arXiv subjects

Ivan V. Kazachkov

Publications and source records attributed to Ivan V. Kazachkov.

13 recordsLinked to original sources

arXiv2018

Derivation of the nonlinear equations for surface of fluid adhering to a moving plate withdrawn from a liquid pool

Many technological processes include preparing some special materials adhering to a product surface. For example, this problem is important for the magnetic tape producing, wire adhering, etc. For a surface withdrawn from the molten metal or the other liquid material there is a problem to determine a profile of a film surface. It is subject of this paper. We developed the mathematical model for the simulation of the adhering process of viscous liquid film to a slowly moving plate, which is vertically withdrawn from the molten metal or the other fluid capacity. The Navier-Stokes equations for a film flow on a surface of the withdrawn plate are considered with the corresponding boundary conditions, and the polynomial approximation is used for the film flow profile. The equations after integration across the layer of a film flow result in the system of partial differential equations for the wavy surface of a film flow, of flow rate and of flow energy.The derived equations are used for analysis of the nonlinear film flow that determines the quality of a fluid adhering on a surface of the withdrawn plate.

physics.flu-dyn↗

arXiv2018

The principle of maximum in the imitative control tasks

The article is devoted to the problem of applying the maximum principle for finding optimal control parameters in simulation tasks of interest for a variety of engineering and industrial systems and processes. Especially important is the problem for such systems where it is practically impossible to organize a control system because of an unknown model or because it is impossible to strictly follow the specified trajectories of control parameters in each particular case. A so-called delta-procedure is constructed that converges and allows one to obtain an approximation and optimal control of the system in a finite number of steps with a given accuracy delta. The theorem on the delta-procedure is proved and illustrative examples are given. Some features of the application of the proposed algorithm to real problems of simulation control are discussed, e.g. the optimal number of points dividing the time interval under consideration, and tasks for further individual research.

math.OC↗

arXiv2018

Heterogeneous Turbulent Jets of the Mutually Immiscible Liquids: the Mixing and Heat Transfer Processes

Many natural and technical processes deal with the turbulent mixing and heat transfer in the jet of mutually immiscible liquids, which represent an important class of the modern multiphase systems dynamics. The differential equations for axisymmetrical two-dimensional stationary flow and the integral correlations in a cylindrical coordinate system are considered for the free and confined jets. The parameters of the turbulent mixing in a free jet and in two-phase flow in a chamber are modelled and analyzed. One example is also done for high-temperature flow of the liquid metal melt cooled by water in a simulation of the hypothetic severe accidents at the nuclear power plant is presented and compared to the experimental data. The algorithm and the results obtained may be of interest for some research and industrial tasks, where calculation of the parameters of multiphase turbulent mixing and heat transfer are important.

physics.flu-dyn↗

arXiv2018

The dynamics of thin gas layer moving between two fluids

The dynamics and stability of a thin gas layer moving between two fluid layers moving in the same or opposite direction is studied. The linear evolutionary equations describing the spatial-temporal dynamics of the interface perturbations between gas and two fluid layers are derived for the flat two-dimensional case. Integral correlations across the layer are obtained, and the various kinds of time dependent base states are found. A linear stability is considered for the system using non-stationary equation array derived. The equation array consists of the two one-dimensional non-stationary equations of a seventh and fourth order. The results of the numerical study of the governing evolution equations support the results of the analysis for more simple limit cases. It is found that the thin sheet gas flow in-between two liquid layers is unstable and the peculiarities are found and discussed together with some applications available.

physics.flu-dyn↗

arXiv2018

About the Problem of Utilization the Low-Potential Heat and Recent Perspective Developments

Problem of utilization of the low-potential heat and its perspectives are considered and one example from the author works is presented in detail. Description of the project and the results obtained are presented by a development of the Liquid Metal Magnetohydrodynamic (LMMHD) Gravitational Mini Power Plant (GMPP) for utilization of the low-potential heat from any available low-exergy sources, which are the huge sources of the wasted energy around the globe. Project is based on the experience by the LMMHD energy transformation with gravitational vapour/gas-lift driving principle. An example of the GMPP was developed and designed for small local consumers (100kW-1MW) for the application in the geothermal low-temperature sources 150-250C, big ferries (unused hot waters from engine), hot waters and gases from metallurgical and chemical factories, and many other similar customers. The drawings for the construction have been made and the optimal parameters computed for some potential liquid metal working media and two variants of the unit modules assembling have been elaborated (parallel assembling for getting the desired voltage or consecutive assembling for obtaining the desired current in the electrical network). The optimal height of the liquid metal circulating loop was obtained in the range 10-15 m, and the voltage in a unit 1-2 Volt.

physics.app-ph↗

arXiv2018

Particle cooling in Vaporizing Coolant

The approximate mathematical model for a cooling of the particle in a volatile liquid is developed and analyzed. Despite the precise model is complex and requires the solution of the nonstationary two-phase flow equations with the conjugated heat transfer boundary problem for the particle, vapor, and liquid cooling pool, the considered simple model may be of interest. Vapor is permanently produced and removed from the coolant pool. Analysis of the model obtained resulted in some correlations for the three main parameters of the cooling process, which may be used for estimation of the particle cooling.

physics.app-ph↗

arXiv2018

Derivation and analysis of the nonlinear boundary conditions at the deformable interface between two fluids

The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the non-linear description is performed and analyzed in a wide range of physical situations. The differential equations of the interfacial motion thus obtained may be useful in research of the non-linear development of the classical hydrodynamic instabilities. They should play an important role in the understanding of the hydrodynamic phenomena associated with the flows involving complex interfacial evolution including parametric control of the boundaries in continua (for example, with electromagnetic field or/and vibration).

physics.flu-dyn↗

arXiv2018

Parametric Control of Nonlinear Longitudinal-Rotational Rod Oscillations and Phenomenon of Reverse Rotational Vibrations

The article is devoted to the investigation of the nonlinear effects in a system of the coupled longitudinal-torsional parametric vibrations of a rotating rod. Constructed and investigated mathematical model, based on which we calculated the resonance conditions of the nonlinear oscillations and found the ratio of the parameters that require changing of the sign of the coefficient in front of the term defining the possible reverse of torsional vibrations. The latter is a new phenomenon, a special mode, where the parametric action in the form of longitudinal vibrations at one end of the rod (for example periodic strikes in the rod's end with a certain frequency) can lead to torsional vibrations due to the nonlinear parametric interaction of oscillations. In the context of this, the reverse leads to control not only the rotation parameters, but also the direction of rotation, and there are possible torsional oscillations, which can be used in precision mechanics devices.

physics.app-ph↗

arXiv2018

Controlled Film Flow in Granulation of Metals for the Development of Amorphous Superhard and Functionally Unique New Materials

The problem of granulation is very bright by the granulated materials, as well as by their application. In the paper, some history of the granulation problem during over century and modern applications of the metallic granulates and amorphous materials are given at the beginning. Then the specific own granulation problem is presented, which has concern to the controlled liquid metal jet and film flows for a production of the uniform by size and form particles (granules) cooled with a high rate, to be amorphous or close to the amorphous materials. Such granules of the given size and form are needed for the new material science. The basics of developed theory of the controlled jet and film flow disintegration with further rapid cooling of the drops obtained after flow disintegration are presented together with the new patented granulation devices. The developed methods and devices can be used for production of the amorphous or close to amorphous granules in a wide range of the given sizes, with very narrow (plus-minus 50% deviation of size from the average one).

physics.app-ph↗

arXiv2018

Approaches for Modeling of the Complex Heat and Fluid Flows and Another Physical Processes of Fractal Nature

The paper deals with the fundamental problem of a modeling of the physical, in particular, thermal hydraulic processes, in various media of fractal structure of the natural, technological and technical systems and devices. The examples of a few complex systems (mainly, the physical processes) are shown as the different fractal structures, e.g. the ones obtained by cooling and solidification of the multiphase mixtures. Some materials reveal the structural features having a significant influence on the behaviors of these materials. The thermal hydraulic processes which are going during a melts cooling, with the further water and steam flow through a porous or a channeled media, are presenting the characteristic examples. The best models of the thermal hydraulic and other physical processes in such fractal media should be the ones based on the fractional differential equations. An order of the fractional derivatives in time and space may change in the process. For example, by a cooling of a melt, with a change of the fractal properties of the system, it is going as follows: first, the vapor, water, melt mixture is interacting, then a formation of the solid structure is performing due to solidification of a melt, and a vapor flows through the permeable structure developed in a process. The dynamically changing fractal systems (dynamic fractals) must be modeled by the corresponding equations changing according to the evolving process. Therefore, it is not surprising that so far some of such tasks have not been properly resolved even in a simplified formulation. There are many similar problems in the modern physics, technology, etc., which are discussed in the paper.

physics.comp-ph↗

arXiv2018

To the problem of mathematical and physical modeling of the turbulent jets of mutually immiscible liquids like the oil and water

Peculiarities of the turbulent two phase and multiphase flows of the mutually immiscible liquids and averaged differential equations for their modeling are considered based on the approach, which was first developed and proposed by Prof. A.I. Nakorchevski as an alternative to a number of the well known averaged multiphase dynamics equations. The main difference of the new method was in an averaging of the Navier Stokes equations by phases and components in time instead of the widely spread spatial averaging in multiphase mechanics. What was more, introduction of the so called function indicator of the phases in a flow allowed recognizing the phases in their movement in a multiphase mixture, both theoretically and experimentally. For experimental study the special micro sensor was invented and created, which was successfully applied. In this paper, the method of Nakorchevski is described in application to some multiphase tasks, and a discussion is presented as concern to advantages of the method for study of turbulent two phase flows of water oil immiscible mixture, as well as many other similar mixtures, where it is important to know the peculiarities of the phases movement and their mixing in a multiphase flow.

physics.flu-dyn↗

arXiv2017

Investigation the Critical Levels in Development of the Complex Systems with Shifted Arguments for their Optimal Control

Investigation of the critical levels and catastrophes in the complex systems of different nature is useful and perspective. Mathematical modeling and analysis is presented for revealing and investigation of the phenomena and critical levels in a development of complex systems for various natures associated with diverse complicated factors, in particular with shifted arguments of the system. Intensive research in this direction and developed techniques may optimize management of the complex systems in financial-economic, natural and other fields. Construction of adequate mathematical models for development of complex systems, critical modes and their effective control are important tasks for a wide range of contemporary issues as shown in paper on examples. Critical levels in development of economic, banking, technical, political and other systems are necessary to determine and anticipate, to manage their system requirements and provide stable development, without being hit in a critical situations, leading to growing oscillations of the system settings.

nlin.AO↗

arXiv2015

The Theory and Applications of Parametric Excitation and Suppression of Oscillations in Continua: State of the Art

The results by development of physical, mathematical and numerical models for parametric excitation and suppression of oscillations on the interfaces separating continuous media, for carrying out computing, physical and natural experiments by revealing the new phenomena and parametric effects, and for their use in improvement the existing and creation the perspective highly efficient technological processes are presented. Scientific novelty of this work consists in development of the theory and applications of parametric excitation and suppression of oscillations on the boundaries of continua on the samples of three tasks classes: flat and radial spreading film flows of viscous incompressible liquids, conductive as well as non-conductive ones; surfaces of phase transition from a liquid state into a solid one; and heterogeneous granular media. The external actions considered are: alternating electromagnetic, vibration, acoustic and thermal fields. Along with linear the non-linear parametric oscillations are investigated (including strongly non-linear) too and the results of theoretical studies are confirmed and supplemented with the corresponding experimental data. The general and specific peculiarities of parametrically excited oscillations and the new parametric effects revealed are discussed for technical and technological applications. First the general statement and substantiation of the problems studied is considered, and then the various parametric oscillations in continua are analyzed from common methodological base. Also the assessment of a current state of the problems, analysis of their features, prospects of further development and the main difficulties of the methodological, mathematical and applied character are presented.

physics.flu-dyn↗