Numerical and experimental study on the ability of dynamic roughness to alter the development of a leading edge vortex

Numerical and Experimental Study on the Ability of Dynamic Roughness to Alter the Development of a Leading Edge Vortex


LIST OF TABLES
an increase in drag as well as a large shift in pitching moment [1]. The first evidence of dynamic stall was identified on helicopters. Helicopter design engineers were unable to predict the performance of high speed helicopters using conventional aerodynamics. This led to increased emphasis on unsteady aerodynamics and their effects [2]. McCroskey [3] noted in his text the importance of understanding the unsteadiness encountered in pitching airfoils, especially oscillating airfoils. He suggests that a large hysteresis develops in the fluid-dynamic forces and moments as the airfoil oscillates and the behavior of lift, drag, and that pitching moment cannot be grasped without fully investigating the unsteady motion of the airfoil. Figure 1.1 [2] presents an evolution of the processes that occur during the cycle of a pitching airfoil. This evolution includes the airfoil pitching down after the initial rapid pitch up. Since the discovery of dynamic stall, research has been conducted to not only gain an understanding of the physics occurring, but also to find ways to alter the formation of the LEV.
With the ability to alter the LEV one could further expand the operational envelope of the aircraft. Most of the strategies used to control the LEV originate from research involving laminar boundary layer control. Laminar boundary layer control attempts to inhibit the transition from a laminar boundary layer to a turbulent boundary layer, as well as prevent or enhance flow separation. Skin friction drag can be reduced up to an order of magnitude if the boundary layer is in a laminar state, which correlates to longer range, less fuel consumption, and perhaps increased speed [4]. Some typical boundary layer flow control techniques include classics such as suction, injection, vortex generators, roughness, compliant surfaces; and also recent techniques such as plasma actuators and synthetic jets.
Although these techniques show great promise in research settings there are some common reasons why they are not utilized in practice. A common problem in flow control is that the device actually causes a net increase in energy expenditure. This usually stems from the fact that the device uses more energy than is saved by the increase in aerodynamic efficiency. Also, many of these techniques are only worthwhile at a certain performance condition; while at other times may cause adverse effects. Therefore, a proper flow control apparatus used to alter the LEV occurring during dynamic stall should be tunable to operate at a variety of conditions, such as various Reynolds number (Re) and pitching frequencies. there had been a turbulent boundary layer over the airfoil with no separation bubble present. The region between separation and reattachment is referred to as the separation bubble" [10]. using dynamic roughness to eliminate the leading edge separation bubble by [5]. One can see the reduction in circulation and thus increase in suction pressure due to the presence of dynamic roughness. Success was also found experimentally using both flow visualization as well as surface pressure data, as shown in Figure 1.3. The previous success with eliminating the leading edge separation bubble using dynamic roughness is the basis for evaluating whether it can also alter the LEV of a rapidly pitching airfoil.

Previous Numerical Analysis of Dynamic Stall
Mehta and Lavan [11] studied the laminar unsteady flow around an impulsively started airfoil at angle of attack and low Reynolds number (Re c = 1000) by solving the Navier-Stokes equations in the whole flow field. They noticed the change in position of the front and rear stagnation points, as well as the correlation between the change in lift and the growth of the separation bubbles and vorticity. They also associated the "bursting" of the large leading edge bubble with airfoil stall.
Shida, et al. [12] accounted for compressibility in their simulations of a pitching NACA 0012 airfoil. They matched their results to experiments by McCroskey and Pucci [13], which evaluated oscillating airfoils at much higher Reynolds number (Re c = 4 x 10 6 ) than previously analyzed numerically. In particular, [12] compared lift coefficient and moment coefficient hysteresis acquired numerically to that found in experiment. They found it important for the mesh density to be fine enough to capture the small vortices along the airfoil surface which produce a pressure coefficient curve indicating attached flow.
Visbal and Shang [14] investigated the flow around a rapidly pitching airfoil at a Reynolds  Visbal [15] did additional research concerning the effects of compressibility on dynamic stall.
He concluded the main effects to be a change from trailing-edge stall to leading edge-stall and a reduction in the stall delay and maximum lift. Shih, et al. [16] performed a computational study on a pitching airfoil using the discrete vortex, random walk approximation in tandem with experimental Particle Image Velocimetry (PIV) work done in a water towing tank. The flow regime they focused on was a chord Reynolds number of 5000. The main objective of their study was to evaluate the ability of PIV to study unsteady flows as well as their computational method. They produced numerical results that correlated well with their experimental work, giving confirmation to both methods. Choudhuri, et al. [17] compared results for structured and unstructured meshes for a NACA 0012 airfoil undergoing dynamic stall as well as two separate numerical algorithms. They investigated the unsteady leading-edge boundary layer separation and also gave a classification of critical points as seen in plots of the instantaneous streamlines in  Rothmayer and Bhaskaran [18] noted the development of Rayleigh instabilities in dynamic stall prior to first flow reversal. Their study was restricted to an idealized leading edge, or flow past a parabola. They documented that these Rayleigh instabilities produce a complex cascading of two-dimensional secondary instabilities. Suito, et al. [19] used a multi-directional finitedifference method to analyze the separating strong shear layer during dynamic stall of a NACA 0012 airfoil at a chord Reynolds number of 5.0 x 10 5 . They concluded, "The vortex structures which give rise to the dynamic stall are the same in spite of the differences such as Reynolds number or airfoil motion". Huebsch and Rothmayer [20] investigated the effect of surface roughness on dynamic stall, and particularly simulated ice roughness. They concluded roughness whose characteristic height was smaller than that of the boundary layer height affected the secondary separation mechanism, and also that large-scale roughness can "significantly alter the inception time for the formation of the dynamic-stall vortex (leading edge vortex)".
Further research was performed by Akbari and Price [21] to investigate the effects of pitching frequency and Reynolds number on an oscillating airfoil. They showed that pitching frequency had the most effect on the flow field and the force moments. With higher frequencies flow separation was delayed, which caused the peak lift to occur at a higher angle of attack. The increase in pitching frequency also caused an increase in the "negative damping in the pitching moment coefficient hysteresis loop". It is significant to be able to associate changes in such characteristics with seemingly secondary effects. This confirmed earlier results found by [14].
All computational research mentioned up to this point has been two-dimensional in nature.
Spentzos, et al. [22] performed three-dimensional computational analysis of dynamic stall. They concluded that similarity between two-dimensional and three-dimensional CFD analysis is good only in the mid-span area of a wing. The outboard section is sufficiently affected by the interaction between the LEV and the tip vortex. Visbal [23] performed three-dimensional analysis using an implicit large-eddy simulation (ILES) approach. He focused this study to low Reynolds number conditions (Re c ≤ 6 × 10 4 ) of a plunging airfoil with relatively high frequency and low amplitude. It was shown that although at inception the LEV is laminar, it quickly experiences an abrupt breakdown and undergoes transition. In a follow up study Visbal [24] broadened the flow characteristics by lowering the frequency and increasing the plunging amplitude, relevant to more micro aerial vehicle (MAV) applications. He was able to show for certain Reynolds number regimes the flow will remain effectively laminar throughout the plunging cycle (Re c ≈ 1 × 10 3 ). At around Re c = 5 × 10 3 transitional effects are present, while at Re c = 1.2 × 10 5 a single turbulent LEV is formed.

Previous Experimental Analysis of Dynamic Stall
Martin, et al. [25] performed an experimental study of dynamic stall on a two-dimensional Cambre airfoil (used to study the effects of camber), symmetrical extensions to reduce the leading edge radius, leading edge serrations, and boundary layer trips. This research showed contrary to previous assumptions, "the shed vortex appears to be fed its initial vorticity by the abrupt, unsteady separation of the turbulent boundary layer, not the laminar bubble". This conclusion is particularly significant to the research proposed here since the dynamic roughness is known to alter the leading edge laminar bubble. Walker, et al. [27] studied the effects of pitching rate on flow separation encountered during dynamic stall. Their data consisted of smoke visualization as well as near wall hot-wire velocity measurements. They were able to confirm that an increase in pitching rate translated into a delay in flow separation and "more energetic" suction peak and LEV. Brandon [28] studied the effects of dynamic stall on the aerodynamic characteristics of high performance aircraft. He did wind tunnel testing of a representative fighter aircraft and investigated dynamic effects on lateral stability and available control power during control surface deflections. Brandon concluded that the results seen in simple two dimensional airfoils are similar to those found on a realistic three dimensional aircraft configuration. He also noted that the dynamic lift effects did not significantly alter turn performance, but did have a significant impact on longitudinal and lateral stability. Chandrasekhara and Ahmed [29] recorded laser velocimetry data for an oscillating airfoil. They captured rapid accelerations over a large region of the airfoil with values as high as 1.6U ∞ (free stream velocity) as well as wall effects as far away as half the chord length from the airfoil. These rapid accelerations seem to be the source of the increased suction pressure and, therefore, increased lift. To better understand the evolution of the LEV, Acharya and Metwally [30] performed detailed surface pressure measurements of pitching airfoils. They identified three regions based on the surface pressure plots: a suction peak in the region near the leading edge (LESP), a constant pressure region or pressure plateau (CPP), and a suction peak associated with the dynamic stall vortex (DSVP).
Acharya and Metwally discovered significant differences in the evolution of these regions dependent on whether the pitch rate was relatively "low" are "high". This gave further evidence on the importance of pitch rate in the development of dynamic stall.
Ahmed and Chandrasekhara [31] focused on the down stroke of an oscillating airfoil which encounters dynamic stall on the upstroke. They used the Schlieren method for qualitative analysis of the global flow field, laser Doppler velocimetry (LDV) for velocity measurements, and point diffraction interferometry (PDI) for measuring density and pressure distributions.
They were able to identify the flow reattachment process, which begins when the airfoil is very close to the static stall angle on its downward stroke and corresponds to a large rise in the suction peak. Shih, et al. [32] performed further research, but this time focusing on the flow near the leading and trailing edges. They used PIV to detail the formation of the vortices and their interaction with the boundary layer vorticity. They concluded that the trailing edge flow field only plays a "secondary role" on the dynamic stall process.
Although Bousman [33] himself did not perform an experimental analysis, he did analyze previous dynamic stall data to characterize the relationship between augmented lift, negative pitching moment, and increase in drag, particularly for rotorcraft. He concluded this relationship shows little sensitivity to airfoil profile and Mach number; and is independent of Reynolds number, oscillation frequency, and blade sweep. He highlights the need for the development of multi element airfoils or variable geometry airfoils that can take advantage of the increase in performance occurring during dynamic stall, but prevent the disadvantages such as increased drag and changes in pitching moment. Schreck, et al. [34] conducted shear stress measurements on a NACA 0015 airfoil as it was pitched at a constant rate through dynamic stall. Using the shear stress calculations they identified boundary layer flow reversal preceding eventual LEV formation and convection downstream. Geissler and Haselmeyer [1] studied the effect of transition on dynamic stall onset. They used a variety of tripping devices to study a forced transition flow encountering dynamic stall and concluded the development, shedding, and accumulating of vorticity plays the dominant role in both free transition as well as forced transition.

Dynamic Stall and Biological Flight
Man  Figure 1.7 presents the computational results from [36] along with the smoke visualization captured by [35]. One can clearly see the formation of the LEV and its convection down the span to the wingtip. The dual LEV also seemed to be independent of wing aspect ratio. Lu and Shen [40] followed this up with additional research identifying one major vortex and three minor vortices making up the LEV system on a three dimensional flapping wing.
Muijres, et al. [41] studied slow flying bats utilizing PIV. They observed lift enhancement as much as 40% by way of the LEV. This research was important in showing that lift enhancement by means of leading edge vorticity is not limited to insects, but also larger flyers. Lua, et al. [42] performed an interesting study concerning the use of flexible vs. rigid wings for flapping flight.
The primary purpose of their study was to evaluate the lift force generation created when using a rigid wing as opposed to a flexible wing. They found that there is a critical stiffness coefficient, and if the wing properties fall below this critical point (wing is too flexible) lift generation is reduced. The interesting and relevant result to this research was that they attributed the loss in lift generation to the altering of the LEV due to the motion of the "too flexible" wing. Jones and Babinsky [43] recorded PIV, flow visualization, and force data for a "waving" wing. The waving wing is a three-dimensional simplification of normal flapping flight observed in nature.
The purpose of their study was to evaluate the flow characteristics over a range of Reynolds number (Re c = 10,000 to 60,000). The flow structures over the wing did not appear to change with regards to Reynolds number, but the leading edge vortices appear to grow and shed more quickly at lower Reynolds number, based on a non-dimensional time-scale.

Edge Vortex
As stated above, flow control techniques for dynamic stall are based on their static stall counterparts, i.e., suction, blowing, moving walls. Freymuth et al. [44] recorded smoke flow visualizations of a pitching airfoil with a rotating leading edge. They were able to show elimination of the LEV and documented a minimum circumferential speed needed by the leading edge cylinder to maintain control. This minimum speed was dependent on free stream velocity and pitching rate. Increasing the speed beyond this minimum had no negative effect on separation control. Figure 1.8 is a sample of the results provided by [44]. One can clearly see the elimination of the LEV and dynamic stall by leading edge rotation. Visbal [45] performed computational analysis to study the effects of leading edge suction via boundary layer bleed and tangential surface motion to delay separation and thus delay the onset of the LEV. They were able to show control using both methods. Distributed suction seemed to be more effective than a concentrated suction slot on the airfoil upper surface. A summary of the results from [45] are shown in Figure 1.9. Karim and Acharya [46] performed experimental analysis of LEV control by means of leading edge surface suction. They were able to derive a required suction rate needed to provide adequate control of the LEV. This was done by balancing the rate of suction with the reverseflow accumulation rate. Figure 1.10 is a plot from [46] that provides the suction requirements for different dimensionless pitch rates. With this plot, one can determine the suction requirements during a constant pitch rate maneuver by following a line of constant α + . It is also evident from this plot that to retain complete suppression of the LEV the suction flow rate needs to be increased as the angle of attack increases. Greenblatt [48] evaluated periodic forcing as a means to control dynamic stall. He used surface pressure and wake measurements to evaluate their effectiveness and oriented the blowing slots at 45° and 90° to the chord-line. More success controlling dynamic stall was achieved using the blowing slot oriented 45° to the chord-line and is attributed to "trapping" the bubble upstream of the forcing slot location, but relatively large forcing amplitudes were required to gain control.
The previous research done by Huebsch [9] on dynamic roughness is the main motivation for the current study. Using a two-dimensional Navier-Stokes numerical simulation on a parabola, also used by [18] [20], he was able to delay the formation of the LEV using dynamic roughness actuation. This, in turn, can translate into the airfoil reaching a higher angle of attack before dynamic stall occurs. The delay in the formation of the LEV is shown in Figure 1.11.

Objectives
As shown through previous research LEV alteration, predominantly LEV development delay, has been established through typical laminar boundary layer control techniques. Dynamic roughness has been shown both computationally and experimentally to be a viable laminar boundary layer control technique, at least in steady aerodynamics [5] [6] [9]. It was the goal of this research to expand the applicability of dynamic roughness to alteration of the LEV development on a rapidly pitching airfoil, an unsteady phenomenon. Both a numerical and experimental analysis was conducted to help validate the results and represents the first time such an approach has been used to evaluate the application of dynamic roughness in such an unsteady aerodynamic phenomenon. In the pursuit of this main objective a few other aspects of LEV development were investigated to help validate the results, as well as provide further evidence for previously debated results. A bulleted list is given to outline the objectives sought in the research.
• Can dynamic roughness alter the development of a LEV on a rapidly pitching airfoil?
Particularly, do conditions exist that show dynamic roughness can both delay LEV development to higher angles of attack as well as initiate LEV development at lower angles of attack?
• If so, can a relationship between dynamic roughness properties (frequency of actuation and amplitude) and flow conditions (Reynolds number, airfoil pitching rate) be established?
• How does LEV development vary with airfoil pitching rate and Reynolds number?
• Are 2-D CFD simulations adequate enough to use as a tool to establish LEV "control" parameters based on dynamic roughness settings and flow characteristics?
• Is phase-averaged PIV analysis able to capture LEV development?

Model Design and Fabrication
The NACA 0012 airfoil was chosen as the airfoil to study based on its wide use in previous research both at WVU and in the literature found in regards to dynamic stall. A chord length of 11.5 inches (0.2921 meters) was used to balance the desire to create a model as large as possible while keeping blockage constraints in mind. The motivation behind making the model as large as possible is to ease the fabrication and to increase the durability of the dynamic roughness sections. Although it is recommended to keep blockage below 10%, at the highest angle of attack obtained during the pitching motion (40°) there is a blockage of 16%. Although this is above the recommended value of 10%, previous research indicates significant reductions in blockage effects when studying rapidly pitching airfoils [49].
The airfoil shape and support is provided by four aluminum ribs that were milled from half inch thick aluminum sheets on a numerically controlled Alliant end milling machine. This particular end mill has a resolution of 0.0002 inches. The profile for the airfoil was developed using the NACA four digit airfoil equation, which was then discretized into 141 points with a bias towards to leading edge. A plot of the points is shown in Figure 2.1.    Keyways in the shaft and ribs ensure accurate alignment and spacing as well as to prevent slippage while undergoing the oscillation during experimentation. One can also see how each threaded hole is counter-sunk into the rib to produce a smooth surface on the model.

System
To simulate a pitching airfoil a basic four bar linkage system was designed and fabricated to oscillate an airfoil between some minimum and maximum angle of attack. A 0.5 HP variable speed DC motor drove the system, allowing the operator to vary the pitch rate. The minimum and maximum angle of attack can also be adjusted by changing the lengths of the linkages in the system. The assembled apparatus is shown in Figure 2.5 This method of pitching has been used extensively in previous research. By using such a system the instantaneous angle of attack, α, can be represented by where ( ) is instantaneous angle of attack at time t, 0 is mean angle of attack, 1 is oscillation magnitude, and is circular frequency in rad/s. The circular frequency is often nondimensionalized using (2), and is termed reduced frequency, k.
An oscillation frequency can be introduced whose cycle starts at a minimum angle of attack, pitches to a maximum angle of attack, and returns back to the minimum angle of attack. This oscillation frequency is measured in Hertz and can be related to the circular frequency, and thus the reduced frequency, by (3).

= 2 (3)
The motor is able to operate up to 120 RPM before the unbalanced nature of the mechanism causes significant vibration. This correlates to an oscillation frequency of 2 Hz. This limitation is very suitable for the pitching frequencies desired to study. This is the only setup limitation since the maximum and minimum angle of attack can be altered by changing linkage lengths, as well as the mean angle of attack can be altered by adjust the initial shaft position.
To create dynamic roughness a pneumatic system was developed, as shown in Figure 2.6. A simple 27 cubic centimeter displacement two-stroke motor was connected via hard plastic tubing to the dynamic roughness plenum. A separate 0.5 HP variable speed DC motor drove a beltpulley system that drove the motor, which in turn created an oscillating pressure source for the dynamic roughness plenum. This system allows the frequency of actuation to be accurately controlled. A shortcoming of this approach is the inability to control amplitude with any reasonable accuracy. A small valve is placed near the outlet of the two-stroke motor which can be opened to divert some mass flow, which in turn reduces amplitude. For the present work the valve remained shut to create the maximum possible amplitude, since during preliminary experimental analysis small amplitudes had no noticeable effect on the leading edge vortex. High-speed video was also used to calculate the amplitude of the dynamic roughness elements.
This was accomplished by placing an object of known diameter in close proximity to the dynamic roughness elements during recording. This allowed for a conversion factor to be created between the pixel length on the recording with a physical unit of length. The amplitude of the dynamic roughness elements while being actuated increased with an increase in frequency.
At a controller setting of 3 (20 Hz) the amplitude was measure to be 0.205 mm, and at a setting of 10 (89 Hz) the amplitude was 0.301 mm. The relationship between controller setting and roughness amplitude varied linearly. There was also a difference in measured amplitude based on whether the two-stroke motor was initiated from bottom dead center (so the mass flow rate from the two-stroke motor would initially create a positive pressure) or from top dead center (created an initial suction pressure in the dynamic roughness plenum) in some instances. When a difference did occur, the amplitude was always less when the motor was started from top dead center. The variation in amplitude between piston initial position was less than 5 percent. Even though this is such a small percentage of the amplitude, care was taken to start the dynamic roughness apparatus with the piston initially in the bottom dead center position.

PIV Results
The PIV analysis can be broken down into three groups that can be posed as questions:   The results of the Reynolds number dependence study are summarized in Figure 2 By examining the results shown in Figure 2.9 one can see there is relatively little variation from one Reynolds number to the next. Although there is some discussion as to the dependence on Reynolds numbers by previous researchers [25], the majority conclude that Reynolds number only plays a minor role in dynamic stall [21] [33]. The results shown here tend to confirm the latter. A subtle difference between Reynolds numbers appears to be a small displacement downstream of the major circulation region as Reynolds number is increased.
A similar study was done to investigate the effects of increasing the reduced frequency, and in Once this condition was found the same dynamic roughness actuation frequency was tested at other flow conditions. If Reynolds number was reduced or the reduced frequency was changed LEV delay was lost. An example of such a case is shown in Figure 2.12. At a Reynolds number of 80,000 and a reduced frequency of 0.1 dynamic roughness was not able to make any noticeable differences in LEV development.

Stereoscopic and Planar PIV Discussion
All results presented above have been planar (two-dimensional) in nature. As stated, both planar and stereoscopic PIV data were collected. A brief discussion on any differences in results is offered. To analyze differences one can look at the case in which dynamic roughness had a noticeable effect on LEV development. Presented in Figure 2.13 is a comparison between the planar results with the stereoscopic results.

PIV Uncertainty Analysis
Although there is no universally accepted procedure to performing an uncertainty analysis when conducting PIV experiments, an attempt was made to find an approach that provides, at the very least, a general idea of the uncertainties associated with PIV analysis. A recommended procedure was found that was developed by the International Towing Tank Conference that was very in depth in its scope of possible sources of uncertainty in PIV measurements [50]. The sources of error are vast and the reader is encourage to view the referenced document for a clear understanding of each source. As an example, typical sources of error are shown in Table 2.2.   Table 2.3. Each of these sub-systems is then broken down to see how their associated error sources effects the three basic measurements of velocity, position, and time. The uncertainties for these measurements are provided in Table 2.4, Table 2.5, and Table 2.6, respectively. The process of uncertainty analysis involves estimating the error for each possible source, then applying a sensitivity calculation to that error. Then for each uncertainty type (velocity, position, and time) the uncertainties are root sum squared to provide a total uncertainty. As shown in the following tables, the total uncertainty in x-velocity is 0.35 m/s, the total uncertainty for position is 1.09 mm, and the total uncertainty for time is 1.00 x 10 -8 s.

Computational Mesh and Solver Considerations
Both two-dimensional and three-dimensional simulations were performed to study the effects of dynamic roughness on the development of the LEV. The NACA 0012 airfoil was again chosen to study based on availability of data and the fact that it was used in previous research associated with the current study. Also, there was a desire to compare the computational simulations with the experimental PIV data. The first consideration when developing the computational mesh besides grid density and structure was to understand the manner in which the pitching should be Fluent offers two different methods for mesh motion in the application of a pitching airfoil; "sliding mesh" and "dynamic mesh". In the sliding mesh technique two cell zones are created in such a way to be bounded by at least one "interface zone" where it meets the opposing cell zone.
The interface zones of the two adjacent cell zones are associated with one another to form a "mesh interface". The two cell zones will move relative to each other along the mesh interface.
As the cell zones slide along the mesh interface, node alignment is not required. This node misalignment is highlighted in Figure 3     Guide which states, "the sliding mesh model is the most accurate method for simulating flows in multiple moving reference frames, but also the most computationally demanding" [51]. It is important to note that no significant difference in flow solution was observed between the two methods. Comparison of streamline plots and surface pressure distributions were performed to check correlations between the two mesh techniques, as shown in Figure 3.4 and Figure 3.5. The flow and pitching parameters used for this comparison were those used by [17], which are displayed in corresponds to a functional form of pitch rate that varies with time to produce a smooth acceleration of the airfoil to its asymptotic pitching rate, Ω 0 . This non-dimensional pitch rate is calculated using (4).
where is the airfoil chord length and ∞ is the freestream velocity. The pitching motion is defined by where Ω is the pitch rate in rad/s, 0 is the time at which Ω has reached 99% of the asymptotic value, Ω 0 . The time to reach Ω 0 can be calculated using (6).
Very little difference is observed between the two methods. The most notable difference is the surface pressure distribution near the trailing edge shown in Figure 3.5. Since the area of interest is the near the leading edge, this discrepancy in surface pressure near the trailing edge is negligible. With this knowledge the dynamic mesh approach was used to model both the airfoil rotating in a fixed domain as well as the domain rotating around a fixed airfoil.   As shown in Figure 3.7, there are significant differences between pitching methods. In the simulation where the domain is kept stationary as the airfoil is rotated the results closely match those of [17]. Although the other two methods show different results, they both eventually develop the LEV, albeit at higher "measured" angles of attack.
It is found that the formation of the LEV occurs at 28.79° for the boundary rotation method and at 24.77° for the variable velocity vector method. It is hypothesized in the boundary rotation method there is a lag time associated with the time needed for the rotation of the velocity inlet to propagate throughout the domain. As can be seen in Figure 3.8 the streamlines do not stay perpendicular to the inlet throughout the domain for the rotating boundary method. This is thought to reduce the "effective" angle of attack sensed by the airfoil. The source of variation for the velocity vector method is thought to be due to the fact that there is no way to identify a pitching axis when the velocity is prescribed at the inlet, as well as the time of propagation required for fluid at the inlet to reach the airfoil. As stated previously by [14], pitching axis has significant effects on LEV formation. In addition, this method also neglects the inertial term of the governing equations. Although neglecting this term will alter the "absolute" analysis, it will still qualitatively show the trend of separation, reattachment, and recirculation which is sufficient for comparison for clean and dynamic roughness cases. Therefore, to model the dynamic roughness elements on a moving airfoil the motion of the airfoil itself needs to be accounted for in the node placement given by the UDF. All attempts to accomplish this were unsuccessful. Even though the double precision solver was used, it still appeared to give enough truncation error to misalign the dynamic roughness element nodes. For this reason it was decided to use the variable velocity vector method model the pitching motion of the airfoil. This not only solved the truncation error problem just described, since the airfoil is not moving, but it also allows for a fully structured mesh to be utilized with no need for a Remeshing Zone, as is needed in the pitching method in which the domain is rotated about a fixed airfoil. This decreases computational time, especially in three-dimensional simulations.
It was decided to limit CFD simulations to a Reynolds number of 150,000 due to the laminar solver being used for this study. Although there is most certainly transition and turbulence occurring at this flow velocity, in the region of interest near the leading edge there is laminar separation, which is best modeled by the laminar solver. In the research performed by Gall et al., the laminar solver was also used [6]. The numerical studies using the laminar solver compared well with the experimental work, as is the case in the current study. Although the work described here has a much more unsteady character, it is still hypothesized that the laminar solver is suitable to evaluate the separation and reattachment near the leading edge. With this approach the computational results further downstream on the airfoil should be viewed with skepticism.
A mesh density and temporal grid independence study was conducted at this Reynolds number.
An initial mesh consisting of 103 nodes along the airfoil and 120 nodes normal to the airfoil was developed. The mesh was then refined in 50% increments in both directions until no noticeable changes in solution were observed. Since this is an unsteady flow, the characteristics used for solution independence is the initiation of recirculation and the structure of the LEV at a higher angle of attack.   To study temporal solution independence a non-dimensional time step was utilized. The form is given in (7).
The same approach used to investigate mesh density independence is used to study temporal independence. Figure 3.11 displays the onset on recirculation for four different time steps.
There is almost no difference between solutions. More significant differences can be seen in Figure 3.12 which characterizes the structure of the LEV at a higher angle of attack. An interesting observation made during the temporal study is that it is not simply the structure of the LEV that is different at different time step sizes, but vortex shedding does not become apparent until a non-dimensional time step of 0.001 is used. Based on the grid and temporal independence study Mesh 3 was used with ∆t* = 0.001 for all two-dimensional cases. The revised structured C-grid type mesh is shown in Figure 3.13. The mesh spacing over each dynamic roughness element and the leading edge is 0.001c. The mesh spacing over the remaining surface of the airfoil to the trailing edge has a hyperbolic stretching profile that matches the dynamic roughness element spacing, then stretches to a maximum spacing of 0.027c, then shrinks back to 0.001c at the trailing edge. The normal spacing linearly stretches from 0.00004c at the airfoil surface to 0.02c at the edge of the DR Zone (which is located at a distance 0.65c normal to the airfoil surface). These specifications provide a mesh with a total of 142,822 nodes, as seen in Figure 3.13 and Figure 3.14.  As described above, to model the dynamic roughness the UDF calculates a new node position based on time, required actuation frequency, and actuation amplitude. In both the threedimensional and two-dimensional simulations the chord-wise length of the dynamic roughness element is dictated by the mesh design. In three-dimensional simulations an additional variable is included in the UDF to dictate the span-wise length of the dynamic roughness element; refer to APPENDIX D. The addition of this variable allows the mesh to be developed without having to define the dynamic roughness element's extent in the span-wise direction. It was previously thought that dynamic re-meshing was necessary to allow for the change in mesh geometry caused by the actuation of a dynamic roughness element [5]. Furthermore, dynamic re-meshing requires tetrahedral cells in the zone identified for re-meshing. This approach tends to result in inefficient unstructured mesh zones within the boundary layer at the location of the dynamic roughness elements. Further investigation of the techniques employed by FLUENT to alter the mesh geometry proved this assumption to be false. It was found that if the mesh remains nearly orthogonal to the moving surface then quad shaped cells can be used. Not only this, but the need for dynamic re-meshing is also eliminated and only mesh smoothing is required. This reduces computational time since dynamic re-meshing not only moves nodes to take into account the mesh motion, but also removes or adds nodes as needed to fulfill the mesh density requirements.
By removing the necessity for this extra calculation computational time is reduced. Also, the use of structured quad cells within the boundary layer provides efficient meshes for computational studies and provides the capability of large dynamic roughness amplitudes that were not attainable with the unstructured approach. The evolution as well as the structured quad cell structure of both a two-dimensional dynamic roughness element and cluster of three-dimensional dynamic roughness elements can be referred to in Figure 3.15 and Figure 3.16, respectively.

Two-Dimensional Simulations
As in the experimental analysis, attempts will be made to answer the same three questions posed previously:  How does the LEV development change with respect to Reynolds number?
 How does the LEV development change with respect to reduced oscillation frequency?
 Can dynamic roughness alter the development of the LEV?
 Can a relationship between LEV delay and dynamic roughness characteristics be quantitatively shown?
A consistent repeatable process was developed in regards to running CFD analysis on a rapidly pitching airfoil. At each Reynolds number studied, simulations first were run at zero angle of attack for ten domain flow through times, which is the time it takes for a particle to travel through the entire domain. This result was then used as the initial solution for the pitching case.
In regards to the initial question about Reynolds number dependence, computational results seem to agree with established research as well as the PIV results. As shown in  In terms of LEV development and its dependence on the reduced frequency, the computational results give similar evidence as the PIV analysis. It is clear that as reduced frequency is increased, LEV development is delayed to higher angles of attack. As Reynolds number is increased the ability for dynamic roughness to delay LEV formation increases as well. Since the laminar solver is used, simulations were not performed with a flow condition with a Reynolds number larger than 150,000. Previous research has indicated that some downstream vortex formation may be an artifact of utilizing the laminar solver [9]. To limit the formation of these vortices care was taken to try to remain in a laminar flow regime. To study the effect of amplitude, the previous case of Re = 150,000, k = 0.1, and actuation frequency = 90 Hz was run with an amplitude half of its current size. The results show that even at half the amplitude, LEV development was delayed. The LEV development was not as delayed as with the larger amplitude, but this shows the robustness of dynamic roughness's ability to delay LEV formation, and perhaps its ability to function at off design conditions. If frequency is reduced to 30 Hz the effectiveness of dynamic roughness greatly degrades. Even if the amplitude is increased, this has no effect on LEV delay. Once the amplitude reaches a critical maximum it tends to hasten LEV development. Figure 3.24 has the same flow conditions as previous results, but the frequency of actuation has been reduced to 30 Hz. One can clearly see that LEV development is on par with that of the clean airfoil. One of the most significant discoveries using computational methods was the fact that there appears to be a strict dependence on dynamic roughness actuation frequency and there is not a minimum frequency of actuation "threshold" as is the case in the laminar separation bubble for an airfoil at static angle of attack [5] [6]. This phenomenon is displayed in Figure 3. 25  It is interesting to note that for all the cases in the table shown above a dynamic roughness actuation frequency of 60 Hz produced the most significant delay in LEV development. This leads the author to believe the optimum dynamic roughness frequency of actuation is more coupled with the pitching rate than with flow velocity.   Figure 3.26 is that it appears the curve is starting to reach its asymptotic value as Reynolds number is increasing. This may give the appearance that a fixed value of nondimensional dynamic roughness strength would be suitable for those relatively higher Reynolds numbers, but most likely the onset of turbulent separation and reattachment will alter the required dynamic roughness characteristics. If we take a view slightly to the side of the leading edge and look down the airfoil chord, we notice a small amount of span-wise flow, as shown in Figure 3.28. This span-wise flow may dissipate some energy from the LEV to alter its reattachment point. These subtle differences may also be a result of the use of a mesh more coarse in the three-dimensional studies. The normal and tangential node spacing is slightly larger than the two-dimensional case to keep computational time manageable. Delay of LEV development due to dynamic roughness is similar to the results gathered by twodimensional simulations. An interesting plot was developed and is provided in Figure 3.30. The plot consists of an isosurface plot of a single vorticity magnitude value, contoured by the chord-wise velocity component. With this information it is interesting to see how the vorticity is altered by the dynamic roughness, and seemingly mostly by the first two rows of dynamic roughness elements.

Clean
The very first row seems to develop a very short bulge region, which seems to accelerate flow between adjacent elements. This accelerated flow then creates a long bulge region that seems to remain unaltered by the aft dynamic roughness elements. Although slight differences between two-dimensional and three-dimensional simulations are present, the trend to delay LEV development is the same. With the ability to run simulations on faster computers, a more refined grid may be able to be employed that may bring the twodimensional and three-dimensional simulations closer together in terms of comparison of results.
The main purpose of the three-dimensional simulations was to investigate any span-wise flow that is not captured by the two-dimensional simulations. Since there is very little span-wise flow this provides more validation to the results obtained with two-dimensional analysis.
Nevertheless, each simulation has provided insight into the nature of the dynamic roughness as the airfoil is pitching up. Analyzing both two-dimensional and three-dimensional simulations creates a more complete picture of the flow in and around the dynamic roughness elements.

CHAPTER 4: DISCUSSION
In the research presented, computational and experimental analysis was performed to evaluate the ability of dynamic roughness to alter the development of the leading edge vortex on a pitching airfoil undergoing dynamic stall in a low Reynolds number range of 10 4 ≤ Re c ≤ 1.5 x 10 5 . Both two-dimensional and three-dimensional simulations were completed, as were both planar and stereoscopic PIV analyses. A variety of flow conditions and dynamic roughness characteristics were evaluated. With the results outlined above, dynamic roughness appears to be a good candidate for LEV flow control in certain conditions.
Both experimental and computational results provide further evidence for certain characteristics of dynamic stall that have been previously proposed. LEV development appears to be independent of Reynolds number, as long as the reduced frequency, k, is held constant at each Reynolds number. This fact supports the use of reduced frequency as the characteristic term used to characterize the pitching motion. In contrast to Reynolds number dependency, reduced frequency greatly affects the angle of attack at which LEV development starts, as well as its growth rate. Evidence to support this was observed in both the experimental and computational studies. As reduced frequency is increased, LEV development is delayed to higher angles of attack. This change in LEV development may be related to a vortex shedding frequency change.
It is a hypothesis that there is a relationship between dynamic roughness actuation frequency and vortex shedding frequency. If the vortex shedding frequency could be related to the reduced frequency, which governs the pitching motion, a relationship could be developed between dynamic roughness actuation and reduced frequency. This relationship could easily be inputted to a theoretical flow control system that could sense pitching rate (or be given a prescribed pitching rate) and in turn apply the appropriate frequency of actuation to optimally delay LEV development.
Previous work for static airfoils concluded there was a relationship between dynamic roughness actuation frequency and amplitude [5]. They concluded that if the frequency of actuation was reduced laminar separation could still be prevented, in terms of a laminar separation bubble, if the amplitude increased. This does not seem to be the case for LEV development during dynamic stall. The numerical study showed that even when amplitude was increased to about  CFD results as well as the PIV analysis provides evidence that as Reynolds number increases, the effectiveness of dynamic roughness also increases. This is an interesting discovery since it has been documented and shown in this research that Reynolds number does not have a significant role in LEV formation. If this is the case, then how can Reynolds number indeed be a significant variable in whether dynamic roughness can delay LEV development? One possible answer to this question is perhaps even though the structure and LEV angle of attack onset is not affected by Reynolds number, perhaps there is a slight displacement of the initial separation point downstream during the pitching process. The angle formed by the airfoil surface, separation point, and LEV boundary also appears to be slightly smaller at higher Reynolds number. At some critical Reynolds number these factors may combine to bring the higher momentum fluid close enough to the dynamic roughness elements that it then uses this fluid to energize the fluid flow near the surface of the airfoil enough to delay the recirculation that precedes the vortex formation.
It is clear from the presented results that all methods of analysis show a trend for the ability of dynamic roughness to alter the development of the LEV on a pitching airfoil. It is obvious there are some subtle differences between the methods including recirculation region size and reattachment point. The main source of variation between numerical and experimental data is most likely the presence of free stream turbulence in the wind tunnel that is not modeled in the computational study as well as the absence of the inertial terms in the numerical analysis. Also, a detailed discussion was provided in Chapter 3 concerning the method of pitching simulation.
This will also add to differences between the methods. It was for this reason a two-pronged approach was taken for this research. Showing a trend both computationally and experimentally provide great proof that the trend is not merely a phenomenon associated with one method or the other.

CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS
A brief summary of what this research accomplished is as follows:  For the first time computational and experimental analysis was able to provide proof that dynamic roughness is capable of delaying leading edge vortex (LEV) development on an airfoil undergoing a rapid pitching maneuver. The effectiveness of dynamic roughness increases as Reynolds number is increased and is robust in terms of actuation amplitude, but more sensitive to actuation frequency. Low frequency actuation did not delay the LEV, and in some computational studies at very low Reynolds number even hastened its development.
 Computational and experimental analysis was validated, and in turn provided more evidence to the lack of Reynolds number dependence on LEV development. This research also confirmed the significant dependence LEV development has on reduced frequency, k.
 Through computational analysis it was discovered that there is a departure from what has been observed in steady studies of dynamic roughness as a flow control device. The frequency of actuation required to delay LEV development appears to be a more precise value and not a minimum "threshold".
 A monomial relationship between non-dimensional dynamic roughness strength and Reynolds number was developed.
 Evidence was given that both the planar and stereoscopic PIV experimental technique can be used to capture the development of the LEV, and either is robust enough to phase average even high pitching rates. The difference between stereoscopic and planar results was discussed and further insight desired to understand the contrast.
 Even though it is obvious that three-dimensional flow structures occur during LEV development, the close agreement between two-dimensional and three-dimensional simulations suggests two-dimensional simulations are sufficient to parameterize the effect of dynamic roughness.
It is with hope that this author has at least shown further research in this area of flow control is warranted. Dynamic roughness seems to be a valid flow control device for not only steady laminar flow phenomena like leading edge laminar separation bubbles, but now also for unsteady flow conditions. Future attempts to study dynamic roughness may include:  Development of a more definable, measurable dynamic roughness actuation system. The developed pneumatic system provides the necessary mass flow rate of air in a predictable oscillating fashion, but because there is no lubrication in the motor itself, the motor heats up quickly, which required that heat resistant tubing to be used as the air transfer conduit.
This could include mechanical systems such as cam shafts, or more exotic surface disturbance mechanisms such as piezoelectric materials.
 Development of a pitching mechanism that would allow higher pitching frequencies.
 The PIV system showed it has great ability to be used as a tool to study such unsteady flow. Further investments such as a lens with a longer focal length giving the ability to focus on the leading edge region to produce results with higher resolution within the LEV itself.
 Although it has been stated a search through parameter space for conditions in which LEV development is delayed can be adequately accomplished with two-dimensional CFD, it is apparent that there are interesting structures occurring in the three-dimensional space within the LEV, especially near the dynamic roughness elements. It may prove necessary to develop simulations that incorporate turbulence models, or even Direct Numerical Simulation (DNS).
 More effort could be put for towards creating a UDF that is able to rotate the airfoil while also simulating the dynamic roughness elements. If such a UDF is developed, the inertial terms would no longer be neglected and a more accurate simulation can be obtained.
 This research may also be expanded to biological flight regimes, where it is known some biological fliers take advantage of the LEV development to enhance their lift.

APPENDIX A
User Defined Function (UDF) to rotate an airfoil or domain.

APPENDIX B
User Defined Function (UDF) to apply a variable velocity vector over the velocity inlet boundary.