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Darrieus–Landau Instability
The Darrieus–Landau instability, or density fingering, refers to an instability of chemical fronts propagating into a denser medium, named after Georges Jean Marie Darrieus and Lev Landau. It is a key Combustion instability#Classification of combustion instabilities, instrinsic flame instability that occurs in premixed flames, caused by density variations due to thermal expansion of the gas produced by the combustion process. In simple terms, stability inquires whether a steadily propagating plane sheet with a discontinuous jump in density is stable or not. The analysis behind the Darrieus–Landau instability considers a planar, premixed flame front subjected to very small perturbations. It is useful to think of this arrangement as one in which the unperturbed flame is stationary, with the reactants (fuel and oxidizer) directed towards the flame and perpendicular to it with a velocity u1, and the burnt gases leaving the flame also in a perpendicular way but with velocity u2. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Georges Jean Marie Darrieus
Georges Jean Marie Darrieus (24 September 1888 – 15 July 1979) was a French aerospace engineering, aeronautical engineer in the 20th century. He invented the Darrieus wind turbine, Darrieus rotor, a wind turbine capable of operating from any direction and under adverse weather conditions, and the vertical-axis wind turbine, vertical-axis giromill. The invention is described in the 1931 . Darrieus is also known for introduction of laminated pressplates into the construction of the stators used in synchronous generators thus reducing the core losses. Biography In World War I, Georges Darrieus was appointed as the artillery captain in 1917. References Sources * External linksacademie-sciences.frUS patent 1,835,018 French aerospace engineers Members of the French Academy of Sciences 20th-century French inventors Wind turbines 1888 births 1979 deaths French fluid dynamicists {{France-engineer-stub ... [...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] |
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] |
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 ... [...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] |
Michelson–Sivashinsky Equation
In combustion, Michelson–Sivashinsky equation describes the evolution of a premixed flame front, subjected to the Darrieus–Landau instability, in the small heat release approximation. The equation was derived by Gregory Sivashinsky in 1977, who along the Daniel M. Michelson, presented the numerical solutions of the equation in the same year. Let the planar flame front, in a uitable frame of reference be on the xy-plane, then the evolution of this planar front is described by the amplitude function u(\mathbf x,t) (where \mathbf x=(x,y)) describing the deviation from the planar shape. The Michelson–Sivashinsky equation, reads as :\frac + \frac(\nabla u)^2 - \nu \nabla^2 u - \frac \int , \mathbf k, e^u (\mathbf x,t) d\mathbf kd\mathbf x'=0, where \nu is a constant. Incorporating also the Rayleigh–Taylor instability of the flame, one obtains the Rakib–Sivashinsky equation (named after Z. Rakib and Gregory Sivashinsky), :\frac + \frac(\nabla u)^2 - \nu \nabla^2 u - \frac \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saffman–Taylor Instability
The Saffman–Taylor instability, also known as viscous fingering, is the formation of patterns in a morphologically unstable interface between two fluids in a porous medium or in a Hele-Shaw cell, described mathematically by Philip Saffman and G. I. Taylor in a paper of 1958. This situation is most often encountered during drainage processes through media such as soils. It occurs when a less viscous fluid is injected, displacing a more viscous fluid; in the inverse situation, with the more viscous displacing the other, the interface is stable and no instability is seen. Essentially the same effect occurs driven by gravity (without injection) if the interface is horizontal and separates two fluids of different densities, the heavier one being above the other: this is known as the Rayleigh–Taylor instability. In the rectangular configuration the system evolves until a single finger (the Saffman–Taylor finger) forms, whilst in the radial configuration the pattern grows formin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hele-Shaw Flow
Hele-Shaw flow is defined as flow taking place between two parallel flat plates separated by a narrow gap satisfying certain conditions, named after Henry Selby Hele-Shaw, who studied the problem in 1898. Various problems in fluid mechanics can be approximated to Hele-Shaw flows and thus the research of these flows is of importance. Approximation to Hele-Shaw flow is specifically important to micro-flows. This is due to manufacturing techniques, which creates shallow planar configurations, and the typically low Reynolds numbers of micro-flows. The conditions that needs to be satisfied are :\frac \ll 1, \qquad \frac \frac \ll 1 where h is the gap width between the plates, U is the characteristic velocity scale, l is the characteristic length scale in directions parallel to the plate and \nu is the kinematic viscosity. Specifically, the Reynolds number \mathrm=Uh/\nu need not always be small, but can be order unity or greater as long as it satisfies the condition \mathrm(h/l) \ll 1. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Equations (fluid Dynamics)
In fluid dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. The Euler equations can be applied to incompressible and compressible flows. The incompressible Euler equations consist of Cauchy equations for conservation of mass and balance of momentum, together with the incompressibility condition that the flow velocity is divergence-free. The compressible Euler equations consist of equations for conservation of mass, balance of momentum, and balance of energy, together with a suitable constitutive equation for the specific energy density of the fluid. Historically, only the equations of conservation of mass and balance of momentum were derived by Euler. However, fluid dynamics literature often refers to the full set of the compressible Euler equations – including ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusive–thermal Instability
Diffusive–thermal instability or thermo–diffusive instability is an intrinsic flame instability that occurs both in premixed flames and in diffusion flames and arises because of the difference in the diffusion coefficient values for the fuel and heat transport, characterized by non-unity values of Lewis numbers. The instability mechanism that arises here is the same as in Turing instability explaining chemical morphogenesis, although the mechanism was first discovered in the context of combustion by Yakov Zeldovich in 1944 to explain the cellular structures appearing in lean hydrogen flames. Quantitative stability theory for premixed flames were developed by Gregory Sivashinsky (1977), Guy Joulin and Paul Clavin (1979) and for diffusion flames by Jong S. Kim and Forman A. Williams (1996,1997). Dispersion relation for premixed flames To neglect the influences by hydrodynamic instabilities such as Darrieus–Landau instability, Rayleigh–Taylor instability etc., the analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Pattern
The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state. The pattern arises due to Turing instability which in turn arises due to the interplay between differential diffusion of chemical species and chemical reaction. The instability mechanism is surprising because a pure diffusion, such as molecular diffusion, would be expected to have a stabilizing influence on the system (i.e., complete mixing). Overview In his paper, Turing examined the behaviour of a system in which two diffusible substances interact with each other, and found that such a system is able to generate a spatially periodic pattern even from a random or almost uniform initial condition. Prior to the discovery of this instability mechanism arising due to unequal diffusion coefficients of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
