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 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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Kolmogorov Microscales
In fluid dynamics, Kolmogorov microscales are the smallest scales in turbulent flow. 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 dissipation ...
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Béla Karlovitz
Béla Karlovitz (November 9, 1904 – February 29, 2004) 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. He 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_c is the ...
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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 ...
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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 prov ...
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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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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 * Bill Forman (1915–?), radio announcer and actor *Bruce Forman (born 1956), American jazz guitarist * Carol Forman (1918–1997), American actress * Charles William Forman (1821–1894), Presbyterian missionary in Pakistan * Chr ...
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Schmidt Number
In fluid dynamics, the Schmidt number (denoted ) of a fluid 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 divided by density) to the diffusivity for mass transfer . It physically relates the relative thickness of the hydrodynamic layer and mass-transfer boundary layer. It is defined as: :\mathrm = \frac = \frac = \frac = \frac where (in SI units): * \nu = \tfrac \mu \rho is the kinematic viscosity (m2/s) * is the mass diffusivity (m2/s). * is the dynamic viscosity of the fluid (Pa·s = N·s/m2 = kg/m·s) * is the density of the fluid (kg/m3) * is the Peclet Number * is the Reynolds Number. The heat transfer analog of ...
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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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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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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 ...
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Fluid Dynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion) and (the study of water and other liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moment (physics), moments on aircraft, determining the mass flow rate of petroleum through pipeline transport, pipelines, weather forecasting, predicting weather patterns, understanding nebulae in interstellar space, understanding large scale Geophysical fluid dynamics, geophysical flows involving oceans/atmosphere and Nuclear weapon design, 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 fl ...
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