Mathematical and Computer Modeling of the Forms of Multi-Zone Fuel Elements with Plates

Abstract

Seeing the significant increase in the number of nuclear power plants, as well as models and modifications of nuclear reactors, it becomes important to find out/establish the advantages of certain plants. At the same time, designers face a number of questions for which optimal solutions have not yet been found. At nuclear plants, there is the largest turnover of financial funds and the smallest gain in economy brings huge profits, but one should not forget about reliability and costs during the plant construction. This is a complex problem that is solved at the design stage. Calculations of the reactor at the design stage make it possible to determine the main parameters of the active zone, temperature values, etc. Thermohydraulic calculation of the active zone of the reactor is one of the cornerstones in justifying the safe operation of the nuclear power plant. Calculations of coolant parameters and temperatures of fuel elements are carried out at all stages of designing and proving the safety of nuclear power plants. Twisted pipes and finned heat transfer surfaces are widely used in engineering to increase the effective heat transfer coefficient. In particular, longitudinal, transverse, and spiral edges are used for finning the shells of fuel elements of nuclear reactors and the outer surfaces of steam generator pipes. Finning not only increases the heat transfer surface on the side where the heat transfer coefficient has a low value, but also significantly affects the hydrodynamics of the flow, and thus affects this coefficient. It is obvious that the better the medium is mixed in the main flow and in the intercoral zone, the higher the heat transfer coefficient is. The most profitable forms of fuel elements shells finning are chevron and polyzonal finning, which are performed in the form of a multiturn spiral with a large step. The R-function theory turned out to be quite convenient for building mathematical models of finned shells of fuel elements with straight and helical plates, as well as for building the corresponding objects on a 3D printer. From a practical point of view, the relevance of the problem is also determined by the significant spread of twisted cylindrical bodies, twisted channels, coils in the energy, chemical, oil, gas, metallurgical industries and in heat engineering equipment. The flows that arise at this time make it possible to intensify the processes of heat and mass exchange and achieve savings in energy resources

Method for design of two-level system of active shielding of power frequency magnetic field based on a quasi-static model

“…A feature of the solution of the considered multi-criteria problem is inconsistency of local criteria to each other, which prevents the simultaneous optimization in general by all criteria at the same time [44]. This is due to the fact that minimizing the induction at one point, for example, located in the center of the screening space, leads to an increase in the induction at the points located closer to the power line due to overcompensation of the original magnetic field, and at the same time leads to an increase in the induction of the resulting magnetic field at points located farther than the power line due to undercompensation of the original magnetic field.…”

“…The task of synthesizing a magnetic field control system is usually complicated by significant uncertainties in the mathematical model of the control object [34][35][36][37]. Due to objective circumstances, such as the inaccuracy of the first level model, unmeasured external and internal disturbances, the actual values of the output coordinates will differ from the calculated ones [44][45][46][47]. In this regard, we will consider design of two-level magnetic field control system.…”

The method for design of electromagnetic hybrid active-passive shielding by overhead power lines magnetic field

“…(12) Note that the components of the vector game (11) and vector constraints (12) are the nonlinear functions of the vector of the required parameters [42][43][44][45] and calculated based on the calculations system COMSOL Multiphysics.…”

The method for design of combined electromagnetic shield for overhead power lines magnetic field

“…A sufficient condition for the existence of a saddle point is a change in the sign of the gradient  X f when passing the minimum point from minus to plus, and a change in the signs of the gradient   f when passing the maximum point from plus to minus [44][45][46][47]. These conditions can be formulated as the positive definiteness H X >0 of the matrix of second derivatives -the Hessian matrix with respect to the choice of parameters X, and the negative definiteness H  0 of the Hessian matrix with respect to the parameters δ, i.e.…”