Karlovitz Number
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Karlovitz Number
In combustion, the Karlovitz number is defined as the ratio of chemical time scale t_F to Kolmogorov time scale t_\eta, named after Béla Karlovitz. The number reads as :\mathrm = \frac. In premixed turbulent combustion, the chemical time scale can be defined as t_F = D_T/S_L^2, where D_T is the thermal diffusivity and S_L is the laminar flame speed and the flame thickness is given by \delta_L = D_T/S_L, in which case, :\mathrm = \frac where \eta is the Kolmogorov scale. The Karlovitz number is related to Damköhler number as :\mathrm = \frac if the Damköhler number is defined with Kolmogorov scale. If \mathrm<1, the premixed turbulent flame falls into the category of corrugated flamelets and wrinkled flamelets, otherwise into the thin reaction zone or broken reaction zone flames.


Klimov–Williams criterion

In premixed turbulent combustion, the Klimov–Williams criterion or Klimov–Williams limit, named after
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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 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 ...
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Kolmogorov Microscales
In fluid dynamics, Kolmogorov microscales are the smallest scales in the turbulent flow of fluids. At the Kolmogorov scale, viscosity dominates and the turbulence kinetic energy is dissipated into thermal energy. They are defined by where * is the average rate of dissipation of turbulence kinetic energy per unit mass, and * is the kinematic viscosity of the fluid. Typical values of the Kolmogorov length scale, for atmospheric motion in which the large eddies have length scales on the order of kilometers, range from 0.1 to 10 millimeters; for smaller flows such as in laboratory systems, may be much smaller. In 1941, Andrey Kolmogorov introduced the hypothesis that the smallest scales of turbulence are universal (similar for every turbulent flow) and that they depend only on and . The definitions of the Kolmogorov microscales can be obtained using this idea and dimensional analysis. Since the dimension of kinematic viscosity is length2/time, and the dimension of the energy ...
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Béla Karlovitz
Principal scientific contributions Béla Karlovitz was a Hungarian engineer who pioneered research into the generation of electricity directly from a body of hot moving gas without any mechanical moving parts. This process is known as magnetohydrodynamic generation or MHD generation for short. Béla Karlovitz received his M.E. degree from Technical University, Budapest, Hungary and his E.E. degree from the Federal Institute of Technology, Zurich, Switzerland. Besides his publications in MHD, he is the author of many publications on turbulent flames and combustion instabilities. He was the Head of the Flame Research Section, Explosives and Physical Science Division, Bureau of Mines, Pittsburgh, PA. Subsequently, he was with Combustion and Explosive Research, Inc. in Pittsburgh, PA. In combustion, Karlovitz is known as the first to introduce the concept of flame stretch. The Karlovitz number is named after him. It is a non-dimensional quantity defined as: \mathit = k t_c where t ...
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Thermal Diffusivity
In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It measures the rate of transfer of heat of a material from the hot end to the cold end. It has the SI derived unit of m2/s. Thermal diffusivity is usually denoted by lowercase alpha (), but , , ( kappa), , and 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)). As seen 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 curvature, quantifying the rate at which temperature concavity is "smoothed out". In a sense, thermal diffusivity is a contrasting measure to thermal inertia. In a substance with high thermal diffusivity, heat moves rapidly through it because the substa ...
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Premixed Flame
A premixed flame is a flame formed under certain conditions during the combustion of a premixed charge (also called pre-mixture) of fuel and oxidiser. Since the fuel and oxidiser—the key chemical reactants of combustion—are available throughout a homogeneous stoichiometric premixed charge, the combustion process once initiated sustains itself by way of its own heat release. The majority of the chemical transformation in such a combustion process occurs primarily in a thin interfacial region which separates the unburned and the burned gases. The premixed flame interface propagates through the mixture until the entire charge is depleted. The propagation speed of a premixed flame is known as the flame speed (or burning velocity) which depends on the convection-diffusion-reaction balance within the flame, i.e. on its inner chemical structure. The premixed flame is characterised as laminar or turbulent depending on the velocity distribution in the unburned pre-mixture (which provides ...
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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. 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 ...
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Forman A
Forman may refer to: Places: *Forman, North Dakota, city in Sargent County, North Dakota, United States * Forman, West Virginia, unincorporated community in Grant County, West Virginia, United States * Forman Glacier between Mount Franke and Mount Cole, in the Queen Maud Mountains of Antarctica *Forman Park, in Syracuse, New York Surname: *A. G. Forman CBE (1910–1967), Chief of Naval Staff of the Ghana Navy * Al Forman (1928–2013), baseball umpire *Alexander A. Forman (1843–1922), American soldier in the American Civil War *Alison Forman (born 1969), Australian soccer player *Andrew Forman (1465–1521), Scottish diplomat and Archbishop *Arthur Forman (1850–1905), English schoolmaster and cricketer *Bill Forman (1886–1958), baseball player * Bruce Forman (born 1956), American jazz guitarist *Carol Forman (1918–1997), American actress *Charles William Forman (1821–1894), Presbyterian missionary in Pakistan *Christine Jones Forman, American astrophysicist *Craig Forman ...
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Schmidt Number
Schmidt number (Sc) is a dimensionless number defined as the ratio of momentum diffusivity (kinematic viscosity) and mass diffusivity, and it is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes. It was named after German engineer Ernst Heinrich Wilhelm Schmidt (1892–1975). The Schmidt number is the ratio of the shear component for diffusivity ''viscosity/density'' to the diffusivity for mass transfer ''D''. It physically relates the relative thickness of the hydrodynamic layer and mass-transfer boundary layer. It is defined as: :\mathrm = \frac = \frac = \frac where: * \nu is the kinematic viscosity or (/\,) in units of (m2/s) * D is the mass diffusivity (m2/s). * is the dynamic viscosity of the fluid (Pa·s or N·s/m2 or kg/m·s) * \rho is the density of the fluid (kg/m3). The heat transfer analog of the Schmidt number is the Prandtl number (Pr). The ratio of thermal diffusivity to mass diffusivity is th ...
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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 to be contrasted with 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 In 1864, Peter Waage and Cato Guldberg pioneered the development of chemical kinetics by formulating the law of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.C.M. Guldberg and P. Waage,"Studies Concerning Affinity" ''Forhandlinger i Videnskabs-Selskabet i Christiania'' (1864), 35P. W ...
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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 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 ...
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Dimensionless Numbers Of Fluid Mechanics
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1), ISBN 978-92-822-2272-0. which is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured in seconds). Dimensionless units are dimensionless values that serve as units of measurement for expressing other quantities, such as radians (rad) or steradians (sr) for plane angles and solid angles, respectively. For example, optical extent is defined as having units of metres multiplied by steradians. History Quantities having dimension one, ''dimensionless quantities'', regularly occur in sciences, and are formally treated within the field of d ...
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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. ...
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