scholarly journals Calculation of turbulent diffusion jets under effects of gravity and moving surrounding air

2001 ◽  
Vol 23 (2) ◽  
pp. 87-94
Author(s):  
Bui Van Ga ◽  
Nhan Hong Quang ◽  
Jean Marc Vignon
Keyword(s):  
Velocity Field ◽  
Turbulent Diffusion ◽  
Concentration Field ◽  
Integral Model ◽  
System Of Equations ◽  
Kutta Method ◽  
Air Velocity ◽  
Runge Kutta Method ◽  
Jet Axis ◽  
General Conditions

The basis theory for the turbulent diffusion of jet and flame has been presented previously [1, 2]. But that one applies only in quiet surrounding air with the effects of buoyancy neglected. In the present paper, the theory is developed further by establishing an integral model for a jet in more general conditions with variable inclined angles, under effects of gravity and surrounding air velocity in any direction compared to the jet axis. The system of equations is closed by turbulence k-E model and is solved by 4th order Runge-Kutta method. In the first stage, the model is applied to predict the velocity field, the concentration field and with development of a 0.3 m diameter jet.

scholarly journals Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Najeeb Alam Khan ◽  
Oyoon Abdul Razzaq ◽  
Sankar Parsad Mondal ◽  
Qammar Rubbab
Keyword(s):  
Dynamical Systems ◽  
Fractional Order ◽  
Equilibrium Points ◽  
System Of Equations ◽  
Biological Parameters ◽  
Kutta Method ◽  
Interacting Species ◽  
Runge Kutta Method ◽  
Novel Approach ◽  
Predator Model

Abstract The key objective of this paper is to study the imprecise biological complexities in the interaction of two species pertaining to harvesting threshold. It is explained by taking the prey–predator model with imprecise biological parameters and fractional order generalized Hukuhara (fgH) differentiability. In this vain, different possible systems of the model are constructed, according to the increasing and decreasing behavior of population growth. Feasibility and stability analyses of equilibrium points of the stated models are also discussed by means of variational matrix with Routh–Hurwitz conditions. In addition, the numerical elaborations are carried out by taking parametric expansion of fuzzy fractional Laplace transform (FFLT). This significantly helps the researchers in using a novel approach to analyze the constant solutions of the dynamical systems in the presence of fractional index. This would allow the avoidance of any intricacy that occurs while solving fractional order derivatives. Furthermore, this attempt also provides numerical and pictorial results, obtained through some well-known methods, namely fifth-forth Runge–Kutta method (FFRK), Grunwald–Letnikov’s definition (GL) and Adams–Bashforth method (ABM) that are deemed appropriate to scrutinize the dynamics of the system of equations.

scholarly journals Stresses of feller buncher on thinnings during technological moves

2018 ◽  
Author(s):  
В.А. Александров ◽  
А.В. Александров ◽  
Г.Ш. Гасымов
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
Dynamic Load ◽  
Mathematical Description ◽  
Lagrange Equation ◽  
Process Equipment ◽  
System Of Equations ◽  
Programming Environment ◽  
Kutta Method ◽  
Runge Kutta Method

Разработана математическая модель динамической системы: «Валочно- пакетирующая машина – предмет труда – дерево». Математическое описание составлено в форме уравнения Лагранжа 2-го рода. Система уравнений решена методом Рунге–Кутта, с помощью среды программирования MathCAD. Апробация модели осуществлена на примере серийно выпускаемых валочно-пакетирующих машин ЛП – 19А в режимах разгона и стопорения. Установлено, что динамическая нагрузка на технологическое оборудование при технологических переездах сопоставима с нагрузкой при обработке (пакетировании) дерева. A mathematical model of a dynamic system has been developed: «The feller buncher – subject of labor – the tree». The mathematical description is made up in the form of the Lagrange equation of the 2nd kind. The system of equations is solved by the Runge–Kutta method, using the MathCAD programming environment. Approbation of the model is carried out on the example of the commercially available LP-19A feller buncher machines in acceleration and stopping modes. Concluded that the dynamic load on the process equipment during technological moves is comparable to the load during the processing (packaging) of the tree.

Mathematical Modeling of the Discharged Heat Water Effect on the Aquatic Environment from Thermal Power Plant

2015 ◽  
Vol 16 (5) ◽  
pp. 229-238 ◽  
Author(s):  
Alibek Issakhov
Keyword(s):  
Power Plant ◽  
Velocity Field ◽  
Aquatic Environment ◽  
Thermal Power Plant ◽  
Pressure Field ◽  
Thermal Power ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Operational Capacity

AbstractThe paper presents a mathematical model of the thermal load on the aquatic environment under operational capacity 200 MW of thermal power plant. It is solved by the Navier–Stokes and temperature equations for an incompressible fluid in a stratified medium based on numerical method, the splitting method by physical parameters which approximated the finite volume method. The numerical solution of the equation system is divided into four stages. At the first step it is assumed that the momentum transfer is carried out only by convection and diffusion. Intermediate velocity field is solved by the five-step Runge–Kutta method. At the second stage, the pressure field is solved by the intermediate velocity field. Poisson equation for the pressure field is solved by Jacobi method. The third step is assumed that the transfer is carried out only by pressure gradient. The fourth step of the transport equation for temperature is also solved as momentum equations, with five-step Runge–Kutta method. The obtained numerical results of temperature distribution for operational capacity of 200 MW of three-dimensional stratified turbulent flow were compared with experimental data, which revealed qualitatively and quantitatively approximately the basic laws of hydrothermal processes occurring in the reservoir-cooler.

Vibroloading operators of feller-packaging cars in a mode of transferring of a tree cutting-off device.

2016 ◽  
Author(s):  
А.В. Александров ◽  
В.А. Александров ◽  
Г.Ш. Гасымов
Keyword(s):  
Mathematical Description ◽  
System Of Equations ◽  
Programming Environment ◽  
Kutta Method ◽  
Lagrange Equations ◽  
Runge Kutta Method ◽  
System Operator ◽  
The Subject ◽  
Tree Cutting ◽  
Made In

Разработана динамическая модель системы: «Оператор – валочно-па­кети­рующая машина – предмет труда – дерево». Математическое описание составлено в форме уравнения Лагранжа 2-го рода. Система уравнений решена относительно упругой деформации подвеса сиденья оператора методом Рунге-Кутта, с помощью среды программирования MathCAD. Апробация модели осуществлена на примере серийно выпускаемых валочно-пакетирующих машин ЛП-19А. Developed a dynamic model of the system: «Operator - feller-buncher – the subject of work – a tree». Mathematical description is made in the form of the Lagrange equations of the 2nd kind. The system of equations is solved with respect to the elastic deformation of the suspension driver's seat by the Runge-Kutta method, using a programming environment MathCAD. Testing of the model implemented by the example of commercially available feller buncher LP-19A.

On the Harmonic Oscillations for the Motion of a Dynamical System

2017 ◽  
Vol 13 (2) ◽  
pp. 4657-4670
Author(s):  
W. S. Amer
Keyword(s):  
Dynamical System ◽  
Numerical Solutions ◽  
Equation Of Motion ◽  
Parameter Method ◽  
Kutta Method ◽  
Small Parameter Method ◽  
Harmonic Oscillations ◽  
Pivot Point ◽  
Runge Kutta Method ◽  
High Consistency

This work touches two important cases for the motion of a pendulum called Sub and Ultra-harmonic cases. The small parameter method is used to obtain the approximate analytic periodic solutions of the equation of motion when the pivot point of the pendulum moves in an elliptic path. Moreover, the fourth order Runge-Kutta method is used to investigate the numerical solutions of the considered model. The comparison between both the analytical solution and the numerical ones shows high consistency between them.

Numerical Approximations to Solution of Biochemical Reaction Model

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Transformation Method ◽  
Reaction Model ◽  
Biochemical Reaction ◽  
Graphical Form ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.

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