|
Shvab–Zeldovich Formulation
The Shvab–Zeldovich formulation is an approach to remove the chemical-source terms from the conservation equations for energy and chemical species by linear combinations of independent variables, when the conservation equations are expressed in a common form. Expressing conservation equations in common form often limits the range of applicability of the formulation. The method was first introduced by V. A. Shvab in 1948 and by Yakov Zeldovich in 1949. Method For simplicity, assume combustion takes place in a single global irreversible reaction \sum_^N \nu_i' \real_i \rightarrow \sum_^N \nu_i'' \real_i where \real_i is the ith chemical species of the total N species and \nu_i' and \nu_i'' are the stoichiometric coefficients of the reactants and products, respectively. Then, it can be shown from the law of mass action that the rate of moles produced per unit volume of any species \omega is constant and given by \omega = \frac where w_i is the mass of species i produced or consum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conservation Law (physics)
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of mass-energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge. There are also many approximate conservation laws, which apply to such quantities as mass, parity, lepton number, baryon number, strangeness, hypercharge, etc. These quantities are conserved in certain classes of physics processes, but not in all. A local conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the quantity and the "transport" of that quantity. It states that the amount of the conserved quantity at a point or within a volume can only change by the amount of the quantity which flows in or out of the volume. From Noether's theorem, every dif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yakov Zeldovich
Yakov Borisovich Zeldovich (, ; 8 March 1914 – 2 December 1987), also known as YaB, was a leading Soviet people, Soviet Physics, physicist of Belarusians, Belarusian origin, who is known for his prolific contributions in physical Physical cosmology, cosmology, physics of Plasma physics, thermonuclear reactions, combustion, and Fluid dynamics, hydrodynamical phenomena. From 1943, Zeldovich, a self-taught physicist, started his career by playing a crucial role in the development of the former Soviet atomic bomb project, Soviet program of nuclear weapons. In 1963, he returned to academia to embark on pioneering contributions on the fundamental understanding of the Black hole thermodynamics, thermodynamics of black holes and expanding the scope of physical cosmology. Biography Early life and education Yakov Zeldovich was born into a History of the Jews in Belarus, Belarusian Jewish family in his grandfather's house in Minsk. However, in mid-1914, the Zeldovich family moved to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Mass Action
In chemistry, the law of mass action is the proposition that the rate of a chemical reaction is directly proportional to the product of the activities or concentrations of the reactants. It explains and predicts behaviors of solutions in dynamic equilibrium. Specifically, it implies that for a chemical reaction mixture that is in equilibrium, the ratio between the concentration of reactants and products is constant. Two aspects are involved in the initial formulation of the law: 1) the equilibrium aspect, concerning the composition of a reaction mixture at equilibrium and 2) the kinetic aspect concerning the rate equations for elementary reactions. Both aspects stem from the research performed by Cato M. Guldberg and Peter Waage between 1864 and 1879 in which equilibrium constants were derived by using kinetic data and the rate equation which they had proposed. Guldberg and Waage also recognized that chemical equilibrium is a dynamic process in which rates of reaction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Diffusivity
In thermodynamics, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It is a measure of the rate of heat transfer inside a material and has SI, SI units of m2/s. It is an intensive property. Thermal diffusivity is usually denoted by lowercase alpha (), but , , (kappa), , , D_T are also used. The formula is \alpha = \frac, where : is thermal conductivity (W/(m·K)), : is specific heat capacity (J/(kg·K)), : is density (kg/m3). Together, can be considered the volumetric heat capacity (J/(m3·K)). Thermal diffusivity is a positive coefficient in the heat equation: \frac = \alpha \nabla^2 T. One way to view thermal diffusivity is as the ratio of the time derivative of temperature to its Second derivative#Generalization to higher dimensions, curvature, quantifying the rate at which temperature concavity is "smoothed out". In a substance with high thermal diffusivity, heat moves rapidly through it because the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lewis Number
In fluid dynamics and thermodynamics, the Lewis number (denoted ) 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: * is the thermal diffusivity, * is the mass diffusivity, * is the thermal conductivity, * is the density, * is the mixture-averaged diffusion coefficient, * is 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. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mach Number
The Mach number (M or Ma), often only Mach, (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after the Austrian physicist and philosopher Ernst Mach. \mathrm = \frac, where: * is the local Mach number, * is the local flow velocity with respect to the boundaries (either internal, such as an object immersed in the flow, or external, like a channel), and * is the speed of sound in the medium, which in air varies with the square root of the thermodynamic temperature. By definition, at Mach1, the local flow velocity is equal to the speed of sound. At Mach0.65, is 65% of the speed of sound (subsonic), and, at Mach1.35, is 35% faster than the speed of sound (supersonic). The local speed of sound, and hence the Mach number, depends on the temperature of the surrounding gas. The Mach number is primarily used to determine the approximation with which a flow can be treated as an i ... [...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.%'' or ''% w/w''; 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 tot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Heat
In thermodynamics, the specific heat capacity (symbol ) of a substance is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. It is also referred to as massic heat capacity or as the specific heat. More formally it is the heat capacity of a sample of the substance divided by the mass of the sample. The International System of Units, SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of of water by is , so the specific heat capacity of water is . Specific heat capacity often varies with temperature, and is different for each state of matter. Liquid water has one of the highest specific heat capacities among common substances, about at 20 °C; but that of ice, just below 0 °C, is only . The specific heat capacities of iron, granite, and hydrogen gas are about 449 J⋅kg−1⋅K−1, 790 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formation Enthalpy
In chemistry and thermodynamics, the standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements in their reference state, with all substances in their standard states. The standard pressure value is recommended by IUPAC, although prior to 1982 the value 1.00 atm (101.325 kPa) was used. There is no standard temperature. Its symbol is Δf''H''⦵. The superscript Plimsoll on this symbol indicates that the process has occurred under standard conditions at the specified temperature (usually 25 °C or 298.15 K). Standard states are defined for various types of substances. For a gas, it is the hypothetical state the gas would assume if it obeyed the ideal gas equation at a pressure of 1 bar. For a gaseous or solid solute present in a diluted ideal solution, the standard state is the hypothetical state of concentration of the solute of exactly one mole pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 used: \rho = \frac, where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate this quantity is more specifically called specific weight. For a pure substance, the density is equal to its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium is the densest known element at standard conditions for temperature and pressure. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative den ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amable Liñán
Amable Liñán Martínez (born 1934 in Noceda de Cabrera, Castrillo de Cabrera, León, Spain) is a Spanish aeronautical engineer working in the field of combustion. Biography He holds a PhD in Aeronautical Engineering from the Technical University of Madrid, advised by 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 latter case working directl ... [...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] |
