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.

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.

A Modular Code for Real Time Dynamic Simulation of Gas Turbines in Simulink

2002 ◽  
Vol 128 (3) ◽  
pp. 506-517 ◽  
Author(s):  
S. M. Camporeale ◽  
B. Fortunato ◽  
M. Mastrovito
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Gas Turbine ◽  
Dynamic Behavior ◽  
Gas Turbines ◽  
Simulation Software ◽  
Computational Time ◽  
High Fidelity ◽  
Time Step ◽  
The Mathematical Model

A high-fidelity real-time simulation code based on a lumped, nonlinear representation of gas turbine components is presented. The code is a general-purpose simulation software environment useful for setting up and testing control equipments. The mathematical model and the numerical procedure are specially developed in order to efficiently solve the set of algebraic and ordinary differential equations that describe the dynamic behavior of gas turbine engines. For high-fidelity purposes, the mathematical model takes into account the actual composition of the working gases and the variation of the specific heats with the temperature, including a stage-by-stage model of the air-cooled expansion. The paper presents the model and the adopted solver procedure. The code, developed in Matlab-Simulink using an object-oriented approach, is flexible and can be easily adapted to any kind of plant configuration. Simulation tests of the transients after load rejection have been carried out for a single-shaft heavy-duty gas turbine and a double-shaft aero-derivative industrial engine. Time plots of the main variables that describe the gas turbine dynamic behavior are shown and the results regarding the computational time per time step are discussed.

A High-Fidelity Real-Time Simulation Code of Gas Turbine Dynamics for Control Applications

2002 ◽  
Author(s):  
S. M. Camporeale ◽  
B. Fortunato ◽  
M. Mastrovito
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Gas Turbine ◽  
Dynamic Behavior ◽  
Computational Time ◽  
High Fidelity ◽  
Simulation Code ◽  
Real Time Simulation ◽  
Time Simulation ◽  
The Mathematical Model

A novel high-fidelity real-time simulation code based on a lumped, non-linear representation of gas turbine components is presented. The aim of the work is to develop a general-purpose simulation code useful for setting up and testing control equipments. The mathematical model and the numerical procedure are specially developed in order to efficiently solve the set of algebraic and ordinary differential equations that describe the dynamic behavior of the gas turbine engine. The paper presents the model and the adopted solver procedure. The code, developed in Matlab-Simulink using an object-oriented approach, is flexible and can be easily adapted to any kind of plant configuration. For high-fidelity purposes, the mathematical model takes into account the actual composition of the working gases and the variation of the specific heats with the temperature, including a stage-by-stage model of the air-cooled expansion. Simulation tests of the transients after load rejection have been carried out for a single-shaft heavy-duty gas turbine and a double-shaft industrial engine. Time plots of the main variables that describe the gas turbine dynamic behavior are shown and the results regarding the computational time per time step are discussed.

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.

A Generalized Mathematical Model to Estimate Gas Turbine Starting Characteristics

1982 ◽  
Vol 104 (1) ◽  
pp. 194-201 ◽  
Author(s):  
R. K. Agrawal ◽  
M. Yunis
Keyword(s):  
Mathematical Model ◽  
Ambient Temperature ◽  
Gas Turbine ◽  
System Combination ◽  
Turbine Performance ◽  
Start Up ◽  
Starting Characteristics ◽  
Starting Torque

The paper describes a generalized mathematical model to estimate gas turbine performance in the starting regime of the engine. These estimates are then used to calculate the minimum engine starting torque requirements, thereby defining the specifications for the aircraft starting system. Alternatively, the model can also be used to estimate the start up time at any ambient temperature or altitude for a given engine/aircraft starting system combination.

scholarly journals The Mathematical Model and Numerical Study of Heat and Mass Transfer Processes in the Combustion Chamber of Diesel-Generator Units with a Valve-Inductor Generator

2020 ◽  
pp. 611-625
Author(s):  
Dmitriy V. Guzei ◽  
Andrey V. Minakov ◽  
Vasiliy I. Panteleev ◽  
Maksim I. Pryazhnikov ◽  
Dmitriy V. Platonov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Combustion Chamber ◽  
Heat And Mass Transfer ◽  
Operating Conditions ◽  
Diesel Generator ◽  
Transfer Processes ◽  
Mass Transfer Processes ◽  
Actual Geometry ◽  
The Mathematical Model

The mathematical model of heat and mass transfer processes in the combustion chamber of diesel generator units with valve inductor generators has been developed. The mathematical model takes into account the actual geometry of the combustion chamber and the operating conditions of the diesel engine. A study of the main characteristics of a diesel generator in a wide range of modes of operation has been carried out. In addition to energy characteristics, environmental parameters have been considered

scholarly journals A Generalized Mathematical Model to Estimate Gas Turbine Starting Characteristics

1981 ◽  
Author(s):  
R. K. Agrawal ◽  
M. Yunis
Keyword(s):  
Mathematical Model ◽  
Ambient Temperature ◽  
Gas Turbine ◽  
System Combination ◽  
Turbine Performance ◽  
Start Up ◽  
Starting Characteristics ◽  
Starting Torque

The paper describes a generalized mathematical model to estimate gas turbine performance in the starting regime of the engine. These estimates are then used to calculate the minimum engine starting torque requirements, thereby defining the specifications for the aircraft starting system. Alternatively, the model can also be used to estimate the start up time at any ambient temperature or altitude for a given engine/aircraft starting system combination.

The influence of operating experiences in the design of the IVAR thermal drying plant expansion in Stavanger, Norway

2004 ◽  
Vol 49 (10) ◽  
pp. 179-184
Author(s):  
O. Tornes ◽  
A. Whipps
Keyword(s):  
Treatment Plant ◽  
Design Stage ◽  
Municipal Sludge ◽  
Complex Process ◽  
Start Up ◽  
Plant Expansion ◽  
Thermal Drying ◽  
Dust Explosions ◽  
Energy Balances ◽  
Mass And Energy Balances

The Regional Wastewater Treatment Plant of North J¾ren (IVAR IKS) serves the Stavanger conurbation with a population equivalence of 240,000. The site was the first in Norway to operate a thermal drying and a pelletising plant for municipal sludge. Since the start up in 1992, IVAR has encountered most of the operational problems typically associated with thermal drying processes. Considerable modifications have been made and lessons learnt resulting in the plant being one of the few thermal drying facilities in Norway which continues to operate successfully. In general, thermal drying is often considered as a costly, energy demanding and complex process requiring careful attention to safety aspects such as risks of self-combustion, fires and dust explosions. The paper presents general considerations of operating experiences influencing the procurement and design stage of the new extended IVAR thermal drying plant. Furthermore, topical issues important for resolution of thermal drying problems are also discussed. Mass and energy balances for the Stavanger plant are presented.

scholarly journals Nonlinear Digital Simulation and Minimum Fuel Control of a Jet Type Gas Turbine Power Generating Unit

1978 ◽  
Author(s):  
D. Weiner ◽  
F. S. Aschner ◽  
J. Dayan
Keyword(s):  
Mathematical Model ◽  
Mathematical Programming ◽  
Gas Turbine ◽  
Digital Simulation ◽  
Measured Data ◽  
Gas Generator ◽  
Nonlinear Simulation ◽  
Power Generating Unit ◽  
Simulation Results ◽  
The Mathematical Model

This paper discusses the digital nonlinear simulation of a twin-spool gas generator-free turbine power generating unit. The mathematical model derived is flexible and can be easily converted to suit any other gas turbine. Simulation results were verified by comparison to measured data. The model was applied to optimize a fuel control schedule by methods of Mathematical Programming, taking into account the constraints imposed by the protective control of the system.

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.

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