Two-dimensional Coordinate System Research Articles

Creation of a universal computing program to control the quality of educational services provided by NUOS in the international arena

Providing timely and high-quality educational services for a foreign customer is a critical task determining the university’s reputation in the international arena and, consequently, subsequent international orders. In the conditions of competition in the global market of educational services, it is necessary to constantly confirm the high standards of the university. It is suggested to apply general calculation of a quantitative assessment of the quality of training in the project management of foreign students’ education in joint programs with international partners. To significantly reduce the time of calculation, a universal computing program has been created. This program allows processing extensive data blocks with visualization of the results in the two-dimensional coordinate system. The results make it possible to quickly make adjustments in the educational process in order to improve the quality of educational services to international customers.

Periodic Orbits of the First Kind in the CR4BP When the Second Primary Is a Triaxial Rigid Body

The present paper deals with the existence of periodic orbits in the Circular Restricted Four-Body Problem (CR4BP) in two-dimensional co-ordinate system when the second primary is a triaxial rigid body and the third primary of inferior mass (in comparison of the other primaries) is placed at triangular libration point L4 of the Circular Restricted Three-Body Problem (CR3BP). With the help of generating solutions, we formed a basis for the existence of periodic orbits, then an analytical approach given by Hassan et al. [1], was applied to our model of equilateral triangular configuration. It is found that in general solution also; the character of periodic orbits is conserved. For verification of the existence of periodic orbits, we have applied the criterion of Duboshin [2] and found satisfied.

Analytical Calculation and Analysis of Main Generator Inductance of Aero Brushless Three-stage Synchronous Starter/Generator System

Precise electro-magnetic parameters are significant in the investigation of characteristic for brushless synchronous starter/generator system, especially the inductance during the starting process.This paper presented an analytical method for inductance calculation, which analysed the influence of stator windings’ parallel structure on inductance calculation and took the skewed slot structure into consideration. Due to the skewed slot structure, applicable two-dimensional coordinate systems were established .This proposed method could save time in calculation according to the simplification to some extent. The results of analytical method were presented and compared with the simulation results. The reason for the differences has been analyzed.

Eddy current loss in double-sided cored slotless type permanent magnet linear synchronous generator using analytical method

This paper describes the eddy current loss analysis of a double-sided cored slotless-type permanent magnet linear synchronous generator using the space harmonic method. To calculate the eddy current, an analytical solution was derived by applying the Maxwell equation, magnetic vector potential, and Faraday’s law in a two-dimensional (2-D) Cartesian coordinate system. Based on the armature reaction field distribution produced by the armature winding current, we obtained an analytical solution for the eddy current density distribution. Then, an analytical solution for eddy current loss induced in a permanent magnet (PM) was derived using the equivalent electrical resistance calculated from the PM’s volume and eddy current density distribution solution. Finally, the resulting current was determined based on analysis of the eddy current loss. The analytical results produced using this application of the space harmonic method were validated extensively through comparison with finite element method results.

Simplified Implementation Scheme for Space Vector Pulse Width Modulation of <italic>n</italic>-Level Inverter With Online Computation of Optimal Switching Pulse Durations

Space vector modulation (SVM) control of multilevel inverters (MLIs) is very popular. However, it gets extremely challenging with the increase in the number of output voltage levels due to the emergence of subtriangles in the various sectors of the hexagon, which results in increased computational complexity and storage requirements of switching states and corresponding pulse durations. Currently, this is handled through laborios offline computations in conjunction with the visual inspection of the space vector hexagon and its various sectors. This paper aims to simplify the implementation of the SVM scheme for an n -level MLI by proposing generalized equations that not only facilitate direct online computation of control pulses and obviate the requirement of lookup tables but also result in optimized switching. Yet, the on-time computations of the various MLI switches are still based on simple two-dimensional Cartesian co-ordinate system combined with the basic two-level inverter implementation. The proposed scheme makes use of a unique l-factor approach, which directly identifies the location of the various subtriangles in the space vector hexagon and leads to direct online computations of the control pulses. The proposed scheme is validated by simulations and experimental results for three- and five-level diode clamped MLI.

Numeric simulation of wet-steam two-phase condensing flow in a steam turbine cascade

Research on the wet-steam condensing flow problem is important for improving steam turbine efficiency. This paper derived a total variation diminishing (TVD) discrete method for a two-dimensional curvilinear coordinate system, which discretizes a control equation via a difference scheme that can accurately describe the transonic flow of compressible gas and capture abrupt parameter changes. This method can be applied to improve the shock wave capture accuracy in a cascade passage. A Cascade in White test is chosen as the study object to obtain test data to verify the accuracy of the proposed model. The calculation results indicate that the condensation process has a significant impact on the local flow parameters and that the distribution gradient of the parameters for the liquid phase is relatively large in the condensation position. The degree of subcooling of wet steam is the primary factor that influences the parameter distribution for the liquid phase in the main flow.

A general disk form formulation for thermo-elastic analysis of functionally graded thick shells of revolution with arbitrary curvature and variable thickness

The present research develops a general formulation for thermo-elastic analysis of a functionally graded thick shell of revolution with arbitrary curvature and variable thickness subjected to thermo-mechanical loading by using higher-order shear deformation theory. Mechanical properties except Poisson’s ratio are assumed to vary along a two-dimensional coordinate system with arbitrary functional distribution. Given that the thick shell is divided into some virtual disks and replacing various variable terms by their constant values, a set of differential equations for constant thickness are obtained for each virtual disk. By applying continuity conditions between the virtual disks, the general solution of the thick shell is obtained. The final relations are derived in general state for every arbitrary structure and material property distributions. Although previous publications presented a general formulation for thick shells of revolution, to the best of the authors’ knowledge, a closed-form solution is not provided.

Three-dimensional accuracy with two-dimensional computation speed: using the Kiva™ numerical framework to improve foundation heat transfer calculations

Calculation of heat transfer from building foundations is a computationally intensive three-dimensional problem that can require several weeks to solve using current computing hardware. The Kiva numerical framework was developed to compare foundation heat transfer calculation methods and determine approaches that reduce computation time without sacrificing a balance of capability, ease-of-use, and accuracy. This paper demonstrates the application of the Kiva framework to determine an accurate method of approximating three-dimensional heat transfer effects using two-dimensional coordinate systems. In two-dimensions, problems that would otherwise take days or weeks to solve can be solved in less than a minute. Three existing two-dimensional approximation methods along with a new boundary layer adjustment method are tested across a range of foundation types, shapes, and insulation configurations. The boundary layer adjustment method is shown to provide results within 3% mean absolute deviation from the three-dimensional solution.

Two-Dimensional study of heat transfer characteristics flow in a corrugated channel

The present work consists of a numerical study of turbulent incompressible two-dimensional flow with heat transfer in a corrugated channel using a computer code. The k-e model is used for turbulence modeling. The governing continuity, momentum and energy equations are written in two-dimensional Cartesian coordinate system and are numerically solved using finite volume method. This study concerns the effect of the Reynolds number based on the hydraulic diameter and the thermal behavior of the hydraulic channel. The thermal and dynamic fields of the flow in the corrugated channel were obtained in a satisfactory manner. Satisfactory results about velocity distributions, pressure and temperature allowed us to understand the behavior of the Nusselt number and friction coefficient along the walls of corrugated channel. A comparison between the numerical and experimental results shows a good agreement. DOI: http://dx.doi.org/10.5755/j01.mech.22.2.13321

Long-range propagation of nonlinear infrasound waves through an absorbing atmosphere.

The Navier-Stokes equations are solved using a finite-difference, time-domain (FDTD) approach for axi-symmetric environmental models, allowing three-dimensional acoustic propagation to be simulated using a two-dimensional Cylindrical coordinate system. A method to stabilize the FDTD algorithm in a viscous medium at atmospheric densities characteristic of the lower thermosphere is described. The stabilization scheme slightly alters the governing equations but results in quantifiable dispersion characteristics. It is shown that this method leaves sound speeds and attenuation unchanged at frequencies that are well resolved by the temporal sampling rate but strongly attenuates higher frequencies. Numerical experiments are performed to assess the effect of source strength on the amplitudes and spectral content of signals recorded at ground level at a range of distances from the source. It is shown that the source amplitudes have a stronger effect on a signal's dominant frequency than on its amplitude. Applying the stabilized code to infrasound propagation through realistic atmospheric profiles shows that nonlinear propagation alters the spectral content of low amplitude thermospheric signals, demonstrating that nonlinear effects are significant for all detectable thermospheric returns.

Analytical and Numerical Study of Nearshore Multiple Oscillating Water Columns

In the present study, the performance of two chamber nearshore oscillating water columns (OWCs) in finite water depth is analyzed based on the linearized water wave theory in the two-dimensional Cartesian coordinate systems. The barriers are assumed to be fixed and the turbine characteristics are assumed linear with respect to the fluctuations of volume flux and pressure inside the chamber. The free surface inside the chambers is modeled as a nonplane wave surface. Two different mathematical models are employed to solve the hydrodynamic problem: the semi-analytic method of matched eigenfunction expansion and the numerical scheme of boundary integral equation method (BIEM). The numerical results are compared with the semi-analytic results and show good agreement. The effects of the distance between the barriers and the length of the barriers on the efficiency of the OWC device are investigated. The results of two chambers OWC are also compared with the results for an equivalent single OWC chamber. Further, the effect of the water depth on the capacity of the wave power absorption is discussed.

The aero-acoustic Galbrun equation in the time domain with perfectly matched layer boundary conditions.

This paper presents a solution for aero-acoustic problems using the Galbrun equation in the time domain with a non-uniform steady mean flow in a two-dimensional coordinate system and the perfectly matched layer technique as the boundary conditions corresponding to an unbounded domain. This approach is based on an Eulerian-Lagrangian description corresponding to a wave equation written only in terms of the Lagrangian perturbation of the displacement. It is an alternative to the Linearized Euler Equations for solving aero-acoustic problems. The Galbrun equation is solved using a mixed pressure-displacement Finite Element Method. A complex Laplace transform scheme is used to study the time dependent variables. Several numerical examples are presented to validate and illustrate the efficiency of the proposed approach.

Approach to the Deviation Representation of Non-ideal Cylindrical Surfaces Based on the Curvilinear Coordinate System

Surface deviations of parts have vital impact on the function and performance of products, and should be controlled in manufacturing. Deviation representation facilitates the analysis of product function and performance, as well as the control of manufacturing process. In this paper, a novel deviation representation method for cylindrical surface is proposed. Instead of the Cartesian coordinate system, a two-dimensional curvilinear coordinate system is established on the ideal cylindrical surface to represent the surface. By adding a deviation dimension in the curvilinear coordinates, a deviation coordinate system is constructed to represent the non-ideal cylindrical surface. The data mapping between the two coordinate systems is presented and typical cylindrical surfaces with deviations are provided as examples to illustrate the formulated deviation representation approach.

Improved nanostructure reconstruction by performing data refinement in optical scatterometry

Recently, we have indirectly demonstrated that nanostructure reconstruction accuracy is degraded by the outliers in optical scatterometry, and we have applied the robust estimation method to suppress these outliers. However, the existence of a possible heavy masking effect could result in the risk of low measurement accuracy, since the detection of outliers is simply based on the judgment of residual value. In this work, a novel method is introduced to directly detect outliers, which can provide the intuitional display of outliers in a two-dimensional coordinate system. Moreover, a robust correction step based on the principle of least trimmed squared estimator regression is proposed to replace the conventional Gauss–Newton iteration step, by which the more reliable and accurate nanostructure reconstruction is achieved. The improved reconstruction of a one-dimensional etched Si grating has demonstrated the feasibility of the proposed methods.

The Symplectic Method in Polar Coordinates for Linear Viscoelastic Materials

In this study, the symplectic method is applied to a two-dimensional annular-sector viscoelastic domain under the polar coordinate system. By applying variable separation approach, all fundamental solutions are derived in analytical form. Furthermore, using the method of variable substitution, lateral conditions are transformed into finding a particular solution for the governing equations, and this particular solution is derived with the use of eigensolution expansion. In the numerical example, the boundary condition problem is discussed in detail to analyze the stress response of viscoelastic solids.

МОДЕЛЮВАННЯ ШВИДКОСТІ РОЗПОДІЛУ ПОВІТРЯ У ВІДСІКУ ВИПАРНИКА ХОЛОДИЛЬНОЇ УСТАНОВКИ РЕФРИЖЕРАТОРНОГО КОНТЕЙНЕРА

The study is aimed at solving the problem of convective heat transfer calculating in the tubular evaporator unit of refrigerating container, which is equipped with fan forced convection. The mathematical model of the problem as a differential equation that establishes the energy conservation law in the air cells through the surface of which its movement is carried out is given. Inthe process of the convective heat transfer around the evaporator problem calculating the link between the basic physical quantities in the air − temperature fields and velocity of its movement was considered. Close relationship of obtained temperature values and air velocity at the outlet from evaporator unit as boundary conditions for further calculation of temperature field in the refrigerator compartment of refrigerating container was proved. Statement of the problem and its simulation wereperformed in a two-dimensional coordinate system, and software environment COMSOL Multiphysics, Femlab 3.0, Fluid Dynamics - Incompressible Navier-Stokes - Convection and Conduction was applied for its solution. he accomplished calculations have shown that the integral temperature value at the outlet of the evaporator unit, was calculated taking into account air velocity, which is lower than its values obtained without air movement consideration. The results of the study should be useful during the research of the convective heat transfer phenomenon in the different refrigerating devices, allow to choose evaporator and fan capacity morereasonably under conditions of obtaining the desired cooling mode for perishable products as well asin the learning process

МОДЕЛЮВАННЯ ЗАДАЧІ КОНВЕКТИВНОГО ТЕПЛООБМІНУ В ХОЛОДИЛЬНІЙ ШАФІ РЕФРИЖЕРАТОРНОГО КОНТЕЙНЕРА

Materials of the study are directed on the solving the problem of air velocity calculating in a confined volume of refrigerating chamber of 20 foot refrigerated container with forced air convection from Carrier Transicold producer firm and on this basis –of convective heat transfer. Problem simulation has been performed in a two-dimensional coordinate system using COMSOL Multiphysics, Femlab 3.0, Fluid Dynamics - Incompressible Navier-Stokes - Convection and Conduction software. As an object of research differential equations of air movement impulse and transfer of energy with it were applied. As a subject of research was selected thermal physical phenomena inside and around the net volume of empty and loaded refrigerated container at air movement. Significant impact of the air movement on the temperature distribution inside the refrigerating container chamber has been established.The obtained results allow to get closer to the theoretical evaluation of the refrigerating machine efficiency in an ordered mode during changes of thermophysical parameters of cargo volume and the environment during perishable products transportation. Tested method is useful for application by scientists and post-graduate students engaged in theoretical simulation of heat transfer problems in the field of refrigeration engineering.

Turbulent forced convection of nanofluid over a heated shallow cavity in a duct

This work presents a numerical investigation of turbulent forced convection of a nanofluid over a heated cavity in a horizontal duct. The objective of this study is to show the effects of nanofluid on heat transfer in such a configuration. The two-dimensional Cartesian coordinate system is used to solve the governing equations which are conservations of mass, momentum and energy. The numerical predictions based on finite volume method are performed by ANSYS FLUENT 14.0 CFD code. Numerical simulations are carried out for pure water and four different nanofluids (water–Cu, water–CuO, water–Ag and water–Al2O3). The results are analyzed through the thermal and dynamical fields with a particular interest to the kinetic energy, skin friction coefficient and Nusselt number evolutions. The range of parameters of Reynolds number is 40,000≤Re≤100,000 and different nanoparticle volume fractions. The maximum shear stress is obtained for the lightest nanoparticle of smaller thermal conductivity (Al2O3). It is found that the average Nusselt number increases with the volume fraction of nanoparticles for the whole tested range of Reynolds number. The nanoparticle type on average Nusselt number has an insignificant effect; the smallest values are obtained for the heavier particle with greatest value of thermal conductivity (Ag). Two correlations of average Nusselt number versus Reynolds number and volume fraction of each type of nanoparticles over the cavity wall are proposed in this paper.

Solution of Radiative Transfer Equation using Discrete Transfer Method for two-dimensional participating medium

The present work reports the development and application of a simplified numerical approach for solving the transient Radiative Transfer Equation (RTE) using Discrete Transfer Method (DTM) in two-dimensional coordinate system. The numerical formulation of the proposed scheme is discussed in detail and its application in the context of understanding light propagation phenomenon in laser-irradiated numerically simulated biological tissue phantoms has been demonstrated. The developed mathematical model has first been benchmarked against the results published in the literature for the same operating conditions. Thereafter, the results of a detailed parametric study have been presented to investigate the effects of optical properties of the biological phantom on the intensity distribution within the two-dimensional tissue phantom, net transmittance and reflectance, etc. The effect of anisotropy of the tissue medium has also been studied to understand the phenomenon of light propagation within the body of the sample. Based on the results of the study, it has been inferred that the developed numerical methodology for two-dimensional Discrete Transfer Method successfully predicts the physics of the phenomena of light propagation within the tissue phantom and compares well with the other conventionally employed numerical models for solving the Radiative Transfer Equation.

Computation of Lightning Electromagnetic Pulses With the Constrained Interpolation Profile Method in the 2-D Cylindrical Coordinate System

In this paper, a procedure for computing transient electromagnetic fields with the constrained interpolation profile (CIP) method in the two-dimensional (2-D) cylindrical coordinate system has been derived. Then, it has been applied to analyzing electromagnetic pulses produced by a current wave propagating upward along a vertical lightning return-stroke channel. CIP-computed waveforms agree well with corresponding waveforms computed using analytical expression of Uman et al. or the finite-difference time-domain method.