Simulation-based Graphic Method for Dynamic System Modeling

The first step for engineering students to understand the practical system is to describe the system,which means to establish the mathematic model for the considered system.However,traditional mathematical modeling techniques are not readily assimilated by students,because the traditional modeling needs to obey the complicated physical laws for different engineering areas and requires a highly iterative process.In this paper,the simulation-based graphic modeling method is introduced to help students model the system and improve their performance in engineering education.The results from the questionnaire indicate that the simulation-based graphic method can help students to do the modeling of the system and improve their performance compared to the traditional ways.

Dynamic Factor Method of Computing Dynamic Mathematical Model for System Simulation

The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of the dynamic mathematical model is researched. By means of theoretical analysis, the error formulas, the error sign criteria and the error relationship criterion of the implicit Euler method and the trapezoidal method are given, the dynamic factor affecting the computational accuracy has been found, the formula and the methods of computing the dynamic factor are given. The computational accuracy of the dynamic mathematical model like this can be improved by use of the dynamic factor.

Mathematical Model of Heat Treatment and Its Computer Simulation

Computer simulation on heat treatment is the foundation of intelligent heat treatment. The simulations of temperature field, phase transformation, stress/strain complicate quenching operation were realized by using the model of three dimensional non linear finite element method and the treatment methods of abruptly changing interface conditions. The simulation results basically fit those measured in experiments. The intelligent sealed multipurpose furnace production line has been developed based on the combination of computer simulation on gaseous carburizing and computer control technology. More than 3000 batches of workpieces have been processed on this production line, and all are up to standard. The application of computer simulation technology can significantly improve the loading ability and relia bility of nitriding and carburizing workpieces, reduce heat treatment distortion, and shorten carburizing duration. It is recommended that the reliable product design without redundancy should be performed with the combination of the CAD of mechanical products, the CAE of materials selection and heat treatment, and the dynamic evaluation technology of product reliability.

MATHEMATICAL MODEL AND COMPUTER SIMULATION OF MOISTURE TRANSFER PROCESS DURING SINTERING

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The mathematical model and simulation of the electrostatic suspension system in the vertical direction

In order to research the vibration law of electrostatic suspension systems in the vertical direction, the mathematical model as a nonlinear differential equation is established. A series of simulation is carried out. The results show that the solution of the differential equation is a periodic function. The amplitude becomes bigger with the original velocity increased. The period becomes smaller with the original velocity increasing. The numerical methods are presented to derive the amplitude and the frequency, and the results coincide with that of the simulation. The condition during which the simple harmonic vibration arises is pointed out. The expressions for the amplitude and the period of simple harmonic vibration are derived respectively, and the results are the same with that of the simulation. This study is helpful for researching the vibration characteristics of the electrostatic suspension system. The external disturb should be controlled to lower the amplitude and the frequency of the vibration.

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.

Basic mathematical model for the normal black smoker system and the hydrothermal megaplume formation

A tube model to simulate the normal black smoker system has been built, where the Darcy flow equation, the Ergun equation and the turbulent pipe flow equation are used respectively to describe the dynamic process of different key areas in the hydrothermal circulation system. At the same time, a convection - diffuse Equation for the temperature field is used for describe the exchange of thermal energy and the law of temperature variation. Combining the above facts and using efficient mathematical algorithms and programming with the MatLab programming language, the variation curves of temperature, pressure and mass flow rate are determined, while also the dynamic heat equilibrium and pressure equilibrium within the black smoker system are analyzed. On the basis of the model of the normal black smoker system, a megaplume formation model is further built. For instance, the hydrothermal venting plume on the Juan de Fuca Ridge has been simulated and the simulation results are fairly consistent with Baker＇ s imputed data in 1986. On the basis of the above productive simulation, a series of factors for megaplume formation and the effectiveness of the main parameters of the periodicity of the megaplume formation, temperature and the maximum mass flow rate are systematically discussed. Main conclusions are as follows： The normal black smoker system can evolve into a megaplum eruption. In fact, the passageway of the hydrothermal discharge is blocked by the hydrothermal sediments during the black smoker period, which leads to a hydrothermal fluid accumulation, rise of temperature and increase of buoyancy pressure under the seabed. After a period of 2 - 3 a, the megaplume hydrothermal eruption will occur when the increasing buoyancy pressure is high enough to crack the blockage （cap）. Meanwhile, the temperature of the heat source must exceed 500 ℃, while the highest temperature of the eruption fluid may be high up to 413 ℃, which is fairly consistent with the surveying data. If the temperature of the heat source were to be higher than 500 ℃, then the critical period for the megaplume formation could be obviously curtailed to be less than 1 a, while the critical temperature and the maximum mass flow rate are nearly invariable. As the permeability increases, the maximum mass flow rate increases gradually close to a steady value.

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.

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

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Flow field simulation and establishment for mathematical models of flow area of spool valve with sloping U-shape notch machined by different methods

Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived.The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notch on the spool,such as mass flow rates,flow coefficients,efflux angles and steady state flow forces under different operating conditions.At last,the reliability of the mathematical model of the flow area for the sloping U-shape notch orifice on the spool was demonstrated by the comparison between the orifice area curve derived and the corresponding experimental data provided by the test.It is presented that the bottom arc of sloping U-shape notch(ABU) should not be omitted when it is required to accurately calculate the orifice area of ABU.Although the theoretical flow area of plain bottom sloping U-shape notch(PBU) is larger than that of ABU at the same opening,the simulated mass flow and experimental flow area of ABU are both larger than these of PBU at the same opening,while the simulated flow force of PBU is larger than that of ABU at the same opening.Therefore,it should be prior to adapt the ABU when designing the spool with proportional character.

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.

Mathematical Modelling and Simulation of <i>β</i>-Cell Mass, Insulin and Glucose Dynamics: Effect of Genetic Predisposition to Diabetes

Worldwide, diabetes is affecting 370 million people, causing nearly five million deaths and absorbing more than 471 billion USD per year. Mathematical models have been developed to simulate, analyse and understand the dynamics of β-cells, insulin and glucose. In this paper, we consider the effect of genetic predisposition to diabetes on dynamics of β-cells, glucose and insulin. We assume that the β-cell dynamics is governed by the differential equation: . The model indicates different behaviours according to the presence or absence of genetic predisposition. In presence of predisposition (ε = 1), the model shows three equilibrium points: a stable physiological equilibrium point (G = 100, I = 20, β = 600), a stable trivial pathological equilibrium point (G = 600, I = 0, β = 0) and a saddle point (G = 250, I = 9.8, β = 129.36). In absence of predisposition (ε = 0), the model has only two equilibrium points: an unstable pathological equilibrium point (G = 600, I = 0, β = 0) and a stable physiological equilibrium point (G = 82.6, I = 23, β = 900). In order to see how physical activity, obesity and other factors affect insulin sensitivity, simulations are carried out with different values of insulin induced glucose uptake rate (c), β-cell maximum insulin secretory rate (d) and environmental capacity (K).

Simulation of a Mathematical Model Minimizing Energy Consumption in SDN Type Networks

Several works by the authors have shown that energy consumption in communication networks does not only depend on the traffic load but on all connected equipment in the network. We have contributed a new mathematical model and a new energy saving strategy with Software Defined Network (SDN) technology [1]. Our Model solution is based on the Modified SPRING Protocol (MSP). In this paper, we simulated our work and compared it to that of the authors [2] and [3]. The OMNET++ simulator was used for our work. Thus, the results of the simulations gave a delay that tends to zero, a packet loss of the order of 10% and a constant jitter of 4% better than the previous authors.

Modeling and Simulations in Symmetrical Supercapacitors Using Time Domain Mathematical Expressions

This study presents the deduction of time domain mathematical equations to simulate the curve of the charging process of a symmetrical electrochemical supercapacitor with activated carbon electrodes fed by a source of constant electric potential in time ε and the curve of the discharge process through two fixed resistors. The first resistor RCo is a control that aims to prevent sudden variations in the intensity of the electric current i1(t) present at the terminals of the electrochemical supercapacitor at the beginning of the charging process. The second resistor is the internal resistance RA of the ammeter used in the calculation of the intensity of the electric current i1(t) over time in the charging and discharging processes. The mathematical equations generated were based on a 2R(C + kUC(t)) electrical circuit model and allowed to simulate the effects of the potential-dependent capacitance (kUC(t)) on the charge and discharge curves and hence on the calculated values of the fixed capacitance C, the equivalent series resistance (ESR), the equivalent parallel resistance (EPR) and the electrical potential dependent capacitance index k.

Mathematical Model for Takeoff Simulation of a Wing in Proximity to the Ground

飞机飞结束到从提高的效率由于的扎根的利益减少导致拖并且增加的电梯。在这研究，一个数学模型被开发用一个反复的边界元素方法(IBEM ) 和有限差别计划在地面附近模仿一个翅膀的起飞。二独立亚代码和母亲代码，启用在亚代码之间的通讯，被开发为 Wing-In-Ground (假发) 效果的自激解决。在翅膀上施加的空气动力学的力量被第一亚代码用 IBEM 计算，并且翅膀的垂直排水量由用有限差别计划的第二亚代码是计算的。二亚代码和罐头在秒以内为翅膀和操作高度的气体动力学解决的母亲代码命令。发达代码系统被用来为一个 NACA6409 翅膀的力量，速度，和排水量解决在一 40，和 20 ?

Research and Application Prospect of Computer Simulation on Heat Treatment Process

In this paper, a modified temperature-phase transformation-stress/strain field coupled 3D non-linear mathematical model was used in the computer simulation on heat treatment processes of workpieces including catch jaw, anchor ring, cold roller, large-scale bearing roller, nitriding crank shaft, etc. The simulation on complicated technologies such as pre-cooled quenching, double media quenching, self-tempering, difference temperature heating, nitriding distortion was carried out. The optimum design of heat treatment technology has been realized. The successful application of computer simulation on heat treatment have also been demonstrated.

Experimental optimization and mathematical modeling of supercritical carbon dioxide extraction of essential oil from Pogostemon cablin

The supercritical carbon dioxide extraction was applied to obtain essential oil from Pogostemon cablin in this work.Effect of extraction parameters including temperature,pressure,extraction time and particle size on extraction yield was investigated,and the response surface methodology with a Box–Behnken Design was used to achieve the optimized extraction conditions.The maximum yield of essential oil was 2.4356%under the conditions of extraction temperature 47°C,pressure 24.5 MPa and extraction time 119 min.Moreover,based on the Brunauer–Emmett–Teller theory of adsorption,a mathematical modeling was performed to correlate the measured data.The model shows a function relationship between extraction yield and time by a simple equation with three significantly adjustable parameters.These model parameters have been optimized through simulated annealing algorithm.The predicted data from the mathematical model show a good agreement with the experimental data of the different extraction parameters.

Mathematical Simulation and Design of Three-Phase Bubble Column Reactor for Direct Synthesis of Dimethyl Ether from Syngas

A three-phase reactor mathematical model was set up to simulate and design a three-phase bubble column reactor for direct synthesis of dimethyl ether （DME） from syngas, considering both the influence of part inert carrier backmixing on transfer and the influence of catalyst grain sedimentation on reaction. On the basis of this model, the influences of the size and reaction conditions of a 100000 t/a DME reactor on capacity were investigated. The optimized size of the 10000 t/a DME synthesis reactor was proposed as follows： diameter 3.2 m, height 20 m, built-in 400 tube heat exchanger （Ф 38×2 mm）, and inert heat carrier paraffin oil 68 t and catalyst 34.46 t. Reaction temperature and pressure were important factors influencing the reaction conversion for different size reactors. Under the condition of uniform catalyst concentration distribution, higher pressure and temperature were proposed to achieve a higher production capacity of DME. The best ratio of fresh syngas for DME synthesis was 2.04.

A continuous and high-efficiency process to separate coal bed methane with porous ZIF-8 slurry:Experimental study and mathematical modelling

Coal bed methane has been considered as an important energy resource.One major difficulty of purifying coal bed methane comes from the similar physical properties of CH_4 and N_2.The ZIF-8/water-glycol slurry was used as a medium to separate coal bed methane by fluidifying the solid adsorbent material.The sorption equilibrium experiment of binary mixture(CH_4/N_2)and slurry was conducted.The selectivity of CH_4 to N_2 is within the range of 2-6,which proved the feasibility of the slurry separation method.The modified Langmuir equation was used to describe the gas-slurry phase equilibrium behavior,and the calculated results were in good agreement with the experimental data.A continuous absorption-adsorption and desorption process on the separation of CH_4/N_2 in slurry is proposed and its mathematical model is also developed.Sensitivity analysis is conducted to determine the operation conditions and the energy performance of the proposed process was also evaluated.Feed gas contains 30 mol%of methane and the methane concentration in product gas is 95.46 mol%with the methane recovery ratio of 90.74%.The total energy consumption for per unit volume of product gas is determined as 1.846 kWh Nm^(-3).Experimental results and process simulation provide basic data for the design and operation of pilot and industrial plant.