SIMPLIFIED MATHEMATICAL MODEL OF A MAGNETIC SYSTEM WITH A CIRCULAR MAGNETIC CONDUCTOR

A simplified design of a magnetic system with a circular magnetic core is presented and its mathematical model is developed to determine the magnetic flux. Transition from a cylindrical coordinate system to a rectangular coordinate system.

Extreme wave run-up on steep rock coasts

<p>Some rock coasts around the world feature very steep slopes immediately adjacent to the shore. If surface waves propagate on such a steep bottom slope, they experience only slight amplification until very close to shore. In this situation, unexpectedly large wave events may occur near the shore. We combine insight from solutions of a simplified mathematical model with statistical analysis and with observations at the Norwegian coast to conclude that even under moderate wave conditions, very large run-up can occur at the shore.</p><p>M. Bjørnestad and H. Kalisch, “Extreme wave runup on a steep coastal profile,” AIP Advances 10, 105205 (2020)</p>

Development of simplified mathematical model of P-88 recovery boiler for operating modes at loads near the nominal

To improve the design of the elements of combined-cycle plants, and their structural and mode optimization, mathematical models are required. These models show energy efficiency indicators of the equipment under changing operating conditions. Modeling of recovery boilers is traditionally carried out with the application of specialized software systems that implement submodels of thermal-hydraulic calculations of the elements of the boiler water-steam and gas paths. This approach makes it difficult to solve practical tasks, since it requires licensed software and appropriate qualifications of an engineer. The current direction of solving this problem is statistical processing of the results of calculation data obtained with the application of specialized software systems, and development of a simplified mathematical model in the form of regression dependencies of boiler performance on variable parameters. In this study, the problem is solved in relation to the P-88 boiler of the combined-cycle plant-325 power unit in the load range near the nominal one. The initial mathematical model is developed with the application of the software package “TRAKT” designed for verification and engineering design of boilers. The simplified mathematical model is based on the methods of regression analysis of statistical data. The accuracy of the model is estimated based on the operational data of the combined-cycle plant -325 power unit. The authors have developed the mathematical model of the P-88 recovery boiler, which allows to determine the main performance indicators of the boiler when the electric power of the gas turbine and the outdoor air temperature are changing at the loads near the nominal value. The performance indicators are determined without application of specialized software for design calculation of the boiler. The accuracy of the initial mathematical model implemented in the software package “TRACT” is characterized by deviation of the calculation results data from the operational data in the corresponding modes of no more than 2 %. The additional uncertainty value introduced into the calculation results data does not exceed 1,5 % when we transfer from the initial mathematical model to the simplified one. The resulting mathematical description will allow solving the problems of mode optimization and evaluating the efficiency of the recovery boiler and the power unit under changing operating conditions.

Internal Leakages in a Water Hydraulic Pump with Gears From Plastic

Plastics are used more and more in hydraulic systems. The chemical properties of the plastics favour the use of working fluids alternative to mineral oil, e.g. water. The conditions in the manufacturing process, e.g. injection moulding, limit the achievement of high working pressures in the hydraulic elements. Internal leakage reduces the efficiency of the hydraulic pump with plastic gears. The article presents the results of internal leakage tests of a water-supplied hydraulic pump. Gears made of various materials (PPS+GF40 and PEEK) have been used in the research, made by two methods: injection moulding and machining. A simplified mathematical model of the dependence of leakages on pressure and rotational speed has been developed. The influence of the materials and manufacturing methods used on the pump operation is discussed.

Creating a mathematical model of the impact of radiation-hazardous objects on the environment during a fire.

On the basis of the new data on the assessment of the removal from fires from stocks in the combustible material and the speed of weak grassroots fires spread, the wind rose in the Chernobyl Exclusion Zone and the capabilities of the HotSpot software package, there has been developed a mathematical model of real-time assessment of the consequences of accidents that may occur in the areas of radiation-hazardous objects during fires. The proposed model was verified on the basis of comparison with the data obtained during a large-scale fire in the Chernobyl Exclusion Zone in April 2020, and the maps of the Chernobyl Exclusion Zone’s air and soil contamination with 137Cs and 90Sr were made. Using the proposed mathematical model, there has been carried out the analysis of the degree of danger that may create radiation-hazardous objects in case of fire directly on the territory of their location. In the paper, there are also considered the examples of the sanitation point (SP) «Rudnia-Veresnia», SP «Rozsokha» and the «Point of vehicle washing near the ChNPP cooling reservoir» in comparison with the current contamination of air and soil around these facilities with radionuclides. The results of the conducted analysis have been used to make a conclusion about the insignificant impact on the environment of the Chernobyl Exclusion Zone compared to the current level of air pollution and the surface of its territory. Estimates of radiation exposure from SP «Rudnia-Veresnia», SP «Rozsokha» and the «Point of vehicle washing near the ChNPP cooling reservoir» to the environment have been obtained with the help of a simplified mathematical model. These data have a significant correlation with the actual data obtained in April 2020 (during a large-scale fire in the Chernobyl Exclusion Zone) in the areas of location of the points of the automated system of radiation condition control, and places of work, temporary and permanent stay of the personnel and the population. Therefore, the created simplified mathematical model can also be used to assess the radiation impact on the environment in the implementation of emergencies of various kinds at other numerous radiation-hazardous facilities of the ChEZ.