Turbulence statistical

In isotropic turbulence, statistical measures of fluctuations are equal in all directions. 

Second, due to the difficulty of accessing multiphase flows with laser-based flow diagnostics, there is very little experimental data available for validating multiphase turbulence models to the same degree as done in single-phase turbulent flows. For example, thanks to detailed experimental measurements of turbulence statistics, there are many cases for which the single-phase k- model is known to yield poor predictions. Nevertheless, in many CFD codes a multiphase k-e model is used to supply multiphase turbulence statistics that cannot be measured experimentally. Thus, even if a particular multiphase turbulent flow could be adequately described using an effective viscosity, in most cases it is impossible to know whether the multiphase turbulence model predicts reasonable values for... 

Owing to the complexity of multi-point descriptions, almost all CFD models for complex turbulent flows are based on one-point turbulence statistics. As shown in Section 2.1, one-point turbulence statistics are found by integrating over the velocity sample space, e.g.,... 

Table 2.4. The turbulence statistics and unclosed quantities appearing in the transport equations for high-Reynolds-number inhomogeneous turbulent flows. 

For convenience, the turbulence statistics used in engineering calculations of inhomogeneous, high-Reynolds-number turbulent flows are summarized in Table 2.4 along with the unclosed terms that appear in their transport equations. Models for the unclosed terms are discussed in Chapter 4. 

Thus, like the turbulence dissipation rate, the scalar dissipation rate of an inert scalar is primarily determined by the rate at which spectral energy enters the scalar dissipation range. Most engineering models for the scalar dissipation rate attempt to describe (kd, t) in terms of one-point turbulence statistics. We look at some of these models in Chapter 4. 

For simple flows where the mean velocity and/or turbulent diffusivity depend only weakly on the spatial location, the Eulerian PDF algorithm described above will perform adequately. However, in many flows of practical interest, there will be strong spatial gradients in turbulence statistics. In order to resolve such gradients, it will be necessary to use local grid refinement. This will result in widely varying values for the cell time scales found from (7.13). The simulation time step found from (7.15) will then be much smaller than the characteristic cell time scales for many of the cells. When the simulation time step is applied in (7.16), one will find that Ni must be made unrealistically large in order to satisfy the constraint that Nf > 1 for all k. 

First, the distribution of the concentration of the tracer is estimated based on the turbulent statistical characteristics such as the mean velocity profile and the intensity of velocity fluctuations. (The method for obtaining the distribution of the tracer concentration is given in detail in the original paper.5 Second, mixedness M based on the distribution of the concentration of the tracer in the cross-section at an arbitrary distance along the axial direction is calculated by using Eq. (2.18). 

Traditional scale-up rules Table 4.2 (These scale-up rules have been used for many types of equipment scale-ups, e.g., the stirred vessel for mixing of the fluids that have no reaction ability. It is clarified that the distribution of the dimensionless turbulent statistical values by making use of impeller tip velocity UT(= ND) becomes identical regardless of impeller rotational... 

Zhang, W., Hamer, A., Klassen, M., Carpenter, D., and Roby, R. Turbulence statistics in a fire room model by large eddy simulation. Fire Safety Journal, 2002. 37(8), 721-752. 

Kim, J., Moin, P., and Moser, R. D., Turbulence Statistics in fully-developed channel flow at low Reynolds number. J. Fluid Mech. T1,133 (1987). 

The first stage in FCM calculations for complex flows is to compute the mean flow and the turbulence statistics and then to use these data in computations of the concentration distribution. As explained in Section 2.3, for well separated buildings, (b/d 1), in the atmospheric boundary layer (e.g. in the suburban situation), the usual methods... 

Plant canopies exhibit remarkable turbulence statistics, which makes canopy aerodynamics a topic of substantial scientific interest. Of particular note are the degree to which vertical and streamwise velocities are correlated, and the high degree of skewness in these two velocity components. The correlation coefficient that relates stream-wise and vertical velocities, defined as... 

The turbulence statistics included in the right-hand-side of (6.38) have similar profile shapes across a free-shear-layer, with maximum values uw = -0.01 AC/2, u 2 = 0.03AU2,w 2 = 0.015AU2, and v 2 = 0.02AU2, where AU = u2 - ux is the velocity... 

Table 6.1 Turbulence statistics evaluated at the top of canopy. In all cases H/h> 2 and 6e < 1, to ensure that shear-layer dynamics are not influenced by other boundaries. Uh not available for Katul and Change [329], so an estimated value is based on Amiro Pine [9].

Rotach, M.W. (1995) Profiles of turbulence statistics in and above an urban street canyon, Atmospheric Environment 29, 1473-1486. 

Prof. Julian Hunt (University College London) introduces a classification of the types of turbulent flow through canopies of different kinds of geometry and length scale. He shows how, by integrating recently developed concepts by many authors, a more comprehensive understanding of eddy structure and turbulence statistics is now emerging. In the atmosphere where canopies may extend over tens of kilometres in... 

As indicated in the introduction (Section 4.2.3.1) of this section, many different techniques may be applied to induce irregular movement which will cause collisions and, if sufficiently high adhesion forces are present, bonding (agglomeration). In addition to rotating discs, drums, mixers of all kinds, fluidized beds, vibrating and shaking conveyors, etc., many other methods to produce turbulent, statistic particle movement are possible. 

RANS, under which the Reynolds-averaged Navier Stokes equations are solved using some type of closure assumption to account for the Reynolds stress terms. RANS provides the values of the mean wind velocity and estimates of the turbulence statistics within the model domain. 

Multiply the result of step 3 by other turbulent quantities and time- or ensemble average to 4eld the transport equations for turbulence statistics such as the Reynolds stresses and the turbulent kinetic energy. 

Shih T-H, Liou WW, Shabbir A, Zhu J (1995) A New k-e Eddy Viscosity Model for High Reynolds Number Turbulent Elows. Comp Eluids 24(3) 227-238 Smith LM, Reynolds WC (1992) On the Yakhot-Orszag renormalization group method for deriving turbulence statistics and models. Phys Fluids A 4(2) 364-390... 

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