Turbulence Kolmogorov length scale

Rate of turbulence production (m s ) Velocity of a turbulent eddy of size X Rate of turbulence dissipation (m s ) Kolmogorov length scale (m)... 

Cherry and Papoutsakis [33] refer to the exposure to the collision between microcarriers and influence of turbulent eddies. Three different flow regions were defined bulk turbulent flow, bulk laminar flow and boundary-layer flow. They postulate the primary mechanism coming from direct interactions between microcarriers and turbulent eddies. Microcarriers are small beads of several hundred micrometers diameter. Eddies of the size of the microcarrier or smaller may cause high shear stresses on the cells. The size of the smallest eddies can be estimated by the Kolmogorov length scale L, as given by... 

An alternative approach (e.g., Patterson, 1985 Ranade, 2002) is the Eulerian type of simulation that makes use of a CDR equation—see Eq. (13)—for each of the chemical species involved. While resolution of the turbulent flow down to the Kolmogorov length scale already is far beyond computational capabilities, one certainly has to revert to modeling the species transport in liquid systems in which the Batchelor length scale is smaller than the Kolmogorov length scale by at least one order of magnitude see Eq. (14). Hence, both in RANS simulations and in LES, species concentrations and temperature still fluctuate within a computational cell. Consequently, the description of chemical reactions and the transport of heat and species in a chemical reactor ask for subtle approaches as to the SGS fluctuations. 

In this definition, ps and pt are the solid and fluid densities, respectively. The characteristic diameter of the particles is ds (which is used in calculating the projected cross-sectional area of particle in the direction of the flow in the drag law). The kinematic viscosity of the fluid is vf and y is a characteristic strain rate for the flow. In a turbulent flow, y can be approximated by l/r when ds is smaller than the Kolmogorov length scale r. (Unless the turbulence is extremely intense, this will usually be the case for fine particles.) Based on the Stokes... 

This model further assumes that the size of the parent particles is in the inertial subrange of turbulence. Therefore, it implies that dmin < d < dmax provided that dmin > Ad, where Ad is the Kolmogorov length scale of the underlying turbulence. Otherwise, dmin is taken to be equal to Ad. However, no assumption needs to be made about the minimum and maximum eddy size that can cause particle breakage. All eddies with sizes between the Kolmogorov scale and the integral scale are taken into account. 

For the species concentration field, the scalar integral scale and the Batchelor scale characterize respectively the largest and the smallest eddies. In most cases, the scalar integral scale is approximately equal to the turbulence integral scale. The Batchelor length scale, on the other hand, is related to the Kolmogorov length scale via the Schmidt number, Sc=nlpD ... 

Balachandar (2009) translated turbulence intensity into the ratio of integral length scale to Kolmogorov length scale of the turbulent flow field (see also below) which in fact is a function of the bulk flow Reynolds number. Kim and Balachandar (2012) also emphasized the role of selfrinduced vortex... 

Homann et al (2015) concluded the relevant parameter to be the ratio of the viscous boundary layer thickness to the Kolmogorov length scale of the ambient turbulent flow. Other authors—such as MageUi et al (1990), Brucato et al (1998), and PineUi et al (2004)—considered the ratio of particle size to the Kolmogorov length scale r] rather than a ratio of time scales and correlate their experimental data with this length scale ratio only. This approach will be discussed in greater detail in the next section. 

Two important length scales for describing turbulent mixing of an inert scalar are the scalar integral scale L, and the Batchelor scale A.B. The latter is defined in terms of the Kolmogorov scale r] and the Schmidt number by... 

The time step required for accurate solutions of (4.3) is limited by the need to resolve the shortest time scales in the flow. In Chapter 3, we saw that the smallest eddies in a homogeneous turbulent flow can be characterized by the Kolmogorov length and time scales. Thus, the time step h must satisfy3 /V l/2... 

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