Characteristic eddy

Figure 4.13 Characteristic eddy constructed from the first two eigenmodes and first three wavenumbers of a 3-dimensional EOF analysis of the three velocity components, scalar concentration, and static pressure. Contours of streamwise velocity fluctuation. Solid lines - positive dashed lines - negative bold line - zero.

The equation for turbulent dispersion was based on the classical development of Chen and Middleman (1967) (see Section 12-2), with the energy dissipation term calculated for drag on a cylinder. Two cases were assumed for the dissipation volume in the wake region behind the cylindrical impeller blade. The first was that an eddy length proportional to the cylinder diameter determined the dissipation volume. The second was that this volume was proportional to the velocity of the cylinder (tip speed) and a characteristic eddy decay time. Equation (12-74) results from the second case. It showed reasonable agreement with data taken at higher speeds. 

Moin, P. and Moser. R.D. (1989) Characteristic eddy decomposition of turbulence in a channel. J. Fluid Mech., 200. 471-509. 

So in order to improve selective characteristics of eddy current testing one should minimize phase change under interference factors influence. Analysis of the above characteristics has indicated that in case of interacting under-surface defects, there is an optimal frequency providing the best sensitivity to defect in amplitude. 

Methods from the theory of LTI-systems are practicable for eddy-current material testing problems. The special role of the impulse response as a characteristic function of the system sensor-material is presented in the theory and for several examples. 

So, a comparison of different types of magnetic field sensors is possible by using the impulse response function. High amplitude and small width of this bell-formed function represent a high local resolution and a high signal-to-noise-characteristic of a sensor system. On the other hand the impulse response can be used for calculation of an unknown output. In a next step it will be shown a solution of an inverse eddy-current testing problem. 

Davies (Turbulence Phenomena, Academic, New York, 1972) presents a good discussion of the spectrum of eddy lengths for well-developed isotropic turbulence. The smallest eddies, usually called Kolmogorov eddies (Kolmogorov, Compt. Rend. Acad. Sci. URSS, 30, 301 32, 16 [1941]), have a characteristic velocity fluctuation given by... 

Most of the energy dissipation occurs on a length scale about 5 times the Kolmogorov eddy size. The characteristic fluctuating velocity for these energy-dissipating eddies is about 1.7 times the Kolmogorov velocity. 

Figure 4-143 represents a computer-generated plot that demonstrates the effectiveness of eddy current brakes in preventing overspeed of the string. The lower curve assumes the butterfly valve characteristic is linear from 60° open to the closed position. The rate of closure is 3.25 sec. (Butterfly valves are normally used to throttle the expander inlet gas.)... 

HOTMAC/RAPTAD requires very extensive meteorological and terrain data input. The program user s guide and diagnostics are inadequate. HOTMAC does not model multiple scale eddy turbulence and does not provide for dispersion of gases that are denser-than air. It must be tailored to reflect the climatic characteristics of specific sites. 

Fine suspensions are reasonably homogeneous and segregation of solid and liquid phases does not occur to any significant extent during flow. The settling velocities of the particles are low in comparison with the liquid velocity and the turbulent eddies within the fluid are responsible for the suspension of the particles. In practice, turbulent flow will always be used, except when the liquid has a very high viscosity or exhibits non-Newtonian characteristics. The particles may be individually dispersed in the liquid or they may be present as floes. 

The principal characteristic of a particle which determines the dominant suspension mechanism is its terminal falling velocity. Particles with low falling velocities will be readily suspended by the action of the eddies, whereas the dispersive forces will be most important with particles of high falling velocities. In a particular case, of course, the fluid velocity will also be an important factor, full suspension of a given particle occurring more readily at high velocities. 

There are two principal characteristics of turbulence. One is the scale which is a measure of the mean size of the eddies, and the other is the intensity which is a function... 

In the mid-latitude region depicted in Fig. 7-5, the motion is characterized by large-scale eddy transport." Here the "eddies" are recognizable as ordinary high- and low-pressure weather systems, typically about 10 km in horizontal dimension. These eddies actually mix air from the polar regions with air from nearer the equator. At times, air parcels with different water content, different chemical composition and different thermodynamic characteristics are brought into contact. When cold dry air is mixed with warm moist air, clouds and precipitation occur. A frontal system is said to exist. Two such frontal systems are depicted in Fig. 7-5 (heavy lines in the midwest and southeast). 

Ekambra etal. [21] compared the results from ID, 2D, and 3D simulations of a bubble column with experimental results. They obtained similar results for holdup and axial velocity, while eddy viscosity, Reynolds stresses, and energy dissipation were very different in the three simulations as shown in Figure 15.7. This example also illustrates the importance of selecting the right variables for model vahdation. A 2D model will yield good results for velocity but will predict all variables based on turbulent characteristics poorly. 

In fluid dynamics the behavior in this system is described by the full set of hydrodynamic equations. This behavior can be characterized by the Reynolds number. Re, which is the ratio of characteristic flow scales to viscosity scales. We recall that the Reynolds number is a measure of the dominating terms in the Navier-Stokes equation and, if the Reynolds number is small, linear terms will dominate if it is large, nonlinear terms will dominate. In this system, the nonlinear term, (u V)u, serves to convert linear momentum into angular momentum. This phenomena is evidenced by the appearance of two counter-rotating vortices or eddies immediately behind the obstacle. Experiments and numerical integration of the Navier-Stokes equations predict the formation of these vortices at the length scale of the obstacle. Further, they predict that the distance between the vortex center and the obstacle is proportional to the Reynolds number. All these have been observed in our 2-dimensional flow system obstructed by a thermal plate at microscopic scales. ... 

Hydrodynamic effects on suspended particles in an STR may be broadly categorized as time-averaged, time-dependent and collision-related. Time-averaged shear rates are most commonly considered. Maximum shear rates, and accordingly maximum stresses, are assumed to occur in the impeller region. Time-dependent effects, on the other hand, are attributable to turbulent velocity fluctuations. The relevant turbulent Reynolds stresses are frequently evaluated in terms of the characteristic size and velocity of the turbulent eddies and are generally found to predominate over viscous effects. 

Flow of the liquid past the electrode is found in electrochemical cells where a liquid electrolyte is agitated with a stirrer or by pumping. The character of liquid flow near a solid wall depends on the flow velocity v, on the characteristic length L of the solid, and on the kinematic viscosity (which is the ratio of the usual rheological viscosity q and the liquid s density p). A convenient criterion is the dimensionless parameter Re = vLN, called the Reynolds number. The flow is laminar when this number is smaller than some critical value (which is about 10 for rough surfaces and about 10 for smooth surfaces) in this case the liquid moves in the form of layers parallel to the surface. At high Reynolds numbers (high flow velocities) the motion becomes turbulent and eddies develop at random in the flow. We shall only be concerned with laminar flow of the liquid. 

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