scholarly journals Study of Different Alternatives for Dynamic Simulation of a Steam Generator Using MATLAB

Fluids ◽  
2021 ◽  
Vol 6 (5) ◽  
pp. 175
Author(s):  
Cristhian Álvarez ◽  
Edwin Espinel ◽  
Carlos J. Noriega
Keyword(s):  
Differential Equation ◽  
Steam Generator ◽  
Steam Pressure ◽  
Order Method ◽  
Runge Kutta ◽  
Main Components ◽  
Energy Balances ◽  
Alternative Solutions ◽  
Implementation In Matlab ◽  
Mass And Energy Balances

This work presents the simulation of a steam generator or water-tube boiler through the implementation in MATLAB® for a proposed mathematical model. Mass and energy balances for the three main components of the boiler - the drum, the riser and down-comer tubes - are presented. Three alternative solutions to the ordinary differential equation (ODE) were studied, based on Runge–Kutta 4th order method, Heun’s method, and MATLAB function Ode45. The best results were obtained using MATLAB® function Ode45 based on the Runge–Kutta 4th Order Method. The error was less than 5% for the simulation of the steam pressure in the drum, the total volume of water in the boiler, and the mixture quality in relation to what was reported.

scholarly journals MODELAGEM E SIMULAÇÃO DINÂMICA DA FASE GASOSA DE UM FORNO ROTATIVO PARA INDÚSTRIA DE CELULOSE

e-xacta ◽  
2016 ◽  
Vol 9 (2) ◽  
Author(s):  
Barbara Burgarelli Alves de Aguiar ◽  
Marcelo Cardoso ◽  
Esly Ferreira da Costa Júnior
Keyword(s):  
Differential Equations ◽  
Gas Phase ◽  
Large Scale ◽  
Maximum Temperature ◽  
Outlet Temperature ◽  
Pulp Industry ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Energy Balances ◽  
Mass And Energy Balances

<p>O forno rotativo tem sido utilizado em larga escala em vários processos unitários nas indústrias, como por exemplo: a calcinação. Este artigo apresenta o desenvolvimento da modelagem da fase gasosa para a simulação dinâmica de um forno de cal da indústria de celulose. O modelo é representado por um sistema de equações diferenciais parciais, considerando os balanços de massa e energia do processo. Esse sistema de equações é discretizado espacialmente, transformado em equações diferenciais ordinárias e resolvido pelo software MATLAB<sup>®</sup> utilizando o método de Runge-Kutta de 4ª ordem. O modelo proposto prediz o perfil de temperatura, massa específica e velocidade da fase gasosa. Essa simulação alcança o estado estacionário em 60s e o gás atinge a temperatura máxima de 1480K e a temperatura de saída de 550K. Os dados obtidos foram comparados com a literatura e pode-se observar que estão condizentes com a realidade operacional do forno.</p><p>ABSTRACT</p><p>The rotary kiln has been used in large scale in several unit processes in industries such as: calcination. This paper presents the development of modeling of the gas phase to the dynamic simulation of a lime kiln in the pulp industry. The model is represented by a system of partial differential equations, considering the mass and energy balances of the process. This system of equations is discretized spatially, transformed into ordinary differential equations, and solved by MATLAB<sup>®</sup> software using the Runge-Kutta method of 4th order. The model predicts the temperature profile, density and velocity of the gas phase. This simulation achieves the steady state in 60 seconds and gas reaches the maximum temperature of 1480K and 550K outlet temperature. The data were compared with the literature, and it can be noted that are consistent with the kiln operating reality.</p>

Innovative energy and mass balance of a continuous evaporating crystallizer

2019 ◽  
pp. 646-654
Author(s):  
Jan Iciek ◽  
Kornel Hulak ◽  
Radosław Gruska
Keyword(s):  
Energy Balance ◽  
Mass Balance ◽  
Working Conditions ◽  
Crystallization Process ◽  
Heat Losses ◽  
Inert Gas ◽  
Gas Removal ◽  
Energy Balances ◽  
Heat Released ◽  
Mass And Energy Balances

The article presents the mass and energy balances of the sucrose crystallization process in a continuous evaporating crystallizer. The developed algorithm allows to assess the working conditions of the continuous evaporating crystallizers and the technological and energy parameters. The energy balance algorithm takes into account the heat released during the crystallization of sucrose, which was analyzed in this study, heat losses to the environment and heat losses due the vapor used for inert gas removal.

scholarly journals Enhancing Accuracy of Runge–Kutta-Type Collocation Methods for Solving ODEs

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 174
Author(s):  
Janez Urevc ◽  
Miroslav Halilovič
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Integration ◽  
Integral Form ◽  
Collocation Methods ◽  
Nonlinear Odes ◽  
New Class ◽  
New Methods ◽  
Runge Kutta

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation. The approach enables enhancing the accuracy of the established collocation Runge–Kutta methods while retaining the same number of stages. We demonstrate that, with the proposed approach, the Gauss–Legendre and Lobatto IIIA methods can be derived and that their accuracy can be improved for the same number of method coefficients. We expressed the methods in the form of tables similar to Butcher tableaus. The performance of the new methods is investigated on some well-known stiff, oscillatory, and nonlinear ODEs from the literature.

scholarly journals On Runge-Kutta processes of high order

1964 ◽  
Vol 4 (2) ◽  
pp. 179-194 ◽  
Author(s):  
J. C. Butcher
Keyword(s):  
Differential Equation ◽  
High Order ◽  
Runge Kutta ◽  
Image Position

An (explicit) Runge-Kutta process is a means of numerically solving the differential equation , at the point x = x0+h, where y, f may be vectors.

Mass and energy balances of an autothermal pilot carbonization unit

2019 ◽  
Vol 120 ◽  
pp. 144-155 ◽  
Author(s):  
Andrea Maria Rizzo ◽  
Marco Pettorali ◽  
Renato Nistri ◽  
David Chiaramonti
Keyword(s):  
Energy Balances ◽  
Mass And Energy Balances

scholarly journals A continuum model for meltwater flow through compacting snow

2017 ◽  
Vol 11 (6) ◽  
pp. 2799-2813 ◽  
Author(s):  
Colin R. Meyer ◽  
Ian J. Hewitt
Keyword(s):  
Continuum Model ◽  
Pore Space ◽  
Water Storage ◽  
Greenland Ice Sheet ◽  
Percolation Process ◽  
Surface Mass ◽  
Run Off ◽  
Flow Through ◽  
Energy Balances ◽  
Mass And Energy Balances

Abstract. Meltwater is produced on the surface of glaciers and ice sheets when the seasonal energy forcing warms the snow to its melting temperature. This meltwater percolates into the snow and subsequently runs off laterally in streams, is stored as liquid water, or refreezes, thus warming the subsurface through the release of latent heat. We present a continuum model for the percolation process that includes heat conduction, meltwater percolation and refreezing, as well as mechanical compaction. The model is forced by surface mass and energy balances, and the percolation process is described using Darcy's law, allowing for both partially and fully saturated pore space. Water is allowed to run off from the surface if the snow is fully saturated. The model outputs include the temperature, density, and water-content profiles and the surface runoff and water storage. We compare the propagation of freezing fronts that occur in the model to observations from the Greenland Ice Sheet. We show that the model applies to both accumulation and ablation areas and allows for a transition between the two as the surface energy forcing varies. The largest average firn temperatures occur at intermediate values of the surface forcing when perennial water storage is predicted.

scholarly journals On the integration processes of A. Huťa

1963 ◽  
Vol 3 (2) ◽  
pp. 202-206 ◽  
Author(s):  
J. C. Butcher
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Sixth Order ◽  
Order Accuracy ◽  
First Order ◽  
Runge Kutta ◽  
Image Position

Huta [1], [2] has given two processes for solving a first order differential equation to sixth order accuracy. His methods are each eight stage Runge-Kutta processes and differ mainly in that the later process has simpler coefficients occurring in it.

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