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Liñán's Diffusion Flame Theory
Liñán diffusion flame theory is a theory developed by Amable Liñán in 1974 to explain the diffusion flame structure using activation energy asymptotics and Damköhler number asymptotics.Liñán, A., Martínez-Ruiz, D., Vera, M., & Sánchez, A. L. (2017). The large-activation-energy analysis of extinction of counterflow diffusion flames with non-unity Lewis numbers of the fuel. Combustion and Flame, 175, 91-106. Liñán used counterflowing jets of fuel and oxidizer to study the diffusion flame structure, analyzing for the entire range of Damköhler number. His theory predicted four different types of flame structure as follows, * ''Nearly-frozen ignition regime'', where deviations from the frozen flow conditions are small (no reaction sheet exist in this regime), * ''Partial burning regime'', where both fuel and oxidizer cross the reaction zone and enter into the frozen flow on other side, * ''Premixed flame regime'', where only one of the reactants cross the reaction zone, in ... [...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 la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion Flame
In combustion, a diffusion flame is a flame in which the oxidizer and fuel are separated before burning. Contrary to its name, a diffusion flame involves both diffusion and convection processes. The name diffusion flame was first suggested by S.P. Burke and T.E.W. Schumann in 1928, to differentiate from premixed flame where fuel and oxidizer are premixed prior to burning. The diffusion flame is also referred to as nonpremixed flame. The burning rate is however still limited by the rate of diffusion. Diffusion flames tend to burn slower and to produce more soot than premixed flames because there may not be sufficient oxidizer for the reaction to go to completion, although there are some exceptions to the rule. The soot typically produced in a diffusion flame becomes incandescent from the heat of the flame and lends the flame its readily identifiable orange-yellow color. Diffusion flames tend to have a less-localized flame front than premixed flames. The contexts for diffusion may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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) \p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Damköhler Numbers
The Damköhler numbers (Da) are dimensionless numbers used in chemical engineering to relate the chemical reaction timescale ( reaction rate) to the transport phenomena rate occurring in a system. It is named after German chemist Gerhard Damköhler. The Karlovitz number (Ka) is related to the Damköhler number by Da = 1/Ka. In its most commonly used form, the Damköhler number relates the reaction timescale to the convection time scale, volumetric flow rate, through the reactor for continuous (plug flow or stirred tank) or semibatch chemical processes: : \mathrm = \frac In reacting systems that include interphase mass transport, the second Damköhler number (DaII) is defined as the ratio of the chemical reaction rate to the mass transfer rate : \mathrm_ = \frac It is also defined as the ratio of the characteristic fluidic and chemical time scales: : \mathrm = \frac Since the reaction timescale is determined by the reaction rate, the exact formula for the Damköhler number v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stagnation Point Flow
In fluid dynamics, stagnation point flow represents the flow of a fluid in the immediate neighborhood of a stagnation point (or a stagnation line) with which the stagnation point (or the line) is identified for a potential flow or inviscid flow. The flow specifically considers a class of stagnation points known as saddle points where the incoming streamlines gets deflected and directed outwards in a different direction; the streamline deflections are guided by separatrices. The flow in the neighborhood of the stagnation point or line can generally be described using potential flow theory, although viscous effects cannot be neglected if the stagnation point lies on a solid surface. Stagnation point flow without solid surfaces When two streams either of two-dimensional or axisymmetric nature impinge on each other orthogonally, a stagnation plane is created, where the incoming streams are diverted tangentially outwards; thus on the stagnation plane, the velocity component normal to t ... [...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/ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lewis Number
The Lewis number (Le) is a dimensionless number defined as the ratio of thermal diffusivity to mass diffusivity. It is used to characterize fluid flows where there is simultaneous heat and mass transfer. The Lewis number puts the thickness of the thermal boundary layer in relation to the concentration boundary layer. The Lewis number is defined as :\mathrm = \frac = \frac . where \alpha is the thermal diffusivity and D the mass diffusivity, \lambda the thermal conductivity, \rho the density, D_ the mixture-averaged diffusion coefficient, and c_p the specific heat capacity at constant pressure. In the field of fluid mechanics, many sources define the Lewis number to be the inverse of the above definition. The Lewis number can also be expressed in terms of the Prandtl number and the Schmidt number : :\mathrm = \frac. It is named after Warren K. Lewis (1882–1975), who was the first head of the Chemical Engineering Department at MIT. Some workers in the field of combustion assume (i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stagnation Point Flow
In fluid dynamics, stagnation point flow represents the flow of a fluid in the immediate neighborhood of a stagnation point (or a stagnation line) with which the stagnation point (or the line) is identified for a potential flow or inviscid flow. The flow specifically considers a class of stagnation points known as saddle points where the incoming streamlines gets deflected and directed outwards in a different direction; the streamline deflections are guided by separatrices. The flow in the neighborhood of the stagnation point or line can generally be described using potential flow theory, although viscous effects cannot be neglected if the stagnation point lies on a solid surface. Stagnation point flow without solid surfaces When two streams either of two-dimensional or axisymmetric nature impinge on each other orthogonally, a stagnation plane is created, where the incoming streams are diverted tangentially outwards; thus on the stagnation plane, the velocity component normal to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Activation Energy
In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol). Activation energy can be thought of as the magnitude of the potential barrier (sometimes called the energy barrier) separating minima of the potential energy surface pertaining to the initial and final thermodynamic state. For a chemical reaction to proceed at a reasonable rate, the temperature of the system should be high enough such that there exists an appreciable number of molecules with translational energy equal to or greater than the activation energy. The term "activation energy" was introduced in 1889 by the Swedish scientist Svante Arrhenius. Other uses Although less commonly used, activation energy also applies to nuclear reactions and various other physical phenomena. Te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liñán's Equation
In the study of diffusion flame, Liñán's equation is a second-order nonlinear ordinary differential equation which describes the inner structure of the diffusion flame, first derived by Amable Liñán in 1974. The equation reads as :\frac =(y^2-\zeta^2)e^ subjected to the boundary conditions : \begin \zeta\rightarrow -\infty : &\quad \frac=-1,\\ \zeta\rightarrow \infty : &\quad \frac=1 \end where \delta is the reduced or rescaled Damköhler number and \gamma is the ratio of excess heat conducted to one side of the reaction sheet to the total heat generated in the reaction zone. If \gamma>0, more heat is transported to the oxidizer side, thereby reducing the reaction rate on the oxidizer side (since reaction rate depends on the temperature) and consequently greater amount of fuel will be leaked into the oxidizer side. Whereas, if \gamma\delta_E. The solution is unique for \delta>\delta_I, where \delta_I is the ignition Damköhler number. Liñán also gave a correlation formul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emmons Problem
In combustion, Emmons problem describes the flame structure which develops inside the boundary layer, created by a flowing oxidizer stream on flat fuel (solid or liquid) surfaces. The problem was first studied by Howard Wilson Emmons in 1956. The flame is of diffusion flame type because it separates fuel and oxygen by a flame sheet. The corresponding problem in a quiescent oxidizer environment is known as Clarke–Riley diffusion flame. Burning rateWilliams, F. A. (2018). Combustion theory. CRC Press. Consider a semi-infinite fuel surface with leading edge located at x=0 and let the free stream oxidizer velocity be U_\infty. Through the solution f(\eta) of Blasius equation f+ff''=0 (\eta is the self-similar Howarth–Dorodnitsyn coordinate), the mass flux \rho v (\rho is density and v is vertical velocity) in the vertical direction can be obtained :\rho v = \rho_\infty \mu_\infty \sqrt \left(f'\rho \int_0^\eta \rho^ \ d\eta - f\right), where :\xi = \int_0^x \rho_\infty \mu_\in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clarke–Riley Diffusion Flame
In combustion, Clarke–Riley diffusion flame is a diffusion flame that develops inside a naturally convected boundary layer on a hot fuel surface with quiescent oxidizer environment, first studied and experimentally verified by John Frederick Clarke and Norman Riley in 1976.Clarke, J. F., & Riley, N. (1976). Free convection and the burning of a horizontal fuel surface. Journal of Fluid Mechanics, 74(3), 415-431. This problem is an extension of Emmons problem. See also *Emmons problem *Liñán's diffusion flame theory Liñán diffusion flame theory is a theory developed by Amable Liñán in 1974 to explain the diffusion flame structure using activation energy asymptotics and Damköhler number asymptotics.Liñán, A., Martínez-Ruiz, D., Vera, M., & Sánchez, A. ... References Fluid dynamics Combustion {{combustion-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
