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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] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Clavin
Paul Clavin is a French scientist at Aix-Marseille University, working in the field of combustion and statistical mechanics. He is the founder of Institute for Research on Nonequilibrium Phenomena (IRPHE). Biography Paul Clavin obtained his first degree at ENSMA and then a Master's degree in Mathematics and Plasma Physics. For his PhD, he joined Ilya Prigogine in Brussels from 1967 to 1970 and then returned to Poitiers. Paul Clavin moved to Aix-Marseille University in the late 1970s and created the combustion research group. Clavin served as the chair of the Physical Mechanics at Institut Universitaire de France from 1993 to 2004 and the administrator from 2000 to 2005. He received Ya.B. Zeldovich Gold Medal from The Combustion Institute in 2014 and a fellow of The Combustion Institute. A workshop titled ''Out-of-Equilibrium Dynamics'' was conducted in 2012 in honor of Clavin's 70th birthday. He is the recipient of Grand Prix award from French Academy of Sciences in 1998 and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
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 heavier fluid. Philip Drazin, Drazin (2002) pp. 50–51. Examples include the behavior of water suspended above oil in the gravity of Earth, mushroom clouds like those from volcanic eruptions and atmospheric nuclear explosions, supernova explosions in which expanding core gas is accelerated into denser shell gas, merging binary quantum fluids in metastable configuration, instabilities in plasma fusion reactors and inertial confinement fusion. Concept Water suspended atop oil is an everyday example of Rayleigh–Taylor instability, and it may be scientific modeling, modeled by two completely plane-parallel layers of immiscible fluid, the denser fluid on top of the less dense one and both subject to the Earth's gravity. The Mechanical equili ... [...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] |
Temperature Dependence Of Viscosity
Viscosity depends strongly on temperature. In liquids it usually decreases with increasing temperature, whereas, in most gases, viscosity ''increases'' with increasing temperature. This article discusses several models of this dependence, ranging from rigorous first-principles calculations for monatomic gases, to empirical correlations for liquids. Understanding the temperature dependence of viscosity is important for many applications, for instance engineering lubricants that perform well under varying temperature conditions (such as in a car engine), since the performance of a lubricant depends in part on its viscosity. Engineering problems of this type fall under the purview of tribology. Here dynamic viscosity is denoted by \mu and kinematic viscosity by \nu. The formulas given are valid only for an absolute temperature scale; therefore, unless stated otherwise temperatures are in kelvins. Physical causes Viscosity in gases arises from molecules traversing layers of flow an ... [...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] |
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] |
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] |
Rayleigh Number
In fluid mechanics, the Rayleigh number (, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a certain lower range denotes laminar flow; a value in a higher range, turbulent flow. Below a certain critical value, there is no fluid motion and heat transfer is by conduction rather than convection. For most engineering purposes, the Rayleigh number is large, somewhere around 106 to 108. The Rayleigh number is defined as the product of the Grashof number (), which describes the relationship between buoyancy and viscosity within a fluid, and the Prandtl number (), which describes the relationship between momentum diffusivity and thermal diffusivity: . Hence it may also be viewed as the ratio of buoyancy and viscosity forces multiplied by the ratio of momentum and thermal diffusivities: . It is closely related to the Nusselt number (). D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prandtl Number
The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as:where: * \nu : momentum diffusivity ( kinematic viscosity), \nu = \mu/\rho, ( SI units: m2/s) * \alpha : thermal diffusivity, \alpha = k/(\rho c_p), (SI units: m2/s) * \mu : dynamic viscosity, (SI units: Pa s = N s/m2) * k : thermal conductivity, (SI units: W/(m·K)) * c_p : specific heat, (SI units: J/(kg·K)) * \rho : density, (SI units: kg/m3). Note that whereas the Reynolds number and Grashof number are subscripted with a scale variable, the Prandtl number contains no such length scale and is dependent only on the fluid and the fluid state. The Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity. The mass transfer analog of the Prandtl number is the Schmidt number and the ratio of the Pran ... [...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] |
