scholarly journals Chaos Predictability in a Chemical Reactor

2020 ◽  
Vol 30 (11) ◽  
pp. 2050221
Author(s):  
Marek Berezowski
Keyword(s):  
Mathematical Model ◽  
Chemical Reactor ◽  
Transient Chaos ◽  
Distant Future ◽  
State Variable ◽  
First Case ◽  
Start Up ◽  
System Temperature ◽  
Intermittent Chaos ◽  
The Mathematical Model

The dynamics of the tubular chemical reactor with mass recycle was examined. In such a system, temperature and concentrations may oscillate chaotically. This means that state variable values are then unpredictable. In this paper, it has been shown that despite the chaos, the behavior of such a reactor can be predictable. It has been shown that this phenomenon can occur in two cases. The first case concerns intermittent chaos. It has been shown that intermittent outbursts can occur at regular intervals. The second case concerns transient chaos, i.e. a situation when chaos occurs only for a certain period of time, e.g. only during start-up. This phenomenon makes it impossible to predict what will occur in the reactor in the nearest time, but, makes it possible to precisely determine the values of the variables even in the distant future. Both of these phenomena were tested by numerical simulation of the mathematical model of the reactor.

Investigation of a Nonlinear Numerical Mathematical Model of a Multi-Shaft Gas Turbine Unit

2003 ◽  
Author(s):  
Soo Yong Kim ◽  
Valeri P. Kovalevsky
Keyword(s):  
Mathematical Model ◽  
Combustion Chamber ◽  
Gas Turbine ◽  
Ambient Air ◽  
Static Characteristic ◽  
Start Up ◽  
Static Calculation ◽  
Energy Balances ◽  
The Mathematical Model ◽  
Mass And Energy Balances

The development of numerical mathematical model to calculate both the static and dynamic characteristics of a multishaft gas turbine consisting of a single combustion chamber, including advanced cycle components such as intercooler and regenerator is presented in the paper. The mathematical model is based on the simplified assumptions that quasi-static characteristic of a turbo-machine and injector is used, total pressure loss and heat transfer relation for static calculation neglecting fuel transport time delay can be employed. The supercharger power has a cubical relation to its rotating velocity. The accuracy of each calculation is confirmed by monitoring mass and energy balances, and comparative calculations with different time steps of integration. The features of the studied gas turbine scheme are the starting device with compressed air bottles and injector supercharging air directly ahead of the combustion chamber. The start-up algorithms are reviewed at different geometrical characteristics of the injector and temperatures of ambient air.

scholarly journals Dynamic Simulation of High-Speed Induction Motor

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2713
Author(s):  
Maria Dems ◽  
Krzysztof Komeza ◽  
Jacek Szulakowski ◽  
Witold Kubiak
Keyword(s):  
Mathematical Model ◽  
Induction Motor ◽  
High Speed ◽  
Start Up ◽  
Modified Equations ◽  
Higher Power ◽  
The Mathematical Model ◽  
Dynamic Phenomena ◽  
Dynamic States

In the drives of high-speed devices, such as a blood centrifuge, dynamic states also play an important role in terms of the time and quality of the tests performed. The article presents the application of modified equations resulting from the mathematical model of an induction motor to model dynamic phenomena during motor start-up, both with mains supply and with frequency start-up. The applied solution considers the phenomenon of current displacement in the rotor bar and the phenomenon of saturation. The comparison of the obtained results with the experiment shows that the method is sufficiently accurate. The obtained results can also be extended to higher power machines and to modeling other dynamic states.

A feedback temperature control in a chemical reactor with high inertia of its cooling system

1984 ◽  
Vol 49 (7) ◽  
pp. 1642-1652 ◽  
Author(s):  
Josef Horák ◽  
František Jiráček ◽  
Libuše Ježová
Keyword(s):  
Mathematical Model ◽  
Temperature Control ◽  
Cooling System ◽  
Batch Reactor ◽  
Time Derivative ◽  
Exothermic Reaction ◽  
Chemical Reactor ◽  
The One ◽  
The Mathematical Model ◽  
The Given

In this work we compare simple algorithms for the one-off feedback temperature control of the reaction mixture in a batch reactor during an exothermic reaction. The aim of the control was to maintain the temperature of the mixture within the given range, and simultaneously, to minimize the number of the regulator switchings. The temperature control of the mixture was being performed at conditions when working states of the reactor in an open regulation loop are unstable and when the response of the cooler to regulation is slow. The following control algorithms were compared: P - regulator, PD - regulator and algorithms based on a prediction mathematical model including its adaptive variant. The results indicate that the algorithms based on the mathematical model are more efficient. However, the precision of the control can be diminished due to error in the time derivative of the temperature of the reaction mixture which forms the input to the prediction model. The adaptive variant of the algorithms was advantageous in cases when it was necessary to make up for significant errors in initial estimates of parameters of the prediction mathematical model.

Dynamic Analysis on the Starting Process of First Conveyor’s Scraper Chain

2016 ◽  
Vol 851 ◽  
pp. 279-285 ◽  
Author(s):  
Qiang Li ◽  
Ming Yu Zhang ◽  
Jun Mao
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Characteristic Analysis ◽  
Technical Parameters ◽  
Adjustment Time ◽  
Start Up ◽  
Starting Process ◽  
Set Up ◽  
The Mathematical Model ◽  
Dynamics Characteristic

For the study of first conveyor chain dynamics behavior when it is started and seek the theory basis for the chain breakage on first conveyor, set up the mathematical model of the first conveyor and its scraper chain by using finite-element method. And then did the dynamics characteristic analysis between scraper chains with material, set up the differential equation. Took advantage of the mathematical model and the differential equation, and combined with the type of EBZ160 road header's technical parameters, did dynamic simulation. It draw a conclusion that during the start-up process the chain speed fluctuates a large range between, the maximum stress value on scraper chain is 1.15×104N appeared after 1s, chain tension adjustment time is about 10s, the biggest adjustment time is 12s.

The Mathematical Model Identification and State Variable Estimation for Gyro Drift

1985 ◽  
Vol 18 (5) ◽  
pp. 1055-1059
Author(s):  
Y-X Lin ◽  
C-J Rao ◽  
W-B Zhang ◽  
S-Y Fang
Keyword(s):  
Mathematical Model ◽  
Model Identification ◽  
State Variable ◽  
The Mathematical Model ◽  
Gyro Drift

Modelin and analysis of nonideal polyphase diode converters

SIMULATION ◽  
1971 ◽  
Vol 17 (6) ◽  
pp. 237-243 ◽  
Author(s):  
Michael J. Smith
Keyword(s):  
Mathematical Model ◽  
Digital Computer ◽  
Linear Time ◽  
Piecewise Linear ◽  
Invariant State ◽  
Computer Solution ◽  
Linear Time Invariant ◽  
State Variable ◽  
Time Invariant ◽  
The Mathematical Model

The mathematical model of the diode proposed in this investigation for the analysis of nonideal poly phase converters has finite forward and reverse resistances. Since current-dependent diode impedances exist at all times, only one set of piecewise-linear time-invariant state-variable equations is required to describe the nonideal polyphase diode converter completely. A digital computer solution of the state- variable equations was obtained to verify the inte grity and tractability of this method of analysis.

Fuel Flexibility at Ignition Conditions for Industrial Gas Turbines

2013 ◽  
Author(s):  
Anders Larsson ◽  
Anton Berg ◽  
Alessio Bonaldo
Keyword(s):  
Mathematical Model ◽  
Gas Turbine ◽  
Gas Turbines ◽  
Inert Gases ◽  
Ignition Energy ◽  
Minimum Ignition Energy ◽  
Fuel Flexibility ◽  
Start Up ◽  
Gas Fuel ◽  
The Mathematical Model

The variety of gaseous fuels that Siemens Industrial Turbomachinery (SIT) is requested to consider during sales enquiries has prompted product development projects that have allowed to continuously increase gas turbine fuel flexibility. The fuel flexibility often has to be guaranteed at all engine load conditions including ignition. The gas turbine ignition capabilities have therefore been analyzed in order to assess the engines current capabilities and identify further potentials. The authors’ approach for ignition fuel flexibility has been to model the minimum ignition energy (MIE) required for successful ignition and to validate the model by experiments conducted under test conditions reproducing engine start up flows at a combustion test rig. The experiments were performed using two hydrocarbon gases individually mixed with two inert gases at various concentrations. The mathematical model predicting the minimum ignition energy is applicable also to hydrocarbon and inert gases mixtures that were not used during the experimental campaign. The model was studied and developed in order to produce a tool for support of gas fuel enquiries received during the sales phase. In accordance to the predictions of the mathematical model, the experimental validation in the paper shows that the difference in MIE required to ignite the gas fuel composition depends on the inert gas used as well as the hydrocarbon used. The MIE model showed the capability of assessing if a specific gas composition can be used as a reliable start-up fuel.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

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