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Markstein Number
In combustion engineering and explosion studies, the Markstein number (named after George H. Markstein who first proposed the notion in 1951) characterizes the effect of local heat release of a propagating flame on variations in the surface topology along the flame and the associated local flame front curvature. There are two dimensionless Markstein numbers:Clavin, Paul, and Geoff Searby. Combustion Waves and Fronts in Flows: Flames, Shocks, Detonations, Ablation Fronts and Explosion of Stars. Cambridge University Press, 2016. one is the curvature Markstein number and the other is the flow-strain Markstein number. They are defined as: :\mathcal_c = \frac, \quad \mathcal_s = \frac where \mathcal_c is the curvature Markstein length, \mathcal_s is the flow-strain Markstein length and \delta_L is the characteristic laminar flame thickness. The larger the Markstein length, the greater the effect of curvature on localised burning velocity. George H. Markstein (1911—2011) showed that ... [...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 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 ... [...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] |
Dimensionless Numbers Of Fluid Mechanics
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined Unit of measurement, units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific Unit of volume, units of volume used, such as in milliliters per milliliter (mL/mL). The 1, number one is recognized as a dimensionless Base unit of measurement, base quantity. Radians serve as dimensionless units for Angle, angular measurements, derived from the universal ratio of 2π times the radius of a circle being equal to its circumference. Dimensionless quantities play a crucial role serving as parameters in differential equations in various technical disciplines. In calculus, concepts like the unitless ratios ... [...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 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clavin–Garcia Equation
Clavin–Garcia equation or Clavin–Garcia dispersion relation provides the relation between the growth rate and the wave number of the perturbation superposed on a planar premixed flame, named after Paul Clavin and Pedro Luis Garcia Ybarra, who derived the dispersion relation in 1983. The dispersion relation accounts for Darrieus–Landau instability, Rayleigh–Taylor instability The Rayleigh–Taylor instability, or RT instability (after Lord Rayleigh and G. I. Taylor), is an instability of an Interface (chemistry), interface between two fluids of different densities which occurs when the lighter fluid is pushing the hea ... and diffusive–thermal instability and also accounts for the temperature dependence of transport coefficients. Dispersion relation Let k and \sigma be the wavenumber (measured in units of planar laminar flame thickness \delta_L) and the growth rate (measured in units of the residence time \delta_L^2/D_ of the planar laminar flame) of the perturbations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matalon–Matkowsky–Clavin–Joulin Theory
The Matalon–Matkowsky–Clavin–Joulin theory refers to a theoretical hydrodynamic model of a premixed flame with a large-amplitude flame wrinkling, developed independently by Moshe Matalon & Bernard J. Matkowsky and Paul Clavin & Guy Joulin, following the pioneering study by Paul Clavin and Forman A. Williams and by Pierre Pelcé and Paul Clavin. The theory, for the first time, calculated the burning rate of the curved flame that differs from the burning rate of the planar flame due to flame stretch, associated with the flame curvature and the strain imposed on the flame by the flow field. Burning rate formula According to Matalon–Matkowsky–Clavin–Joulin theory, if S_L and \delta_L are the laminar burning speed and thickness of a planar flame (and \tau_L=D_/S_L^2 be the corresponding flame residence time with D_ being the thermal diffusivity in the unburnt gas), then the burning speed S_T for the curved flame with respect to the unburnt gas is given by :\frac = 1 + \m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
G Equation
G, or g, is the seventh letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages, and others worldwide. Its name in English is ''gee'' (pronounced ), plural ''gees''. The lowercase version can be written in two forms: the single-storey (sometimes "opentail") and the double-storey (sometimes "looptail") . The former is commonly used in handwriting and fonts based on it, especially fonts intended to be read by children. History The evolution of the Latin alphabet's G can be traced back to the Latin alphabet's predecessor, the Greek alphabet. The voiced velar stop was represented by the third letter of the Greek alphabet, gamma (Γ), which was later adopted by the Etruscan language. Latin then borrowed this "rounded form" of gamma, C, to represent the same sound in words such as ''recei'', which was likely an early dative form of '' rex'', meaning "king", as found in an "early Latin inscription." Over time, how ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dilogarithm
In mathematics, the dilogarithm (or Spence's function), denoted as , is a particular case of the polylogarithm. Two related special functions are referred to as Spence's function, the dilogarithm itself: :\operatorname_2(z) = -\int_0^z\, du \textz \in \Complex and its reflection. For , an infinite series also applies (the integral definition constitutes its analytical extension to the complex plane): :\operatorname_2(z) = \sum_^\infty . Alternatively, the dilogarithm function is sometimes defined as :\int_^ \frac dt = \operatorname_2(1-v). In hyperbolic geometry the dilogarithm can be used to compute the volume of an ideal simplex. Specifically, a simplex whose vertices have cross ratio has hyperbolic volume :D(z) = \operatorname \operatorname_2(z) + \arg(1-z) \log, z, . The function is sometimes called the Bloch-Wigner function. Lobachevsky's function and Clausen's function are closely related functions. William Spence, after whom the function was named by early write ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Conductivity
The thermal conductivity of a material is a measure of its ability to heat conduction, conduct heat. It is commonly denoted by k, \lambda, or \kappa and is measured in W·m−1·K−1. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. For instance, metals typically have high thermal conductivity and are very efficient at conducting heat, while the opposite is true for insulating materials such as mineral wool or Styrofoam. Metals have this high thermal conductivity due to free electrons facilitating heat transfer. Correspondingly, materials of high thermal conductivity are widely used in heat sink applications, and materials of low thermal conductivity are used as thermal insulation. The reciprocal of thermal conductivity is called thermal resistivity. The defining equation for thermal conductivity is \mathbf = - k \nabla T, where \mathbf is the heat flux, k is the thermal conductivity, and \nabla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zel'dovich 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 asym ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Explosion
An explosion is a rapid expansion in volume of a given amount of matter associated with an extreme outward release of energy, usually with the generation of high temperatures and release of high-pressure gases. Explosions may also be generated by a slower expansion that would normally not be forceful, but is not allowed to expand, so that when whatever is containing the expansion is broken by the pressure that builds as the matter inside tries to expand, the matter expands forcefully. An example of this is a Volcano, volcanic eruption created by the expansion of magma in a magma chamber as it rises to the surface. Supersonic explosions created by high explosives are known as detonations and travel through shock waves. wikt:subsonic, Subsonic explosions are created by low explosives through a slower combustion process known as deflagration. Causes For an explosion to occur, there must be a rapid, forceful expansion of matter. There are numerous ways this can happen, both natura ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
