Effects of the competition between leading and trailing edge 62

The previous section discussed the competition between leading and trailing edge flows. The impact that this competition has on the wake characteristics is now discussed in terms of this notion. The elliptical leading edge is taken as the base case and the trailing edge vortex shedding proceeds generally as that described by Gerrard (1966) although with relatively thicker boundary layers than those in the wake of circular cylinders. As leading edge separation is introduced, vortices are shed from the leading edge. From the results herein, these structures are detectable at the trailing edge for the cases when the leading edge separation angle is greater than 45°. These structures disturb the strong periodicity associated with the persistent trailing edge vortex shedding of the elliptical leading edge. With increasing leading edge separation angle, these disturbances are also increasingly three-dimensional with poor spanwise correlation. This type of disruption is hypothesized to lower the shedding frequency which is in agreement with suggestions made by Gerrard (1966). Gerrard (1966) hypothesized that the more difficult the interaction between opposing shear layers, the lower the shedding frequency. Coupling these disruptions with the observation that there is no significant jump between leading and trailing edge domination (e.g., Figure 3.17, Figure 3.18), an explanation for the linear variation of the Strouhal number is now suggested.

Simpson (1989) expects a roughly linear variation in the reattachment length with increasing separation angle as was also found herein. The mean reattachment length is a reasonable approximation to the size of the leading edge disturbances, thus the linear variation in the Strouhal number could simply be the result of a linearly increasing leading edge disturbance. If there was a strong dependence on the synchronization between these two locations, as there is at low Reynolds numbers, one would expect

shedding frequencies to be selected on the basis of one or more instabilities. For example, Liu (2009) showed that there are bounding options for frequency selection at low Reynolds numbers. The lower bound is the case of the ILEV instability for

rectangular cylinders which has a stepwise variation in the chord based Strouhal number with elongation ratio and the upper bound is the elliptical leading edge which shows a linear variation with separation angle. They also show that for the case of a leading edge separation angle of 45°, the frequency locks to one mode before switching to another once the chord is slightly elongated. The results herein, with the lack of frequency communication between these locations show that this is not the mechanism which occurs at higher Reynolds numbers. Rather it is suggested that it is simply the scale of the leading edge disturbance which most affects shedding frequency and could explain the linear variation observed in Figure 3.3.

The leading edge separation angle is also observed to have a significant effect on the fluctuating lift; however, the existence of a peak lift fluctuation is in contrast with the linear decrease of shedding frequency. These results might have been anticipated by the hypotheses of Gerrard (1966) who suggested that even if the frequency is decreased due to a disturbance, this disruption can also lead to less vorticity cancelled out by reduced entrainment of oppositely signed vorticity which in turn increases circulation in the shed vortex and, ultimately, the fluctuating lift. This point was also addressed in Chapter 2 where higher wake vortex circulations and lift fluctuations were found for the case of a triangular-edged elongated bluff body compared to a body with a higher shedding frequency.

The present results show that the fluctuations in the base pressure can be higher in magnitude close to the boundary of the base region (y → 0.5t) for the case of γ = 30° compared with the elliptical nosed body even though they share the same mean and fluctuating base pressure (i.e., that measured at y = 0). This observation suggests formation of the vortices closer to the top of the base region than the middle. The formation of vortices closer to the top of the base region can either be attributed to the increased circulation (of the same sign) drawing the growing vortex towards the edge of the base region or a reduction in the entrainment of the opposing shear layer due to the

leading edge disturbance. Either one or both may be occurring and this type of

interaction will produce higher lift fluctuations compared with the elliptical leading edge for much the same reasons as suggested by Gerrard (1966). As the separation angle is increased further (i.e. γ > 60°), the flow from the leading edge becomes highly three- dimensional, the strength of the TEVS is decreased and thus its ability to correlate the trailing edge flow is also decreased thus, once again, lowering the lift fluctuations. Another factor limiting the lift fluctuations at higher separation angles is the observed suppression of bursting events. Bursting events are known to be associated with strong shedding and high lift fluctuations for circular cylinders (Szepessy and Bearman, 1992). The burst events identified herein are shown to produce the highest lift fluctuations for the bodies with small separation angles. Thus, the suppression of bursting events is expected to lower the time-averaged lift fluctuations. However, it remains unclear if it is the scale of the leading edge disturbance which suppresses bursting at the trailing edge or if it is the high three-dimensionality for large leading edge separation angles. Burst events were observed to be preceded by strong three-dimensional correlation near the trailing edge (also observed by Szepessy and Bearman, 1992 for circular cylinders); however, the poor correlation of structures shed from the leading edge at high leading edge separation angles does not allow this precursor to bursting events and correlation near the trailing edge remains poor. Thus, the dominance of the leading edge flow is suggested to be the reason for reduced burst events which are primarily a feature of trailing edge vortex shedding.