A mathematical model of the cool-flame oxidation of acetaldehyde

1971 ◽  
Vol 322 (1550) ◽  
pp. 377-403 ◽  
Keyword(s):  
Mathematical Model ◽  
Negative Temperature ◽  
Isothermal Oxidation ◽  
Limited Range ◽  
Detailed Model ◽  
Cool Flame ◽  
Induction Periods ◽  
Cool Flames ◽  
Satisfactory Account ◽  
Flame Oxidation

A detailed mathematical model of the non-isothermal oxidation of acetaldehyde has been found to give a realistic simulation of (i) single and multiple cool flames, their limits, amplitudes and induction periods; (ii) two-stage ignition; and (iii) the negative temperature coefficient for the maximum rate of slow combustion. A simplified form of the model, valid over a limited range of conditions, has been subjected to mathematical analysis to provide interpretations of the effects simulated by the detailed model. It is concluded that cool flames are thermokinetic effects often, but not exclusively, of an oscillatory nature, and that a satisfactory account of cool-flame phenomena must necessarily take reactant consumption into account.

A mathematical model for hydrocarbon autoignition at high pressures

1975 ◽  
Vol 346 (1647) ◽  
pp. 515-538 ◽  
Keyword(s):  
Mathematical Model ◽  
High Pressures ◽  
The Other ◽  
Chain Mechanism ◽  
Rapid Compression Machine ◽  
High Pressure And Temperature ◽  
Cool Flame ◽  
Induction Periods ◽  
Branched Chain ◽  
Low Pressures

We have developed a generalized mathematical model for the autoignition of hydrocarbons under the conditions of high pressure and temperature achieved in a rapid-compression machine. The model is able to simulate the essential phenomena of the two-stage autoignition of alkanes under these conditions; these are a well-defined cool flame that is often quenched rapidly and completely before the onset of a sharp ignition. It also pre­dicts correctly the transition to single-stage autoignition at even higher temperatures and the variation with temperature of the characteristic induction periods. The model is based on a degenerate-branched-chain mechanism. We show that it must contain as necessary features two termination processes, one linear and the other quadratic in radial concen­tration, and two routes for the formation of branching agent, one of which involves intermediate products of oxidation. The model also predicts, without any adjustment of the kinetic parameters, the essential pheno­mena of cool-flame and ignition behaviour that are observed at low pressures.

Low-temperature oxidation and cool flames of propane

1954 ◽  
Vol 221 (1145) ◽  
pp. 151-170 ◽  
Keyword(s):  
Low Temperature ◽  
Thermal Instability ◽  
Analytical Study ◽  
Simple Explanation ◽  
Low Temperature Oxidation ◽  
Temperature Oxidation ◽  
Cool Flame ◽  
Cool Flames ◽  
Oxidation Of Hydrocarbons ◽  
Flame Oxidation

A detailed analytical study of the cool-flame oxidation of propane has been carried out using a continuous-flow technique with a view to the further elucidation of the mechanism of the low-temperature oxidation of hydrocarbons. The formation of the three theoretically possible aldehydes has been demonstrated and the initially formed peroxide shown to be hydrogen peroxide. Measurements of the yields of the different products formed under varying conditions of temperature, composition and time of contact have been made and correlated with measurements of the luminous intensity and temperature of the flame. The results confirm the earlier conclusions of Norrish (1948) that aldehydes are the important branching agents in the temperature range of 300 to 400°C, and a detailed scheme based on that proposed earlier has been developed to account for the observations. The scheme has further been shown to allow of a simple explanation of the origin of the periodic character of the cool flame in terms of the thermal instability of the normal slow reaction.

The non-isothermal oxidation of 2-methylpentane I. The properties of cool flames

1966 ◽  
Vol 293 (1434) ◽  
pp. 378-394 ◽  
Keyword(s):  
High Pressure ◽  
Pressure Rise ◽  
Isothermal Oxidation ◽  
Temperature Sensitive ◽  
Gaseous Mixtures ◽  
Cool Flame ◽  
Cool Flames ◽  
Slow Combustion ◽  
Subsequent Passage ◽  
Limiting Pressure

The conditions of pressure and temperature under which gaseous mixtures of 2-methylpentane with oxygen react non-iso thermally have been established. At temperatures greater than 307 °C, 1:2 fuel-oxygen mixtures of sufficiently high pressure ignite by a one-stage mechanism. At lower temperatures, the limiting pressure for ignition decreases and the resulting ignition is a two stage phenomenon, the passage of a cool flame preceding that of the hot flame. At similar temperatures but lower pressures, multiple and single cool flames propagate but do not lead to ignition. Correlation of the intensities of and rates of pressure rise due to cool flames with the limiting conditions for low temperature ignition has shown that cool flames affect profoundly the subsequent passage of a hot flame and that this effect is not purely thermal. The complexity of the limiting pressure/temperature relationship for cool flame propagation shows that the transition from slow combustion to cool flame is dependent upon several temperature-sensitive branching reactions. Moreover, the formation of periodic cool flames would appear to necessitate the participation, even under given conditions of pressure and temperature, of more than one branching agent.

The cool-flame oxidation of 3-ethylpentane

1971 ◽  
Vol 325 (1563) ◽  
pp. 469-492 ◽  
Keyword(s):  
Carbon Number ◽  
Sole Source ◽  
Initial Reaction ◽  
Cool Flame ◽  
Cool Flames ◽  
Lower Molecular Mass ◽  
Flame Region ◽  
Group Migration ◽  
Flame Oxidation ◽  
Alkylperoxy Radicals

Detailed studies have been carried out of the combustion of 3-ethylpentane with special reference to the chemical changes taking place in the cool-flame region, where at least 74 individual products are formed. At ca . 300 °C, the first products to appear are 3-ethylpent-1-ene and 3-ethylpent-2-ene, C 7 O -heterocycles and alkenes of carbon number less than seven; the rates of consumption of 3-ethylpentane and of formation of all products increase dramatically just before propagation of the first cool-flame but do not vary appreciably when subsequent cool-flames pass. As the temperature is raised to ca . 400 °C, the quantities of 3-ethylpentane consumed and of lower molecular mass products formed increase markedly while the amounts of most C 7 products decrease. Consideration of the analytical results indicates that alkylperoxy radical isomerization plays an important part in the primary chain-propagation cycle both in and out of the cool-flame region and at temperatures as high as 400 °C. It appears that the initial reaction of alkyl radicals with oxygen takes place, largely, if not exclusively, by direct addition to form alkylperoxy radicals. Different modes of isomerization of these radicals leads to the wide variety of products found and decomposition of the a-hydroperoxyalkyl radicals by direct loss of HO 2 is probably the sole source of the conjugate alkenes. The results also provide the first recorded evidence of ethyl group migration during alkylperoxy radical isomerization.

scholarly journals Starting generator driving torque modeling in the studies of synchronous starting of synchronous machines

2002 ◽  
Vol 15 (3) ◽  
pp. 399-408
Author(s):  
Zoran Stajic ◽  
Dragan Petrovic ◽  
Dusan Arnautovic
Keyword(s):  
Mathematical Model ◽  
Linear Function ◽  
Polynomial Approximation ◽  
System Model ◽  
Synchronous Machines ◽  
Model Function ◽  
Detailed Model ◽  
Pumped Storage ◽  
Driving Torque ◽  
Time Linear

The paper deals with significance of the starting generator (SG) driving torque modeling in the studies of synchronous starting of synchronous machines (SSSM). The detailed mathematical model of SSSM in reversible pumped storage plant (RPSP) "Bajina Basta" is derived. Because it is very difficult to include the detailed model of the SG turbine in the system model, function of SG driving torque is modeled approximately. The most frequent case in SSSM studies is its approximation with a time linear function, until it reaches the value that should provide rotating of both machine rotors with synchronous velocities, which is also used in the paper Afterwards, three different cases are considered: constant, linear and polynomial approximation in terms of SG rotor velocity. Numerical results obtained by applying developed models to a particular case of synchronous starting are compared with the corresponding experimental results. In this way, it is shown that the application of the most frequently used SG driving torque modeling leads to the erroneous results. The advantages of the polynomial approximation suggested in the paper and its validity is demonstrated.

Extended validation of a ground-based three-axis spacecraft simulator model

2020 ◽  
pp. 095441002093896
Author(s):  
H Sh Ousaloo ◽  
Gh Sharifi ◽  
B Akbarinia
Keyword(s):  
Mathematical Model ◽  
Attitude Control ◽  
Aerodynamic Drag ◽  
Center Of Mass ◽  
Model Development ◽  
Optimization Method ◽  
Experimental Results ◽  
Spacecraft Dynamics ◽  
Detailed Model ◽  
Mass Properties

The ground-based spacecraft dynamics simulator plays an important role in the implementation and validation of attitude control scenarios before a mission. The development of a comprehensive mathematical model of the platform is one of the indispensable and challenging steps during the control design process. A precise mathematical model should include mass properties, disturbances forces, mathematical models of actuators and uncertainties. This paper presents an approach for synthesizing a set of trajectories scenarios to estimate the platform inertia tensor, center of mass and aerodynamic drag coefficients. Reaction wheel drag torque is also estimated for having better performance. In order to verify the estimation techniques, a dynamics model of the satellite simulator using MATLAB software was developed, and the problem reduces to a parameter estimation problem to match the experimental results obtained from the simulator using a classical Lenevnberg-Marquardt optimization method. The process of parameter identification and mathematical model development has implemented on a three-axis spherical satellite simulator using air bearing, and several experiments are performed to validate the results. For validation of the simulator model, the model and experimental results must be carefully matched. The experimental results demonstrate that step-by-step implementation of this scenario leads to a detailed model of the platform which can be employed to design and develop control algorithms.

Experiments with cool flames. I—induction periods

1950 ◽  
Vol 46 (0) ◽  
pp. 824-835 ◽  
Author(s):  
F. E. Malherbe ◽  
A. D. Walsh
Keyword(s):  
Induction Periods ◽  
Cool Flames

Regenerative Gas Turbines With Divided Expansion

2004 ◽  
Author(s):  
Brian Elmegaard ◽  
Bjo̸rn Qvale
Keyword(s):  
Mathematical Model ◽  
Gas Turbines ◽  
High Efficiency ◽  
Limited Range ◽  
Simulation Program ◽  
Operating Parameters ◽  
Gas Generator ◽  
Extensive Simulation ◽  
Power Turbine ◽  
The Mathematical Model

Recuperated gas turbines are currently drawing an increased attention due to the recent commercialization of micro gas turbines with recuperation. This system may reach a high efficiency even for the small units of less than 100kW. In order to improve the economics of the plants, ways to improve their efficiency are always of interest. Recently, two independent studies have proposed recuperated gas turbines to be configured with the turbine expansion divided, in order to obtain higher efficiency. The idea is to operate the system with a gas generator and a power turbine, and use the gas from the gas generator part for recuperation ahead of the expansion in the power turbine. The present study is more complete than the predecessors in that the ranges of the parameters have been extended and the mathematical model is more realistic using an extensive simulation program. It is confirmed that the proposed divided expansion can be advantageous under certain circumstances. But, in order for todays micro gas turbines to be competitive, the thermodynamic efficiencies will have to be rather high. This requires that all component efficiencies including the recuperator effectiveness will have to be high. The advantages of the divided expansion manifest themselves over a rather limited range of the operating parameters, that lies outside the range required to make modern micro turbines economically competitive.

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