scholarly journals A Novel Exact Analytical Solution Based on Kloss Equation towards Accurate Speed-Time Characteristics Modeling of Induction Machines during No-Load Direct Startups

2021 ◽  
Vol 11 (11) ◽  
pp. 5102
Author(s):  
Martin Ćalasan ◽  
Mohammed Alqarni ◽  
Marko Rosić ◽  
Nikola Koljčević ◽  
Basem Alamri ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Computer Simulation ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
Induction Machines ◽  
Voltage Sags ◽  
Local Power ◽  
Acceleration Time ◽  
Protection Relay ◽  
Good Agreement

The acceleration time of induction machines (IMs) is essential for proper protection-relay settings of the machine to prevent voltage sags in local power areas. In this paper, mathematical modeling of IMs’ speed-time characteristics during no-load direct startup has been presented. Unlike the approaches presented in the literature, the proposed approach includes the bearing losses, in which two expressions of the speed-time characteristics of IMs during no-load direct startup are derived. The first expression was derived based on the Kloss equation used for representing the torque, and the second expression was derived based on the torque expression determined from the Thevenin equivalent circuit of the machine. The derived expressions’ accuracy was validated using laboratory measurement and computer simulation approaches. The results obtained show a good agreement between the measured and simulated speed-time characteristics of two IMs. Finally, the proposed formulations can provide a simple analytical base to enable accurate IM modeling.

An Integral Equation Method for Predicting Acoustic Emission within Enclosures

1985 ◽  
Vol 199 (2) ◽  
pp. 133-137 ◽  
Author(s):  
D T I Francis ◽  
M M Sadek
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Acoustic Emission ◽  
Analytical Solution ◽  
Numerical Solution ◽  
Finite Element Methods ◽  
Exact Analytical Solution ◽  
Integral Equation Method ◽  
Absorption Characteristics ◽  
Good Agreement

A method is presented for calculating the acoustic emission of a vibrating body within an enclosure whose surface has known absorption characteristics. It is based on a numerical solution of the Helmholtz integral equation. Solutions are given for the case of a pulsating sphere within a sphere, and good agreement with the exact analytical solution is reported. The method is of value for small and medium scale problems at lower frequencies, where traditional techniques are less reliable. It is also potentially less demanding computationally than finite element methods.

A Comparison of Micro-PIV Experiments in a Mini-Channel to Numerical and Analytical Solutions

2003 ◽  
Author(s):  
D. Newport ◽  
D. Curtin ◽  
M. Davies
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Exact Analytical Solution ◽  
Measurement Tool ◽  
Channel System ◽  
Micro Piv ◽  
Software Packages ◽  
Micro Systems ◽  
Experimental Rig ◽  
Good Agreement

In this paper, measurements are presented of the velocity profile in a mini-channel at different locations. The channel is rectangular in cross-section, approximately 1.2mm wide, 1.4mm deep and 29mm long. A micro-PIV system was used to obtain the velocity profiles at the inlet, mid-length and exit of the channel. The raw image maps were processed using three different commercial PIV software packages, and compared to an exact analytical solution. The mini-channel system was also simulated using a commercial CFD code as a further check on the dataset, and the experimental rig itself. It was found that the different processing procedures had little influence on the micro-PIV data, and good agreement was found with theory, numerical prediction and experiment. This establishes confidence in micro-PIV as a measurement tool in micro-systems.

scholarly journals MATHEMATICAL MODELING OF EXPERIMENT ON BERKOVICH NANOINDENTATION OF ZRN COATING ON STEEL SUBSTRATE

2020 ◽  
Vol 27 ◽  
pp. 18-21
Author(s):  
Evgeniy Sadyrin ◽  
Andrey Vasiliev ◽  
Sergei Volkov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Analytical Solution ◽  
Contact Problem ◽  
Half Space ◽  
Steel Substrate ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Good Agreement

In the present paper the experiment on Berkovich nanoindentation of ZrN coating on steel substrate is modelled using the proposed effective mathematical model. The model is intended for describing the experiments on indentation of samples with coatings (layered or functionally graded). The model is based on approximated analytical solution of the contact problem on indentation of an elastic half-space with a coating by a punch. It is shown that the results of the model and the experiment are in good agreement.

scholarly journals Modeling methodology of locally non-equilibrium heat conductivity processes

Vestnik IGEU ◽  
2020 ◽  
pp. 65-71
Author(s):  
A.V. Eremin
Keyword(s):  
Mathematical Modeling ◽  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Equation ◽  
Exact Analytical Solution ◽  
Separation Of Variables ◽  
Infinite Plate ◽  
Transfer Processes ◽  
Non Equilibrium

With the development of laser technologies and the ability to carry out processing steps under extreme conditions (ul-trahigh temperatures, pressures and their gradients), the interest in studying the processes that occur under locally non-equilibrium conditions has grown significantly. The key directions for the description of locally non-equilibrium pro-cesses include thermodynamic, kinetic and phenomenological ones. The locally non-equilibrium transfer equations can also be derived from the Boltzmann equation by using the theory of random walks and molecular-kinetic methods. It should be noted that some options of locally non-equilibrium processes lead to conflicting results. This study aims to develop a method for mathematical modeling of locally nonequilibrium heat conduction processes in solids, which allows determining their temperature with high accuracy during fast and high-intensity heat transfer processes. As applied to heat transfer processes in solids, a generalized heat equation that takes into account the relaxation properties of materials is formulated. The exact analytical solution is obtained using the Fourier method of separation of variables. The methodology for mathematical modeling of locally non-equilibrium transfer processes based on modified conservation laws has been developed. The generalized differential heat equation which allows performing N-fold relaxation of the heat flow and temperature in the modified heat balance equation has been formulated. For the first time, an exact analytical solution to the unsteady heat conduction problem for an infinite plate was obtained taking into account many-fold relaxation. The analysis of the solution to the boundary value problem of locally nonequilibrium heat conduction enabled to conclude that it is impossible to instantly has establish a boundary condition of the first kind. It has been demonstrated that each of the following terms in the relaxed heat equation has an ever smaller effect on the heat transfer process. The obtained results can be used by the scientific and technical personnel of organizations and higher educational institutions in the study of fuel ignition processes, the development of laser processing of materials, the design of highly efficient heat transfer equipment and the description of fast-flowing heat transfer processes.

scholarly journals The exact analytical solution of the dual-phase-lag two-temperature bioheat transfer of a skin tissue subjected to constant heat flux

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Hamdy M. Youssef ◽  
Najat A. Alghamdi
Keyword(s):  
Heat Flux ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
Constant Heat Flux ◽  
Bioheat Transfer ◽  
Skin Tissue ◽  
Phase Lag ◽  
Dual Phase ◽  
Constant Heat ◽  
Two Temperature

Abstract This work is dealing with the temperature reaction and response of skin tissue due to constant surface heat flux. The exact analytical solution has been obtained for the two-temperature dual-phase-lag (TTDPL) of bioheat transfer. We assumed that the skin tissue is subjected to a constant heat flux on the bounding plane of the skin surface. The separation of variables for the governing equations as a finite domain is employed. The transition temperature responses have been obtained and discussed. The results represent that the dual-phase-lag time parameter, heat flux value, and two-temperature parameter have significant effects on the dynamical and conductive temperature increment of the skin tissue. The Two-temperature dual-phase-lag (TTDPL) bioheat transfer model is a successful model to describe the behavior of the thermal wave through the skin tissue.

scholarly journals Semi-Analytical Solution to Assess CO2 Leakage in the Subsurface through Abandoned Wells

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2452
Author(s):  
Tian Qiao ◽  
Hussein Hoteit ◽  
Marwan Fahs
Keyword(s):  
Analytical Solution ◽  
Storage Site ◽  
Co2 Leakage ◽  
Transient Pressure ◽  
Flow Paths ◽  
Abandoned Wells ◽  
Diffusivity Equation ◽  
Carbon Dioxide Co2 ◽  
Good Agreement

Geological carbon storage is an effective method capable of reducing carbon dioxide (CO2) emissions at significant scales. Subsurface reservoirs with sealing caprocks can provide long-term containment for the injected fluid. Nevertheless, CO2 leakage is a major concern. The presence of abandoned wells penetrating the reservoir caprock may cause leakage flow-paths for CO2 to the overburden. Assessment of time-varying leaky wells is a need. In this paper, we propose a new semi-analytical approach based on pressure-transient analysis to model the behavior of CO2 leakage and corresponding pressure distribution within the storage site and the overburden. Current methods assume instantaneous leakage of CO2 occurring with injection, which is not realistic. In this work, we employ the superposition in time and space to solve the diffusivity equation in 2D radial flow to approximate the transient pressure in the reservoirs. Fluid and rock compressibilities are taken into consideration, which allow calculating the breakthrough time and the leakage rate of CO2 to the overburden accurately. We use numerical simulations to verify the proposed time-dependent semi-analytical solution. The results show good agreement in both pressure and leakage rates. Sensitivity analysis is then conducted to assess different CO2 leakage scenarios to the overburden. The developed semi-analytical solution provides a new simple and practical approach to assess the potential of CO2 leakage outside the storage site. This approach is an alternative to numerical methods when detailed simulations are not feasible. Furthermore, the proposed solution can also be used to verify numerical codes, which often exhibit numerical artifacts.

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