) is further improved by introducinga parameterization for cumulus convection into it. Numerical experiments by this improved model mani-fest quasi-three week oscillations both in the location of the simulated subtropical high at upper tropo-sphere along cast-west direction and in the simulated vertical velocities and precipitation over South Asia,which is similar to those in the real atmosphere. The results of the experiments and the computationsof parameters of energetics show that introducing moist processes is a necessary condition for stimulat-ing and maintaining the low-frequency oscillations, and that moist convection can also obviously shortenoscillation periods, which is generally in agreement with the conclusions in another paper~([2]) of theauthors.     

Modelling and simulation of hydro-gel growth mechanism by analysis of experimental data

We have experimentally studied the growth process of a water-absorbing polymer commonly known as hydro-gel. We took a number of spherical beads, immersed them in pure water, measured their diameters at regular intervals of time and plotted graphs showing the change in volume with the time of immersion, to analyze their swelling properties. We have formulated a dynamical model on the basis of curve-fitting to our experimental data. Our mathematical modelling is devoted solely towards the explanation of the swelling of spherical hydro-gels and we have interpreted our observations on these basis. And finally evaluating the constants of the process, we have shown that the results obtained from our modelling and numerical simulation exactly match the experimental data. The justification of this new approach lies in its successful application for the complete explanation of our observations through numerical and analytical ways.     

Two-layer model description of polymer thin film dynamics

Experiments in the past two decades have shown that the glass transition temperature of polymer films can become noticeably different from that of the bulk when the film thickness is decreased below ca. 100 nm. It is broadly believed that these observations are caused by a nanometer interfacial layer with dynamics faster or slower than that of the bulk. In this paper, we examine how this idea may be realized by using a two-layer model assuming a hydrodynamic coupling between the interfacial layer and the remaining, bulk-like layer in the film. Illustrative examples will be given showing how the two-layer model is applied to the viscosity measurements of polystyrene and polymethylmethacrylate films supported by silicon oxide, where divergent thickness dependences are observed.     

ON NONLINEAR GRAVITY TRAVELLING WAVE

In this paper, a two--layer model with dispersive and dissipative effects but without Co-?iolis effect is investigated. It is proved that in the model, under certain parameter condi-tions, there exists monotone travelling wave as well as oscillation travelling wave in additionto the nonlinear periodic solution and solitary wave. The conditions for their existence areprovided. It is particularly pointed out that the pattern of the oscillation travelling wave issimilar to that of the pressure upwelling wave of a squall line which passes certain region.     

Comparative study of kinetic modeling for the oxidative coupling of methane by genetic and marquardt algorithms

Overall kinetic studies on the oxidative coupling of methane, OCM, have been conducted in a tubular fixed bed reactor, using perovskite titanate as the reaction catalyst. The appropriate operating conditions were found to be: temperature 750-775 ℃, total feed flow rate of 160 ml/min, CH4/O2 ratio of 2 and GHSV of 100 min-1. Under these conditions, C2 yield of 28% was achieved. Correlations of the kinetic data have been performed with lumped rate equations for C2 and COx formation as functions of temperature, O2 and CH4 partial pressures. Six models have been selected among the common lumped kinetic models. The selected models have been regressed with the experimental data which were obtained from the Catatest system by genetic algorithm in order to obtain optimized parameters. The kinetic coefficients in the overall reactions were optimized by different numerical optimization methods such as: the Levenberg-Marquardt and genetic algorithms and the results were compared with one another. It has been found that the Santamaria model is in good agreement with the experimental data. The Arrhenius parameters of this model have been obtained by linear regression. It should be noted that the Marquardt algorithm is sensitive to the first guesses and there is possibility to trap in the relative minimum.     

Simulation of noise characteristic effects on stochastic resonance in Belousov-Zhabotinsky flow reaction

A three-variable model, which was proposed to account for the stochastic resonance (SR) in Belousov-Zhabotinsky (B-Z) reaction in a continuous-flow stirred-tank reactor, is investigated when the control parameter kr, the flow rate, is modulated by noise near supercritical Hopf bifurcation point. Using the computer simulation, noise-induced oscillations are observed, and the signal-to-noise ratio (SNR) goes through a maximum with the increment of noise intensity, which means occurrence of stochastic resonance. in addition, we have also investigated the effects of correlation time of colored noise and the duration time of white noise on the system's dynamics.     

SOLITARY INTERNAL GRAVITY INERTIAL WAVE IN A STRATIFIED ATMOSPHERE AND NONLINEAR PROCESSES FOR THE FORMATION OF SQUALL LINES

In this paper the KdV equation is derived from the three dimensional primitive equations for a class of finite amplitude waves in a stratified basic flow. The solitary wave solution is given for a simple case where a constant and uniformly stratified basic flow is confined in a region bounded by solid walls with rectangular cross section. The properties of the solitary wave solution can give a possible explanation for the preferential occurrence of a squall line or storm cell train at the left side of a low level jet and the concurrent fluctuation in the low level jet. For more general cases, i. e. sheared basic flow and nonuniform stratification, the qualitative response of the wave amplitude to the symmetric baroclinic stability of the basic flow is analysed. The results indicate that the vertical circulation in a solitary wave will possibly be dramatically intensified in a local area where the stability is weak or negative.