Application of numerical simulation on optimum design of two-dimensional sedimentation tanks in the wastewater treatment plant

The paper establishes the relationship between the settling efficiency and the sizes of the sedimentation tank through the process of numerical simulation, which is taken as one of the constraints to set up a simple optimum designing model of sedimentation tank. The feasibility and advantages of this model based on numerical calculation are verified through the application of practical case.

Mathematical model for the thermal process of controlled cooling of wires and its numerical simulation

The mathematical model for the thermal process of billets rolling has beenestablished, including transporting in air and temperature-holding cover, descaling withhigh-pressure water, and the process of rolling and cooling in water box. The calculated data by themodel have been compared with the measured data and the results show that the model is right andcreditable. Based on the model, the main thermal characters of rolling line have been simulated andthe influence of all the parameters on the temperature of rolling has been analyzed.

Numerical modeling method on the movement of water flow and suspended solids in two-dimensional sedimentation tanks in the wastewater treatment plant

Taking the distributing calculation of velocity and concentration as an example, the paper established a series of governing equations by the vorticity stream function method, and dispersed the equations by the finite differencing method. After figuring out the distribution field of velocity, the paper also calculated the concentration distribution in sedimentation tank by using the two dimensional concentration transport equation. The validity and feasibility of the numerical method was verified through comparing with experimental data. Furthermore, the paper carried out a tentative exploration into the application of numerical simulation of sedimentation tanks.

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

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Numerical Simulation of a Mathematical Model for Dry/Wet-Spun Nascent Hollow Fiber Membrane

In an effort to find the effect of mass transfer, surface tension and drag forces on the velocity distribution, the mathematical model of the velocity profile of a nascent hollow fiber during membrane formation in the air gap region was numerically simulated by using the Runge-Kutta method (fourth-order method). The effect of mass transfer on velocity distribution based on the complicated function (G(Cs h)) was presented and the effects of a complicated function were studied in two cases: in the first case, G(Cs h) was constant; in the second, G(Cs h) was variable. The latter was done by varying with the concentration of solvent in a nascent hollow fiber through the air-gap region. One empirical equation was used to describe this change and the predicted values had a better agreement with the experimental values. To verify the model hypotheses, hollow fiber membranes were spun from 20∶80 polybenzimidazole/polyetherimide dopes with 25.6 wt% solid in N, N-dimethylacetamide (DMAc) using water as the external and internal coagulants. Based on the experimental results of dry-jet wet-spinning process for the fabrication of hollow fiber membranes, it is found that the model calculated values were in a good agreement with the experimental values.

Numerical Simulation Analysis of a Mathematical Model of Circadian Pacemaker Neurons

Sim and Forger have proposed a mathematical model of circadian pacemaker neurons in the suprachiasmatic nucleus (SCN). This model, which has been formulated on the Hodgkin-Huxley mo-del, is described by a system of nonlinear ordinary differential equations. An important feature of the SCN neurons observed in electrophysiological recording is spontaneous repetitive spiking, which is reproduced using this model. In the present study, numerical simulation analysis of this model was performed to evaluate variations in two system parameters of this model: the maximal conductance of calcium current (gCa) and the maximal conductance of sodium current (gNa). Simulation results revealed the spontaneous repetitive spiking states of the model in the (gCa, gNa)-pa-rameter space.

Experimental study and numerical simulation of the sludge concentration in a sedimentation tank

Sedimentation tanks and clarifiers play a significant role in an active sludge system, and the efficiency of the whole system is closely related with the design and operation of the sedimentation tanks. This paper focuses on the sludge concentration in each cross-section of the sedimentation tank. We measured the sludge concentration to explore its distribution inside the tank, carried in-situ tests to research the fluid pattern and real operational rules of the sedimentation tank. We also used the computational fluid dynamics (CFD) software, PHOENICS 3.5, to simulate the solid-liquid two-phase fluid inside the tank and describe the sludge concentration distribution. The numerical results indicate obviously a sludge-water interface and a compression interface inside the sedimentation tank, a stratified sedimentary region with uniform concentration and a compression region with high concentration at the bottom of the tank. Although the simulated concentrations deviated slightly from those of in-situ tests, they were still acceptable for identifying the sludge interfaces and fluid pattern inside a sedimentation tank, which are important parameters for optimizing the tank size and improving the settling efficiency.

Experimental research and numerical simulation of the multi-field performance of cemented paste backfill:Review and future perspectives

Cemented paste backfill(CPB)technology is a green mining method used to control underground goaves and tailings ponds.The curing process of CPB in the stope is the product of a thermo-hydro-mechanical-chemical multi-field performance interaction.At present,research on the multi-field performance of CPB mainly includes indoor similar simulation experiments,in-situ multi-field performance monitoring experiments,multi-field performance coupling model construction of CPB,and numerical simulation of the multi-field performance of CPB.Because it is hard to study the in-situ multi-field performance of CPB in the real stope,most current research on in-situ multi-field performance adopts the numerical simulation method.By simulating the conditions of CPB in the real stope(e.g.,maintenance environment,stope geometry,drainage conditions,and barricade and backfilling rates),the multi-field performance of CPB is further studied.This paper summarizes the mathematical models employed in the numerical simulation and lists the engineering application cases of numerical simulation in the in-situ multi-field performance of CPB.Finally,it proposes that the multi-field performance of CPB needs to strengthen the theoretical study of multi-field performance,form the strength design criterion based on the multi-field performance of CPB,perform a full-range numerical simulation of the multi-field performance of CPB,develop a pre-warning technology for the CPB safety of CPB,develop automatic and wireless sensors for the multi-field performance monitoring of CPB,and realize the application and popularization of CPB monitoring technology.

Mathematical modelling and numerical optimization of particle heating process in copper flash furnace

A mathematical model of the particle heating process in the reaction shaft of flash smelting furnace was established and the calculation was performed.The results indicate that radiation plays a significant role in the heat transfer process within the first 0.6 m in the upper part of the reaction shaft,whilst the convection is dominant in the area below 0.6 m for the particle heating.In order to accelerate the particle ignition,it is necessary to enhance the convection,thus to speed up the particle heating.A high-speed preheated oxygen jet technology was then suggested to replace the nature gas combustion in the flash furnace,aiming to create a lateral disturbance in the gaseous phase around the particles,so as to achieve a slip velocity between the two phases and a high convective heat transfer coefficient.Numerical simulation was carried out for the cases with the high-speed oxygen jet and the normal nature gas burners.The results show that with the high-speed jet technology,particles are heated up more rapidly and ignited much earlier,especially within the area of the radial range of R=0.3−0.6 m.As a result,a more efficient smelting process can be achieved under the same operational condition.

Mathematical model and numerical method for spontaneous potential log in heterogeneous formations

This paper introduces a new spontaneous potential log model for the case in which formation resistivity is not piecewise constant. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on the interfaces. It has beer/ shown that the elliptic interface problem has a unique weak solution. Furthermore, a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic problems. Numerical results show validity and effectiveness of the proposed method.

Mathematical and Numerical Modelling of Copper Tube Extrusion after Optimizing Geometrical and Operating Parameters

This study aimed to optimize cross-sectional area of the extruder and the flow rate of the material through the extruder. Extrusion process was first modelized using the continuum mechanics method before being simulated with the commercial software LS-DYNA using the Johnson-Cook model based on the finite element method after optimization of the factors with simplex algorithm. The study was carried out on a connecting rod: diameter of 145 mm, cross-section of 1.65 m2, length of 0.25 m, volume of 0.41 m3 and a mass of 37 kg. Optimum parameters obtained were temperature of 850℃, flow rate of 0.237 m/s, die diameter of 19.2 mm, pin diameter of 14 mm, extrusion strength of 565.6 kN and press pressure of 245 GPa. From these factors, a blank was obtained with external and internal diameters of 19.2 and 14 mm respectively over a length of 28 m with a thickness of 2.6 mm. Simulation using LS-DYNA software resulted in a difference in values of 7.4% between optimization and simulation when the difference of 2.4% was found between modelling and simulation. These values make the process optimal for industrial application to improve the extrusion requirements of copper tubes.

NUMERICAL SIMULATIONS OF TEMPERATURE FIELD IN DIRECT METAL LASER SINTERING PROCESS

A mathematical model is developed for simulating the heat transferring behavior in a direct metal laser sintering process. The model considers the thermal phenomena involved in the process, including conduction, radiation, and convection. A formula for the calculation of the heat conductivity of a sintering system containing solid phase, liquid phase, and gas phase is given. Due to the continuous movement of the laser beam, a local coordinate system centered on the laser beam is used to simplify the analytical calculation. Assuming that it is approximately a Gaussian laser beam, the heat conduction equation is resolved based on the assumption of the thermal insulating boundary conditions and the fixed thermal physical parameters. The FORTRAN language is employed to compile the program to simulate the temperature field in the direct copper powder sintering process. It shows a good agreement with the preliminary experimental results.[KH3/4D]

Mathematical model and numerical investigation of the influence of spray drying parameters on granule sizes of mold powder

In this work,the formation mechanism of the droplet-to-granule was investigated in detail based on mold powder manufacturing.A specific mathematical model of two-stage spray drying was established to describe droplet and granule motion,heat and mass transfer,and granule morphology during spray drying.Then,the relationships between spray drying parameters(inlet temperature,atomization pres-sure,slurry mass flow rate)and the properties of the drying tower(temperature and velocity fields)and mold powder granules(temperature,evaporation rates,moisture content,and diameter)were simulated and calculated using ANSYS/Fluent software.To ensure that the granule size of mold powder was controlled within the ideal range(0.2-0.6 mm)for producing granules with appropriate mechanical and metallurgical properties,the following optimum spray drying parameters were chosen based on the results of the numerical simulation:inlet temperatures,873 K;slurry atomization pressure,1.8 MPa;slurry mass flow rate,0.05 kg s-1.Among these parameters,the slurry mass flow rate has the most significant effect on granule size.

Numerical modelling and simulation analysis of wind blades:a critical review

Wind energy has emerged as a promising renewable energy source and wind turbine technology has developed rapidly in recent years.Improved wind turbine performance depends heavily on the design and optimization of wind blades.This work offers a critical evaluation of the state of the art in the field of numerical modelling and simulation analysis,which have become crucial for the design and optimization of wind blades.The evaluation of the literature includes considerable research on the application of numerical methods for the structural and aerodynamic performance of wind blades under various operating situations,as well as for analysis and optimization of wind blades.The article illustrates how numerical techniques can be used to analyse wind blade performance and maximize design efficiency.The study of blade performance under various wind conditions has also been made possible through the use of simulation analysis,thus enhancing the efficiency and dependability of wind turbines.Improvements in wind turbine efficiency and dependability,and ultimately the move towards a more sustainable energy future,will be greatly helpful for the development of numerical modelling and simulation techniques.

Numerical modeling of DPSK pressure signals and their transmission characteristics in mud channels

A numerical model and transmission characteristic analysis of DPSK （differential phase shift keying） pressure signals in mud channels is introduced. With the control logic analysis of the rotary valve mud telemetry, a logical control signal is built from a Gate function sequence according to the binary symbols of transmitted data and a phase-shift function is obtained by integrating the logical control signal. A mathematical model of the DPSK pressure signal is built based on principles of communications by modulating carrier phase with the phase-shift function and a numerical simulation of the pressure wave is implemented with the mathematical model by MATLAB programming. Considering drillpipe pressure and drilling fluid temperature profile along drillpipes, the drillpipe of a vertical well is divided into a number of sections. With water-based drilling fluids, the impacts of travel distance, carrier frequency, drillpipe size, and drilling fluids on the signal transmission were studied by signal transmission characteristic analysis for all the sections. Numerical calculation results indicate that the influences of the viscosity of drilling fluids and volume fraction of gas in drilling fluids on the DPSK signal transmission are more notable than the others and the signal will distort in waveform with differential attenuations of the signal frequent component.

Numerical Study of Solid-Liquid Two-Phase Flow in StirredTanks with Rushton Impeller(Ⅱ) Prediction of Critical Impeller Speed

Three-dimensional solid-liquid flow is mathematically formulated by means of the 'two-fluid' approach and the two-phase k-ε-AP turbulence model. The turbulent fluctuation correlations appearing in the Reynolds time averaged governing equations are fully incorporated. The solid-liquid flow field and solid concentration distribution in baffled stirred tanks with a standard Rushton impeller are numerically simulated using an improved 'inner-outer'iterative procedure. The flow pattern is identified via the velocity vector plots and a recirculation loop with higher solid concentration is observed in the central vicinity beneath the impeller. Comparison of the simulation with experimental data on the mean velocities and the turbulence quantities of the solid phase is made and quite reasonable agreement is obtained except for the impeller swept volume. The counterpart of liquid phase is presented as well.The predicted solid concentration distribution for three experimental cases with the average solid concentration up to 20% is also found to agree reasonably with the experimental results published in the literature.

Numerical Simulation for Evolutionary History of Three-Dimensional Basin

Numerical simulation or evolutionary history of an oil and gas-bearing basin is to repeat geological and thermodyanomic history of basin evolution on a computer and then to quantitate petroleum generation,accumulation and migration.The mathemat-ical model describing geological and thermodynamic history of the basin evolution ischaracterised by an initial-boundary value problem of a system of nonlinear partial dif-ferential equations. In the present paper, a numerical method for three-dimensionalproblem and the analysis of its stability are established and a numerical result for apractical model is given, which shows that the abnormal pressure and paleo-temperat-ure computed are reasonable and display physical characteristics clearly as well.

Three-dimensional tidal current numerical model of the Oujiang Estuary

The characteristics of three-dimensional （3-D） tidal current in the Oujiang Estuary are investigated according to in situ observations. The Oujiang Estuary has features of irregular coastline, complex topography, many islands, moveable boundary, and submerged dyke, therefore, σ 3-D numerical model oil an unstructured triangular grid has been degeloped. The σ coordinate transforination, the moveable boundary and submerged dyke treatment techniques were employed in the model so it is suitable for the tidal simulations in the Oujing Estuary with submerged dyke and moveable boundary problems. The model is evaluated with the in situ data, and the results show that the calculated water elevations at 19 stations and currents at 19 profiler stations are in good agreement with measured data both in magnitude and phase. This numerical model is applied to the 3-D tidal circulation simulations of experiments in stopping flow transport through the South Branch of the Oujiang Estuary, and the feasibility to cutoff the flow in the South Branch of the Oujiang Estuary is demonstrated by numerical simulation experiments. The developed numerical model simulated the 3-D tidal current circulations in complicated coastal and estuarine waters very well.

New Model and Simulation of Condenser for Ship Nuclear Power Plant

A new reasonably perfect dynamic mathematic model has been established for condenser used in ship nuclear power plant according to its structural features and operating principle. The model has been solved by the Runge-Kutta method. And an analysis program has been developed for dynamic numerical simulation under steady operation condition, disturbance condition, and accident condition. The dynamic characteristics of condenser has been calculated and analyzed under several kinds of disturbances, and the results of calculation are in good agreement with the theoretical analysis.

Numerical Simulation of Wave Height and Wave Set-Up in Nearshore Regions

Based on the time dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation, and then a practical method for the simulation of wave height and wave set- up in nearshore regions is presented. The variation of the complex wave amplitude is numerically simulated by use of the parabolic mild slope equation including the effect of wave energy dissipation due to wave breaking. The components of wave radiation stress are calculated subsequently by new expressions for them according to the obtained complex wave amplitude, and then the depth-averaged equation is applied to the calculation of wave set-up due to wave breaking. Numerical results are in good agreement with experimental data, showing that the expression for the energy dissipation factor is reasonable and that the new method is effective for the simulation of wave set-up due to wave breaking in nearshore regions.