METHOD OF THEORY OF DIMENSIONS IN EXPERIMENTAL RESEARCH OF SYSTEMS AND PROCESSES

The method and parameters of experimental modelling of systems and processes in mechanical engineering are substantiated. The theory of similarity and dimensionality is used as an intermediate link between theory and experiment. The dimension of the factor space depends on the number of factors. The set of factors is grouped into dimensionless similarity criteria. The selected criteria are in certain dependence, such as the Galileo test, Euler and Reynolds numbers. Examples of application in experimental studies are given. The use of dimension theory in a factor-planned experiment allows reducing the number of factors, simplifies the mathematical interpretation of the response criterion and provides a graphical representation in the form of 3-D model.

Elaboration of a criterion heat transfer equation of electrostatic fields influence in kerosene medium at free convection and deposit formation

The paper focuses on the problem of deposit formation in engines and power plants operating on liquid hydrocarbon fuels and coolers, and analyzes hydrocarbon deposit formation on heated fuel-delivery metal at increased temperature. First, an experimental setup was created to study the effect of electrostatic fields on the heat transfer intensification in liquid aviation kerosene TS-1 and the process of deposit formation on a heated working plate. Then, the effect of electric wind on thermal processes was visualized using the Tepler optical setup and the influence of electrostatic fields on the processes of heat transfer of deposit formation in the kerosene medium when using coaxial needles as electrodes was studied. Finally, findings of the research were generalized and a new criterion equation with a created dimensionless similarity number of electric convection and deposit formation simplex was introduced.

Computational analysis of water based Cu - Al2O3/H2O flow over a vertical wedge

Theoretical and numerical investigation of the fluctuating mixed convection of hybrid nanofluid flow over a vertical Riga wedge is considered in this analysis. Two kinds of solid nanoparticles with base fluid at vertical Riga wedge is studied. Thermal and velocity slip impacts on vertical Riga wedge are investigated in the current study. We discussed both the unsteady and steady cases. The water has low thermal conductivity. We added the nanoparticle [Formula: see text] and [Formula: see text] which increases the thermal conductivity of the base fluid. This phenomena increase the heat transfer rate at the surface Riga plate. Partial differential equations are reduced into an ordinary differential equation by means of dimensionless similarity variables. The resulting ordinary differential equations are further solved through numerical and perturbation methods. Thickness of momentum boundary layer is reduced because of the solid nanoparticle rises in all cases of [Formula: see text], [Formula: see text], [Formula: see text]and[Formula: see text]. Our results are more agreeing with the decay results of Bachok et al. and Yacob et al. when rest of the physical parameters dimensions.

Working process for installing snow melting plants with active working element

Based on the operating experience analysis of snow melting plants and the proposed patent solutions for their improvement, a new design is developed. Operability of the new design, in which rotation of the working bodies is carried out under the influence of the supplied coolant’s pressure, is confirmed. The study of the working process is based on an experimental method based on physical modeling. The influence of individual factors affecting the intensity and efficiency and enabling to determine the dimensionless similarity equations, is studied. Based on the results obtained, a pilot plant is designed, created, and tested under real operating conditions.

Analysis of dimensionless similarity complexes’ influence on steam-assisted gravity drainage using the integral model

This article analyzes dimensionless complexes of similarity sensitivity of steam-assisted gravity drainage (SAGD) model. The application of SAGD for development of hard-to-recover reserves is complicated by the need to choose a rational development system. Therefore, the task of modeling the process of SAGD with subsequent analysis of sensitivity of technological indexes from the essential parameters and characteristics of the reservoir is relevant. Existing works have not conducted a comprehensive analysis of all values influence. Such analysis is conducted for the first time in this article. This work aims to analyze the influence of main characteristics (steam injection rate, steam temperature, well pattern, depression and repression on wells, reservoir thickness, heat capacity) on technological parameters of SAGD. The main methods include de-dimensioning of the physical and mathematical model of the process and calculations using an explicit finite-difference scheme. Dimensionless similarity complexes with a significant contribution to SAGD are distinguished. Values of sweep efficiency and cost-effective time at different values of selected dimensionless complexes of similarity are defined. The greatest influence on SAGD is affected by three dimensionless similarity complexes, characterizing respectively the ratio of water and oil flows, heat losses vertically and horizontally, and the development system. The results show that there are some effective values of depression on the formation and the distance between pairs of wells. Based on the results of calculations, the authors provide recommendations for the future application of the method on a real field.

An Investigation of Acoustic Similarity on an Underwater Structure

An acoustic similarity due to two geometrically similar structures which are vibrating in heavy flow, such as in water, is investigated. The acoustic similarity states that for two geometrically similar structures, if a group of dimensionless similarity numbers are constant, the dimensionless acoustic pressure coefficient keep constant at the corresponding acoustic field points for the two flow–loaded vibrating structure systems. Numerical simulations and experiment results are presented to validate the acoustic similarity. This acoustic similarity may be useful when a small structure is employed to investigate the acoustic performance of large scale structure.

Fractional Giona-Roman Equation on Heterogeneous Fractal Structures in External Force Fields and Its Solutions

We introduce a heterogeneous fractional Giona-Roman equation (HFGRE) on heterogeneous fractal structure media describing systems involving external force fields. The HFGRE is shown to obey generalized Einstein relation, and its stationary solution is the Boltzmann distribution. It is proved that the asyrnptotic shape of its solution is a stretched Gaussian and that its solution can be expressed in the form of a function of a dimensionless similarity variable for the case of constant potentials, linear potentials, harmonic potentials, analytic potentials, logarithm potentials and generic potentials.

Instabilities of a Hall plasma flowing across a magnetic field

Under certain restrictions imposed on the plasma parameters, an analytical 2D solution to the magnetohydrodynamic equations, taking into account the Hall effect [of the HMHD (Hall magnetohydrodynamic) equations], is found for the case when plasma flows across a magnetic field. This solution has the form of the sum of a rather arbitrary steady flow and a small time-dependent disturbance. We show that waves of a purely acoustic nature can propagate against the background of the flow. The magnetic field manifests itself in this process only in that it produces an effective gravity force, the “gravitational” acceleration being proportional ωeτe. Like acoustic-gravity waves in the atmosphere, such quasiacoustic-gravity (QAG) waves in a plasma increase greatly in their amplitude as they propagate “upward,” that is, in this case, to the anode of an accelerating plasma channel. The existence of a rather general dimensionless similarity criterion is also shown. It can be found directly from the structure of the HMHD equations without any restrictions as to the plasma parameters.