Bulletin of Dnipropetrovsk University. Series: Mechanics

17-28

Authors: O. O. Kochubey, E. V. Kravec

The calculations of viscous incompressible flows in the cavity with a movable top side and also in the cavity with free surface by finite elements method at 0-500 numbers of Reynolds are executed. The mathematical models in dimensionless variables ‘velocity-pressure’ of the flows in the cavities with and without a movable top side are brought. The advantage and disadvantage of mathematical formulations of problem for the considering cases are specified. The influence of cavity geometry with attitude of depth to width ratio 0.5; 1.0; 2.0 to the system of vortex formation is been investigated. The profiles of speed longitudinal and transversal components in the central sections of square cavity with a movable side and also map of stream-lines, isolines of two speed components and isobars for cavities with presence and absence of movable side are brought. The detailed comparative analysis of the flow in the cavities with and without a movable top side is carried out. The effect of a movable top side presents/absence on distribution of the velocity, pressure fields, and also on conformity to law of formation main and secondary vortex systems in cavities are found. The comparing of the results received with numerical researches of other authors is executed.

38-48

Authors: S. V. Tarasov, D. A. Redchic, O. B. Polevoy, I. B. Chashina, S. V. Moiseenko

A review of the current state and tendencies of development of wind power in the world and in Ukraine was carried out. The models and methods for calculating the aerodynamic characteristics of vertical-axis wind turbines were considered. The role of computational fluid dynamics in the aerodynamic design of complex systems was described. The problems of solving of Navier–Stokes equations and turbulence modeling were considered. A review and classification of applied programs packages of computational fluid dynamics was carried out. The results of numerical simulation of aerodynamics of Darrieus and Savonius rotors with two and three blades are discussed. The Reynolds averaged Navier–Stokes equation was applied to a numerical simulation of aerodynamics of Darrieus and Savonius rotors with two and three blades. The one-equation turbulence models were used. The solution of a system of initial equations is obtained with the help of implicit finite-volume numerical algorithm which was based on the artificial compressibility method. In multidomain areas overlapped structured grids were applied. The results of calculation of Darrieus and Savonius rotors with different quantity and geometrical performances of blades are submitted. The analysis of flow field near rotors was carried out. The main stages of development of vortex were allocated. The influence of Reynolds numbers, tip-speed-ratios and solidity on power characteristics of Darrieus and Savonius rotors was found.

53-60

Authors: N. N. Bilyaev, T. I. Rusakova

The development of methodology and software for holding a numericl calculation to research the level of atmospheric air pollution in the area of thermoelectric plant influation, as a result of its work there are gas pollutions that act into the atmosphere. The methodology for atmospheric air pollution level research (when thermoelectric plant functions) is based on math model for calculation the pollution consentration (nitrogen dioxide) that takes into account processes of nitrogen dioxide chemical transformation in atmosphere. Numerical methodology is based on the combined solutions to the convex and diffuse admixture transfer equations for every pollutant that comes from the plants and forms in chemical reactions in atmosphere. Implicit difference schemes are used in this methodology. Based on this math model, the software is worked out for carrying out some experments to research the level of atmospheric air pollution caused by thermoelectric plant emissions. As a result of these calculations, there are detected some atmospheric air zones that are polluted by nitrogen dioxide worked out by Pridniprovskiy thermoelectric plant. Several areas, which are subjected to contamination, are also detected. This study takes into account weather conditions. The software is necessary for obtaining some quantitative results to estimate the level of pollution consentration in atmosphere. The whole research can provide ecological security in large objects functioning that impact on the environment.

70-81

Authors: V. S. Podgurenko

The process of structural perfection of the wind energy systems is analysed. The modern wind power stations (WPS) are created as a rule with the use of wind turbines by power 2-4 MWt. The single power of wind turbines, maximally attained about 8 MWt, that is the limit of modern economic feasibilities of assembling works. Thus, the increase of single power of wind turbines in the conflict with the classic chart of wind energy extraction is used now, in this connection further development of wind energetic is thought to use of the new ways of taking the wind power and to refuse from the ol constructions of the WPS. The new wind energy system of new turbogenerator type with the direct driving by academician of the Engineering academy of Ukraine and academician of international engineering academy, the famous inventor of Ukraine Nikolay Stepanovich Golubenko is considered. The characteristics of the fundamentally new constructors schema are analysed – the new wind energy system with turbogenerator solves the problem of increase of single power to 40-50 MWt. There is opening in the article, that N. S. Golubenko had done the revolution in the wind energetic and energetic in total, and this achievement is put in a row with the greatest world achievements in the wind energetic area of science and technique. Personality aspects assisting the origin of opening in science and technique on the example of separate prominent scientists and designers are also proposed.

91-99

Authors: J. I. Nikolaenko, S. V. Moiseenko, O. A. Samoylenko

The work is dedicated to building the broadest family of basises of bicubic finite element and the allocation of its quasi-harmonic basises. The five-parameter family of complete basises and threeparameter family of bicubic finite element basises, complete with respect to all harmonic polynomials up to the third degree inclusive were built. Two quasi-harmonic basises that accurately approximate the harmonic functions were extracted from the three-parameter family. Mandatory conditions such as: the function of its site is one, in otherwise - zero, were used in the construction of the basis functions in the form of bicubic polynomials. Completeness condition was added to these conditions, which provides an accurate approximation of linear functions, as well as the symmetry (geometry) finite element was taken into account. The sum of squared deviations Laplacians values of basis functions from zero was taken as an additional measure of the basis functions harmony. Relative error, meansquare deviation, the Gram matrix of these bases and the condition number were calculated for comparison of properties of considered basises.