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.

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 Debates as an Integral Part of the Learning Process

In this report, we want to touch upon two aspects of teaching mathematics in middle and high school. The first of them is the eternal question of how to teach, to motivate students and make them involved in the educational process, particularly in mathematics, where the most important factor is the natural gifts. The second aspect concerns the question which became very urgent in the modern world： what, in fact, we want to teach the students in a world over-saturated with information of any kind. As a result of the information blowup, two aspects emerge. On the one hand, straight passing over the skills and knowledge to the students becomes irrelevant today （just like a teacher or lecturer, merely speaking to an audience, who is not that relevant for young people, accustomed from childhood to perceive information through dynamic color visuals）. On the other hand, there is a change in emphasis in the objective function of the educational process from gaining knowledge to acquisition of skills of working with information, consideration and estimation, and choosing of the optimal strategy of a number of possibilities. This trend can be seen in the selection of problems in the international examination PISA （Program for international Student Assessment）, in the new curriculum in mathematics and in the selection of problems in the matriculation exams. These considerations （along with others） make teachers took for rtew forms of teaming, more appropriate to the demands of modernity. In this report we suggest the idea of using a mathematical competition called ＂Mathematical debate＂ （mathematical fight） as an integral part of the educational process at different levels of learning mathematics, as an appropriate tool.

Novel kinetic model for the simulation analysis of the butanol productivity of Clostridium acetobutylicum ATCC 824 under different reactor configurations

Acetone–butanol–ethanol(ABE)fermentation process can be exploited for the generation of butanol as biofuel,however it does need to overcome its low volumetric solvent productivity before it can commercially compete with fossil fuel technologies.In this regard,mathematical modelling and simulation analysis are tools that can serve as the base for process engineering development of biological systems.In this work,a novel phenomenological kinetic model of Clostridium acetobutylicum ATCC 824 was considered as a benchmark system to evaluate the behaviour of an ABE fermentation under different process configurations using both free and immobilized cells:single stage batch operation,fed-batch,single stage Continuous Stirred Tank Reactor(CSTR)and multistage CSTRs with and without biomass recirculation.The proposed model achieved a linear correlation index r^2=0.9952 and r^2=0.9710 over experimental data for free and immobilized cells respectively.The predicted maximum butanol concentration and productivity obtained were 13.08 g·L^(-1)and 1.9620 g·L^(-1)·h^(-1)respectively,which represents an increase of 1.01%and 990%versus the currently developed industrial scale process reported currently into the literature.These results provide a reliable platform for the design and optimization of the ABE fermentation system and showcase the adequate predictive nature of the proposed model.

A model for expansion ratio in liquid-solid fluidized beds

Liquid-solid fluidized beds are used in mineral processing industries to separate particles based on parti- cle size, density, and shape. Understanding the expanded fluidized bed is vital for accurately assessing its performance. Expansion characteristics of the fluidized bed were studied by performing several experi- ments with iron ore, chromite, quartz, and coal samples. Using water as liquid medium, experiments were conducted to study the effects of particle size, particle density, and superficial velocity on fluidized bed expansion. The experimental data were utilized to develop an empirical mathematical model based on dimensional analysis to estimate the expansion ratio of the fluidized bed in terms of particle character- istics, operating and design parameters. The predicted expansion ratio obtained from the mathematical model is in good agreement with the experimental data.