Scale turbulence

When using LES, the time-dependent three-dimensional momentum and continuity are solved for. A subgrid turbulence model is used to mode the turbulent scales that are smaller than the cells. Instead of the traditional time averaging, the equations for using LES are filtered in space, and is a function of space and time. 

Heckman, Behavior of Turbulent Scales in Hypersonic Sphere Wakes , Rept No DREV-R-696/73 Contract DAAH01-69-C-0921, ARPA Order — 133, Defence Res Est, Valcartier (Can) (1973) 42) Ya.L. Al pert, Waves and Satel-... 

Ultrasonic Doppler velocimetry is a nonintrusive technique that has been developed into a very useful technique for opaque liquid flows [3]. This technique provides good measurement of velocity new high-frequency techniques give a space resolution on the millimeter level, and even the large turbulent scales can be resolved. 

In reactor design, it is very important to know how and where turbulence is generated and dissipated. In a liquid phase, it is also important that the smallest eddies are sufficiently small. The ratio between the reactor scale (I) and the smallest turbulent scale, the Kolmogorof scale rj), usually scales as L/x]aR . The Kolmogorov scale can also be estimated from the viscosity and the power dissipation T] = (v 30 xm in water with a power input of 1W kg and from the Bachelor scale 3 pm in liquids. For a liquid, the estimation of the time... 

Usually, however, the stresses are modeled with the help of a single turbulent viscosity coefficient that presumes isotropic turbulent transport. In the RANS-approach, a turbulent or eddy viscosity coefficient, vt, covers the momentum transport by the full spectrum of turbulent scales (eddies). Frisch (1995) recollects that as early as 1870 Boussinesq stressed turbulence greatly increases viscosity and proposed an expression for the eddy viscosity. The eventual set of equations runs as... 

Two questions arise from this result. Do lobsters use only chemical and not mechanosensory information, and why do lobsters not use ground reference and head up-current Since turbulent odor dispersal is based on water flow patterns, we must investigate the role of microflow patterns in plume orientation behavior. As for ground reference, we speculate that the flow patterns of the lobster s natural environment may be too complex to allow for efficient rheotactic behavior in odor source localization. This complexity is most likely caused by a mismatch between turbulent scales and animal body size and sampling scales. 

Re = 3.65 X 10 for turbulence-free flow). No effect of turbulence scale was detected. The data of Torobin and Gauvin do not (C7, Ul) readily extrapolate to those of Dry den et al Whether the mismatch results from differences between fixed and entrained particles or from differences in turbulence characteristics is not clear. In the absence of further experimental data, Re can be estimated by modifying the empirical equations proposed by Clift and Gauvin (C7), neglecting the weak effect of d/L ... 

Experimental data are available for large particles at Re greater than that required for wake shedding. Turbulence increases the rate of transfer at all Reynolds numbers. Early experimental work on cylinders (VI) disclosed an effect of turbulence scale with a particular scale being optimal, i.e., for a given turbulence intensity the Nusselt number achieved a maximum value for a certain ratio of scale to diameter. This led to speculation on the existence of a similar effect for spheres. However, more recent work (Rl, R2) has failed to support the existence of an optimal scale for either cylinders or spheres. A weak scale effect has been found for spheres (R2) amounting to less than a 2% increase in Nusselt number as the ratio of sphere diameter to turbulence macroscale increased from zero to five. There has also been some indication (M15, S21) that the spectral distribution of the turbulence affects the transfer rate, but additional data are required to confirm this. The major variable is the intensity of turbulence. Early experimental work has been reviewed by several authors (G3, G4, K3). 

Two other points about the present state of experimental work should be mentioned. One is that measurements of turbulence scale and intensity are necessarily made in the cold flow the flame may upset the flow field, even generating added turbulence as suggested by Karlovitz (42). The second point is that the flame can never be thought of as burning in a region with constant scale and intensity throughout, not only because of the ordinary decay of turbulent fluctuations, but also because there may be (as in Bunsen... 

The three main numerical approaches used in turbulence combustion modeling are Reynolds averaged Navier Stokes (RANS) where all turbulent scales are modeled, direct numerical simulations (DNS) where all scales are resolved and large eddy simulations (LES) where larger scales are explicitly computed whereas the effects of smaller ones are modeled ... 

The third level of combustion simulations is direct numerical simulations (DNS) where the full instantaneous Navier-Stokes equations are solved without any model for turbulent motions all turbulence scales are explicitly determined and their effects on combustion are captured. DNS would predict all time variations of temperature (Fig. 7.4) exactly like a high-resolution sensor would measure them in an experi-... 

Questions of the degree of perfection of mixing have plagued the use of the concept of the well-stirred reactor. In general, high turbulence intensities, small turbulence scales, slow rates of reaction, high reactor temperatures, small amounts of heat release, and relatively weak dependences of rates on temperature favor achievement of experimental results to which the concept can be applied, since under these conditions mixing rates are enhanced in comparison with reaction rates, and influences of nonuniformities within the reactor are minimized. Further information on favorable conditions may be found in Chapter 10. 

If Prandtl or Schmidt numbers differ appreciably from unity, as in liquids or ionized gases, then a number of additional interesting aspects of cascade phenomena arise, and additional turbulence scales with distinguished attributes may be defined. We do not discuss these topics but instead refer the reader to C. H. Gibson, Phys. Fluids 11, 2305 (1968). 

V / oX / )]" a relationship that enables lines of constant values of Ri to be plotted, as shown. Turbulence Reynolds numbers quoted in the literature are often based on the Taylor scale, equation (31), instead of the integral scale these are directly related to and are denoted by in Figure 10.5. In addition to the ratio IJd) of the smallest turbulence scale to the laminar-flame thickness, the ratio of the largest scale (the integral scale) to the flame thickness, //<5, is a relevant parameter. Lines of constant values of //(5, generated from equation (30), also are shown in Figure 10.5. 

Laminar flames in turbulent flows are subjected to strain and develop curvature as consequences of the velocity fluctuations. These influences modify the internal structure of the flame and thereby affect its response to the turbulence. The resulting changes are expected to be of negligible consequence at sufficiently large values of Jb in Figure 10.5, but as turbulence scales approach laminar-flame thicknesses, they become important. Therefore, at least in part of the reaction-sheet regime, consideration of these effects is warranted. The effects of curvature were discussed in Section 9.5.2.3. Here we shall focus our attention mainly on influences of strain. 

As is discussed above, within a canopy, the turbulence scales are constrained by the size and spacing of the stems and branches. If the stem Reynolds number is high enough, the stem wakes generate eddies of scale d. These eddies may grow, but only... 

Valerio S., Vanni M., Barresi A.A., Contribution of different turbulent scales to mixing and reaction between unpre-mixed reactants, Chem. Eng. Sci. 49 (1994) 24 B, p. 5159-5174... 

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