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Activation Energy Asymptotics
Activation energy asymptotics (AEA), also known as large activation energy asymptotics, is an asymptotic analysis used in the combustion field utilizing the fact that the reaction rate is extremely sensitive to temperature changes due to the large activation energy of the chemical reaction. History The techniques were pioneered by the Russian scientists Yakov Borisovich Zel'dovich, David A. Frank-Kamenetskii and co-workers in the 30s, in their study on premixed flames and thermal explosions (Frank-Kamenetskii theory), but not popular to western scientists until the 70s. In the early 70s, due to the pioneering work of Williams B. Bush, Francis E. Fendell, Forman A. Williams, Amable Liñán and John F. Clarke, it became popular in western community and since then it was widely used to explain more complicated problems in combustion. Method overview In combustion processes, the reaction rate \omega is dependent on temperature T in the following form ( Arrhenius law), :\omega(T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotic Analysis
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as becomes very large, the term becomes insignificant compared to . The function is said to be "''asymptotically equivalent'' to , as ". This is often written symbolically as , which is read as " is asymptotic to ". An example of an important asymptotic result is the prime number theorem. Let denote the prime-counting function (which is not directly related to the constant pi), i.e. is the number of prime numbers that are less than or equal to . Then the theorem states that \pi(x)\sim\frac. Asymptotic analysis is commonly used in computer science as part of the analysis of algorithms and is often expressed there in terms of big O notation. Definition Formally, given functions and , we define a binary relation f(x) \sim g(x) \q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Frederick Clarke
John Frederick Clarke FRS (1 May 1927 – 11 June 2013) was a professor, an aeronautical engineer, and a pilot. Biography After his schooling, he got training from Fleet Air Arm as a Navy Pilot and then from Royal Air force at Lossiemouth. He left Navy and worked few months at Armstrong Siddeley Motors, but his interest were in academics. Subsequently he quit the job and joined Queen Mary College in Aeronautical engineering course in 1949. He married Jean Gentle in 1953. His thesis advisor Norman A.V. Piercy died in 1953,Winny, H. F. (1953). Prof. NAV Piercy. Nature, 171(4353), 593-594. then he temporarily advised by Leslie G. Whitehead and then finally by Alec David Young. He received his PhD at Queen Mary College in 1957. He briefly worked for English Electric company from 1955 to 1957. In 1958 he joined Cranfield University as a lecturer and stayed there till 1991. After his retirement he continued to do research for a decade. His research interests were Shock waves, deto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burke–Schumann Limit
In combustion, Burke–Schumann limit, or large Damköhler number limit, is the limit of infinitely fast chemistry (or in other words, infinite Damköhler number), named after S.P. Burke and T.E.W. Schumann, due to their pioneering work on Burke–Schumann flame. One important conclusion of infinitely fast chemistry is the non-co-existence of fuel and oxidizer simultaneously except in a thin reaction sheet. The inner structure of the reaction sheet is described by Liñán's equation. Limit description In a typical non-premixed combustion (fuel and oxidizer are separated initially), mixing of fuel and oxidizer takes place based on the mechanical time scale t_mdictated by the convection/diffusion (the relative importance between convection and diffusion depends on the Reynolds number) terms. Similarly, chemical reaction takes certain amount of time t_c to consume reactants. For one-step irreversible chemistry with Arrhenius rate, this chemical time is given by :t_c = \left(B e^\ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zeldovich–Frank-Kamenetskii Equation
ZFK equation, abbreviation for Zeldovich–Frank-Kamenetskii equation, is a reaction–diffusion equation that models premixed flame propagation. The equation is named after Yakov Zeldovich and David A. Frank-Kamenetskii who derived the equation in 1938 and is also known as the Nagumo equation. The equation is analogous to KPP equation except that is contains an exponential behaviour for the reaction term and it differs fundamentally from KPP equation with regards to the propagation velocity of the traveling wave. In non-dimensional form, the equation reads :\frac = \frac + \omega(\theta) with a typical form for \omega given by :\omega =\frac \theta(1-\theta) e^ where \theta\in ,1/math> is the non-dimensional dependent variable (typically temperature) and \beta is the Zeldovich number. In the ZFK regime, \beta\gg 1. The equation reduces to Fisher's equation for \beta\ll 1 and thus \beta\ll 1 corresponds to KPP regime. The minimum propagation velocity U_ (which is usually th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Method Of Matched Asymptotic Expansions
In mathematics, the method of matched asymptotic expansions is a common approach to finding an accurate approximation to the solution to an equation, or system of equations. It is particularly used when solving singularly perturbed differential equations. It involves finding several different approximate solutions, each of which is valid (i.e. accurate) for part of the range of the independent variable, and then combining these different solutions together to give a single approximate solution that is valid for the whole range of values of the independent variable. In the Russian literature, these methods were known under the name of "intermediate asymptotics" and were introduced in the work of Yakov Zeldovich and Grigory Barenblatt. Method overview In a large class of singularly perturbed problems, the domain may be divided into two or more subdomains. In one of these, often the largest, the solution is accurately approximated by an asymptotic series found by treating the prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heat Release Parameter
In combustion, heat release parameter (or gas expansion parameter) is a dimensionless parameter which measures the amount of heat released by the combustion process. It is defined as :\alpha = \frac where *T_b is the burnt gas temperature *T_u is the unburnt mixture temperature. In typical combustion process, \alpha\approx 0.7-0.9. For isobaric combustion, using ideal gas law, the parameter can be expressed in terms of density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...,Clavin, P. (1985). Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Progress in energy and combustion science, 11(1), 1-59. i.e., :\alpha = \frac = \frac. The ratio of burnt gas to unburnt gas temperature is :\frac = \frac=\frac. See also * Zel'dovich number References {{Reflist, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zel'dovich Number
The Zel'dovich number is a dimensionless number which provides a quantitative measure for the activation energy of a chemical reaction which appears in the Arrhenius exponent, named after the Russian scientist Yakov Borisovich Zel'dovich, who along with David A. Frank-Kamenetskii, first introduced in their paper in 1938. In 1983 ICDERS meeting at Poitiers, it was decided to name after Zel'dovich.Clavin, P. (1985). Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Progress in energy and combustion science, 11(1), 1-59. It is defined as :\beta = \frac \cdot \frac where *E_a is the activation energy of the reaction *R is the universal gas constant *T_b is the burnt gas temperature *T_u is the unburnt mixture temperature. In terms of heat release parameter \alpha, it is given by :\beta = \frac \alpha For typical combustion phenomena, the value for Zel'dovich number lies in the range \beta\approx 8-20. Activation energy asymptotics Activation energy asym ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Gas Constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance, i.e. the pressure–volume product, rather than energy per temperature increment per ''particle''. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation. The gas constant is the constant of proportionality that relates the energy scale in physics to the temperature scale and the scale used for amount of substance. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of units of energy, temperature and amount of subs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arrhenius Law
In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that the van 't Hoff equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and reverse reactions. This equation has a vast and important application in determining the rate of chemical reactions and for calculation of energy of activation. Arrhenius provided a physical justification and interpretation for the formula. Laidler, K. J. (1987) ''Chemical Kinetics'', Third Edition, Harper & Row, p. 42 Currently, it is best seen as an empirical relationship.Kenneth Connors, Chemical Kinetics, 1990, VCH Publishers It can be used to model the temperature variation of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally-induced processes/re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amable Liñán
Amable Liñán Martínez (born Noceda de Cabrera, Castrillo de Cabrera, León, Spain in 1934) is a Spanish aeronautical engineer considered a world authority in the field of combustion. Biography He holds a PhD in Aeronautical Engineering from the Technical University of Madrid, advised by :es:Gregorio Millán Barbany and Degree of Aeronautical Engineer from the Caltech advised by Frank E. Marble. He is currently Professor of Fluid Mechanics and professor emeritus at the Higher Technical School of Aeronautical Engineers of the Polytechnic University of Madrid (attached to the Department of Motorcycle and Thermofluidodynamics of said school). He has taught at universities in California, Michigan and Princeton University in the United States and in Marseilles in France, among others. Since 1997 he is an adjunct professor at Yale University. Research He has focused his research studies on the basic problems of combustion, both reactor and planetary probe dynamics, in the lat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion does not always result in fire, because a flame is only visible when substances undergoing combustion vaporize, but when it does, a flame is a characteristic indicator of the reaction. While the activation energy must be overcome to initiate combustion (e.g., using a lit match to light a fire), the heat from a flame may provide enough energy to make the reaction self-sustaining. Combustion is often a complicated sequence of elementary radical reactions. Solid fuels, such as wood and coal, first undergo endothermic pyrolysis to produce gaseous fuels whose combustion then supplies the heat required to produce more of them. Combustion is often hot enough that incandescent light in the form of either glowing or a flame is produce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
