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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] |
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] |
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] |
Burke–Schumann Flame
In combustion, a Burke–Schumann flame is a type of diffusion flame, established at the mouth of the two concentric ducts, by issuing fuel and oxidizer from the two region respectively. It is named after S.P. Burke and T.E.W. Schumann, who were able to predict the flame height and flame shape using their simple analysis of infinitely fast chemistry (which is now called as Burke–Schumann limit) in 1928 at the First symposium on combustion. Mathematical description Consider a cylindrical duct with axis along z direction with radius a through which fuel is fed from the bottom and the tube mouth is located at z=0. Oxidizer is fed along the same axis, but in the concentric tube of radius b outside the fuel tube. Let the mass fraction in the fuel tube be Y_ and the mass fraction of the oxygen in the outside duct be Y_. Fuel and oxygen mixing occurs in the region z>0. The following assumptions were made in the analysis: * The average velocity is parallel to axis (z direction) of the ... [...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] |
Reynolds Number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow ( eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full-size ve ... [...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] |
Pre-exponential Factor
In chemical kinetics, the pre-exponential factor or A factor is the pre-exponential constant in the Arrhenius equation#Equation, Arrhenius equation (equation shown below), an empirical relationship between temperature and Reaction rate constant, rate coefficient. It is usually designated by A when determined from experiment, while Z is usually left for collision frequency. The pre-exponential factor can be thought of as a measure of the frequency of properly oriented collisions. It is typically determined experimentally by measuring the rate constant k at a particular temperature and fitting the data to the Arrhenius equation. The pre-exponential factor is generally not exactly constant, but rather depends on the specific reaction being studied and the temperature at which the reaction is occurring. A=\frac The units of the pre-exponential factor A are identical to those of the rate constant and will vary depending on the order of the reaction. For a first-order reaction, it has ... [...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] |
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 substanc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass Fraction (chemistry)
In chemistry, the mass fraction of a substance within a mixture is the ratio w_i (alternatively denoted Y_i) of the mass m_i of that substance to the total mass m_\text of the mixture. Expressed as a formula, the mass fraction is: : w_i = \frac . Because the individual masses of the ingredients of a mixture sum to m_\text, their mass fractions sum to unity: : \sum_^ w_i = 1. Mass fraction can also be expressed, with a denominator of 100, as percentage by mass (in commercial contexts often called ''percentage by weight'', abbreviated ''wt%''; see mass versus weight). It is one way of expressing the composition of a mixture in a dimensionless size; mole fraction (percentage by moles, mol%) and volume fraction ( percentage by volume, vol%) are others. When the prevalences of interest are those of individual chemical elements, rather than of compounds or other substances, the term ''mass fraction'' can also refer to the ratio of the mass of an element to the total mass of a sampl ... [...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] |
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., MartÃnez-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] |
