Intensity of turbulence

Inertial forces are developed when the velocity of a fluid changes direction or magnitude. In turbulent flow, inertia forces are larger than viscous forces. Fluid in motion tends to continue in motion until it meets a sohd surface or other fluid moving in a different direction. Forces are developed during the momentum transfer that takes place. The forces ac ting on the impeller blades fluctuate in a random manner related to the scale and intensity of turbulence at the impeller. 

Intensity of turbulence These factors, represented by the standard deviations of the horizontal wind direction, Og, the standard deviation of the vertical wind component, a, and the gustiness as measured by the standard deviation of the wind speed, all have significant bearing on the dispersion of emissions from a stack. 

The dynamics of reactor flow is also important for its effect on the crystal agglomeration, since the intensity of turbulent shear dominates the orthoki-netic mechanism for both processes of aggregation and disruption. The mean shear rate is estimated as (see Harnby etai, 1992)... 

The intensity of turbulence I is defined as the ratio of the mean value of the fluctuating component of velocity to the steady state velocity, For flow in the A-direction parallel to a surface this may be written as ... 

The intensity of turbulence will vary with the geometry of the flow system. Typically, for a fluid flowing over a plane surface or through a pipe, it may have a value of between... 

Insulation see also lagging 554 Intelligent transmitters 240,241,242 Intensity of turbulence 701 Interface evaporation 484 Interfacial turbulence 618 Internal energy 27,44... 

One of the simplest approaches to quantify the pressure field downstream of the constriction used to generate cavitation is to assume linear pressure recovery profile. Yan et al. [8] have used similar approach also considering a single bubble to be existing independent of the other bubbles. Such an approach may be adequate when the intensity of turbulence is quite low i.e. for a venturi type constriction or any other constriction with a smooth variation in the cross-sectional flow area. The pressure recovery from the point at which cavitation starts to any downstream pipe position can be approximated by a linear expression with respect to the distance downstream of the constriction. In such a case, the local pressure at any downstream position can be estimated as ... 

S T increases with increasing intensity of turbulence ahead of the flame. Many have found the relationship to be approximately linear. (This point will be discussed later.)... 

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... 

Supersonic combustion depends considerably (along with the kinetics) on the intensity of turbulent mixing. The significant factors in supersonic mixing enhancement are (1) the decrease in mixing intensity in supersonic flows, and... 

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). 

Fig. 10.12 Effect of intensity of turbulence on the local Nusselt number for a sphere in an air stream at Re = 2 x 10". Data of Galloway and Sage (G5).

There is conflicting evidence regarding the extent to which imposed vibrations increase particle to fluid heat and mass transfer rates (G2), with some authors even claiming that transfer rates are decreased. For sinusoidal velocity variations superimposed on steady relative motion, enhancement of transfer depends on a scale ratio A/d and a velocity ratio Af /Uj (G3). These quantities are rather like the scale and intensity of turbulence (see Chapter 10). For Af /Uj < l/2n, the vibrations do not cause reversal in the relative motion and the enhancement of mass transfer has been correlated (G3) by... 

To understand the principal idea of Deacon s model we have to remember the key assumption of the film model according to which a bottleneck boundary is described by an abrupt drop of diffusivity, for instance, from turbulent to molecular conditions (see Fig. 19.3a). Yet, theories on turbulence at a boundary derived from fluid dynamics show that this drop is gradual and that the thickness of the transition zone from fully turbulent to molecular conditions depends on the viscosity of the fluid. In Whitman s film model this effect is incorporated in the film thicknesses, 8a and 8W (Eq. 20-17). In addition, the film thickness depends on the intensity of turbulent kinetic energy production at the interface as, for instance, demonstrated by the relationship between wind velocity and exchange velocity (Figs. 20.2 and 20.3). 

Now we turn our attention to flowing waters. Here the physics of the boundary is influenced by two kinds of motion, the motions induced by the wind and the water currents, respectively. The latter will be extensively discussed in Chapter 24. At this point it is sufficient to introduce the most important concept in fluid dynamics to quantify the intensity of turbulent motion and to assess the relative importance of several simultaneous processes of turbulent kinetic energy production. 

Increasing the oxygen concentration of the ambient gas has a profound effect in increasing the extinction velocity of wetted spheres (1). In the same work, the scale and intensity of turbulence in a gas stream have been found to have a strong influence on the extinction velocity. 

Approach-flow turbulence does not change the correlation of burner blow-off data by means of gb. With supported flames, contradictory results have been reported. Scurlock found that as the intensity of turbulence was increased, the blow-off velocity decreased (64), while other work indicated the opposite effect (75). Turbulent flash-back is of interest, but it is not ordinarily encountered. 

Mention may be made here that in the case of a pipe in turbulent flow, the intensity of turbulence along the axis is about 3 percent of the mean... 

The fundamental objection to the above relations is that they are derived assuming steady-state flow. In practice, the intensity of turbulence in agitated slurry reactors is time dependent. Also, an accurate estimate of the relative velocity between the liquid and solid is often difficult.45,12S The relative velocity has been related to various system parameters by Kuboi et al.67,68... 

If a flow in the tank is turbulent, either because of high power levels or low viscosity, then a typical velocity pattern at a point would be illustrated by Fig. 3. The velocity fluctuation i can be changed into a root mean square value (RMS), which has great utility in estimating the intensity of turbulence at a point. So in addition to the definitions above, based on average velocity point, we also have the same quantities based on the root mean square fluctuations at a point. We re interested in this value at various rates of power dissipation, since energy dissipation is one of the major contributors to a particular value of RMS v. ... 

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