Zeldovich–Liñán–Dold Model
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Zeldovich–Liñán–Dold Model
In combustion, Zeldovich–Liñán–Dold model or ZLD model or ZLD mechanism is a two-step reaction model for the combustion processes, named after Yakov Borisovich Zeldovich, Amable Liñán and John W. Dold. The model includes a chain-branching and a chain-breaking (or radical recombination) reaction. The model was first introduced by Zeldovich in 1948, later analysed by Liñán using activation energy asymptotics in 1971 and later refined by John W. Dold in the 2000s.Dold, J. W. (2007). Premixed flames modelled with thermally sensitive intermediate branching kinetics. Combustion Theory and Modelling, 11(6), 909-948. The ZLD mechanism mechanism reads as :\begin \rm & \quad \rm + \rm \rightarrow 2\rm \\ \rm & \quad \rm + \rm \rightarrow \rm +\rm +\rm \end where \rm is the fuel, \rm is an intermediate radical, \rm is the third body and \rm is the product. This mechanism exhibits a ''linear or first-order recombination''. The model originally studied before Dold's refinement per ...
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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 activation energy must be supplied 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. The study of combustion is known as combustion science. Combustion is often a complicated sequence of elementary reaction, elementary Radical (chemistry), 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 e ...
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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, who worked in chemical engineering, thermodynamics, and fluid dynamics. The Karlovitz number (Ka) is related to the Damköhler number by Da = 1/Ka. In its most commonly used form, the first Damköhler number (DaI) relates particles' characteristic residence time scale in a fluid region to the reaction timescale. The residence time scale can take the form of a convection time scale, such as 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 first Damköhler number can be written as the ratio of the chemical reaction rate to the mass transfer rate : \mathrm_ = \frac It is also defin ...
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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 activation energy must be supplied 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. The study of combustion is known as combustion science. Combustion is often a complicated sequence of elementary reaction, elementary Radical (chemistry), 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 e ...
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Chemical Kinetics
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is different from chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction. History The pioneering work of chemical kinetics was done by German chemist Ludwig Wilhelmy in 1850. He experimentally studied the rate of inversion of sucrose and he used integrated rate law for the determination of the reaction kinetics of this reaction. His work was noticed 34 years later by Wilhelm Ostwald. In 1864, Peter Waage and Cato Guldberg published the law ...
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Peters Four-step Chemistry
Peters four-step chemistry is a systematically reduced mechanism for methane combustion, named after Norbert Peters, who derived it in 1985. The mechanism reads as :\begin & \text && \ce \\ & \text && \ce \\ & \text && \ce \\ & \text && \ce \end The mechanism predicted four different regimes where each reaction takes place. The third reaction, known as radical consumption layer, where most of the heat is released, and the first reaction, also known as fuel consumption layer, occur in a narrow region at the flame. The fourth reaction is the hydrogen oxidation layer, whose thickness is much larger than the former two layers. Finally, the carbon monoxide Carbon monoxide (chemical formula CO) is a poisonous, flammable gas that is colorless, odorless, tasteless, and slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the si ... oxidation layer is the largest of them all, corresponding to the second rea ...
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Zel'dovich Mechanism
Zel'dovich mechanism is a chemical mechanism that describes the oxidation of nitrogen and NO''x'' formation, first proposed by the Russian physicist Yakov Borisovich Zel'dovich in 1946. The reaction mechanisms read as : + O _1 + : + O2 _2 + where k_1 and k_2 are the reaction rate constants in Arrhenius law. The overall global reaction is given by : + 2NO The overall reaction rate is mostly governed by the first reaction (i.e., rate-determining reaction), since the second reaction is much faster than the first reaction and occurs immediately following the first reaction. At fuel-rich conditions, due to lack of oxygen, reaction 2 becomes weak, hence, a third reaction is included in the mechanism, also known as extended Zel'dovich mechanism (with all three reactions), : + _3 + Assuming the initial concentration of NO is low and the reverse reactions can therefore be ignored, the forward rate constants of the reactions are given by :\begin k_ &= 1.47\times 10^ \, T^ \m ...
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Heat Release Parameter
In combustion, heat release parameter (or gas expansion parameter) is a dimensionless parameter which measures the amount of heat released by an adiabatic combustion process. It is defined as :q = \frac where *T_ is the adiabatic flame temperature *T_u is the unburnt mixture temperature. In typical combustion process, q\approx 2-7. 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 ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...,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., :q = \frac = \frac. The ratio of burnt gas to unburnt gas temperature is :\frac =1+q. Gas expansion ratio The gas expansion ratio is simply defined by ...
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Molecular Weight
A molecule is a group of two or more atoms that are held together by Force, attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and ''molecule'' is often used when referring to polyatomic ions. A molecule may be homonuclear, that is, it consists of atoms of one chemical element, e.g. two atoms in the oxygen molecule (O2); or it may be heteronuclear, a chemical compound composed of more than one element, e.g. water (molecule), water (two hydrogen atoms and one oxygen atom; H2O). In the kinetic theory of gases, the term ''molecule'' is often used for any gaseous particle regardless of its composition. This relaxes the requirement that a molecule contains two or more atoms, since the noble gases are individual atoms. Atoms and complexes connected by non-covalent interactions, such as hydrogen bonds or ionic ...
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Zeldovich Number
The Zeldovich 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 Zeldovich, who along with David A. Frank-Kamenetskii, first introduced in their paper in 1938. In 1983 ICDERS meeting at Poitiers, it was decided that the non-dimensional number will be named after Zeldovich.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 q, it is given by :\beta = \frac \frac For typical combustion phenomena, the value for Zel'dovich number lies in the range \beta\approx 8-20. Activation energy asy ...
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Yakov Borisovich Zeldovich
Yakov Borisovich Zeldovich (, ; 8 March 1914 – 2 December 1987), also known as YaB, was a leading Soviet physicist of Belarusian origin, who is known for his prolific contributions in physical cosmology, physics of thermonuclear reactions, combustion, and hydrodynamical phenomena. From 1943, Zeldovich, a self-taught physicist, started his career by playing a crucial role in the development of the former Soviet program of nuclear weapons. In 1963, he returned to academia to embark on pioneering contributions on the fundamental understanding of the thermodynamics of black holes and expanding the scope of physical cosmology. Biography Early life and education Yakov Zeldovich was born into a Belarusian Jewish family in his grandfather's house in Minsk. However, in mid-1914, the Zeldovich family moved to Saint Petersburg. They resided there until August 1941, when the family was evacuated together with the faculty of the Institute of Chemical Physics to Kazan to avoid the ...
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Rate Constant
In chemical kinetics, a reaction rate constant or reaction rate coefficient () is a proportionality constant which quantifies the rate and direction of a chemical reaction by relating it with the concentration of reactants. For a reaction between reactants A and B to form a product C, where :A and B are reactants :C is a product :''a'', ''b'', and ''c'' are stoichiometric coefficients, the reaction rate is often found to have the form: r = k mathrmm mathrm Here is the reaction rate constant that depends on temperature, and and are the molar concentrations of substances A and B in moles per unit volume of solution, assuming the reaction is taking place throughout the volume of the solution. (For a reaction taking place at a boundary, one would use moles of A or B per unit area instead.) The exponents ''m'' and ''n'' are called partial orders of reaction and are ''not'' generally equal to the stoichiometric coefficients ''a'' and ''b''. Instead they depend on the reactio ...
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Activation Energy
In the Arrhenius model of reaction rates, activation energy is the minimum amount of energy that must be available to reactants for a chemical reaction to occur. The activation energy (''E''a) of a reaction is measured in kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol). Activation energy can be thought of as a 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. Temperature ...
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