Freestream turbulence

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 range between these small and large particles is less well understood although some experimental studies have been reported (K9, Ul). Similar problems arise in interpretation as with accelerated motion (see Chapter 11). Measurements are commonly correlated by a turbulence-dependent drag coefficient, which contains a number of possible acceleration-dependent components. With fundamental understanding so poorly advanced, it is impossible to say to what extent results are specific to the experimental conditions employed. 

As a rough guide, a particle follows the fluid motion faithfully if its relaxation time, a 2y + l)/9v, is small compared with the period of oscillation (L12), i.e., if 

The approach of representing the fluid and particle motion by their component frequencies is only valid if drag is a linear function of relative velocity and acceleration, i.e., if the particle Reynolds number is low. This is the reason for the restriction on small particles noted earlier. The terminal velocity of the particle relative to the fluid is superimposed on the turbulent fluctuations and is unaffected by turbulence if Re is low (see Chapter 11). 

If the particle Re is well above the creeping flow range, mean drag may be increased or decreased by freestream turbulence. The most significant effect is on the critical Reynolds number. As noted in Chapter 5, the sharp drop in Cd at high Re results from transition to turbulence in the boundary layer and consequent rearward shift in the final separation point. Turbulence reduces Re, presumably by precipitating this transition.  

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As in Chapter 5, it is convenient to define Re as the Reynolds number at which Cd falls to 0.3. Freestream turbulence may be characterized by the relative intensity ... 

Re- = dU i/v. These simplifications are only valid in Stokes flow, and can lead to substantial errors at higher Re [see, e.g., (R7)]. The effect of freestream turbulence can be included, via the correlations in Chapter 10, provided that the turbulence intensity can be estimated. Alternatively, one of the available correlations for drag in accelerated motion through a turbulent fluid can be used [see (C9)], although these are only applicable for limited ranges of experimental conditions. 

For a 5 m/s flow, then, we might expect SO2 deposition velocities of about 0.56 - 0.9 cm./sec. on a rough or corrugated building with external freestream turbulence, but only about 0.56 cm./sec. on a smooth building. Note that these values are considerably lower than obtained from outdoor corrosion tests on small plates (discussed above). 

The conditions under which transition occurs depend on the geometrical situation being considered, on the Reynolds number, and on the level of unsteadiness in the flow well away from the surface over which the flow is occurring [2], [30]. For example, in the case of flow over a flat plate as shown in Figure 5.6, if the level of unsteadiness in the freestream flow ahead of the plate is very low, transition from laminar to turbulent boundary layer flow occurs approximately when ... 

Lin, N., Reed, H.L. and Saric, W.S. (1992). Effect of leading edge geometry on boundary-layer receptivity to freestream sound. In Instability, Transition and Turbulence. (Eds. M.Y. Hussaini, A. Kumar and C.L. Streett), Springer,New York. 

The first test case, useful for future comparison, involved the measurements without any obstructions. That is, a typical boundary layer over a relatively smooth surface (the wind tunnel ground plane covered with plywood) was studied. No unexpected phenomena were found, thereby validating the thermal anemometry technique and acquisition algorithms employed, for flows with a predominant wind direction. For a freestream speed of / , the time-averaged velocity and turbulence intensity distributions are shown in Fig. 3.39,(A). These data allow the determination of the boundary... 

The second case is the wake behind a single obstruction in the form of a D-tree described earlier. For a freestream speed of Um = 8 m/s, the measurements were carried out along several vertical lines within the wake behind the tree , as shown in Fig. 3.40,(A). The mean velocity and turbulence intensity profiles over the vertical line (9,1) that lies in the wake at a distance of 2.5h behind the D-tree are shown in Figs. 3.40,(B) and (C), curves 2, along with the corresponding profiles in the oncoming flow upstream of the obstruction (curves 1) for the purpose of comparison. The aerodynamic wake results in the velocity reduction to Uw 6 m/s and the increased... 

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