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.

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.

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 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.

SIMULATED MATHEMATICAL MODEL FOR HIGH PRESSURE CYLINDER WALL TEMPERATURE OF HOMEMADE TURBINE

In order to balance the contradiction between the demand of high precision and that of short time interval of model computing for the power plant simulator, a set of simulated mathematical models are constructed. The model describes the cylinder wall temperature located at four key positions of the high pressure cylinder. The simulated model is confirmed to be not only simple but also precise via comparison between the simulated results and the autoptic data of a power plant.

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.

Dynamic Behavior and Deformation Analysis of the Fish Cage System Using Mass-Spring Model

Fish cage systems are influenced by various oceanic conditions, and the movements and deformation of the system by the external forces can affect the safety of the system itself, as well as the species of fish being cultivated. Structural durability of the system against environmental factors has been major concern for the marine aquaculture system. In this research, a mathematical model and a simulation method were presented for analyzing the performance of the large-scale fish cage system influenced by current and waves. The cage system consisted of netting, mooring ropes, floats, sinkers and floating collar. All the elements were modeled by use of the mass-spring model. The structures were divided into finite elements and mass points were placed at the mid-point of each element, and mass points were connected by springs without mass. Each mass point was applied to external and internal forces, and total force was calculated in every integration step. The computation method was applied to the dynamic simulation of the actual fish cage systems rigged with synthetic fiber and copper wire simultaneously influenced by current and waves. Here, we also tried to find a relevant ratio between buoyancy and sinking force of the fish cages. The simulation results provide improved understanding of the behavior of the structure and valuable information concerning optimum ratio of the buoyancy to sinking force according to current speeds.

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.

Modeling and simulation of circulating fluidized bed reactors applied to a carbonation/calcination loop

A fluid dynamic model for a gas-solid circulating fluidized bed （CFB） designed using two coupled riser reactors is developed and implemented numerically with code programmed in Matlab. The fluid dynamic model contains heat and species mass balances to calculate temperatures and compositions for a carbonation/calcination loop process. Because of the high computational costs required to resolve the three-dimensional phenomena, a model representing a trade-offbetween computational time requirements and accuracy is developed. For dynamic processes with a solid flux between the two reactor units that depends on the fluid dynamics of both risers, a dynamic one-dimensional two-fluid model is sufficient. A two-fluid model using the constant particle viscosity closure for the stress term is used for the solid phase, and an algebraic turbulence model is applied to the gas phase. The numerical model implementa- tion is based on the finite volume method with a staggered grid scheme. The exchange of solids between the reactor units constituting the circulating fluidized bed （solid flux） is implemented through additional mass source/sink terms in the continuity equations of the two phases, For model validation, a relevant experimental analysis provided in the literature is reproduced by the numerical simulations, The numerical analysis indicates that sufficient heat integration between the two reactor units is important for the performance of the circulating fluidized bed system, The two-fluid model performs fairly well for this chemical process operated in a CFB designed as two coupled riser reactors. Further analysis and optimization of the solution algorithms and the reactor coupling strategy is warranted.

Randomness in the Hybrid Modeling and Simulation of Insulin Secretion Pathways in Pancreatic Islets

Insulin secreted by pancreatic islet ˇ-cells is the principal regulating hormone of glucose metabolism.Disruption of insulin secretion may cause glucose to accumulate in the blood, and result in diabetes mellitus.Although deterministic models of the insulin secretion pathway have been developed, the stochastic aspect of this biological pathway has not been explored. The first step in this direction presented here is a hybrid model of the insulin secretion pathway, in which the delayed rectifying KCchannels are treated as stochastic events. This hybrid model can not only reproduce the oscillation dynamics as the deterministic model does, but can also capture stochastic dynamics that the deterministic model does not. To measure the insulin oscillation system behavior, a probability-based measure is proposed and applied to test the effectiveness of a new remedy.