APPLICATION OF ULTRAMICROELECTRODES IN STUDIES OF HOMOGENEOUS CATALYTIC REACTIONS .3. THE CONDITION FOR QUASI-1ST AND 2ND-ORDER HOMOGENEOUS CATALYTIC REACTIONS AT ULTRAMICRODISK ELECTRODES IN THE STEADY-STATE

The conditions for quasi-first and second order homogeneous catalytic reactions and their variation with each other at an ultramicrodisk electrode in the steady state are discussed in this paper. The order of reaction can be controlled by changing the dimension of the ultramicroelectrode: the second order reaction can be changed to quasi-first by decreasing the dimension of the ultramicroelectrode. An example of this is given. The main factor effect on the reaction order is the dimension of the ultramicroelectrode. The K4Fe(CN)6-aminopyrine system is selected to confirm the theory, the experiments showing that the system is a second order reaction at a 432 mum microelectrode, and a quasi-first order reaction at a 19 mum ultramicroelectrode. The kinetic constant of the system can be determined by applying the previous theory of homogeneous catalytic reaction.

Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea

Large amplitude internal solitary waves (ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean. We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea (19A degrees 35'N, 112A degrees E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors, and an acoustic Doppler current profiler (ADCP). We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories. Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width. Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries (KdV) theory than the first-order KdV model. These results indicate that the northwestern South China Sea (SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.

Perturbational Finite Volume Method For The Solution of 2-D Navier-Stokes Equations on Unstructured and Structured Colocated Meshes

Based on the first-order upwind and second-order central type of finite volume( UFV and CFV) scheme, upwind and central type of perturbation finite volume ( UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from 0.3 to 0. 8 and convergence perform excellent with Reynolds number variation from 102 to 104.

双曲守恒型方程的二阶摄动有限差分格式

对双曲守恒型方程，将其一阶迎风格式空间差商的常系数摄动展开为时间步长和空间步长的幂级数，通过确定幂级数系数而获得二阶精度的摄动有限差分（PFD）格式。进而从双曲守恒型方程的通量分裂型一阶迎风格式出发，通过娄似的摄动展开方法，获得空间精度为二阶的通量分裂形式的摄动有限差分（FPFD）格式。这两类格式保留了一阶守恒迎风格式的简洁结构形式，使用三节点即可达到二阶精度，又避免了三点二阶格式的非物理数值振荡。并将这两类格式推广应用到双曲守恒型方程组，最后通过模型方程和一维激波管流动的数值算例验证了格式的高精度、高分辨率性质。

Thermocapillary Effect in a Thermal Rheological Jet

The process of die swell in polymer jets is an important feature within polymer processing and can be explained through a study of its rheological effects. The existence of a thermocapillary effect, driven by the gradient of its surface tension, should be considered when examining a thermal jet that has a non-uniform temperature distribution on its free surface, as in various polymer processings. Both the rheological effect and thermocapillary effect on die swell can be studied numerically through a finite element method as used on a two-dimensional and unsteady model, in which a Coleman-Noll second-order fluid model is employed. The results show that the expanding angle depends on both the rheological property of the fluid and the pressure at the vessel exit. Although both the thermocapillary and the rheological effects contribute to the cross-section expansion of the fluid jet, the latter is more important in determining the expansion.

Calculations of longitudinal and transverse velocity structure functions using a vortex model of isotropic turbulence

The longitudinal structure function (LSF) and the transverse structure function (TSF) in isotropic turbulence are calculated using a vortex model. The vortex model is composed of the Rankine and Burgers vortices which have the exponential distributions in the vortex Reynolds number and vortex radii. This model exhibits a power law in the inertial range and satisfies the minimal condition of isotropy that the second-order exponent of the LSF in the inertial range is equal to that of the TSF. Also observed are differences between longitudinal and transverse structure functions caused by intermittency. These differences are related to their scaling differences which have been previously observed in experiments and numerical simulations.

Navier-Stokes方程二阶速度滑移边界条件的检验

对微尺度气体流动，Navier-Stokes方程和一阶速度滑移边界条件的结果与实验数据相比，在滑移区相互符合，在过渡领域则显著偏离，为改善Navier-Stokes方程在过渡领域的表现，有些研究者尝试引入二阶速度滑移边界条件，如Cercignani模型，Deissler模型和Beskok-Karniadakis模型．以微槽道气体流动为例，将Navier-Stokes方程在不同的二阶速度滑移模型下的结果与动理论的直接模拟Monte Carlo（DSMC）方法和信息保存（IP）方法以及实验数据进行比较．在所考察的3种具有代表性的二阶速度滑移模型中，Cercignani模型表现最好，其所给出的质量流率在Knudsen数为0．4时仍与DSMC和IP结果相符；然而，细致比较表明，Cercignani模型给出的物面滑移速度及其附近的速度分布在滑流区和过渡领域的分界处（Kn=0．1）已明显偏离DSMC和IP的结果．

一个基于非均匀网格上的二阶基本无振荡差分格式

在基本无振荡格式的构造中，将通常的对流通量f的逼近方式推广到对通量导数的逼近，这一构造方法可以有效地应用到非均匀或非结构网格。直接基于非均匀网格上，构造了一个二阶的基本无振荡(ENO)差分格式。该格式具有形式简单，对网格的划分灵活，与传统格式相比不增加计算量等优点，儿个数值算例证明了格式的有效性。

Simulation of Coal Combustion by AUSM Turbulence-Chemistry Char Combustion Model and a Full Two-Fluid Model

An algebraic unified second-order moment (AUSM) turbulence-chemistry model of char combustion is introduced in this paper, to calculate the effect of particle temperature fluctuation on char combustion. The AUSM model is used to simulate gas-particle flows, in coal combustion in a pulverized coal combustor, together with a full two-fluid model for reacting gas-particle flows and coal combustion, including the sub-models as the k-epsilon-k(p) two-phase turbulence niodel, the EBU-Arrhenius volatile and CO combustion model, and the six-flux radiation model. A new method for calculating particle mass flow rate is also used in this model to correct particle outflow rate and mass flow rate for inside sections, which can obey the principle of mass conservation for the particle phase and can also speed up the iterating convergence of the computation procedure effectively. The simulation results indicate that, the AUSM char combustion model is more preferable to the old char combustion model, since the later totally eliminate the influence of particle temperature fluctuation on char combustion rate.

Studies of the Effect of a Coal Concentrator on NO Formation in Swirling Coal Combustion

To develop low-pollution burners, the effect of a coal concentrator on NO formation in swirling coal combustion is studied using both numerical simulation and experiments. The isothermal gas-particle two-phase velocities and particle concentration in a cold model of swirl burners with and without coal concentrators were measured using the phase Doppler particle anemometer (PDPA). A full two-fluid model of reacting gas-particle flows and coal combustion with an algebraic unified second-order moment (AUSM) turbulence-chemistry model for the turbulent reaction rate of NO formation are used to simulate swirling coal combustion and NO formation with different coal concentrators. The results give the turbulent kinetic energy, particle concentration, temperature and NO concentration in cases of with and without coal concentrators. The predicted results for cold two-phase flows are in good agreement with the PDPA measurement results, showing that the coal concentrator increases the turbulence and particle concentration in the recirculation zone. The combustion modeling results indicate that although the coal concentrator increases the turbulence and combustion temperature, but still can remarkably reduce the NO formation due to creating high coal concentration in the recirculation zone.

An Improved Ce/Se Scheme And Its Application To Detonation Propagation

An improved two-dimensional space-time conservation element and solution element ( CE/ SE) method with second-order accuracy is proposed, examined and extended to simulate the detonation propagations using detailed chemical reaction models. The numerical results of planar and cellular detonation are compared with corresponding results by the Chapman-Jouguet theory and experiments, and prove that the method is a new reliable way for numerical simulations of detonation propagation.

Quasi-Dammann Grating With Proportional Intensity Array Spots

A quasi-Dammann grating is proposed to generate array spots with proportional-intensity orders in the far field. To describe the performance of the grating, the uniformities of the array spots are redefined. A two-dimensional even-sampling encode scheme is adopted to design the quasi-Dammann grating. Numerical solutions of the binary-phase quasi-Dammann grating with proportional-intensity orders are given. The experimental results with a third-order quasi-Dammann grating, which has an intensity proportion of 3:2:1 from zero order to second order, are presented. (C) 2008 Optical Society of America

Coupling Of Evaporation And Thermocapillary Convection In A Liquid Layer With Mass And Heat Exchanging Interface

We propose and analyse a new model of thermocapillary convection with evaporation in a cavity subjected to horizontal temperature gradient, rather than the previously studied model without evaporation. The pure liquid layer with a top free surface in contact with its own vapour is considered in microgravity condition. The computing programme developed for simulating this model integrates the two-dimensional, time-dependent Navier-Stokes equations and energy equation by a second-order accurate projection method. We focus on the coupling of evaporation and thermocapillary convection by investigating the influence of evaporation Biot number and Marangoni number on the interfacial mass and heat transfer. Three different regimes of the coupling mechanisms are found and explained from our numerical results.

Hydrodynamic interaction between two vertical cylinders in water waves

The hydrodynamic interaction between two vertical cylinders in water waves is investigated based on the linearized potential flow theory. One of the two cylinders is fixed at the bottom while the other is articulated at the bottom and oscillates with small amplitudes in the direction of the incident wave. Both the diffracted wave and the radiation wave are studied in the present paper. A simple analytical expression for the velocity potential on the surface of each cylinder is obtained by means of Graf's addition theorem. The wave-excited forces and moments on the cylinders, the added masses and the radiation damping coefficients of the oscillating cylinder are all expressed explicitly in series form. The coefficients of the series are determined by solving algebraic equations. Several numerical examples are given to illustrate the effects of various parameters, such as the separation distance, the relative size of the cylinders, and the incident angle, on the first-order and steady second-order forces, the added masses and radiation-damping coefficients as well as the response of the oscillating cylinder.