Scales of turbulence

Prandtl mixing length, length scale of turbulence... 

Turbulent Flow in Stirred Vessels Turbulence parameters such as intensity and scale of turbulence, correlation coefficients, and... 

An idea of the scale of turbulence can be obtained by measuring instantaneous values of velocities at two different points within the fluid and examining how the correlation coefficient for the two sets of values changes as the distance between the points is increased. 

When these are close together, most of the simultaneously measured velocities will relate to fluid in the same eddy and the correlation coefficient will be high. When the points are further apart the correlation coefficient will fall because in an appreciable number of the pairs of measurements the two velocities will relate to different eddies. Thus, the distance apart of the measuring stations at which the correlation coefficient becomes very poor is a measure of scale of turbulence. Frequently, different scales of turbulence can be present simultaneously. Thus, when a fluid in a tube flows past an obstacle or suspended particle, eddies may form in the wake of the particles and their size will be of the same order as the size of the particle in addition, there will be larger eddies limited in size only by the diameter of the pipe. 

More recently, experimental studies have been carried out using a similar device but with an annular external hot coflow of burned gases that allowed one to operate within a much larger velocity range. Chen et al. [26] and more recently Chen and Bilger [27,28] have studied the perturbations that the smallest scales of turbulence can impose to the local flamelet structures. Those studies are of paramount importance, first because they have allowed to get deeper insights into the local structure... 

Turbulent nonpremixed flames contain a wide range of lengfh scales. For a given flame geomefry, fhe largest scales of furbulence are determined by the overall width of an unconfined jef flame or by fhe dimensions of the hardware that contain the flow. Therefore, the largest scales of turbulent motion are typically independent of Reynolds number. As the Re5molds number increases. 

Since in the case of turbulent stress the ratio of particle diameter dp to length scale of turbulence qp is decisive for the stress regime (see Fig. 1) the model particle systems must have properties which guarantee dp/qp values which are in the same range as for the biological particle systems. 

The ratio Zt/Zp is in technical reactors much higher than 1. It becomes, e.g. also for a small scale reactor of V-IOOL (H/D = 2 D = 0.4 m) equipped with three turbines (d/D = 0.3) and working at a average impeller power per mass of only = lmVs in media with water like viscosity to Zt/Zp>36...72. The maximal energy dissipation in the impeller zones, required for the calculation of length scale of turbulence here taken from Eq. (20). 

Stresses acting on micro-organisms in (a) to (c) are derived on the premise that the flow forces originate from the turbulent motion of the carrier medium. In almost all cases, turbulence is assumed to be locally isotropic and homogeneous which greatly simplifies the analysis and allows the application of the Kolmogoroff s theory of turbulence to the problem [81]. The Kolomogoroff micro-scale of turbulence,... 

The properties of the turbulence are different at the two extremes of the scale of turbulence. The largest eddies, known as the macroscale turbulence, contain most of the turbulent kinetic energy. Their motion is dominated by inertia and viscosity has little direct effect on them. In contrast, at the microscale of turbulence, the smallest eddies are dominated by viscous stresses, indeed viscosity completely smooths out the microscale turbulence. 

The packing particle density and fraction voids strongly affect the radial scale of turbulence (Ab) larger scales are found for beds containing denser particles at a given fraction voids. The scale of turbulence has a maximum value at e = 0.7. 

The scale of concentration fluctuation (A) is affected by the fraction voids in the same manner as the scale of turbulence, but it is not greatly influenced by the particle density. The scales of concentration fluctuation show that there are isoconcentration eddies several times the size of a packing particle. ... 

The motion of a particle in a turbulent fluid depends upon the characteristics of the particle and of the turbulent flow. Small particles show a fluctuating motion resulting from turbulent fluid motion. Generally speaking, a particle responds to turbulent fluctuations with a scale larger than the particle diameter (K9). A particle which is much larger than the scale of turbulence shows relatively little velocity fluctuation. The effect of turbulence is then to modify the flow field around the particle, so that the drag may be affected. 

The largest scale of turbulence is roughly equal to the smallest overall scale of the flow field. This may be seen in comparing the size of eddies at the edge of the smoke or steam plume to the width of the plume. 

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