Analysis of the Working Process and Mechanical Losses in a Stirling Engine for a Solar Power Unit

1999 ◽  
Vol 121 (2) ◽  
pp. 121-127 ◽  
Author(s):  
Kh. Kh. Makhkamov ◽  
D. B. Ingham
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Power Unit ◽  
Computational Simulation ◽  
Mass Conservation ◽  
Stirling Engine ◽  
Computational Results ◽  
Working Process ◽  
Euler’S Method ◽  
Governing System

In this paper a second level mathematical model for the computational simulation of the working process of a 1-kW Stirling engine has been used and the results obtained are presented. The internal circuit of the engine in the calculation scheme was divided into five chambers, namely, the expansion space, heater, regenerator, cooler and the compression space, and the governing system of ordinary differential equations for the energy and mass conservation were solved in each chamber by Euler’s method. In additional, mechanical losses in the construction of the engine have been determined and the computational results show that the mechanical losses for this particular design of the Stirling engine may be up to 50% of the indicated power of the engine.

Study on Mathematical Model in Working Process of Automotive Air Conditioning Scroll Compressor

2015 ◽  
Vol 741 ◽  
pp. 572-576
Author(s):  
Yu Fan Zhang ◽  
Zhi Hao Ji ◽  
Jin Yan Liu ◽  
Shu Sheng Xiong ◽  
Xiao Bo Huang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Thermodynamic Model ◽  
Air Conditioning ◽  
Mass Conservation ◽  
Back Pressure ◽  
Working Process ◽  
Scroll Compressor ◽  
Performance Simulation ◽  
Automotive Air Conditioning ◽  
Compressor Performance

In order to study the working features of automotive air conditioning scroll compressor, this paper uses mathematical model of working process to analyze it. After studying working process, a equation of suction volume is given. The thermodynamic model of compression chamber and back pressure chamber includes mass conservation and energy conservation. Based on Hydromechanics, leakage models of radial leakage and tangential leakage are discussed. The model lays a foundation of automotive air conditioning scroll compressor performance simulation.

scholarly journals A mathematical model for the virtual simulator of the power unit electrical part

2022 ◽  
Vol 1216 (1) ◽  
pp. 012009
Author(s):  
P Baran ◽  
Y Varetsky ◽  
V Kidyba ◽  
Y Pryshliak
Keyword(s):  
Mathematical Model ◽  
Power Plant ◽  
Differential Equations ◽  
Power System ◽  
Real Time ◽  
Power Unit ◽  
Operating Conditions ◽  
Auxiliary System ◽  
Algebraic Differential Equations ◽  
Electrical Part

Abstract The mathematical model is developed for a virtual training system (simulator) of the power unit electrical part operators of a thermal (nuclear) power plant. The model is used to simulating the main operating conditions of the power unit electrical part: generator idling, generator synchronization with the power system, excitation shifting from the main unit to the backup one and vice versa, switching in the power unit auxiliary system, and others. Furthermore, it has been implemented modelling some probable emergency conditions within a power plant: incomplete phase switching, damage to standard power unit equipment, synchronous oscillations, asynchronous mode, etc. The model of the power unit electrical part consists of two interacting software units: models of power equipment (turbine, generator with excitation systems, auxiliary system) and models of its control systems, automation, relay protection and signalling. The models are represented by the corresponding algebraic-differential equations that provide real-time mapping power unit processes at the operator’s request. The developed model uses optimal solving algebraic-differential equations to ensure the virtual process behaviour in real-time. In particular, the implicit Euler method is used to solve differential equations, which is stable when simulating processes in significant disturbances, such as accidental disconnection of the unit from the power system, tripping and energizing loads, generator excitation loss, etc.

Mathematical model for the ciliary-induced transport of seminal liquids through the ductuli efferentes

2017 ◽  
Vol 10 (03) ◽  
pp. 1750031 ◽  
Author(s):  
A. A. Farooq ◽  
A. M. Siddiqui
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Couple Stress ◽  
Reproductive Tract ◽  
Couple Stress Fluid ◽  
Graphical Form ◽  
Axially Symmetric ◽  
Governing System ◽  
Ciliary Motion ◽  
Two Dimensional Flow

This study describes the consequences of the ciliary motion on the transport of seminal liquid through the ductus efferentes of the male reproductive tract. By assuming the seminal liquid as a couple stress fluid, we have formulated a mathematical model for a two-dimensional flow through an axially symmetric tube whose inner surface is ciliated in the form of a metachronal wave. The governing system consists of nonlinear coupled partial differential equations which is reduced to a system of ordinary differential equations by utilizing the long wavelength approximation in an environment of the inertia free flow. Exact solutions for the velocity distribution, the pressure gradient and the stream function are obtained in terms of the couple stress parameters and the ciliary metachronism. Special attention is given to the pumping and the trapping characteristics due to the cilia motility. The study reveals that the ciliary pumping has to be more efficient to transport a couple stress fluid as compared to a Newtonian fluid. Moreover, the theoretical results for the couple stress fluid are found to be in good agreement with those reported by [T. J. Lardner and W. J. Shack, Cilia transport, Bull. Math. Biophys. 34 (1972) 325–335]. The analytical results are also displayed in graphical form.

scholarly journals Modeling of Boring Mandrel Working Process with Vibration Damper

Materials ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1931 ◽  
Author(s):  
Kirill Sentyakov ◽  
Jozef Peterka ◽  
Vitalii Smirnov ◽  
Pavol Bozek ◽  
Vladislav Sviatskii
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Field Tests ◽  
Operator Method ◽  
Vibration Damper ◽  
Working Process ◽  
Mass System ◽  
Inertial Body ◽  
The Laplace Transform ◽  
Made In

The article considers the issue of modeling the oscillations of a boring mandrel with vibration damper connected to the mandrel with a viscoelastic coupling. A mathematical model of the boring mandrel oscillations, machine support and inertial body (damper) is developed in the form of a differential equations system. The model is made in the form of a four-mass system of connected bodies. The solution to the differential equations system was found using the finite difference method, as well as the operator method with the use of the Laplace transform. As the simulation result, it was found that the use of vibration damper can significantly reduce the amplitude of the boring mandrel natural vibrations when pulsed, and also significantly reduce the forced vibrations amplitude when exposed to periodic disturbing forces. The developed mathematical model and algorithms for the numerical solution to the differential equations allowed us to choose the optimal parameters of the boring mandrel damping element. The obtained data will be used to create a prototype boring mandrel and conduct field tests.

scholarly journals A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity Dynamics

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Rafael J. Villanueva ◽  
Abraham J. Arenas ◽  
Gilberto González-Parra
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Difference Scheme ◽  
Numerical Scheme ◽  
Modern Society ◽  
Health Concern ◽  
Euler’S Method ◽  
Positivity Condition ◽  
Obesity Epidemic ◽  
Essential Properties

The obesity epidemic is considered a health concern of paramount importance in modern society. In this work, a nonstandard finite difference scheme has been developed with the aim to solve numerically a mathematical model for obesity population dynamics. This interacting population model represented as a system of coupled nonlinear ordinary differential equations is used to analyze, understand, and predict the dynamics of obesity populations. The construction of the proposed discrete scheme is developed such that it is dynamically consistent with the original differential equations model. Since the total population in this mathematical model is assumed constant, the proposed scheme has been constructed to satisfy the associated conservation law and positivity condition. Numerical comparisons between the competitive nonstandard scheme developed here and Euler's method show the effectiveness of the proposed nonstandard numerical scheme. Numerical examples show that the nonstandard difference scheme methodology is a good option to solve numerically different mathematical models where essential properties of the populations need to be satisfied in order to simulate the real world.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

scholarly journals Exhaust Noise Reduction by Application of Expanded Collecting System in Pneumatic Tools and Machines

Energies ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1592
Author(s):  
Dominik Gryboś ◽  
Jacek S. Leszczyński ◽  
Dorota Czopek ◽  
Jerzy Wiciak
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Noise Reduction ◽  
Sound Pressure ◽  
Acoustic Pressure ◽  
Pressure Level ◽  
Computational Results ◽  
Noise Measurements ◽  
Exhaust Noise ◽  
Collecting System

In this paper, we demonstrate how to reduce the noise level of expanded air from pneumatic tools. Instead of a muffler, we propose the expanded collecting system, where the air expands through the pneumatic tube and expansion collector. We have elaborated a mathematical model which illustrates the dynamics of the air flow, as well as the acoustic pressure at the end of the tube. The computational results were compared with experimental data to check the air dynamics and sound pressure. Moreover, the study presents the methodology of noise measurement generated in a pneumatic screwdriver in a quiet back room and on a window-fitting stand in a production hall. In addition, we have performed noise measurements for the pneumatic screwdriver and the pneumatic screwdriver on an industrial scale. These measurements prove the noise reduction of the pneumatic tools when the expanded collecting system is used. When the expanded collecting system was applied to the screwdriver, the measured Sound Pressure Level (SPL) decreased from 87 to 80 dB(A).

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

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