Introduction
Motivation
In the years since then, the technology for conventional rotary wind turbines (the modern incarnation of which is called Horizontal Axis Wind Turbines or HAWTs) has advanced considerably, with gains in actual operating efficiency significantly outpacing alternative flow collector designs (Sivaram et al., 2018). Since this configuration can lead to the simultaneous potential for thrust production and energy harvesting, as described by Beal et al. 2006), these experiments bridge the gap between studies mainly on thrust performance (where active flapping is assumed to require a net energy expenditure) and power production capacity (where a net power gain is possible despite the required energy input).
Flapping Foils in a Uniform Free Stream for Power and Propulsion . 3
Le Fouest et al. 2021) present a modern study of the static stall process for a NACA 0018 airfoil under similar experimental conditions to those in this thesis. This discrepancy is likely due to the strong dependence of the size and character of the suction zone on the Reynolds number (which is more than 100 times larger in the current study, as well as in those of Lefebvre and Jones (2019) and Beal et al.
Cyber-Physical Fluid Mechanics for Unsteady Aerodynamics Testing 18
In the pushed case, the airfoil executed the same preplanned trajectory regardless of flow conditions. As in the thrust case, we see it as the upper side of the airfoil.
Experimental Setup and Data Processing Methodology
Introduction
Experiments conducted in the NOAH Water Channel at the California Institute of Technology form the basis of the contributions presented in this thesis. In the following chapters, however, the results from the experiments described here are presented in an order that goes more naturally from basic observations to those more specified for particular engineering goals.
Basic Experimental Configuration for All Experiments
In addition, the presence of the cylinder in the tunnel creates a large change in the average downstream conditions due to a high blocking ratio. We note that the resolution of the sensor in the axes of interest is 0.01 N, provided by the manufacturer.
Experimental Setup for the Mechanical Free-Response System
This corresponds to an accuracy error at the largest measured values, approximately on the order of the standard deviation. It is interesting to note that the accuracy of the sensor seems to deteriorate over time: for future measurement campaigns, recalibration by the manufacturer is recommended.
The Captive Trajectory System and Captive Airfoil Experiments
Finally, the appropriate amplitude for the driven sinusoidal motion was determined by analogy with the time-averaged kinetic energy ĀÆšø of the airfoil in the MFRS experiments. For the Passive Captive Airfoil experiments discussed in Chapters 4 through 6, the CTS is used to provide real-time control of the airfoil's motion based on programmed dynamics.
Particle Image Velocimetry
Another source of error in the calculated trajectories stems from the uncertainty about the actual mass of the airfoil (and associated mounting hardware) needed to calculate the actual impulse,š¼š. Moreover, the real mass of the system is a known source of error for CPFD systems of this type: Mackowski and Williamson (2011) acknowledge the real mass of their similar configuration as a source of error in the realized trajectories (regardless of its specification of correct) , and recommend making sure that
Data Processing Methods
In addition, this condition results in the broadening of the combined wake signature upon impacting the airfoil. We again examine a phase-averaged picture of the airfoil's behavior in the same way as in previous sections.
Characterization of the Behaviour of an Airfoil Driven in the
Introduction
In this chapter, both the incoming flow from the cylinder and the resulting shear force acting on the airfoil are characterized. Then the phase-averaged dynamics of the airfoil and its resulting thrust and power extraction potential are presented.
Characterization of the Cylinder Wake
Phase-averaged contours of the Ī2Criterion are used to create the visualization, following the method presented in Chapter 2. This may be due to an offset in the placement of the cylinder in the tunnel, as discussed in Chapter 2.
Experimental Setup for Driven Airfoil Experiments
This was necessary to improve the robustness of the triggering algorithm to noise in the measured force signal and to prevent false triggers. For more information and justification for this restriction, please see the discussion of Guided Aircraft Experiments in Chapter 2.
Frequency and Amplitude Variation in Oncoming Forcing
As in the case of the amplitude, the fact that the airfoil is in motion relative to the flow when š¹š¦ is measured has the potential to affect the observed forcing frequencies. The limits for frequency at which periods are rejected for phase averaging are given by the grayed-out regions in the Figure.
Lift, Thrust and Power Produced by a Driven Airfoil
These questions are particularly important for experiments where the airfoil is actuated in the š„ direction (all the experiments in this section discuss the š¦ direction or transverse. In addition, the mean pressure coefficientš¶š is also positive: the airfoil therefore simultaneously produces net thrust.
Quasi-steady Thrust Production and the Katzmayr Effect
In the illustration, the airfoil has a geometric angle of attack of 0Ā° (it is directed directly upstream). This implies that the thrust experienced by the airfoil at this point in the cycle can be largely attributed to the Katzmayr Effect, developed using results from the steady theory of thin airfoils.
Phase-Averaged Interactions with Upstream Vorticity
TE vortex is mainly shed from the pressure side of the airfoil as a cylinder vortex approaches the leading edge. In the š/2š = 0.57 panel, we see that airfoil-derived CW vortices formed during the upward portion of the airfoil's motion (the first three panels) have detached from the leading edge and convected downstream.
Time Evolution of the Combined Airfoil-Cylinder Wake
The CV vortex above the airfoil then generates a Trailing Edge Vortex (TEV) with the same orientation that enters the flow behind the airfoil, as discussed with reference to flow snapshots in the previous section. In the present case, the timing of vortex shedding appears to be strongly related to the passage of cylinder vortices.
Thrust and Power Production Effects on the Mean Airfoil-Cylinder
In contrast, we see that the presence of an airfoil has a strong influence on the observed downdraft profiles. We also note that the velocity deficit region appears to have been extended in the š¦-direction, supporting the observation that the cylindrical vortices are displaced further from the centerline by the presence of the wing.
Summary of Airfoil Interactions with Oncoming Vorticity
First, we consider the moment of phase 1 in Figure 3.15, when the airfoil is at its minimum position in the frame. This TEV is in the process of merging with the lower roller vortex CW v.
Effect of Static Angle of Attack Offset on Airfoil Behaviour
In addition, especially for the HAoA+ case there appears to be increased variability in all measured quantities, especially in the first half of the cycle. 0.5 0 0.5 Figure 3.20: View of the phase-averaged Ī2 criterion values āāat the indicated points in the vortex shedding cycle, for an airfoil with a static displacement angle of attackš¼0 =+10Ā°, corresponding to Case HAoA+.
Chapter 3 Interim Summary and Conclusions
Despite the lack of coherent LEV formation, there is significant hysteresis in the behavior of the profile over one cycle. The adjustment of the (dimensional) values āāof the two parameters used in the simplified friction model (š¹šinš¹š¶) in tandem with the parameters [š, š, š] for the assembly system was carried out as follows.
Passive Captive Airfoil Motion in 1 Dimension: Optimizing
Introduction
Building from the characterization of the actuated airfoil in the wake of a circular cylinder provided in Chapter 3, this chapter presents the behavior of a similar but distinct passive captive system. Small differences in the behavior of the passive airfoil due to its ability to respond to changes in the oncoming flow are described.
Experimental Setup for the Passive Captive Airfoil
Overall, the interaction between the airfoil and the oncoming vortex is very similar to that observed in the driven case, presented in Chapter 3. Similar variations in the amplitude of the lift experienced were observed in the driven case, and discussed in Chapter 3.
Optimizing 1-Dimensional Passive Motions for Energy Harvesting . 100
For the conservative case described in the previous section, the natural frequency of the system was chosen to match the vortex shedding frequency (šš ā šš) based on references such as Su and Breuer (2019) and Kinsey and Dumas (2008). To explore this in more detail, Figure 4.18 shows successive frames of the Ī2 scale for the Case 2 system, similar to the figures presented for Case 0 and Case 1 in the previous sections.
Thrust Production with the Spring-Mass-Damper Mounting System . 121
Similar to the findings of these authors, we see a slight increase in the magnitude of lift experienced as the airfoil approaches the cylinder. The bottom two figures show the behavior of the airfoil as a function of time during the entire run.
Passive Captive Motion in 2 Dimensions: An Airfoil Swims
Introduction
However, they could not demonstrate that the airfoil actually translated upstream due to experimental limitations (Beal et al., 2006). Motion in the transverse direction was governed by the same dynamics as described in Chapter 4, while the streamwise dynamics were programmed to follow š¹š„ =š šš„.
Experimental Setup for 2-Dimensional Airfoil Motion
Further discussion of the choice of the virtual dampingšš„ is included in the following section. This represents the noise floor of the system when the CTS is not moving in the š„ direction (and although y direction movement is allowed, it is very small).
Passive Captive Airfoil Motion in 2 Dimensions
During each experiment, there is a strong relationship between the moments of high thrust and the transverse position of the airfoil. It can be seen from the figure that the airfoil generates most of its useful thrust in the cylinder centerline region while traveling at maximum š¦-velocity.
Interactions with Oncoming Flow
This similarity in behavior is to be expected, since the yaw speedš„ of the airfoil is small in this. Similar to the 1D case, this demonstrates the utility of passive transverse dynamics in allowing airfoil behavior to adapt to moderate changes in the frequency content of the forward force.
Chapter 5 Interim Summary and Conclusions
To address these issues, we present a statistical description of the behavior of the MFRS in the next section. This makes sense, since much of the work done on the airfoil is repurposed to overcome the effects of friction.
Realistic Engineering Behaviour and the Effects of Friction
Introduction
Although it does not model the underlying physics associated with friction in the system, this model adequately reproduces the qualitative behavior of the airfoil, as well as statistics describing its motion. Through this simple realization of friction in the mounting system, access to reproducible and tunable behavior is made available to facilitate investigation of the effect of friction on vortex interactions as well as system performance.
Characterization of Behaviour for the Mechanical Free-Response
Moreover, as summarized in Table 6.2, we see that for most of the trials considered, the airfoil has a positive angle of attack. To characterize the behavior of the MFRS experiment (the "output" of our system), we consider the speed of the airfoil.
Modelling Frictional Behaviour using the Captive Trajectory System 154
The percentage of time spent on station for the Captive passive airfoil should be similar to the MFRS Experiment, or approximately 50% of the time. To explore this further, we consider the corresponding observed airfoil velocity histograms for the RF and HF trials.
Fluid-Structure Interaction and Emergent Behaviours
In the second left-hand panel, the airfoil experiences a local maximum inš¼effe when stationary. In the third left-hand panel, the airfoil experiences a large positive velocity, which has caused its apparent angle of attack to decrease from the previous maximum.
Chapter 6 Interim Summary and Conclusions
Conclusions & Future Work
