and Computational Methods

doi: 10.18698/2309-3684-2024-3-100119

In various technical systems hydraulic devices are widely used to ensure the synchronous movement of executive bodies — unregulated chokes, flow dividers, regulators and/or flow stabilizers. The latter are characterized by the fact that their functioning occurs in the range of pressure drops of liquid amounting to several hundred atmospheres. The issues related to the numerical simulation of non-stationary physical processes in the flow stabilizer the design of which is protected by a patent of the Russian Federation for the invention are considered. The results of computer modeling based on a theoretical model with concentrated parameters, the use of the finite-difference implicit Geer method for solving a system of rigid differential equations are presented. The problem of optimal improvement of the design of such flow stabilizer in accordance with the selected criterion is formulated and solved. This optimization criterion is to ensure the condition of the minimum possible positive statism of the flow-drop (static) characteristic in conditions of wide change in the pressure drop on the device and the effect of the axial component of the hydrodynamic force. The problem of optimal design improvement was solved using one of the widely used evolutionary optimization algorithms — genetic algorithm with real coding. The results of computational experiments in modeling physical processes of the analysis problem correspond to the available experimental data that were previously obtained by the authors of the work. It is shown that improvement of the existing design of the flow stabilizer is possible — the angle of inclination of the flow-drop characteristic to the horizontal axis has decreased almost twofold. At the same time, it was possible to obtain higher accuracy of maintaining volumetric flow rate of the liquid. This accuracy is on the order of ±7,5 % of the nominal (tuning) value of the flow stabilizer. For comparison, the accuracy of maintaining the volume flow rate of the liquid before performing the optimization procedure was about ±10 %.

Иванов М.Ю., Бушуев А.Ю., Щербаков Н.С., Реш Г.Ф. Компьютерное моделирование динамических процессов в гидравлическом стабилизаторе расхода и его оптимизация на основе эволюционного алгоритма. Математическое моделирование и численные методы, 2024, № 3, с. 100-119.

doi: 10.18698/2309-3684-2023-2-6789

The problems of mathematical modeling of three–dimensional laminar and turbulent motion of a viscous incompressible fluid in multilayer permeable structures – porous mesh materials are considered. Each layer of the material is a woven metal mesh with square cells of micron sizes. Porous mesh materials are widely used in space, chemical, oil and gas, nuclear and other industries, for example, as hydraulic filters. Such materials have a complex internal structure and a variety of possible geometric configurations. Therefore, in the general case, the nature of the functional dependence of the hydraulic resistance that a material sample exerts on the flow of fluid flowing in its pore channels from the Reynolds number is not known. To determine this dependence on the existing material, as well as to create a material with a predetermined hydraulic resistance, computational fluid dynamics tools were used. The domestic engineering analysis system "Logos" and the author's program code developed in Keldysh Research Center were used. The physical parameters of liquid mass transfer in a porous filter material and its hydraulic resistance are determined by the methods of control volumes on an unstructured computational grid for integrating the Navier-Stokes equations and Lattice Boltzmann Method. It is established that the theoretical methods used allow us to estimate from above the functional dependence of the hydraulic resistance of a porous mesh material on the Reynolds number in the range of values from 0.01 to 500. To verify the mathematical model an experimental setup was made with the help of which a cycle of hydraulic spills of sample of porous mesh material was performed. The numerical solutions obtained are consistent with the available analytical dependencies obtained in the works of domestic and foreign scientists and the results of experimental studies.

Городнов А.О., Лаптев И.В., Сидоренко Н.Ю., Иванов М.Ю., Малахов А.С., Реш Г.Ф. Математическое моделирование процессов ламинарной и турбулентной фильтрации жидкой несжимаемой среды в пористых сетчатых материалах. Математическое моделирование и численные методы, 2023, № 2, с. 67–89.

doi: 10.18698/2309-3684-2020-1-103117

A software environment was developed for computer-aided design of optimal throttle hydraulic synchronization systems of actuators of various functional purposes operating under conditions of external alternating-sign force effects. The criterion of an optimization procedure was the minimization of a mismatch time of relative movement of actuators during operation. A compute core of an object-oriented code was constructed on the basis of a dynamic mathematical model of a synchronization system consisting of four power cylinders. A model problem was solved with the help of the created software environment. This model problem demonstrated the efficiency of the proposed multidimensional optimization process. The methodology was based on the use of the well-known heuristic method (binary coded genetic algorithm) and the subsequent improvement (in the sense of a given objective functional) of the obtained solution by a method on the basis of the Hooke-Jeeves algorithm. Recommendations on the practical application of the software and mathematical support for achieving the best convergence to the extreme value of a vector of controlled parameters were formulated.

Бушуев А.Ю., Иванов М.Ю., Коротаев Д.В., Реш Г.Ф. Программная среда dgsSynchCAD для моделирования и автоматизированной эвристической оптимизации дроссельных гидросистем синхронизации. Математическое моделирование и численные методы. 2020. № 1. с 103–117.