Porosity design procedure at the directed solidification of castings

One of the main tasks in developing a technical process to manufacture castings is to organize risering at the stage of solidification, which ensures the set level on shrinkable porosity and shrinkage cavities. As known, generally, the risering zone consists of a feeder zone and a feeding butt end zone. In references the terms of final (end) effect action or an effective area of the casting edge is possible to encounter rather than the term of feeding butt end zone.The values of feeding butt end zone are used to calculate a directional solidification in the casting mould. The design procedure of a directional solidification of castings is follows. The first design section is advised to settle down at the distance equal to the zone of feeding butt end. The subsequent design sections are advisable to settle down at distances a little bit less, than the zone of feeding butt end. The padding (lap) value ought to be selected to provide the later solidification of the upper sections of casting with respect to the sections lying below.A series of special experiments on castings of the simple configuration (slabs and bars) defines a value of the feeding zone of a butt end and makes it out as the regressional dependences of the feeding butt end zone on the characteristic sizes of this or that casting. Thus, considerable material and time expenditures are demanded to define the value of the feeding butt end zone to be used further, including calculation of directional solidification of castings.The paper offers a design procedure to calculate a zone of the feeding butt end via computing simulation of solidification in a casting mould thereby sharply reducing expenditures for searching the desirable values. To reveal spaces in the casting, staggered with shrinkable porosity, the new criteria of porosity developed in BMSTU are used.The paper shows a possibility to use the effective size as a characteristic parameter of casting for dependence of the feeding butt end zone thus providing this dependence universality and a possibility to use it for making any shaped casting, but not just the castings of a simple configuration.</p

Beta-approximation of the two-particle distribution function for the chains of phase oscillators

Abstract: When constructing the BBGKY hierarchy for systems with strong local interaction (liquids, magnetic materials) the key problem is the issue of approximation of the two-particle distribution function. The traditional approximation of multiplicativity that leads to the theory of the mean field often gives qualitatively incorrect results. In this paper, we consider a ring chain of phase oscillators with interaction only between the nearest neighbors, in a thermostat. On the basis of the analysis of the results of ab initio calculations, an approximation is constructed for the two-particle distribution function. It results in the one-particle Fokker-Planck equation with a self-consistent integral force. The results of the modeling based on the resulting equation are in a good agreement with the ab initio calculations. The obtained results may be of great importance in the construction of self-consistent models of systems with strong local interaction and temperature fluctuations.Note: Research direction:Mathematical modelling in actual problems of science and technic

The problem of the phase oscillators chain kinetic simulation

Abstract: One of the main problems of kinetic theory is the method of taking the correlations between intensively interacting particles into account on the BBGKY hierarchy truncation. This question becomes critical for the nonequilibrium processes in fluids and condensed matter. The classical multiplicative approximation which leads to the mean field approach often results in the qualitatively wrong behaviour of a system. In this work the looped phase oscillators chain connected to the heat bath was studied. The interaction is limited to the nearest particles. Results for the direct numerical solution of the problem were compared to the outcome of simulations based on kinetic theory with different approximations. It is showed that Self-consistent moments approach provides acceptable values of the mean energy and the relaxation time for the certain interval of the temperatures.Note: Research direction:Mathematical modelling in actual problems of science and technic