Fluid turbulence

Turbulence in any system is characterized by chaotic motion of the fluid/particles in time and space. The fluid velocity vector, u, at any time is the sum of u, the time average velocity, and u[, the instantaneous fluctuating component 

The instantaneous fluctuating component (m ) can be negative or positive. However, the time average of m, m = 0. The amplitude of (m ) is conventionally expressed as and is always positive. is considered as a measure 

Turbulence intensity is a major factor governing transport processes. It will be shown later that simple, measurable parameters or parameters that can be readily calculated are useful as a substitute for the somewhat esoteric turbulence intensity. Such a substitute can then be used to obtain correlations for mass transfer coefficient in multiphase reactors. 

Most complex phenomena are made tractable using cases that are far simpler than the real phenomena. Examples of this type of approach abound in many areas of sci-ence/engineering starting with the ideal gas law for predicting fluid properties. This ideal case is then considered as the basis, and the deviations from this ideal case (fugacity/activity coefficient) represent the behavior of the real system. In the case of turbulence, two classes are defined. 

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Example The equation dQ/dx = (A/f/)(3 6/3f/ ) with the boundary conditions 0 = OatA.=O, y>0 6 = 0aty = oo,A.>0 6=iaty = 0, A.>0 represents the nondimensional temperature 6 of a fluid moving past an infinitely wide flat plate immersed in the fluid. Turbulent transfer is neglected, as is molecular transport except in the y direction. It is now assumed that the equation and the boundary conditions can be satisfied by a solution of the form 6 =f y/x ) =j[u), where 6 =... 

GASFLOW models geometrically complex containments, buildings, and ventilation systems with multiple compartments and internal structures. It calculates gas and aerosol behavior of low-speed buoyancy driven flows, diffusion-dominated flows, and turbulent flows dunng deflagrations. It models condensation in the bulk fluid regions heat transfer to wall and internal stmetures by convection, radiation, and condensation chemical kinetics of combustion of hydrogen or hydrocarbon.s fluid turbulence and the transport, deposition, and entrainment of discrete particles. 

Whenee the fluid turbulence attrition rate is given by... 

Before discussing the on.set, and nature, of fluid turbulence, it is convenient to first recast the Navier-Stokes equations into a dimensionless form, a trick first used by Reynolds in his pioneering experimental work in the 1880 s. In this form, the Navier-Stokes equations depend on a single dimensionless number called Reynolds number, and fluid behavior from smooth, or laminar, flow to chaos, or turbulence,... 

How does this relate to fluid turbulence The idea is that there exists a critical value of the Reynolds number, TZe, such that intermittent turbulent behavior can appear in the system for TZ > TZe- Moreover, if the behavior of the Lorenz system correctly identifies the underlying mechanism, it may be predicted that, as TZ changes, (1) the duration of the intermittently turbulent behavior will be random, and (2) the mean duration of the laminar phases in between will vary as... 

The conveying of fine particles in vertical pipes of diameters 25 mm, 50 mm, and 75 mm has been studied by BoOTHROYD(75 . He measured the pressure gradient in the pipeline, and found that the frictional pressure drop was less than that for air alone in the 25 mm pipe, but was greater in the larger pipes. This effect was attributed to the fact that the extent to which the fluid turbulence was affected by the presence of the particles was markedly influenced by pipe size. 

A screen with 100 U.S. mesh (149 micrometer) openings was placed at the bottom of the test column to prevent the production of coarse sand particles from the test column. To avoid injection fluid turbulence disturbing the test sand, a 7.5g layer of 20-40 U.S. mesh sand was placed on top of the test sand. All fluids except polymer solutions were filtered prior to injection. Polymer solutions were injected at 5 psia and immediately followed by aqueous fluid at 40 psig. Effluent fluids were collected and filtered through 0.45 micron paper to collect the produced fine particles. 

Most examples of flow in nature and many in industry are turbulent. Turbulence is an instability phenomenon caused, in most cases, by the shearing of the fluid. Turbulent flow is characterized by rapid, chaotic fluctuations of all properties including the velocity and pressure. This chaotic motion is often described as being made up of eddies but it is important to appreciate that eddies do not have a purely circular motion. 

McComb, W.D., The Physics of Fluid Turbulence, Oxford, Oxford University Press, 1990. 

A fluidized bed is made up of a mass of particles buoyed up out of permanent contact with each other by a flowing fluid. Turbulent activity in such a bed promotes high rates of heat and mass transfer and uniformity of temperature and composition throughout. The basic system includes a solids feeding device, the fluidizing chamber with a perforated distributing plate for the gas, an overflow duct for removal of the dry product, a cyclone and other equipment for... 

Once particles are present in a volume of gas, they collide and agglomerate by different processes. The coagulation process leads to substantial changes in particle size distribution with time. Coagulation may be induced by any mechanism that involves a relative velocity between particles. Such processes include Brownian motion, shearing flow of fluid, turbulent motion, and differential particle motion associated with external force fields. The theory of particle collisions is quite complicated even if each of these mechanisms is isolated and treated separately. 

The effect of fluid turbulence, in so far as a suspension of particles is concerned, is to cause the particles to be agitated in conformity with the motion of the fluid. This effect applies generally to small particles which do not settle rapidly, and to concentrations not so great as to interfere with the free motion of turbulence in the fluid. Under these conditions, in the case of a fluid moving over a bed of fine materials, we may write that... 

At low velocities between the metal and the solution, the solution flow is laminar, while at high velocities it is turbulent. The transition velocity depends on the geometry, flow rate, liquid viscosity, and surface roughness. The Reynolds number accounts for these effects and predicts the transition from laminar to fluid turbulent flow. The Reynolds number is the ratio of convective to viscous forces in the fluid. For pipes experiencing flow parallel to the centerline of the pipe (4,8) ... 

Erosion corrosion is caused by the conjoint action of corrosion and mechanical abrasion by a moving fluid or suspended material in the fluid. Turbulent flow or jets of liquid on a metal surface may lead to erosion corrosion. The mechanical action of the fluid removes the protective corrosion deposit, thus exposing fresh metal to the corrosive. As corrosion products build up, they are removed and so the process continues. The surface of a piece of metal exposed to this type of corrosion has a characteristic structure (Fig. 8). 

The parameter D is usually called a turbulent (or eddy) diffusion coefficient when it arises from fluid turbulence its value varies enormously from one situation to another, depending on the intensity of turbulence and on whether the environmental medium is air or water. The diagram in Fig. 1-6 shows the Fickian mass flux arising from a concentration gradient in a smoke plume. 

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