By investigating the energy and frequency of the large scale structures in the wake, some interesting observations can be made, which are summarised below and their
5.3. DISCUSSION AND CONCLUSION
importance discussed.
● There is no apparent difference in the behaviour of the large scale structures in the wake of a disk and a square.
● The frequency at which the large scale structures shed is the same for all plates considered, given that they have the same `= √A and are subjected to the same freestream velocity U∞.
● The energy of these structures is influenced by the smaller scales of the plates. ● A maximum decrease in Ξ of 15% in the spatial area considered here is observed
between the square plate and the Df = 1.5(3).
● For a given downstream and radial distance, the decrease in the energy of the large scale structures can be as much as 80%
● The energy of the large scale structures decay at a slower rate for the fractal plates compared to the non-fractal plates.
● The amount of the energy of the large scale structures coming from the stream- wise fluctuating velocity increases with increasing fractal dimension and iter- ation.
The lack of any discernible difference of the large scale structures in the wake of the disk and the square is surprising since one would have expected the corners of the square plate to be a factor, but this does not appear to be the case at this Reynolds number and over the spatial extent investigated. Interestingly however, it appears that the ‘global’ length scale of the plate controls the frequency of the vortex shedding i.e. ` = √A, whilst the smaller ‘local’ length scales around the perimeter of the plate appear to have some influence on the energy. By using fractal patterns it is possible to increase the number of these ‘local’ length scales whilst keeping the frontal area constant, and hence we find that as both fractal dimension and iteration increase, the energy of the large scale structure decrease as shown in figure 5.7. Although the energy is lower for the fractal plates to begin with, as much
as 80% for a given aximuthal angle at a given downstream and radial distance (figure 5.1), they seem to retain their energy for longer as can be seen in figure 5.5, and the amount of energy coming from the radial velocity component is noticeably smaller compared to the stream wise velocity, suggesting that the wake may be more steady. Understanding how these large scale structures behave is vital in also under- standing the self-similar properties of the wake. Bevilaqua and Lykoudis [1978] raised the issue that the development of the self-similar wake may not simply be down to the momentum deficit of the wake generator but that the eddy structure might also play some role in determining the similarity characteristics of the axisym- metric wake. Cannon [1991] took this one step further by varying the solidity (ratio between solid to open area) of his disks and found a correlation whereby increasing the solidity of the disk created a wider wake. As well as changing the solidity of the body, Cannon investigated the effect of actively forcing the large scale structures in the wake of a bullet shaped object, where it was found that by increasing the forcing frequency, the wake would become larger. In his conclusion, Cannon states that there are parallels between the changes observed by changing the solidity and the forcing frequency.
Nevertheless, both of these studies have been helpful in understanding the results we present here. Unlike these two studies, we have plates where the frontal area doesn’t change, we still have a re-circulating region and large scale shedding, yet we still observe a clear change in the spreading parameter of wake. Therefore although the observation made by Cannon was correct whereby increasing the solidity of the wake caused an increase in the wake width, there was no clear link as to why this was the case, although it was hinted at.
It is now known that as we increase the fractal dimension and iteration of the plates, the energy of the large scale structures decreases - see figure 5.6(b). Parallels could be made to a porous plate where the re-circulating region disappears after a certain threshold - see Castro [1971] for regular array of porous holes and chapter 6 for fractal porosity. As the porosity increases the vortex structure behind the plate changes, going from a clear vortex shedding mechanism to, as Bevilaqua and Lykoudis [1978] explain in their study, vortex pair eddies that one would find for a
5.3. DISCUSSION AND CONCLUSION 1.2 1.3 1.4 1.5 1.6 10 12 14 16 18 20 Ξ = (2π /ℓ)R5ℓ25ℓξdx CV = (2 π / ℓ 3 ) R25 ℓ 5 ℓ δ ∗ 2 d x
Figure 5.8: Relationship between volume of wake and the energy of the large scale structures Ξ for large plates ` = 128mm. (∎) - square, (△) - Df=1.3(1), (▷) - Df=1.3(2), (▽) - Df=1.3(3), (◁) - Df=1.3(4),
(◇) - Df=1.3(5), (▲) - Df = 1.5(1), (▶) - Df = 1.5(2), (▼) -
Df = 1.5(3)
porous wake without a re-circulating region. Although we do not have any idea of how large these structures are, we do have a measure of their energy, as calculated with equation 5.2 and shown in figure 5.6(b). By combining this data with the volume coefficient calculated in the previous chapter, we can see if there is any correlation between the two. This is shown in figure 5.8 where there appears to be a strong correlation. As the fractal dimension and iteration of the plates increases, both the volume of the wake and the energy of the large scale structures decrease, with this decrease being 15% for Ξ and 35% for CV when comparing the square
and the Df = 1.5(3). Hence these findings may suggest that the size of the wake is
correlated with the intensity of the large scale structures, however we do not know if the size of these structures have changed.
Part III
Applications of fractal-generated
wakes
Chapter 6
Aero-acoustic performance of fractal
spoilers
∗
6.1
Introduction
One of the major environmental problems facing the aviation industry is that of aircraft noise. The work presented in this chapter, done as part of the European Union’s Optimisation for Low Environmental Noise Impact Project (OPENAIR), looks at reducing spoiler noise while maintaining aerodynamic performance, through means of large-scale fractal porosity. It is hypothesised that the highly turbulent flow generated by fractal grids from the way the multiple-length scales are organised in space, would reduce the impact of the recirculation region and, with it, the low- frequency noise it generates. In its place, a higher frequency noise is introduced, which is more susceptible to atmospheric attenuation and is less offensive to the human ear.
Figure 6.1: Contribution of total aircraft noise at take-off and landing ac- cording to Owens [1979]