Chapter III: Characterization of the Behaviour of an Airfoil Driven in the
3.9 Thrust and Power Production Effects on the Mean Airfoil-Cylinder
and net thrust are generated over one vortex shedding cycle. Therefore, we expect that the presence of the airfoil will induce changes to the oncoming cylinder wake, both by repositioning cylinder-derived vorticity, and by qualitatively changing the structure of the combined wake region. This was confirmed in the previous sections, which describe time-dependent interactions between the airfoil and oncoming vor- ticity, as well as the resulting vortical structures formed in the near-airfoil region. To make a quantitative link between the thrust production and power extraction of the airfoil and the resulting mean combined airfoil-cylinder wake is more challenging however, due to several complicating factors present in this system.
Firstly, due to the relatively high Reynolds number, wake vorticity quickly becomes disorganized downstream of the airfoil, and the finite size of the field of view
means that vorticity is convected out of the frame. This makes it challenging to qualitatively view the wake structures without the aid of frozen-flow visualizations (discussed in detail in Chapter 2), which provide a temporal rather than spatial picture of wake evolution, and therefore illuminate wake behaviour only in a very limited spatial region. Secondly, the upstream circular cylinder induces its own drag wake in the region near the airfoil, which forms a backdrop upon which the action of the airfoil is added; since the presence of the airfoil has the potential to alter the drag characteristics of the cylinder itself, determining wake effects due to the airfoil’s presence may not solely reflect the action of thrust and/or drag on the foil only. Lastly, the foil extracts net power from the flow while simultaneously producing thrust. Since energy is extracted from the flow by the foil, we expect that the combined wake region will be de-energized relative to the cylinder case, in direct opposition to our expectation of jet formation (energized flow) in the near wake due to the production of thrust.
To begin to untangle these effects, Figure 3.14 shows mean profiles of the𝑥-direction velocity, ¯𝑈 for one station upstream of the airfoil, and three stations downstream.
For comparison, profiles at the same locations in the flow with no airfoil present are also included. For the first station located at−1.1𝐷 from the cylinder trailing edge (ahead of the airfoil location), the profiles correspond quite closely, showing that the airfoil’s presence has a limited effect on the mean flow at this location. The slightly larger velocity deficit for the airfoil case could be the result of a small deviation between sets of data in the free-stream velocity,𝑈∞. This value was assumed to be 0.32 m/s for all data collected, but in reality varied slightly from day to day in experiments due to small variations in tunnel fill level.
By contrast, we see that the airfoil’s presence has a strong impact on the observed downstream profiles. Close to the airfoil’s trailing edge at approximately−4.1𝐷, we see that instead of the parabolic-type profile observed for the cylinder case, the mean velocity has two troughs surrounding a central peak (jet) region, which occurs near the mean 𝑦-position of the airfoil. This energized jet region is a result of the shedding of trailing edge vorticity, which appears in alternating ‘stripes’ behind the airfoil in the wake visualization for the Driven Airfoil Experiments in Figure 3.13.
As large cylinder vortices encounter the airfoil, they generate high-velocity flow from the airfoil’s trailing edge, some component of which points in the downstream direction. This can be seen in Figure 3.12, where regions of energized𝑈are visible near the airfoil’s trailing edge particularly in panels 2 and 3. The two troughs in𝑈
0D -1.1D -3.1D -4.1D -5.1D 6.1D 0
D
-1 0 1
Figure 3.14: Mean𝑥-direction velocity ( ¯𝑈) field for the Driven Airfoil Experiments, with𝑦-direction profiles shown at 3 stations. Blue lines ( ) show ¯𝑈for the Driven Airfoil Experiments, while yellow lines ( ) show ¯𝑈for Cylinder-Only experiments (discussed in Section 3.2) at the same locations in𝑥 , 𝑦space for reference. Velocity profiles are shown with𝑈∞ subtracted, so that portions of profiles to the right of their corresponding black dashed lines indicate velocities larger than𝑈∞.
pictured above and below this jet region (such that the velocity deficit at the trough locations is larger than the corresponding cylinder-only profile) could be a result of the formation of LEVs or other flow separation near the airfoil’s surface, which is then shed into the flow above and below the airfoil, and convected downstream. It is interesting to note the asymmetry in the deficit magnitude above and below the airfoil - this could be linked to the asymmetry in thrust behaviour observed over one vortex shedding cycle. We also note that the velocity deficit region appears to have been expanded in the 𝑦-direction, lending support to the observation that cylinder vortices are repositioned farther away from the centerline by the presence of the airfoil.
At the farther downstream stations, located at −5.1𝐷 and −6.1𝐷, we see that although the effect of airfoil-derived vorticity on the𝑈-velocity has been attenuated, the overall profiles of ¯𝑈 remain wider in the 𝑦-direction than in the cylinder-only case. This implies that the expansion of the cylinder wake by the airfoil persists even far downstream of the foil, consistent with the idea of an expanding wake discussed in the previous section.
Comparing again to the simpler uniform free-stream case, for a symmetric foil undergoing heave-only motion Andersen et al. (2017) found that 2P-type wakes were observed in both thrust and drag producing regimes. However, the unifying feature that they observed in cases where thrust was produced (in agreement with many previous studies) was that at 4 chord lengths downstream of the trailing edge, the mean flow in the streamwise direction was positive, or in the mean the airfoil’s wake formed a jet. Thrust-producing 2P wakes were shown to have energetic regions
away from the centerline that created jet-like flow strong enough to overcome a region of net drag directly behind the airfoil, which leads to a positive mean momentum flux. It is interesting to note the emergence of an opposite pattern here, linked to the upstream orientation of the generated pairs of counter-rotating vortices, most clearly seen in Figure 3.15 in the following section. Computing mean momentum flux at each station in Figure 3.14, we also find that when the airfoil is present, the mean momentum flux is slightly reduced compared to that for the cylinder-only case, although this calculation is highly sensitive to the mean flow velocity on a particular day of testing. This is consistent with the idea that the foil extracts net energy from the flow, or that not all of the available momentum harvested from oncoming vorticity is used to generate net thrust.