Mean turbulent energy structure

The acronyms for closure type used in this review are as follows FVF, fluctuating velocity field MVF, mean-velocity field MVFN, Newtonian MVF MTE, mean turbulent energy MTEN, Newtonian MTE MTOS, structural MTE MTEN/L, MTEN closure with dynamical length scale equation MRS, mean Reynolds-stress MRS/L, MRS closure with dynamical length scale equation. 

Earlier it was stated that the structure of a turbulent velocity field may be presented in terms of two parameters—the scale and the intensity of turbulence. The intensity was defined as the square root of the turbulent kinetic energy, which essentially gives a root-mean-square velocity fluctuation U. Three length scales were defined the integral scale l0, which characterizes... 

Earlier it was stated that the structure of a turbulent velocity field may be presented in terms of two parameters—the scale and the intensity of turbulence. The intensity was defined as the square root of the turbulent kinetic energy, which essentially gives a root-mean-square velocity fluctuation U. Three length scales were defined the integral scale /q, which characterizes the large eddies the Taylor microscale X, which is obtained from the rate of strain and the Kolmogorov microscale 1, which typifies the smallest dissipative eddies. These length scales and the intensity can be combined to form not one, but three turbulent Reynolds numbers Ri = U lo/v, Rx. = U X/v, and / k = U ly/v. From the relationship between Iq, X, and /k previously derived it is found that / ... 

As discussed in Chapter 3, with LES, the smallest scale to be resolved is chosen to lie in the inertial sub-range of the energy spectrum, which means the so-called sub-grid scale (SGS) wave numbers are not resolved. As LES can capture transient large-scale flow structures, it has the potential to accurately predict time-dependent macromixing phenomena in the reactors. However, unlike DNS, a SGS model representing interaction of turbulence and chemical reactions will be required in order to predict the effect of operating parameters on say product yields in chemical reactor simulations. These SGS models attempt to represent an inherent loss of SGS information, such as the rate of molecular diffusion, in an LES framework. Use of such SGS models makes the LES approach much less computationally intensive than the DNS approach. DNS... 

Turbulent flow in the jackets with triangular helical ducts is simulated applied CFD software. The fully developed flow field and the distribution of the turbulence kinetic energy are obtained. When turbulent fluid flows in the jackets, the structure of secondary flow in the cross section is steady two vortices. The turbulent kinetic energy near the outer walls is larger than that near the inner wall. The fRe oc on the inner wall is almost symmetric about / = 0 and the variation of/ iocai on the outer walls with y is vastly different from that on the inner wall. In the study range, the mean coefficient of resistance on the outer walls is about 1.41 1.57 times of that on the inner wall. The effects of Re and k on the flow field, the local coefficient of resistance at the boundary walls and the mean coefficient of resistance are analyzed. With the increase o Re, the intensity of secondary flow and the turbulent kinetic energy are all enhanced and the /K iocai on the boundary walls is increased as well. However, the locai near the center of the inner wall decreases with increasing k. The mean coefficient of resistance can increase as Re or k increases. 

U, L, H are the characteristic velocity, length and layer thickness scales. L/j is the Rossby deformation radius. The Rossby number measures the importance of rotation on the flow, the Burger number measures the stratification in the atmosphere via the Brunt-Vaisala frequency. As it is known, the atmospheric structure in the giant planets in the solar system is in bands. This structure evolves from shallow-water turbulence. Two dimensional turbulence is characterized by an inverse energy cascade—this means a transfer from small to large scales. 

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