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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] |
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] |
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] |
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] |
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] |
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 numbers, 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#Large Damköhler number, 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 Arrheniu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
California Institute Of Technology
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasionally referred to as "CIT", most notably in its alma mater, but this is uncommon. is a private research university in Pasadena, California. Caltech is ranked among the best and most selective academic institutions in the world, and with an enrollment of approximately 2400 students (acceptance rate of only 5.7%), it is one of the world's most selective universities. The university is known for its strength in science and engineering, and is among a small group of institutes of technology in the United States which is primarily devoted to the instruction of pure and applied sciences. The institution was founded as a preparatory and vocational school by Amos G. Throop in 1891 and began attracting influential scientists such as George Ellery H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Function
In mathematics, the error function (also called the Gauss error function), often denoted by , is a complex function of a complex variable defined as: :\operatorname z = \frac\int_0^z e^\,\mathrm dt. This integral is a special (non-elementary) sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real. In statistics, for non-negative values of , the error function has the following interpretation: for a random variable that is normally distributed with mean 0 and standard deviation , is the probability that falls in the range . Two closely related functions are the complementary error function () defined as :\operatorname z = 1 - \operatorname z, and the imaginary error function () defined as :\operatorname z = -i\operatorname iz, where is the imaginary unit Name The name "error function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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 and time. ... [...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 produced. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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