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Particle-laden Flow
Particle-laden flows refers to a class of Two-phase flow, two-phase fluid flow, in which one of the phases is continuously connected (referred to as the continuous or carrier phase) and the other phase is made up of small, immiscible, and typically dilute particles (referred to as the dispersed or particle phase). Fine aerosol particles in air is an example of a particle-laden flow; the aerosols are the dispersed phase, and the air is the carrier phase. The modeling of two-phase flows has a tremendous variety of engineering and scientific applications: pollution dispersion in the atmosphere, fluidization in combustion processes, aerosol deposition in spray medication, along with many others. Governing equations The starting point for a mathematical description of almost any type of fluid flow is the classical set of Navier–Stokes equations. To describe particle-laden flows, we must modify these equations to account for the effect of the particles on the carrier, or vice versa, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-phase Flow
In fluid mechanics, two-phase flow is a flow of gas and liquid — a particular example of multiphase flow. Two-phase flow can occur in various forms, such as flows transitioning from pure liquid to vapor as a result of external heating, separated flows, and dispersed two-phase flows where one phase is present in the form of particles, droplets, or bubbles in a continuous carrier phase (i.e. gas or liquid). Categorization The widely accepted method to categorize two-phase flows is to consider the velocity of each phase as if there is not other phases available. The parameter is a hypothetical concept called Superficial velocity. Examples and applications Historically, probably the most commonly studied cases of two-phase flow are in large-scale power systems. Coal and gas-fired power stations used very large boilers to produce steam for use in turbines. In such cases, pressurised water is passed through heated pipes and it changes to steam as it moves through the pipe. The d ... [...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 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navier–Stokes Equations
In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes). The Navier–Stokes equations mathematically express conservation of momentum and conservation of mass for Newtonian fluids. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing ''viscous flow''. The difference between them and the closely related Euler equations is that Navier–Stokes equations take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eulerian Reference Frame
__NOTOC__ In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time. Plotting the position of an individual parcel through time gives the pathline of the parcel. This can be visualized as sitting in a boat and drifting down a river. The Eulerian specification of the flow field is a way of looking at fluid motion that focuses on specific locations in the space through which the fluid flows as time passes. This can be visualized by sitting on the bank of a river and watching the water pass the fixed location. The Lagrangian and Eulerian specifications of the flow field are sometimes loosely denoted as the Lagrangian and Eulerian frame of reference. However, in general both the Lagrangian and Eulerian specification of the flow field can be applied in any observer's frame of reference, and in any coordinate system used within the chosen f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basset–Boussinesq–Oseen Equation
In fluid dynamics, the Basset–Boussinesq–Oseen equation (BBO equation) describes the motion of – and forces on – a small particle in unsteady flow at low Reynolds numbers. The equation is named after Joseph Valentin Boussinesq, Alfred Barnard Basset and Carl Wilhelm Oseen. Formulation The BBO equation, in the formulation as given by and , pertains to a small spherical particle of diameter d_p having mean density \rho_p whose center is located at \boldsymbol_p(t). The particle moves with Lagrangian velocity \boldsymbol_p(t)=\text \boldsymbol_p / \textt in a fluid of density \rho_f, dynamic viscosity \mu and Eulerian velocity field \boldsymbol_f(\boldsymbol,t). The fluid velocity field surrounding the particle consists of the undisturbed, local Eulerian velocity field \boldsymbol_f plus a disturbance field – created by the presence of the particle and its motion with respect to the undisturbed field \boldsymbol_f. For very small particle diameter the latter is locally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stokes' Law
In 1851, George Gabriel Stokes derived an expression, now known as Stokes' law, for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers in a viscous fluid. Stokes' law is derived by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations.Batchelor (1967), p. 233. Statement of the law The force of viscosity on a small sphere moving through a viscous fluid is given by: :F_ = 6 \pi \mu R v where: * ''F''d is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle * ''μ'' is the dynamic viscosity (some authors use the symbol ''η'') * ''R'' is the radius of the spherical object * ''v'' is the flow velocity relative to the object. In SI units, ''F''d is given in newtons (= kg m s−2), ''μ'' in Pa·s (= kg m−1 s−1), ''R'' in meters, and ''v'' in m/s. Stokes' law makes the following assumptions for the behavior of a particle i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent. Turbulence is caused by excessive kinetic energy in parts of a fluid flow, which overcomes the damping effect of the fluid's viscosity. For this reason turbulence is commonly realized in low viscosity fluids. In general terms, in turbulent flow, unsteady vortices appear of many sizes which interact with each other, consequently drag due to friction effects increases. This increases the energy needed to pump fluid through a pipe. The onset of turbulence can be predicted by the dimensionless Rey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Direct Numerical Simulation
A direct numerical simulation (DNS)Here the origin of the term ''direct numerical simulation'' (see e.g. p. 385 in ) owes to the fact that, at that time, there were considered to be just two principal ways of getting ''theoretical'' results regarding turbulence, namely via turbulence theories (like the direct interaction approximation) and ''directly'' from solution of the Navier–Stokes equations. is a simulation in computational fluid dynamics (CFD) in which the Navier–Stokes equations are numerically solved without any turbulence model. This means that the whole range of spatial and temporal scales of the turbulence must be resolved. All the spatial scales of the turbulence must be resolved in the computational mesh, from the smallest dissipative scales (Kolmogorov microscales), up to the integral scale L, associated with the motions containing most of the kinetic energy. The Kolmogorov scale, \eta, is given by :\eta=(\nu^/\varepsilon)^ where \nu is the kinematic visco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reynolds-averaged Navier–Stokes Equations
The Reynolds-averaged Navier–Stokes equations (RANS equations) are time-averaged equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition, whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities, an idea first proposed by Osborne Reynolds. The RANS equations are primarily used to describe turbulent flows. These equations can be used with approximations based on knowledge of the properties of flow turbulence to give approximate time-averaged solutions to the Navier–Stokes equations. For a stationary flow of an incompressible Newtonian fluid, these equations can be written in Einstein notation in Cartesian coordinates as: \rho\bar_j \frac = \rho \bar_i + \frac \left - \bar\delta_ + \mu \left( \frac + \frac \right) - \rho \overline \right The left hand side of this equation represents the change in mean momentum of a fluid element owing to the unsteadiness in the mean flow and the convection by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Large Eddy Simulation
Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents, and first explored by Deardorff (1970). LES is currently applied in a wide variety of engineering applications, including combustion, acoustics, and simulations of the atmospheric boundary layer. The simulation of turbulent flows by numerically solving the Navier–Stokes equations requires resolving a very wide range of time and length scales, all of which affect the flow field. Such a resolution can be achieved with direct numerical simulation (DNS), but DNS is computationally expensive, and its cost prohibits simulation of practical engineering systems with complex geometry or flow configurations, such as turbulent jets, pumps, vehicles, and landing gear. The principal idea behind LES is to reduce the computational cost by ignoring the smallest length scales, which are the most co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer. The air next to a human is heated resulting in gravity-induced convective airflow, airflow which results in both a velocity and thermal boundary layer. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the velocity boundary layer is the part of the flow close to the wing, where viscous forces distort the surrounding non-viscous flow. In the Earth's atmosphere, the atmospheric boun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turbophoresis
Turbophoresis is the tendency for particles to migrate in the direction of decreasing turbulence level. The principle tends to segregate particles entrained in high velocity gases axially toward the wall region. Caporaloni et al. (1975) first found that because the vertical gradient of turbulence near a depositing surface is large, turbophoresis is expected to enhance rate of particle deposition onto the surface. It was also predicted independently by Reeks (1983) who derived it rigorously from the particle kinetic equation and showed that it arose from a force balance between the net drag force and the gradient of the particle kinetic stresses acting on the particles due to the turbulence. He predicted that this would lead to a buildup of concentration near the wall, a feature which has been observed both experimentally and in Direct Numerical Simulation A direct numerical simulation (DNS)Here the origin of the term ''direct numerical simulation'' (see e.g. p. 385 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
