Dynamics eddy

The physical basis of the use of Fe— Si alloys, commonly called silicon steels, as soft magnetic materials is the fact that both the magnetocrystalline anisotropy isTi and the magnetostriction parameters >.100 and Xm of Fe approach zero with increasing Si content (see Fig. 4.3-5a). The lower the magnitude of these two intrinsic magnetic properties is, the lower are the coercivity He and the AC magnetic losses The total losses ppe consist of the static hysteresis losses p y and the dynamic eddy current losses pw which may be subdivided into a classical p c and an anomalous p eddy current loss term. 

In addition to the distortions caused by the probes, there were also distortions caused by filtering the signals within the eddy-current test instruments. To achieve the highest possible dynamics with the test instruments, high-pass filters with a high rate of rise, but also a long reverberation time were used. Thus, the recorded C-scan pictures sometimes shows strong echo effects. 

If a fluid is placed between two concentric cylinders, and the inner cylinder rotated, a complex fluid dynamical motion known as Taylor-Couette flow is established. Mass transport is then by exchange between eddy vortices which can, under some conditions, be imagmed as a substantially enlranced diflfiisivity (typically with effective diflfiision coefficients several orders of magnitude above molecular difhision coefficients) that can be altered by varying the rotation rate, and with all species having the same diffusivity. Studies of the BZ and CIMA/CDIMA systems in such a Couette reactor [45] have revealed bifiircation tlirough a complex sequence of front patterns, see figure A3.14.16. 

The Prandtl mixing length concept is useful for shear flows parallel to walls, but is inadequate for more general three-dimensional flows. A more complicated semiempirical model commonly used in numerical computations, and found in most commercial software for computational fluid dynamics (CFD see the following subsection), is the A — model described by Launder and Spaulding (Lectures in Mathematical Models of Turbulence, Academic, London, 1972). In this model the eddy viscosity is assumed proportional to the ratio /cVe. 

When the two liquid phases are in relative motion, the mass transfer coefficients in eidrer phase must be related to die dynamical properties of the liquids. The boundary layer thicknesses are related to the Reynolds number, and the diffusive Uansfer to the Schmidt number. Another complication is that such a boundaty cannot in many circumstances be regarded as a simple planar interface, but eddies of material are U ansported to the interface from the bulk of each liquid which change the concenuation profile normal to the interface. In the simple isothermal model there is no need to take account of this fact, but in most indusuial chcumstances the two liquids are not in an isothermal system, but in one in which there is a temperature gradient. The simple stationary mass U ansfer model must therefore be replaced by an eddy mass U ansfer which takes account of this surface replenishment. 

Another detailed method of determining pressures is computational fluid dynamics (CFD), which uses a numerical solution of simplified equations of motion over a dense grid of points around the building. Murakami et al. and Zhoy and Stathopoulos found less agreement with computational fluid dynamics methods using the k-e turbulence model typically used in current commercial codes. More advanced turbulence models such as large eddy simulation were more successful but much more costly. ... 

David.son, L, Large eddy simulation A dynamic one-equation subgrid model for three-dimensional recirculating flow. In llth Int. Symp. on Turbulent Shear Flow, vol. 3, pp. 26.1-26.6, Grenoble, 1997. 

We recall from our earlier discussion of chaos in one-dimensional continuous systems (see section 4.1) that period-doubling is not the only mechanism by which chaos can be generated. Another frequently occurring route to chaos is intermittency. But while intermittency in low dimensional dynamical systems appears to be constrained to purely temporal behavior [pomeau80], CMLs exhibit a spatio-temporal intermittency in which laminar eddies are intermixed with turbulent regions in a complex pattern in space-time. 

For an incompressible viscous fluid (such as the atmosphere) there are two types of flow behaviour 1) Laminar, in which the flow is uniform and regular, and 2) Turbulent, which is characterized by dynamic mixing with random subflows referred to as turbulent eddies. Which of these two flow types occurs depends on the ratio of the strengths of two types of forces governing the motion lossless inertial forces and dissipative viscous forces. The ratio is characterized by the dimensionless Reynolds number Re. 

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. ... 

In the velocity field of the determining eddies, which is characterized by the turbulent fluctuation velocity the particles experience a dynamic stress according to the Reynolds stress Eq. (2) ... 

For the following we assume that the atmospheric variations in C02 and in its carbon isotopic composition are entirely due to atmospheric system disturbances, such as the input of 14C-free C02 from fossil C02 production, and deviations from the average rate of 14C production by cosmic radiation. The system dynamics, i.e., the exchange coefficients and the eddy diffusivity are kept constant. We approximate the fossil C02 input p(t) by... 

Of all of the methods reviewed thus far in this book, only DNS and the linear-eddy model require no closure for the molecular-diffusion term or the chemical source term in the scalar transport equation. However, we have seen that both methods are computationally expensive for three-dimensional inhomogeneous flows of practical interest. For all of the other methods, closures are needed for either scalar mixing or the chemical source term. For example, classical micromixing models treat chemical reactions exactly, but the fluid dynamics are overly simplified. The extension to multi-scalar presumed PDFs comes the closest to providing a flexible model for inhomogeneous turbulent reacting flows. Nevertheless, the presumed form of the joint scalar PDF in terms of a finite collection of delta functions may be inadequate for complex chemistry. The next step - computing the shape of the joint scalar PDF from its transport equation - comprises transported PDF methods and is discussed in detail in the next chapter. Some of the properties of transported PDF methods are listed here. 

A large-eddy simulation scheme for turbulent reacting flows. Physics of Fluids A Fluid Dynamics 5,1282-1284. 

Germano, M., U. Piomelli, P. Moin, and W. H. Cabot (1991). A dynamic subgrid-scale eddy viscosity model. Physics of Fluids 7, 1760-1765. 

Vedula, P., P. K. Yeung, and R. O. Fox (2001). Dynamics of scalar dissipation in isotropic turbulence A numerical and modeling study. Journal of Fluid Mechanics 433, 29-60. Verman, B., B. Geurts, and H. Kuertan (1994). Realizability conditions for the turbulent stress tensor in large-eddy simulations. Journal of Fluid Mechanics 278, 351-362. Vervisch, L. (1991). Prise en compte d effets de cinetique chimique dans lesflammes de diffusion turbulente par Tapproche fonction densite de probabilite. Ph. D. thesis, Universite de Rouen, France. 

CE is a technique with a very high power of resolution. This is attributed to low diffusion and high plate numbers obtained from the absence of band-broadening factors (e.g., eddy diffusion, equilibrium dynamics, etc.) other than diffusion, which is also minimized by short analysis time. 

Boris, J.P., F. F. Grinstein, E. S. Oran, and R. L. Kolbe. 1992. New insights into large eddy simulation. Fluid Dynamics Research 10 199-228. 

Jaberi, F. A., and S. A. James. 1998. A dynamic similarity model for large eddy simulation of turbulent combustion. J. Physics Fluids 10(7) 1775-77. 

---