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.

Governing Equation and Mathematical Simulation on Ablation and Transpiration Control

This paper represents a physical model of two -dimensional transpiration cooling control system with surface heating and ablating. The governing equation is derived and the third boundary conditions are given. They constitute a two -dimensional variable -domain distributed parameter control system in which the control parameter appears in both the governing equation and the boundary conditions. Applying time semi-step alternating direction method to difference this mathematical model, the tridiagonal difference equations are obtained. For a flying shell of electromagnetic railgun, the mathematical simulation results agree with the realistic physical process, and the control parameter not only can control the temperature of heat shield, but also can control the boundary motion effectively.

A study on mathematical simulation of spray forming process

An integrated approach for modeling the entire spray forming process is presented in this paper, and the program for the simulation is developed. The whole spray forming process can be divided into four calculation processes and the basis for the analysis is the classical k -ε turbulence model which was used to simulate the flow field of gas formed in the chamber. In the atomization model the flow field of gas is coupled with formation, velocity and location of droplet. By means of the above mathematical model, the process of spray forming was simulated.

Mathematical modeling and simulation of the interface region of a tri-layer composite material,brass-steel-brass,produced by cold rolling

The object of this study was to find the optimum conditions for the production of a sandwich composite from the sheets of brass-steel-brass. The experimental data obtained during the production process were used to validate the simulation program, which was written to establish the relation between the interface morphology and the thickness reduction amount of the composite. For this purpose, two surfaces of a steel sheet were first prepared by scratching brushing before inserting it between two brass sheets with smooth surfaces. Three sheets were then subjected to a cold rolling process for producing a tri-layer composite with various thick- nesses. The sheet interface after rolling was studied by different techniques, and the bonding strength for each rolling condition was determined by peeling test. Moreover, a relation between interfacial bonding strength and thickness reduction was found. The simulation results were compared with the experimental data and the available theoretical models to modify the original simulation program with high application efficiency used for predicting the behavior of the interface under different pressures.

Mathematical model and simulation of partial penetrated weld pool

The qualitative analysis on the behavior of partial penetrated weld pool transferring from pulsed peak current to base current in pulsed TIG welding is carried out in this paper. Based on the analysis results, the mathematical models for 3D liquid surface shape of partial penetrated weld pool in pulsed TIG welding are created including surface potential energy model, gravitational energy model and volumetric potential energy. The numerical simulation with these models and the experiments on low carbon steel are carried out using the software Surface Evolver. The simulation results and model are then amended with experimental results. Two important characteristic quantities, the liquid metal coverage ratio and the stripping width of liquid metal, are put forward in this paper, which paves a way for further weld pool full penetration control.

Mathematical Simulation of Nd and Sm Extract Separation in （Nd，Sm）Cl_3－HCL－HEHEHP－Kerosene System

A number of epuilibrium data of single stage in the system (Nd-SM)Cl_3-HCl-H_2O-1mol/L HEHEHP-kerosence was determined On the basis of epuilibrium data, two mathematical describing extract epui-librium of Nd and Sm were developed.The models cover wide available ranges (the total RE concentration inepuilibrated apueous phase is 0. 07～0. 77 mol/L and the acidity is 0. 11～0. 48 mol/L; the mole fraction ofMd or Sm is 0. 020～0. 998) with small average relative errors(The model of Nd is 6. 11 % and the model ofSm is 3. 07 %, respectively ) With the developed models, the extract behaviors of Nd and sM, such as thedistribution of rare earth concentrations in both phase, the effects of acidity, RE concentration, mole fractionof RE in aqueous phase on the RE concentration in organic phase, were researched The separation circuits be-tween Nd and Sm simulated and performed by the experiments in laboratory. The purities obtained prod-uct of Nd_2O_3O_3 as well as Sm_2O_3 were higher than 99%.Two calculation programs were written in BASIC language. One of them is used for publishing epuilibri-um model and another is used for simulation of fractional solvent extraction. The amulation results obtainedmay serve as a reference for designing solvent extraction process.

MATHEMATICAL MODEL AND DIGITAL SIMULATION OF TURBOJET ACCELERATION

The acceleration performance of a turbojet is one of its important characteristics. In terms of control system, the engine is a controlled object. The acceleration performance not only depends on the engine, but also on the controller; therefore both the engine and the controller must be combined in a control system to make research for this performance. This paper presents a mathematical model of the turbojet acceleration control system and digital simulation method. Because the engine acceleration is a large variation transient process, the models of the engine and the controller are described by nonlinear equations. The methods of solving nonlinear equations and iterative techniques of calculating acceleration control system are discussed in this paper. The calculated results, as compared with test results, show that the simulation for this system is satisfactory.

NUMERICAL SIMULATION OF TEMPERATURE FIELDS FOR WELD METAL SOLIDIFICATION CRACKING IN STAINLESS STEELS

This paper has analyzed the influences of the heat input of welding arc, the latent heat of solidifica- tion,fluid flow of liquid metal on the heat conductivity pertaining to welding solidification crack of stainless steels. As a result,two - dimensional heat conduction models with prescribed heat flux mov- ing along the the have been developed that can simulate welding arc, convection and radiation heat loss from top and bottom surfaces of the workpiece. Finally, the finite element model was used to ana- lyze and calculate the temperature field.

Mathematical model of flow characteristic in multi-strand continuous casting tundishes

In this paper, the subject of mathematical model is a series of math expressions, which is used to calculate different regions＇ volume fraction and analyze flow characterization in multi-strand tundish. But research about mathematical model for multi-strand tundish is few, and so far, there has been no acknowledged math model for multi- strand tundish to describe its flow characteristic. If Sahai＇s model, which is originally proposed for the case of single-strand tundish （proposed in reference, and this model is widely used in the world）, is applied to describe flow feature in multi-strand tundish, the calculation results would be unreasonable. Based on the data of watermodel experiment results, the sum of each strand＇s dead region＇s volume fraction is bigger than 100%, and this obviously doesn＇T agree with reality; and the value of dead region＇s volume fraction is calculated to be minus according to mathematical simulation results data in another case. What＇s more, Sahai＇s model does not propose the standard of plotting the RTD-curve, and this makes scholars around the world can＇t achieve consensus of views about plotting RTD-curve. And the model doesn＇t consider the bypass flow and can＇t calculate its volume fraction, but bypass flow is critical to tundish metallurgy. And through Sahai＇s model, the calculation result of plug flow region＇s volume fraction is also not reasonable, because the model doesn＇t well describe the essence of plug flow. So these suggest that it is not reliable to apply Sahai＇s single-strand tundish model to multi-strand tundish case. Then a new model is attempted to propose in this paper for your discussion. In the new model, the standard of plotting RTD curve is definitely proposed, and relative calculation method is also proposed; and the feature of dead region is carefully studied and the model proposes a new method to calculate its volume fraction, and the calculation formula about its volume fraction can be adjustable according the actual demand; what＇s more, the new model considers the bypass flow and proposes a method to calculate its volume fraction for the first time, and then volume fraction of plug flow region, backmix flow region, dead region and bypass flow can be calculated and obtained at the same time; and this new model can better capture the deviation of reality flow pattern from ideal plug flow pattern, and reflects the feature of plug flow.

Mathematical modeling of fluid flow, heat transfer and inclusion transport in a four strand tundish

Mathematical simulation was used for trouble-shooting and optimization. By the mathematical simulation, fluid flow and beat transfer of molten-steel in a four-strand tundish of a billet caster under different conditions （bare tundish and tundish with flow control device） were analyzed, The results showed that （1） the tundish with flow control device （FCD） has an important effect on the fluid pattern and temperature distribution; （2） the unsteady, solving method was used to model the inclusion motions at different time perthds, and it showed that the FCD is advantageous to separate the nonmetallic inclusions. According to the simulation results, the main problem existing in the industry preduction was found, and some helpful rneasurements were executed. Consequently, the large nonmetallic inclusions were separated, and the content of total oxygen was reduced. The qualily of steel was greatly improved.

CFD Simulation on Ethylene Furnace Reactor Tubes

Different mathematical models for ethylene furnace reactor tubes were reviewed. On the basis of these models a new mathematical simulation approach for reactor tubes based on computational fluid dynamics （CFD） technique was presented. This approach took the flow, heat transfer, mass transfer and thermal cracking reactions in the reactor tubes into consideration. The coupled reactor model was solved with the SIMPLE algorithm. Some detailed information about the flow field, temperature field and concentration distribution in the reactor tubes was obtained, revealing the basic characteristics of the hydrodynamic phenomena and reaction behavior in the reactor tubes. The CFD approach provides the necessary information for conclusive decisions regarding the production optimization, the design and improvement of reactor tubes, and the new techniques implementation.

Numerical simulation of temperature fields for weld metal solidification cracking in stainless steels

This paper has analyzed the influences of the heat input of the welding arc, the latent heat of solidification, the fluid flow of liquid metal on the heat conductivity pertaining to the welding solidification crack of stainless steels. As a result, two dimensional heat conduction models with the prescribed heat flux moving along the weld have been developed that can simulate welding arc, convection and radiation heat loss from top and bottom surfaces of the workpiece. Finally, the finite element model was used to analyze and calculate the temperature fields.

Simulation of meniscus fluctuations in the feeding system used in strip casting

The feeding system used in the strip casting process delivers molten metal from the tundish to the pool that is bordered by side dams and rolls and is one of the key units in the production of high quality strip metal. The traditional method for studying this key unit is to use a combination of a water model and a mathematical model. However,the relations in the model with and without roll rotation have not been clearly revealed in previous studies. A 2D transient model based on a continuity equation, momentum equation, turbulent equations, and a VOF equation was established in this study and used to simulate the meniscus fluctuation. A half model with a structured grid was used for the reported simulation. The simulation showed that significant differences existed in the fluctuation in the flow fields and wave length with or without the roll rotation. The wave fluctuation exhibited uncertainty and an unstable character in the roll rotation condition. The level fluctuation employing different process parameters such as rotating speed and immersion depth of tip angle was simulated and compared with and without roll rotation. The study results showed that the meniscus fluctuation of twin-roll strip casting was primarily affected by the roll rotation, and the level fluctuation increased with the increase in rotation velocity and decreased with immersion depth.

Simulation of a Walking Robot-E xoskeleton Movement on a Movable Base

The paper studies the problem of movement of a two-legged walking machine on a movable base.This task is relevant for design rehabilitation and mechanotherapy complexes for people with impaired functions of the musculoskeletal system and presents a mathematical model that allows obtaining the kinematic and dynamic parameters of the movement of the executive units of the device under study.The paper presents a method for planning the trajectory of exoskeleton links,its algorithmic and software implementation.The paper proposes the structure of the automatic link position control system,which ensures the movement of the executive links along a given trajectory.A mathematical apparatus is proposed for studying the dynamics of the controlled movement of the links of the human-machine system of the exoskeleton.The article presents the results of numerical.experiments on the movement of the low-limb exoskeleton leg in the one step mode and analyzes them.

Numerical Simulation of Two-Phase Closed Thermosyphon

Heat transfer and hydrodynamics of two phase closed thermosyphon （TPCT） is studied using finite difference method of Stream function and vorticity. The mathematical model is formed for both vapor phase and liquid film in a non-dimensional form. The momentum and energy equations as parabolic equations have been solved by means of the locally one-dimensional scheme of A.A. Samarskii. The Poisson equation for the stream function has been approximated on the basis of the discrete scheme ＂cross＂. The obtained system of algebraic equations has been solved by the successive over relaxation method. The effect of the Rayleigh number on the velocity and temperature fields in the domain of interest and on the average Nusselt number at the solid-fluid interfaces is investigated. It was found that increase in the Rayleigh number leads to the increment of both the average Nusselt number and the stream function in the vapor zone.

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.

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.

Novel Method Employing Accelerated-Oscillated Wave Saline Solutions to Unblock Blood Vessels—Physics and Fluid Dynamics Perspectives and Simulations

This research assesses the speed of blood flow across blood vessels and more specifically the veins in terms of Reynold’s number (laminar flow vs. turbulence flow) and in terms of overall speed of the blood when being injected with high-speed saline particles. The authors propose a novel technique to generate accelerated-waved particles built from saline solution to enable the unblocking of partially-blocked healthy-walled veins, and to restore normal operations of these veins. The novel technique encompasses a pump that accelerates saline solutions into the blood stream of the vein and these oscillated waves break down the fats or deposits inside the veins in order to help the blood to flow freely without any obstruction. This research simulated the vein with blood stream using characteristics of the vein in terms of vein diameter, blood density, venous blood flow, and the viscosity of the blood at the normal body temperature. The speed of the overall blood flow after the injection of the accelerated saline droplet solution was determined as well as the depth of penetration of the accelerated particles in order to cleanse the inside of the vein. Results are promising in terms of not altering significantly the overall speed of the bloodstream and also in terms of efficacy of the length of the vein which is being cleaned using this accelerated particle method.

Mathematical model of absorption and hybrid heat pump

Recovering waste heat from industrial processes is bene ficial in order to reduce the primary energy demands and heat pumps can be used to this purpose.Absorption heat pumps are energy-saving and environment-friendly because use working fluids that do not cause ozone depletion and can reduce the global warming emissions.The hybrid heat pump processes combine the conventional vapor-compression and the absorption heat pump cycles.Studies about the simulations and modeling of hybrid heat pumps are few in literature.In this research a mathematical model for single effect absorption and hybrid heat pump is carried out with Chem Cad? 6.0.1.LiBr–H_2O is used as working fluid while electrolytic NRTL and electrolytes latent heat are used as thermodynamic model due to the better results.Binary parameters of activity coef ficients are regressed from experimental vapor pressure data while default constants are used for the solubility expressions.A design of heat pumps is developed and a new modeling of generator is analyzed.The coef ficient of performance of absorption heat pump and hybrid heat pump is equal to 0.7 and 0.83 respectively.For absorption heat pump a sensitivity analysis is carried out to evaluate the effect of temperature and pressure generator,the concentration of Li–Br solution on coef ficient of performance,cooling capacity and working fluid temperature.For hybrid heat pump,the different coef ficients of performance,the primary energy ratio,the generator heat,and the compressor power are analyzed for different values of compressor proportion.Results show that comparing the two systems the hybrid pump allows to save more primary energy,costs and carbon dioxide emissions with respect to absorption heat pump with the increasing of compressor proportion parameter.Future researches should focus on the construction of this heat pumps integrated in chemical processes as a biogas plant or trigeneration systems.

Mathematical modeling and analysis of thermodynamic processes in a twin-rotor piston engine

In order to study the major performance indicators of the twin-rotor piston engine(TRPE), Matlab/simulink was used to simulate the mathematical models of its thermodynamic processes. With consideration of the characteristics of the working processes in the TRPE, corresponding differential equations were established and then simplified by period features of the TRPE. Finally, the major boundary conditions were figured out. The changing trends of mass, pressure and temperature of working fuel in the working chamber during a complete engine cycle were presented. The simulation results are consistent with the trends of an actual working cycle in the TRPE, which indicates that the method of simulation is feasible. As the pressure in the working chamber is calculated, all the performance parameters of the TRPE can be obtained. The major performance indicators, such as the indicated mean effective pressure, power to weight ratio and the volume power, are also acquired. Compared with three different types of conventional engines, the TRPE has a bigger utilization ratio of cylinder volume, a higher power to weight ratio and a more compact structure. This indicates that TRPE is superior to conventional engines.