NUMERICAL MODELING OF TURBULENTEVAPORATING GAS-DROPLET TWO-PHASE FLOWS IN AN AFTERBURNER DIFFUSOR OF TURBO-FAN JET ENGINES

The two-dimensional turbulent evaporating gas-droplet two-phase flows in an afterburner diffusor of turbo-fan jet engines are simulated by the k-ε turbulence model and the particle trajectory model. Comparison of predicted gas velocity and temperature distributions with experimental results for the cases without liquid spray shows pretty good agreement. Gas-droplet two-phase flow predictions give plausible droplet trajectories, fuel-vapor concentration distribution, gas-phase velocity and temperature field in presence of liquid droplets. One run of computation with this method is made for a particular afterburner. The results indicate that the location of the atomizers is not favorable to flame stabilization and combustion efficiency. The proposed numerical modeling can also be adopted for optimization design and performance evaluation of afterburner combustors of turbo-fan jet engines.

Numerical Simulation of Diffusion Type Traffic Flow Model Using Second-Order Lax-Wendroff Scheme Based on Exponential Velocity Density Function

In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which provides a non-linear second-order parabolic partial differential equation. The analytical solution of the diffusion-type traffic flow model is very complicated to approximate the initial density of the Cauchy problem as a function of x from given data and it may cause a huge error. For the complexity of the analytical solution, the numerical solution is performed by implementing an explicit upwind, explicitly centered, and second-order Lax-Wendroff scheme for the numerical solution. From the comparison of relative error among these three schemes, it is observed that Lax-Wendroff scheme gives less error than the explicit upwind and explicit centered difference scheme. The numerical, analytical analysis and comparative result discussion bring out the fact that the Lax-Wendroff scheme with exponential velocity-density relation of diffusion type traffic flow model is suitable for the congested area and shows a better fit in traffic-congested regions.

Mathematical Modeling,Field Calibration and Numerical Simulation of Low-Speed Mixed Traffic Flow in Cities

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Debris flow simulation 2D(DFS 2D):Numerical modelling of debris flows and calibration of friction parameters

Debris flows are rapid mass movements with a mixture of rock,soil and water.High-intensity rainfall events have triggered multiple debris flows around the globe,making it an important concern from the disaster management perspective.This study presents a numerical model called debris flow simulation 2D(DFS 2D)and applicability of the proposed model is investigated through the values of the model parameters used for the reproduction of an occurred debris flow at Yindongzi gully in China on 13 August 2010.The model can be used to simulate debris flows using three different rheologies and has a userfriendly interface for providing the inputs.Using DFS 2D,flow parameters can be estimated with respect to space and time.The values of the flow resistance parameters of model,dry-Coulomb and turbulent friction,were calibrated through the back analysis and the values obtained are 0.1 and 1000 m/s^(2),respectively.Two new methods of calibration are proposed in this study,considering the crosssectional area of flow and topographical changes induced by the debris flow.The proposed methods of calibration provide an effective solution to the cumulative errors induced by coarse-resolution digital elevation models(DEMs)in numerical modelling of debris flows.The statistical indices such as Willmott's index of agreement,mean-absolute-error,and normalized-root-mean-square-error of the calibrated model are 0.5,1.02 and 1.44,respectively.The comparison between simulated and observed values of topographic changes indicates that DFS 2D provides satisfactory results and can be used for dynamic modelling of debris flows.

A Numerical Model for Natural Backfill of Pipeline Trenches Subjected to Unidirectional/Oscillatory Flows

A numerical model for the self-burial of a pipeline trench is developed. Morphological evolutions of a pipeline trench under steady-current or oscillatory-flow conditions are simulated with/without a pipeline inside the trench. The oscillatory flow in this study represents the action of waves. The two-dimensional Reynolds-averaged continuity and Navier-Stokes equations with the standard k-ε turbulence closure, as well as the sediment transport equations, are solved with the finite difference method in a curvilinear coordinate system. Both bed and suspended loads of sediment transport are included in the morphological model. Because of the lack of experimental data on the backfilling of pipeline trenches, the numerical model is firstly verified against three closely-relevant experiments available in literature. A detailed measurement of the channel migration phenomenon under steady currents is employed for the assessment of the integral performance of the model. The two experimental results from U-tube tests are used to validate the model's ability in predicting oscillatory flows. Different time-marching schemes are employed for the morphological computation under unidirectional and oscillatory conditions. It is found that vortex motions within the trench play an important role in the trench development.

Validation of the RANS-SOM Combustion Model Using Direct Numerical Simulation of Incompressible Turbulent Reacting Flows

秒顺序时刻燃烧 moGel，由作者求婚了用 incRmpressible 的直接数字的模拟(DNS ) 被验证狂暴的反应 Fhannel 流动。即时 DNS 结果显示出集中和温度变化的近墙的长带结构。DNS 统计结果在关联方程给术语的预算，证明生产和驱散术语是很重要的。DNS 统计数据被用来在 RANS 秒顺序验证闭合模型时刻(SOM ) 燃烧模型。在近墙的修正应该被做的地方，模仿的散开和生产术语与在大多数流动区域的 DNS 数据一致，这被发现，除了在近墙的区域在近墙的修正应该被做的地方，并且为驱散术语的闭合模型需要进一步的改进。代数学的秒顺序时刻(ASOM ) 燃烧模型被 DNS 很好验证。

Numerical Modeling of Porous Structure of Biomaterial and Fluid Flowing Through Biomaterial

A Cellular Automata model of simulating body fluid flowing into porous bioceramic implants generated with stochastic methods is described, of which main parameters and evolvement rule are determined in terms of flow behavior of body fluid in porous biomaterials. The model is implemented by GUI （ Graphical User Interface） program in MATLAB , and the results of numerical modeling show that the body fluid percolation is related to the size of pores and porosity.

A Higher-Efficient Three-Dimensional Numerical Model for Small Amplitude Free Surface Flows

A higher-efficient three-dimensional non-hydrostatic model is developed to simulate small amplitude free surface flows based on a staggered unstructured grid. In this model, a fractional step algorithm is adopted to solve the Navier-Stokes equations in two major steps. A top-layer pressure method is proposed to minimize the number of vertical layers and subsequently the computational cost. Three classical examples of small amplitude free surface flows are used to demonstrate the capability and efficiency of the model. The satisfactory results demonstrated the capability and efficiency of modelling a range of small amplitude free surface flows with only a small number of vertical layers.

Numerical modeling of influence of thermal flow coupling on flow characteristics of molten steel

Using the equation of continuity and the double equation of Navier-Stokes and k-ε, numerical modeling on a single outlet continuous casting tundish has been carried out during the process of non-thermal flow coupling. The flow field distribution inside the tundish was calculated and the viscosity response time was calculated with the mass transfer equation based on the flow field distribution. The flow characteristics of the molten steel inside the tundish were analyzed, with the results of the numerical modeling compared to the hydraulic modeling. The results showed that the Resident Time Distribution （RTD） curves in the latter anatomosed comparatively better. This certified the validity established by the mathematical model. Numerical modeling was carried out on both large and small tundishes during the processes of thermal flow coupling and also thermal non-flow coupling. The results showed that in regards to large tundishes with relatively simple flow processes, using numerical modeling for thermal flow coupling is necessary.

Depth-resolved numerical model of dam break mud flows with Herschel-Bulkley rheology

Mud flows are common phenomena in mountainous areas,which can threaten human safety and cause property losses under certain extreme circumstances.Studying the dynamic characteristics of mud flows,especially in the vertical direction,is helpful for risk reduction and hazard mitigation.In this study,a 2D depth-resolved numerical model based on Herschel-Bulkley rheology was developed to study the vertical structures of unsteady mud flows with a free-surface.The numerical model was solved by the projection method,and the free surface of mud flows was captured through the VOF method.To fully validate this new model,a series of laboratory experiments involving dam break mud flows were conducted,and the mud flow heights,bottom pressures and envelopes of mud residuum were measured.The numerical model proposed in this study was first validated by the steady-state solution for uniform flows of Herschel-Bulkley fluid on an inclined plane.Additionally,the simulated and measured mud flow heights,bottom pressures at different x locations and envelopes with different bed slopes showed good agreement.Furthermore,the numerical results for a Herschel-Bulkley fluid dam break flow were used to validate the proposed model,which further revealed good agreements.After that,the scenarios in which mud flows impact on a structure were numerically studied,and the vertical profiles of the front velocity and impact pressure on the structure were analyzed and discussed.The results show that a plug layer was formed in the mud flow under unsteady and nonuniform flow conditions,and the impact pressure on the structure was dominated by the dynamic pressure.In addition,the vertical position with the maximum impact pressure acting on the structure was not at the bottom or the surface of the mud flows,and the normalized vertical position rose as the yield stress and consistency coefficient increase for Herschel-Bulkley fluids.

Numerical modeling of bed deposition in rapid flow-like landslides:a case study of the Gaolou landslide in Shaanxi Province,China

Some flow-like landslides tend to lose materials while moving on a relatively dry sliding surface.This phenomenon is called bed deposition.In contrast to the bed entrainment phenomenon,bed deposition is relatively poorly understood.Therefore,an improved depth-averaged model is proposed to quantify this phenomenon.The deposition depth is calculated according to the momentum conservation of the deposited mass,and the rheological property of the sliding mass on the bottom is modified considering an abrupt increase in the depth of the sliding surface after deposition.Utilizing the proposed model,the Gaolou landslide,a typical flowlike landside occurring on October 6 th,2006 with an obvious bed deposition phenomenon in Shaanxi Province of China,is simulated to investigate the influence of bed deposition on its propagation process.The results indicate that the proposed model can effectively depict the bed deposition phenomenon in the Gaolou landslide.Bed deposition dissipates part of the kinetic energy of this landslide;thus,the simulated debris inundation area would likely be overestimated when this effect is neglected.On the other hand,the thin liquefied layer formed by the bed deposition process reduces the friction energy dissipation,contributing to the high mobility of this landslide.

NUMERICAL CALCULATIONS OF GASEOUS REACTING FLOWS IN A MODEL OF GAS TURBINE COMBUSTORS

This paper describes the numerical calculations of gaseous reaction flows in a model of gas turbine combustors. The profiles of hydrodynamic and thermodynamic patterns in a three-dimensional combustor model are obtained by solving the governing differential transport equations. The well-established numerical prediction algorithm SIMPLE, the modified k-ε turbulence model and k-ε-g turbulent diffusion flame model have been adopted in computations. The β function has been selected as probability density function. The effect of combustion process on flow patterns has been investigated. The calculated results have been verified by experiments. They are in remarkably good agreement.

Three Dimensional Numerical Modeling of Flow and Pollutant Transport in a Flooding Area of 2008 US Midwest Flood

This paper presents the development and application of a three-dimensional numerical model for simulating the flow field and pollutant transport in a flood zone near the confluence of the Mississippi River and Iowa River during the US Midwest Flood in 2008. Due to a prolonged precipitation event, a levee along the Iowa River just upstream of Oakville, Iowa broke, and the small town was completely flooded for a couple of weeks. During this period, the high water level in the flood zone reached about 2.5 metersabove the ground, and wind was the major force for the flow circulation. It was observed that some pollutants were leaked from the residential and farming facilities and transported into the flood zone. Leaking of pollutants from these facilities was reported by different news media during the flood and was identified using high resolution satellite imagery. The developed 3D numerical model was first validated using experimental measurements, and then applied to the flood inundated zone in Oakville for simulating the unsteady hydrodynamics and pollutant transport. The simulated pollutant distributions were generally in good agreement with the observed data obtained from satellite imagery.

Analyses and Modeling of Laminar Flow in Pipes Using Numerical Approach

This paper investigate some important works done on numerical analysis and modeling of laminar flow in pipes. This review is focused on some methods of approach and the analytical tools used in analyzing of the important parameters to be considered in laminar flow;such as frictional losses, heat transfer etc. in laminar flow in pipes of different shapes, and the importance of laminar flow in its areas of applications. Prominent researchers have approached this from different perspectives. Some carried out analysis on the pressure drop as a function of permeability, some worked on friction factor analysis, some discussed heat transfer effects of laminar flow in the entrance region, while some discussed its applications in various industries. Some of these works were done considering a given form of pipe configuration or shape which is circular pipes. Only a few, of the literature reviewed have related their considerations to different forms of pipes. Most consider pipes to be majorly circular in shape, but in industries today some circular pipes have become elliptical in shape due to long time usage of the pipes, which would have contributed to increase in some different forms of losses in the industries. In engineering, efficiency and effectiveness improvement is the major goal, if a research work has been done, considering the important parameters in laminar flow showing their effects on different forms of pipe configuration as a result of pipe deformation due to usage, huge amount of money will be saved. This will show clearly how the efficiency of a given circular pipe has seriously been affected due to deformation, and the level of loss this has resulted to.

NUMERICAL INVESTIGATION OF THREE-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOWS IN DIVERGENT CURVED CHANNELS AND TURBULENT MODEL STUDY

In order to make the numerical calculation of viscous flows more convenient for the flows in channel with complicated profile governing equations expressed in the arbitrary curvilinear coordinates were derived by means of Favre density-weighted averaged method, and a turbulent model with effect of curvature modification was also derived. The numerical calculation of laminar and turbulent flown in divergent curved channels was carried out by means of parabolizeil computation method. The calculating results were used to analyze and investigate the aerodynamic performance of talor cascades in compressors preliminarily.

Numerical modelling of structural controls on fluid flow and mineralization

This paper presents the results of a set of numerical models focussing on structural controls on hydrothermal mineralization. We first give an overview of natural phenomena of structurally-controlled ore formation and the background theory and mechanisms for such controls. We then provide the results of a group of simple 2D numerical models validated through comparison with Cu-vein structure observed near the Shilu Copper deposit （Yangchun, Guangdong Province, China） and finally a case study of 3D numerical modelling applied to the Hodgkinson Province in North Queensland （Australia）. Two modelling approaches, discrete deformation modelling and continuum coupled deformation and fluid flow modelling, are involved. The 2D model-derived patterns are remarkably consistent with the Cu-vein structure from the Shilu Copper deposit, and show that both modelling approaches can realistically simulate the mechanical behaviours of shear and dilatant fractures. The continuum coupled deformation and fluid flow model indicates that pattern of the Cu- veins near the Shilu deposit is the result of shear strain localization, development of dilation and fluid focussing into the dilatant fracture segments. The 3D case-study models （with deformation and fluid flow coupling） on the Hodgkinson Province generated a number of potential gold mineralization

Numerical modeling of earthen dam breach due to piping failure

Based on model tests of earthen dam breach due to piping failure, a numerical model was developed.A key difference from previous research is the assumption that the cross-section of the pipe channel is an arch, with a rectangle at the bottom and a semicircle at the top before the collapse of the pipe roof, rather than a rectangular or circular cross-section.A shear stress-based erosion rate formula was utilized, and the arched pipe tunnel was assumed to enlarge along its length and width until the overlying soil could no longer maintain stability.Orifice flow and open channel flow were adopted to calculate the breach flow discharge for pressure and free surface flows, respectively.The collapse of the pipe roof was determined by comparing the weight of the overlying soil and the cohesion of the soil on the two sidewalls of the pipe.After the collapse, overtopping failure dominated, and the limit equilibrium method was adopted to estimate the stability of the breach slope when the water flow overtopped.In addition, incomplete and base erosion, as well as one-and two-sided breaches were taken into account.The USDAARS-HERU model test P1, with detailed measured data, was used as a case study, and two artificially filled earthen dam failure cases were studied to verify the model.Feedback analysis demonstrates that the proposed model can provide satisfactory results for modeling the breach flow discharge and breach development process.Sensitivity analysis shows that the soil erodibility and initial piping position significantly affect the prediction of the breach flow discharge.Furthermore, a comparison with a well-known numerical model shows that the proposed model performs better than the NWS BREACH model.

Numerical Simulation on Gas-Solid Two-Phase Turbulent Flow in FCC Riser Reactors(Ⅰ) Turbulent Gas-Solid Flow-Reaction Model

Gas-solid two-phase turbulent flows,mass transfer,heat transfer and catalytic cracking reactions areknown to exert interrelated influences in commercial fluid catalytic cracking(FCC)riser reactors.In the presentpaper,a three-dimensional turbulent gas-solid two-phase flow-reaction model for FCC riser reactors was devel-oped.The model took into account the gas-solid two-phase turbulent flows,inter-phase heat transfer,masstransfer,catalytic cracking reactions and their interrelated influence.The k-V-k_P two-phase turbulence modelwas employed and modified for the two-phase turbulent flow patterns with relatively high particle concentration.Boundary conditions for the flow-reaction model were given.Related numerical algorithm was formed and a nu-merical code was drawn up.Numerical modeling for commercial FCC riser reactors could be carried out with thepresented model.

Multiple car-following model of traffic flow and numerical simulation

On the basis of the full velocity difference （FVD） model, an improved multiple car-following （MCF） model is proposed by taking into account multiple information inputs from preceding vehicles. The linear stability condition of the model is obtained by using the linear stability theory. Through nonlinear analysis, a modified Korteweg-de Vries equation is constructed and solved. The traffic jam can thus be described by the klnk-antikink soliton solution for the mKdV equation. The improvement of this new model over the previous ones lies in the fact that it not only theoretically retains many strong points of the previous ones, but also performs more realistically than others in the dynamical evolution of congestion. Furthermore, numerical simulation of traffic dynamics shows that the proposed model can avoid the disadvantage of negative velocity that occurs at small sensitivity coefficients λ in the FVD model by adjusting the information on the multiple leading vehicles. No collision occurs and no unrealistic deceleration appears in the improved model.