A Numerical Method for Calculating Transmission Coefficients Across Arbitrary Potential Barriers with High Accuracy

We report a new method for calculating transmission coefficients across arbitrary potential barriers based on the Runge-Kutta method. A numerical solution of the Schrodinger equation is calculated using the Runge-Kutta method,and a new model is established to analyze the numerical results to find the transmission coefficient. This technique is applied to various cases, such as parabolic potential barrier and double-barrier structures. Transmission probability with high precision is obtained and discussed. The tunnelling current density through a MOS structure is also explored and the result coincides with the Fowler-Nordheim model,which indicates the applicability of our method.

Numerical simulation of a bubble rising in shear-thinning fluids

The motion of a single bubble rising freely in quiescent non-Newtonian viscous fluids was investigated experimentally and computationally. The non-Newtonian effects in the flow of viscous inelastic fluids are modeled by the Carreau theological model. An improved level set approach for computing the incompressible two-phase flow with deformable free interface is used. The control volume formulation with the SIMPLEC algorithm incorporated is used to solve the governing equations on a staggered Eulerian grid. The simulation results demonstrate that the algorithm is robust for shear-thinning liquids with large density (rho(1)/rho(g) up to 10(3)) and high viscosity (eta(1)/eta(g) up to 10(4)). The comparison of the experimental measurements of terminal bubble shape and velocity with the computational results is satisfactory. It is shown that the local change in viscosity around a bubble greatly depends on the bubble shape and the zero-shear viscosity of non-Newtonian shear-thinning liquids. The shear-rate distribution and velocity fields are used to elucidate the formation of a region of large viscosity at the rear of a bubble as a result of the rather stagnant flow behind the bubble. The numerical results provide the basis for further investigations, such as the numerical simulation of viscoelastic fluids. (C) 2010 Elsevier B.V. All rights reserved.

Numerical simulation of thermal loading produced by shaped high power laser onto engine parts

Recently a new method for simulating the thermal loading on pistons of diesel engines was reported. The spatially shaped high power laser is employed as the heat source, and some preliminary experimental and numerical work was carried out. In this paper, a further effort was made to extend this simulation method to some other important engine parts such as cylinder heads. The incident Gaussian beam was transformed into concentric multi-circular patterns of specific intensity distributions, with the aid of diffractive optical elements (DOEs). By incorporating the appropriate repetitive laser pulses, the designed transient temperature fields and thermal loadings in the engine parts could be simulated. Thermal-structural numerical models for pistons and cylinder heads were built to predict the transient temperature and thermal stress. The models were also employed to find the optimal intensity distributions of the transformed laser beam that could produce the target transient temperature fields. Comparison of experimental and numerical results demonstrated that this systematic approach is effective in simulating the thermal loading on the engine parts. (C) 2009 Elsevier Ltd. All rights reserved.

Numerical simulation of principal tidal constituents in the South China Sea, Gulf of Tonkin and Gulf of Thailand

The principal tidal constituents M-2, S-2, K-1 and O-1 in the South China Sea, Gulf of Tonkin and Gulf of Thailand are simulated simultaneously using the numerical scheme of Kwok et al. (1995 Proceedings of the 1st Asian Computational Fluid Dynamics Conference, pp. 16-19). The average differences between the computed and observed harmonic constants are mostly within 5 cm and 10 degrees for amplitudes and phase-lags, respectively. The simulated tidal regimes in the present model are believed to be more accurate than the previous numerical results. Our studies confirm that a clockwise rotating M-2 amphidromic system lies in the southeast of the Gulf of Thailand and an S-2 amphidromic system at the near-shore area of the northeast South China Sea. The linear tidal energy equation developed by Garrett (1975 Deep-Sea Research 22, 23-35) is generalized to the nonlinear case. Based on the numerical results, the energy budgets in the South China Sea and its subareas, namely the Taiwan Strait, the Gulf of Tonkin, the Gulf of Thailand and the remaining area are investigated. The tidal motion in the Taiwan Strait is maintained mainly by the energy fluxes from the East China Sea for both semidiurnal and diurnal species and partially from the Luzon Strait for semidiurnal species. For the other parts of the South China Sea, the tidal motion is mainly maintained by the energy fluxes through the Luzon Strait. The energy inputs from the tide-generating force are negative for semidiurnal species and positive for diurnal species. (C) 1999 Elsevier Science Ltd. All rights reserved.

Differentiated Control of Web Traffic: A Numerical Analysis

Internet measurements show that the size distribution of Web-based transactions is usually very skewed; a few large requests constitute most of the total traffic. Motivated by the advantages of scheduling algorithms which favor short jobs, we propose to perform differentiated control over Web-based transactions to give preferential service to short web requests. The control is realized through service semantics provided by Internet Traffic Managers, a Diffserv-like architecture. To evaluate the performance of such a control system, it is necessary to have a fast but accurate analytical method. To this end, we model the Internet as a time-shared system and propose a numerical approach which utilizes Kleinrock's conservation law to solve the model. The numerical results are shown to match well those obtained by packet-level simulation, which runs orders of magnitude slower than our numerical method.

A two-dimensional numerical investigation of the oscillatory flow behaviour in rectangular fire compartments with a single horizontal ceiling vent

This paper presents a comparison of fire field model predictions with experiment for the case of a fire within a compartment which is vented (buoyancydriven) to the outside by a single horizontal ceiling vent. Unlike previous work, the mathematical model does not employ a mixing ratio to represent vent temperatures but allows the model to predict vent temperatures a priori. The experiment suggests that the flow through the vent produces oscillatory behaviour in vent temperatures with puffs of smoke emerging from the fire compartment. This type of flow is also predicted by the fire field model. While the numerical predictions are in good qualitative agreement with observations, they overpredict the amplitudes of the temperature oscillations within the vent and also the compartment temperatures. The discrepancies are thought to be due to three-dimensional effects not accounted for in this model as well as using standard ‘practices’ normally used by the community with regards to discretization and turbulence models. Furthermore, it is important to note that the use of the k–ε turbulence model in a transient mode, as is used here, may have a significant effect on the results. The numerical results also suggest that a linear relationship exists between the frequency of vent temperature oscillation (n) and the heat release rate (Q0) of the type n∝Q0.290, similar to that observed for compartments with two horizontal vents. This relationship is predicted to occur only for heat release rates below a critical value. Furthermore, the vent discharge coefficient is found to vary in an oscillatory fashion with a mean value of 0.58. Below the critical heat release rate the mean discharge coefficient is found to be insensitive to fire size.

Numerical simulation of encapsulant curing within a variable frequency microwave processing system

Curing of encapsulant material in a simplified microelectronics package using an open oven Variable Frequency Microwave (VFM) system is numerically simulated using a coupled solver approach. A numerical framework capable of simulating electromagnetic field distribution within the oven system, plus heat transfer, cure rate, degree of cure and thermally induced stresses within the encapsulant material is presented. The discrete physical processes have been integrated into a fully coupled solution, enabling usefully accurate results to be generated. Numerical results showing the heating and curing of the encapsulant material have been obtained and are presented in this contribution. The requirement to capture inter-process coupling and the variation in dielectric and thermophysical material properties is discussed and illustrated with simulation results.

A lysimeter experimental study and numerical characterisation of the leaching of incinerator bottom ash waste

Incinerator bottom ash (IBA) is a residual produced from incinerating municipal solid waste. In the past, IBA presented a big waste disposal problem; however, various recycling approaches have been adopted in recent years to mitigate this problem, as well as to provide a useful alternative to using primary aggregate resources. The use of IBA as an alternative to conventional aggregates in different civil engineering construction applications helps to conserve premium grade aggregate supplies; however, when IBA is in contact with water in the field, as a consequence of precipitation events or changes in water table, elements, such as salts and heavy metals, may be released to the soil and ground water. In this work, IBA waste was mixed with limestone aggregate to produce a blend with acceptable mechanical properties and minimum environmental risks for use as road foundation. The study focused on evaluating potential environmental impacts of some constituents, including sulphate, chloride, sodium, copper, zinc and lead in IBA blends using a lysimeter as a large scale leaching tool. Moreover, a specific scenario simulating field conditions was adopted in the lysimeter to assess the potential impact of changing conditions, such as IBA content in the blend, liquid to solid ratio (L/S) and pH value, on long-term release of heavy metals and salts. Then, numerical modelling was used to predict the release of the aforementioned constituents from IBA based on initial measurement of intrinsic material properties and the kinetic desorption process concept. Experimental results showed that zinc and lead were released in very low concentrations but sodium and sulphate were in high concentrations. The control limestone only blend also demonstrated low release concentrations of constituents in comparison to IBA blends, where constituent concentrations increased with increase in IBA content. Experimental results were compared with numerical results obtained using a non-equilibrium desorption model. Good agreement was found between the two sets of data. 

Numerical Study of Wave Slamming on an Oscillating Flap

Bottom hinged Oscillating Wave Surge Converters (OWSCs) are efficient devices for extracting power from ocean waves. There is limited knowledge about wave slamming on such devices. This paper deals with numerical studies of wave slamming on an oscillating flap to investigate the mechanism of slamming events. In our model, the Navier–Stokes equations are discretized using the Finite Volume method with the Volume of Fluid (VOF) approach for interface capturing. Waves are generated by a flaptype wave maker in the numerical wave tank, and the dynamic mesh method is applied to model the motion of the oscillating flap. Basic mesh and time step refinement studies are performed. The flow characteristics in a slamming event are analysed based on numerical results. Various simulations with different flap densities, water depths and wave amplitudes are performed for a better understanding of the slamming.

Development and Validation of a Procedure for Numerical Vibration Analysis of an Oscillating Wave Surge Converter

During extreme sea states so called impact events can be observed on the wave energy converter Oyster. In small scale experimental tests these impact events cause high frequency signals in the measured load which decrease confidence in the data obtained. These loads depend on the structural dynamics of the model. Amplification of the loads can occur and is transferred through the structure from the point of impact to the load cell located in the foundation. Since the determination of design data and load cases for Wave Energy Converters originate from scale experiments, this lack of confidence has a direct effect on the development.

Numerical vibration analysis is a valuable tool in the research of the structural load response of Oyster to impact events, but must take into account the effect of the surrounding water. This can be done efficiently by adding an added mass distribution, computed with a linearised potential boundary element method. This paper presents the development and validation of a numerical procedure, which couples the OpenSource boundary element code NEMOH with the Finite Element Analysis tool CodeAster. Numerical results of the natural frequencies and mode shapes of the structure under the influence of added mass due to specific structural modes are compared with experimental results.

Numerical studies on bi-directionally coupled directly modulated semiconductor lasers

Results of a numerical study of synchronisation of two directly modulated semiconductor lasers, using bi-directional coupling, are presented. The effect of stepwise increase in the coupling strength (C) on the synchronisation of the chaotic outputs of two such lasers is studied, with the help of parameter space plots, synchronisation error plots, phase diagrams and time series outputs. Numerical results indicate that as C increases, the system achieves synchronisation as well as stability together with an increase in the output power. The stability of the synchronised states is checked by applying a perturbation to the system after it becomes synchronised and then noting the time it takes to regain synchronisation. For lower values of C the system does not regain synchronisation. But, with higher values synchronisation is regained within a very short time.

Numerical study of 2D heat transfer in a scraped surface heat exchanger

A numerical study of fluid mechanics and heat transfer in a scraped surface heat exchanger with non-Newtonian power law fluids is undertaken. Numerical results are generated for 2D steady-state conditions using finite element methods. The effect of blade design and material properties, and especially the independent effects of shear thinning and heat thinning on the flow and heat transfer, are studied. The results show that the gaps at the root of the blades, where the blades are connected to the inner cylinder, remove the stagnation points, reduce the net force on the blades and shift the location of the central stagnation point. The shear thinning property of the fluid reduces the local viscous dissipation close to the singularity corners, i.e. near the tip of the blades, and as a result the local fluid temperature is regulated. The heat thinning effect is greatest for Newtonian fluids where the viscous dissipation and the local temperature are highest at the tip of the blades. Where comparison is possible, very good agreement is found between the numerical results and the available data. Aspects of scraped surface heat exchanger design are assessed in the light of the results. (C) 2003 Elsevier Ltd. All rights reserved.

An evaluation of three upwinding approximations for numerical modeling the flow in tubular membrane of Newtonian and non-Newtonian fluids

In this paper, the laminar fluid flow of Newtonian and non-Newtonian of aqueous solutions in a tubular membrane is numerically studied. The mathematical formulation, with associated initial and boundary conditions for cylindrical coordinates, comprises the mass conservation, momentum conservation and mass transfer equations. These equations are discretized by using the finite-difference technique on a staggered grid system. Comparisons of the three upwinding schemes for discretization of the non-linear (convective) terms are presented. The effects of several physical parameters on the concentration profile are investigated. The numerical results compare favorably with experimental data and the analytical solutions. (C) 2011 Elsevier Inc. All rights reserved.

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.