Free turbulence

Vulis, L. A. 1960. Regarding free turbulent jets computation applying the heat conductivity method. In Proceedings of Acad. Set. Kaz. SSR, Ser. Energy, vol. 2, no. 18. 

This result makes it clear that particle stress is strongly dependent on the interaction between the particles and the interface, so that electrostatic and also hydrophobic and hydrophilic interactions with the phase boundary are particularly important. This means that the stress caused by gas sparging and also by boundary-layer flows, as opposed to reactors with free turbulent flow (reactors with impellers and baffles), may depend on the particle system and therefore applicability to other material systems is limited. 

The stress caused by gas sparging and also by boundary-layer flows, as opposed to reactors with free turbulent flow (reactors with impellers and bafQes), may depend on the particle system. 

For reactors with free turbulent flow without dominant boundary layer flows or gas/hquid interfaces (due to rising gas bubbles) such as stirred reactors with bafQes, all used model particle systems and also many biological systems produce similar results, and it may therefore be assumed that these results are also applicable to other particle systems. For stirred tanks in particular, the stress produced by impellers of various types can be predicted with the aid of a geometrical function (Eq. (20)) derived from the results of the measurements. Impellers with a large blade area in relation to the tank dimensions produce less shear, because of their uniform power input, in contrast to small and especially axial-flow impellers, such as propellers, and all kinds of inclined-blade impellers. 

Due to the variations in physical properties, especially under the influence of buoyancy, the heat transfer can be significantly alterated compared to the well-known conditions at buoyancy-free turbulent flow. [2]... 

The heat transfer at 80 bar, except for vertically upstreaming carbon dioxide, can still be described by the usual heat transfer formulas for buoyancy-free turbulent flow [2], with an uncertainty of 20%.. These results are in accordance with the results of Jurgensen and Mon-tillon [4],... 

The time-varying turbulent motion of the bubble column seems to resemble the free turbulence of open jets (S4) or in the mixing zone of two parallel streams of different velocities (D13). 

Prandtl (P7, S4) established a simplified equation for the apparent kinematic viscosity of free turbulent flow based on experiments with free-turbulent flow by Reichardt (R2). He assumed that the dimensions of the lumps of fluid moving traversally during turbulent mixing are comparable in magnitude to the width of the mixing zone. The virtual kinematic viscosity Pi is now formed by multiplying the maximum difference in time-... 

For integrating Eq. (4-9), vji= ei Er) should be known as a function of and operating variables. However, the momentum diffusivity is the only term we know, with essentially no systematic data for In the case of free turbulence of a homogeneous fluid, the diffusivity of a scalar quantity like heat and mass is estimated to be about two times that of momentum (S4) and the two diffusivities are not far apart for turbulent pipe flow (S8). However, such a relation is not available yet for gas-liquid bubble flow in bubble columns. Generally the local radial mass diffusivity may be expressed by a, with a being a numerical coefficient of order unity. 

Malin, M.R. and Spalding, D.B. (1984), Calculations of intermittency in self-preserving free turbulent jets and wakes, CFDU Report, CFD/84/5, Imperial College, London. 

In his treatise "The local structure of turbulence in an incompressible viscous liquid at very high Reynolds numbers , Kolmogorov [289] considered the elements of free turbulence as random variables, which are in general terms accessible to probability theory. This assumes local isotropic turbulence. Thus the probability distribution law is independent of time, since a temporally steady-state condition is present. For these conditions Kolmogorov postulated two similarity hypotheses ... 

Figure 10.9 The axisymmetric free turbulent jet. The initial region of the axisymmetric jet, extending to 5-10 nozzle diameters, consists of an undisturbed cone of nozzle fluid surrounded by the shear layer. For nucleation-controlled growth, particle formation is conlined to the shear layer.

In a free turbulent jet, the length of the shear layer is 5 to 10 times the nozzle diameter, d. If nucleation is confined to the shear layer, according to (10.61) the particle formation rate is proportional to d and is independent of the initial jet velocity kq. Because the volumetric flowrate of a turbulent Jet ( 2> is proportional to u d and Y to N Q, the panicle concentration in the gas exiting the initial region (/Vj) is proportional to rf/wo- Moreover, because the particle concentration downstream of the shear layer changes only by dilution, N N,d/z, and the group Nu z/d should be constant at any point on the Jet axis fora given initial temperature and vapor concentration conditions. 

Birch, S. F., and J. M. Eggers. 1972. Critical review of the experimental data for developed free turbulent shear layers. NASA Special Publication SP-321. 11-40. 

The turbulent flow in a pipe is quite different in character from the turbulent flow in a wind tunnel or in the lower atmosphere. In the atmosphere or in the central section of a wind tunnel, the nearest wall is so far away that it has little influence on the flow. This kind of flow, substantiallyj uninfluenced by nearby walls, is called free turbulence. In a typical long pipe, the flow is strongly influenced by the nearby presence of a wall. This kind of flow is often called shear turbulence or wall turbulence. 

Figure 16.4 is typical of correlation coefficient measurements in a pipe. In free turbulence one often measures a curve as sketched in Fig. 16.5. The negative correlation coefficient shown in this figure is not an experimental error. Rather it reflects the fact that in free turbulence generally two adjacent eddies will, on average, be moving in opposite directions. Thus, when the probes are placed far enough apart to be normally present in two adjacent eddies, the correlation coefficient will be negative. ...

Typical correlation coefficient measurement for free turbulence. 

Free turbulence has a different experimental character from that of turbulence near a solid wall or a free jet. 

Liepmann, H.W., Laufer, J. (1947). Investigations of free turbulent mixing. NACA TN 1257. Washington DC. 

The classical model of a normal turbulent jet was recently extended to a S3mthetic jet [6, 7]. This is summarized in this section. Axisymmetric free turbulent jets can be solved analytically by using the Prandtl mixing-length model. The model findings are summarized by... 

Equation (6.217) gives for free turbulence (in jets) an approximation to the number of grid points... 

Harsha, P.T., "Free Turbulent Mixing A Critical Evaluation of Theory and Experiment", AEDC-TR-71-36, Arnold Air Force Station, Tennessee, 1971. 

Kornev, N., Hassel, E. (2006). Synthesis of homogenous anisotropic divergence-free turbulent fields with prescribed second-order statistics by vortex dipoles. Physics of Fluids. 19, 068101. 

The mass transfer is connected with transfer of molecules or elements of fluid flow caused ly difference in concentrations, or to be precise in chemical potentials, which is a driving force of this process [10]. It can be divided into four large and important phenomena [10] molecular diffusion in immovable medium, diffusion in liquid in case or laminar flow, mixing in free turbulent flow, and mass transfer betv%en the phases. Speaking for mass transfer we mean further first of all the last of these processes. 

Yu.A. Gostintsev, A.G. Istratov, Yu.V. Shulenin, Self-similar propagation of a free turbulent flame in mixed gas mixtures. Combust. Explo. Shock Waves 24(5), 563-569 (1988)... 

---