ARL-TR-7995 ● APR 2017

US Army Research Laboratory

Computational Investigation of a PitchOscillating Canard on Lift Enhancement and 

Tip Vortex Mitigation

by Joseph D Vasile

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ARL-TR-7995 ● APR 2017

US Army Research Laboratory

Computational Investigation of a PitchOscillating Canard on Lift Enhancement and 

Tip Vortex Mitigation

by Joseph D Vasile

Weapons and Materials Research Directorate, ARL

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Computational Investigation of a Pitch-Oscillating Canard on Lift Enhancement 

and Tip Vortex Mitigation

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6. AUTHOR(S)

Joseph D Vasile

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AH43

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US Army Research Laboratory

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Aberdeen Proving Ground, MD 21005-5066

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ARL-TR-7995

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14. ABSTRACT

A 2-D National Advisory Committee for Aeronautics (NACA) 0012 airfoil and 3-D NACA 0015 canard undergoing a 

dynamic ramp pitch-oscillating motion were investigated computationally. The effect of amplitude and reduced frequency on 

augmenting lift for both configurations was considered. The study showed lift enhancement for both configurations at M∞ = 

0.5 and M∞ = 0.2 for all amplitudes and reduced frequencies at angles of attack poststall. Furthermore, the effect of the 

dynamic motion on the development of the tip vortex was explored. The time-averaged flow solution for the pitch-oscillating 

canard revealed lower vorticity magnitude and less coherence of the tip vortex downstream. For the parameters investigated, 

increasing the amplitude of the oscillation proved to be the most effective in enhancing lift as well as reducing the strength of 

the tip vortex. The encouraging results indicate that further research in unsteady aerodynamics to increase the control 

authority of canard-controlled projectiles is necessary. 

15. SUBJECT TERMS

CFD, dynamic stall, tip vortex, enhanced canard control, lift augmentation

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19a. NAME OF RESPONSIBLE PERSON

Joseph D Vasile

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Contents

List of Figures iv

List of Tables v

Acknowledgments vi

1. Introduction 1

2. Technical Approach 2

2.1 Geometries and Computational Domains 3

2.1.1 Two-Dimensional Airfoil 3

2.1.2 Three-Dimensional Canard 4

2.2 Computational Fluid Dynamics (CFD) Solution Technique 5

2.3 Flowfield and Boundary Conditions 6

3. Results and Discussion 6

3.1 Two-Dimensional Airfoil 6

3.2 Three-Dimensional Canard 9

3.2.1 Unsteady Lift Enhancement 9

3.2.2 Tip Vortex Mitigation 12

4. Conclusion 26

5. References 27

List of Symbols, Abbreviations, and Acronyms 32

Distribution List 33
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iv

List of Figures

Fig. 1 Two-dimensional airfoil geometry with mesh.......................................4

Fig. 2 Three-dimensional canard and computational domain..........................4

Fig. 3 Prescribed dynamic ramp motion for the 2-D airfoil at k2 = 0.5 (a) and 

1.0 (b).....................................................................................................7

Fig. 4 Lift coefficient of dynamic airfoil as a function of equivalent mean 

angle of attack, unfiltered (a, c) and filtered (b, d), for reduced 

frequency of oscillation of k2 = 0.5 (a–b) and 1.0 (c–d), M∞ = 0.5 .......8

Fig. 5 Lift coefficient of dynamic canard as a function of equivalent mean 

angle of attack, unfiltered (a, c) and filtered (b, d), for reduced 

frequency of oscillation of k2 = 0.5 (a–b) and 1.0 (c–d), M∞ = 0.5 .....10

Fig. 6 Lift coefficient of dynamic canard as a function of equivalent mean 

angle of attack, unfiltered (a, c) and filtered (b, d), for reduced 

frequency of oscillation of k2 = 0.5 (a–b) and 1.0 (c–d), M∞ = 0.2 .....11

Fig. 7 Prescribed dynamic motion of 3-D canard for tip vortex mitigation at 

k2 = 1.0, M∞ = 0.5 ...............................................................................12

Fig. 8 Contour of time-accurate nondimensional vorticity magnitude near 

canard tip (y/c = 0.1 inboard from tip) undergoing pitch-oscillation 

about α = 10° at an amplitude of A = 1.5° and reduced frequency 

k2 = 0.5 at M∞ = 0.5 .............................................................................13

Fig. 9 Contour of time-accurate nondimensional vorticity magnitude near 

canard tip (y/c = 0.1 inboard from tip) undergoing pitch-oscillation 

about α = 10° at an amplitude of A = 1.5° and reduced frequency 

k2 = 1.0 at M∞ = 0.5 .............................................................................13

Fig. 10 Contour of time-accurate nondimensional vorticity magnitude near 

canard tip (y/c = 0.1 inboard from tip) undergoing pitch-oscillation 

about α = 10° at an amplitude of A = 5.0° and reduced frequency 

k2 = 0.5 at M∞ = 0.5 .............................................................................14

Fig. 11 Contour of time-accurate nondimensional vorticity magnitude near 

canard tip (y/c = 0.1 inboard from tip) undergoing pitch-oscillation 

about α = 10° at an amplitude of A = 5.0° and reduced frequency 

k2 = 1.0 at M∞ = 0.5 .............................................................................14

Fig. 12 Contour of time-averaged (over the last oscillation cycle) 

nondimensional vorticity magnitude near canard tip (y/c = 0.1 inboard 

from tip) for baseline (a), a = 1.5° (b, d) and A = 5° (c, e) at reduced 

frequencies k2 = 0.5 (b–c) and 1.0 (d–e), M∞ = 0.5 .............................15

Fig. 13 Contour of time-averaged (over the last oscillation cycle) 

nondimensional vorticity magnitude near canard tip (y/c = 0.1 inboard 

from tip) for baseline (a), a = 1.5° (b, d) and A = 5° (c, e) at reduced 

frequencies k2 = 0.5 (b–c) and 1.0 (d–e), M∞ = 0.2 .............................16
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v

Fig. 14 Contour of time-averaged (over the last oscillation cycle) 

nondimensional TKE, near canard tip (y/c = 0.1 inboard from tip) for 

baseline (a), A = 1.5° (b, d) and A = 5° (c, e) at reduced frequencies 

k2 = 0.5 (b–c) and 1.0 (d–e), M∞ = 0.5.................................................18

Fig. 15 Contour of time-averaged (over the last oscillation cycle) 

nondimensional TKE, near canard tip (y/c = 0.1 inboard from tip) for 

baseline (a), A = 1.5° (b, d) and A = 5° (c, e) at reduced frequencies 

k2 = 0.5 (b–c) and 1.0 (d–e), M∞ = 0.2.................................................19

Fig. 16 Contours of time-averaged nondimensional vorticity (a–c), q-criterion 

(d–f), and tangential velocity (g–i) at x/c = 2 downstream of canard tip 

for baseline (a, d, and g), a = 1.5° (b, e, and h), and a = 5° (c, f, and i) 

case at reduced frequency, k2 = 1.0, M∞ = 0.5.....................................21

Fig. 17 Distributions of time-averaged nondimensional vorticity magnitude 

along centerline in both spanwise (z*, solid) and cross-stream 

(y*, dashed) directions at x/c = 1 to 10 downstream of canard tip for 

baseline (a), a = 1.5° (b, d) and 5.0° (c, e), at reduced frequencies, 

k2 = 0.5 (b–c) and 1.0 (d–e), at M∞ = 0.5.............................................22

Fig. 18 Distributions of time-averaged nondimensional tangential velocity 

along centerline in both spanwise (z*, solid) and cross-stream 

(y*, dashed) directions at x/c = 1 to 10 downstream of canard tip for 

baseline (a), a = 1.5° (b, d) and 5.0° (c, e), at reduced frequencies, 

k2 = 0.5 (b–c) and 1.0 (d–e), at M∞ = 0.5.............................................23

Fig. 19 Line plots of time-averaged nondimensional peak vorticity (a), 

tangential velocity (b), circulation (c), Q-criterion (d), and vortex core 

radius (e) at x/c = 1 to 10 downstream of canard tip for baseline, A = 

1.5° , and A = 5° cases at reduced frequencies, k2 = 0.5 and 1.0, at M∞

= 0.5 .....................................................................................................25

List of Tables

Table 1 Computational test matrix......................................................................3
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vi

Acknowledgments

The author would like to thank Dr James DeSpirito, US Army Research Laboratory 

(ARL), for providing the geometry and computational domain for both the 2-D

airfoil and 3-D canard configurations. Furthermore, many thanks to Dr DeSpirito 

and Dr Sidra Silton (ARL) for their help and discussions both relating to this work 

and with regards to computational fluid dynamics fundamentals and techniques. 

This work was supported in part by a grant of high-performance computing time 

from the US Department of Defense High Performance Computing Modernization 

program at the ARL Department of Defense Supercomputing Resource Center 

(DSRC) at Aberdeen Proving Ground, Maryland, and the US Air Force Research 

Laboratory DSRC at Wright Patterson Air Force Base, Dayton, Ohio.
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1

1. Introduction

Current aerodynamic research for guided munitions has primarily been focused on 

improving the maneuverability of projectiles to perform at a wider range of 

engagement and operating conditions.1–6 Moreover, these efforts focus on 

increasing the control authority while concurrently reducing adverse wake effects 

from movable lifting surfaces.7–9 Extensive research has shown significant control 

authority detriment due to the flow interactions between the downwash of trailingedge vortices from control surfaces impacting the tail fins downstream.10–19 To 

address these issues, the US Army Research Laboratory (ARL) is investigating 

techniques that can increase maneuverability by both augmenting lift and 

mitigating the vortex-fin flow interactions. Viable techniques will expand the 

capabilities of guided projectiles, through increased accuracy and precision, against 

both stationary and moving targets. 

One area of research that has demonstrated a significant increase in lift for airfoils 

has been unsteady aerodynamics.20–22 Specifically, the benefit of oscillatory 

pitching and plunging airfoils have been extensively studied.23–29 This dynamic 

motion can result in higher lift as well as delay the onset of stall. The unsteady lift 

augmentation is the product of an airfoil undergoing rapid change in angle of attack, 

which causes a leading-edge vortex to be produced and then shed downstream 

along the suction side of the airfoil. The vortex increases suction pressure as it rolls 

downstream, temporarily increasing lift. This periodic lift augmentation is 

generally referred to as dynamic stall.30–33 A comprehensive collection of studies 

have examined dynamic stall and its application. However, to the best of the 

author’s knowledge, none have studied the viability of using dynamic stall for 

increased performance of canard-controlled projectiles. Furthermore, very little 

work has been performed investigating the effect of dynamic stall on the 

development of the tip vortex. The majority of these studies focus on either 2-D

vortex street34–36 (i.e., spanwise rollers) or rotorcraft applications, specifically 

studying the interaction of rotor blades of a helicopter impacting vortices shed by

preceding rotor blades(i.e., blade-vortex interactions).

37–40

The purpose of the present study is to determine if unsteady pitch-oscillating 

canards could be a viable solution to increase the control authority of guided 

projectiles. The effect of a pitch-oscillating canard for lift augmentation and its 

effectiveness in reducing the strength of the tip vortex to reduce adverse flow 

interactions downstream is investigated. The computational study is split into 2 

investigations. First, lift augmentation for an unsteady 2-D airfoil at M∞ = 0.5 is
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considered. Second, both lift enhancement and tip vortex mitigation of an unsteady 

3-D canard at M∞ = 0.2 and 0.5 are investigated. In both studies, the effect of 

reduced frequency and amplitude of the oscillation on dynamic stall was an area of 

interest. 

2. Technical Approach

The computational investigation is split as follows: 1) a 2-D airfoil (National 

Advisory Committee for Aeronautics [NACA] 0012) study to reduce the number 

of parameters (i.e., reduced frequency and amplitude) for the prescribed ramposcillation that enhances lift at M∞ = 0.5 and 2) a 3-D rectangular planform canard 

(NACA 0015 cross-sectional airfoil) associated with typical dimensions used for 

canard-controlled projectiles at M∞ = 0.5 and 0.2. In addition to assessing lift 

augmentation, the effect of the dynamic motion on the development of the tip 

vortex was investigated.

A ramp-oscillation motion was prescribed for each computational case (see Section 

3.1). The dynamic ramp motion increases the angle of attack of the lifting surface 

linearly while superimposing a high-frequency oscillation about the quarter-chord 

of the airfoil. The mathematical relationship of the rotation of the lifting surface 

with respect to the freestream velocity, about the quarter-chord, as a function of 

time, is described in Eq. 1.

αα(tt) = ωω1tt + AA ∙ ssssss(ωω2tt), (1)

where α(t) is the angle of attack as a function of time, t, ω1, and ω2 are the rate and 

frequency of the linear ramp and oscillation, respectively, and A is the amplitude of 

the oscillation. This dynamic motion was chosen in order to model a practical 

command for canard-controlled projectiles. Furthermore, the dynamic motion was 

selected to exploit the full dynamic motion effect as found in previous unsteady 

aerodynamic studies,

20–33 namely the superposition of rapidly increasing angle of 

attack to delay stall (ramp) and periodic lift augmentation due to classic dynamic 

stall (oscillation). Through the combination of these 2 mechanisms, it was 

hypothesized that the same dynamic effect could be achieved with less amplitude 

of oscillation in both augmenting lift as well as delaying stall. The rate and 

frequency of the dynamic motion was selected based on a reduced frequency value, 

k. As defined in most studies on unsteady aerodynamics, the reduced frequency is 

mathematically expressed in Eq. 2.

kkjj = ωωjjcc

2UU∞

�

jj=1,2

, (2)
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where c is the chord length of the airfoil, U∞ is the freestream velocity, and j denotes 

either the linear ramp rate, 1, or oscillation frequency, 2. For the present study, the 

reduced frequency of the linear ramp rate was held constant at k1 = 0.005. This 

value was selected based on reference values of usual actuator driven canardcontrolled rate (e.g., 5–13 Hz). Note that the dynamic stall effect of enhancing lift 

is not expected to originate from the linear ramp motion due to the relatively low 

reduced frequency value. The dynamic stall effect is dependent on the reduced 

frequency of the oscillation and is most noticeable when the value is greater than 

0.05. The reduced frequency for oscillatory motion was studied at k2 = 0.5 and 1.0. 

Furthermore, 4 amplitudes, A = 0°, 0.5°, 1.5°, and 5°, were investigated for the 

2-D case, whereas 3 amplitudes, A = 0°, 1.5°, and 5°, were studied for the 3-D case. 

For both computational cases, the linear ramp motion (i.e., pitch oscillation set to 

zero amplitude [A = 0°]), was selected for the baseline case. Table 1 summarizes

the test matrix for both computational cases.

Table 1 Computational test matrix

Case M∞ k1 k2 A 

(°)

2-D airfoil 

(NACA 0012)

0.5 0.005 0.5, 1.0 0, 0.5, 1.5, 5

3-D canard

(NACA 0015)

0.2, 0.5 0.005 0.5, 1.0 0, 1.5, 5

2.1 Geometries and Computational Domains

2.1.1 Two-Dimensional Airfoil

The 2-D airfoil used for the initial simulations, shown in Fig. 1, has a chord length, 

c = 1 m, with a cross-sectional profile of a NACA 0012 airfoil. The computational 

domain was meshed with GAMBIT v2.4 from ANSYS Fluent, a C-grid mesh 

containing approximately 55,000 cells, and has an approximate radial distance of 5 

chord lengths from the leading edge of the airfoil to the domain surfaces. The first 

cell spacing was set to 4 × 10–6 m to ensure y+ values were at or below 1.0 along 

the surface of the airfoil for accurate boundary layer prediction. 
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Fig. 1 Two-dimensional airfoil geometry with mesh

2.1.2 Three-Dimensional Canard

The 3-D canard model, shown in Fig. 2, is an unswept, finite canard with a chord 

length, c = 0.021 m, a semi-span, b/2 = 0.063 m, and a cross-sectional NACA 0015 

airfoil profile. The computational domain was meshed with MIME from Metacomp 

Technologies.41 The rectangular domain spans an approximately 48 chord lengths 

equidistant in both streamwise and normal directions from the leading edge of the 

canard. The width of the domain is approximately 22 chord lengths from the root 

of the canard to the outboard domain surface. A mesh density cylinder was used to 

refine the mesh in the region near the canard tip and wake region to resolve the tip 

vortex. The origin of the density box was aligned to the canard tip, with a radius of 

approximately 2 chord lengths, spanning approximately 10 chord lengths 

downstream (Fig. 2b). The total mesh size was approximately 33 M cells, consisting 

of triangular surface cells, with prism layers used along the surface and tetrahedral 

cells for the rest of the domain. The first cell wall spacing of the prism layers was 

set to 2 × 10–6 m to ensure y+ values of less than 1 along the surface of the canard.

Fig. 2 Three-dimensional canard and computational domain
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2.2 Computational Fluid Dynamics (CFD) Solution Technique

The commercially available code, CFD++ v15.1.1 by Metacomp Technologies, 

Inc.,

42 was used for all simulations. The 2-D or 3-D compressible Reynoldsaveraged Navier-Stokes (RANS) equations were numerically solved to compute the 

flow solution for each respective case. Both steady-state and transient simulations 

were employed.

Simulations were performed on the Cray XC40 (Excalibur) and Cray XC30 

(Lightning) supercomputers located at ARL’s Department of Defense 

Supercomputing Resource Center (DSRC) at Aberdeen Proving Ground, Maryland, 

and US Air Force Research Laboratory DSRC at Wright-Patterson Air Force Base, 

Ohio, respectively.

For all steady-state simulations, the solution was advanced toward convergence 

using a point-implicit time-integration scheme with local time-stepping defined by 

the Courant-Friedrichs-Lewy (CFL) number. A linear ramping schedule was used 

to gradually increase the CFL number from 1 to 50 over the first 100 iterations,

after which the CFL remained constant until convergence was reached. The 

multigrid W-cycle method with a maximum of 4 cycles and a maximum of 20 grid 

levels were used to accelerate convergence. Implicit temporal smoothing was 

applied for the increased stability, which is especially useful where strong transients 

arise. The spatial discretization function was a second-order, upwind scheme using 

a Harten-Lax-van Leer-Contact Riemann solver and Metacomp’s multidimensional Total-Variation-Diminishing flux limiter. Convergence for the total 

forces and moments was typically achieved in a few thousand iterations, with 

residuals reducing at 5 orders or more in magnitude. 

For all transient RANS simulations, the dual-time step method was employed with 

the point-implicit time-integration scheme using a global time step and an inner 

time step. For the transient planar pitching simulations, the global time step of the 

transient simulation was selected based on 100 steps per cycle of pitch-oscillation 

with 20 inner iterations per global time step. The number of global time steps were 

selected based on the time it took the dynamic ramp schedule to reach an angle of 

attack of approximately 25°. 

For the 2-D simulation, a realizable k-ε 2-equation turbulence model was used, 

whereas for the 3-D simulation, Menter’s k-ω Shear Stress Transport 

2-equation model was used. For the current study, initialization of the turbulence 

transport was completed by setting the turbulence intensity to 3% and the turbulentto-molecular viscosity ratio to 50, as the length scale was not known. The choice

of turbulence model may be an important factor in numerical modeling of the tip 

vortex and will need to be further investigated. 
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2.3 Flowfield and Boundary Conditions

All computations were completed using a free-stream temperature and pressure of 

288.15 K and 101,325 Pa, respectively. The study was conducted at M∞ = 0.5

(170 m/s) and 0.2 (68 m/s). The wind-axis coordinate system was used such that 

streamwise velocity, U, is positive downstream; cross-stream velocity, V, is 

positive toward the sidewall (inboard direction); and normal velocity, W, is positive 

upward. The free-stream velocity and chord length of the geometries were used to 

nondimensionalize important parameters and coordinates, denoted by an asterisk

(*). The domain was initialized using free-stream conditions everywhere. The farfield boundary was set as “characteristic-based” inflow/outflow. This boundary 

condition takes the specified free-stream conditions and solves a Riemann problem 

at the boundary using the supplied data as a virtual state outside the domain. The 

surfaces of the airfoil and canard were modeled as adiabatic, no-slip, viscous walls 

with solve-to-wall methodology. The sidewall for the 3-D domain was modeled as 

an inviscid slip wall. For the transient simulations, the dynamic motion was 

prescribed through a file-based single-axis rotation, which allowed for the entire

grid to rotate as a function of time. 

3. Results and Discussion

3.1 Two-Dimensional Airfoil

The 2-D NACA 0012 airfoil case was first investigated to determine if the dynamic 

stall effect could be achieved from the prescribed dynamic ramp motion at M∞ = 

0.5. The dynamic ramp schedule of the airfoil at 2 reduced frequencies (k2 = 0.5 

and 1.0) and 4 amplitudes (A = 0.0, 0.5, 1.5, and 5.0) is presented in Figs. 3a and 

3b, respectively. The dynamic ramp schedule is the combination of a linear ramp 

superimposed with a high-frequency oscillation. For this study, the linear rate is 

held constant, while the oscillation frequency was varied. The high-frequency 

oscillation begins when the angle of attack of the airfoil is α = 5°. This angle was 

selected to ensure that the airfoil never experiences a negative angle of attack during 

the ramp schedule. The baseline case is denoted by the dashed black line.
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Fig. 3 Prescribed dynamic ramp motion for the 2-D airfoil at k2 = 0.5 (a) and 1.0 (b)

The sectional lift coefficient, CL, of the airfoil was computed in CFD++ for all 

parameter combinations. The equation for the section lift coefficient for the 2-D

airfoil case is presented in Eq. 3.

CCLL = LL

1

2

ρρ∞UU∞

2 cc , (3)

where L is the lift force, ρ∞ and U∞ are the free-stream density and velocity, 

respectively, and c is the chord length of the airfoil. To compare the lift values 

between the actuated (i.e., oscillatory) cases with the baseline for a given angle of 

attack, the lift coefficient was plotted against the equivalent mean angle of attack 

(i.e., baseline angle of attack). The lift coefficient as a function of angle of attack 

for the baseline (black dashed line) and the dynamic motion cases is presented in 

Fig. 4. The baseline case shows the typical linear increase of lift with increasing 

angle of attack until approximately α = 9°. At this angle the flow begins to separate 

from the upper surface of the airfoil, which causes the lift curve to become 

nonlinear. At α = 14°, the airfoil stalls, characterized by a peak followed by a 

precipitous drop in lift. Further increase in angle of the attack results in unsteady, 

nonlinear lift along with a large increase in drag. For the investigated configuration, 

the lift coefficient oscillates since the airfoil is pitch oscillating about the mean 

angle of attack (Figs. 4a and 4c). The period of the oscillation is correlated to the 

reduced frequency of the prescribed dynamic motion. For all amplitudes, the lower 

reduced frequency, k2 = 0.5, exhibits a longer period as well as larger fluctuations 

in lift than the higher reduced frequency, k2 = 1.0, case. The larger the amplitude 

of oscillation, the larger the fluctuation in lift. For both cases, the lift fluctuation 

remains sinusoidal about the mean angle of attack until approximately α = 9°, when 

the peaks of the lift curve become deformed. The lift fluctuation behaves sinusoidal 

longer for the lower reduced frequency case than the higher-frequency case. These 

fluctuations in lift continue with increase in angle of attack. 
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Fig. 4 Lift coefficient of dynamic airfoil as a function of equivalent mean angle of attack, 

unfiltered (a, c) and filtered (b, d), for reduced frequency of oscillation of k2 = 0.5 (a–b) and 

1.0 (c–d), M∞ = 0.5

The large fluctuations in lift make it difficult to distinguish the full effect of the 

dynamic motion in enhancing lift; therefore, the lift data for both cases was filtered 

and is presented in Figs. 4b and 4d. The lift curves for the actuated cases were 

filtered using a low pass filter to remove the oscillation due to the dynamic motion. 

A fast Fourier transform algorithm was used to analyze the frequency components 

of the lift curve and to perform the filter. From the filtered data for both reduced 

frequencies, the smallest amplitude case, A = 0.5°, seems to have little to no effect 

on enhancing the lift of the airfoil, whereas the largest amplitude case, A = 5°, 

shows considerable lift enhancement at higher angles of attack compared with the 

baseline. Furthermore, the A = 1.5° and 5° cases do not exhibit the precipitous drop 

in lift at α = 14°, therefore indicating that stall was successfully delayed. The results 

from the 2-D case suggest that lift augmentation is possible using a dynamic 

motion. The favorable results from the 2-D case warranted further exploration of 

the dynamic motion effect for 3-D configurations.
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3.2 Three-Dimensional Canard

The 3-D canard (NACA 0015 airfoil) case was studied to investigate the dynamic 

stall effect on a more-realistic control surface with dimensions that are typical of 

canard-controlled projectiles. The favorable results from the 2-D case were used to 

help determine the computational test matrix. Following the same procedure as the 

2-D case, a prescribed ramp-oscillation dynamic motion was simulated for the 3-D

canard case. 

3.2.1 Unsteady Lift Enhancement

Similar to the 2-D airfoil case (Fig. 3), the dynamic ramp schedule of the 3-D canard 

is a linear ramp superimposed with high-frequency oscillation beginning when the 

angle of attack of the airfoil equals α = 5°. Two reduced frequencies (k2 = 0.5 and 

1.0) at 3 amplitudes (A = 0.0, 1.5, and 5.0) were simulated at 2 free-stream Mach 

numbers, M∞ = 0.5 and 0.2. The lift coefficient for the 3-D canard case was 

computed similarly to the 2-D case (Eq. 3) and is mathematically expressed in 

Eq. 4. 

CCLL = LL

1

2

ρρ∞UU∞

2 SS , (4)

where S is the planform area of the canard (i.e., SS = cc ∙ bb/2). The lift coefficient as 

a function of angle of attack for the baseline (black dashed line) and the dynamic 

motion cases at M∞ = 0.5 and 0.2 are presented in Fig. 5 and Fig. 6, respectively. 

Similar to the 2-D case, the baseline lift distribution for the 3-D case increases 

linearly until α = 10° then nonlinearly until reaching a peak at approximately α = 

14° (Fig. 5). Note that the peak value of lift is less than the peak achieved for the 

2-D airfoil case. The reduction in lift is due to the downwash generated by the tip 

vortex. Furthermore, there is a less-pronounced drop in lift after stall. The unfiltered 

data (Fig. 5a and 5c) shows fluctuations in lift at both reduced frequencies and 

increasing fluctuations with increasing amplitude of oscillation. 

Following the same procedure as the 2-D case, the lift coefficient data was filtered 

to remove the frequency associated with the prescribed oscillation frequency. The 

filtered data (Fig. 5b and 5d) show that the dynamic motion is ineffective in 

increasing lift at small angles of attack but is able to increase lift past the stall angle, 

thus delaying the onset of stall. Although the data have been filtered, there is still 

an oscillation of lift present at higher angles of attack, suggesting that the inherent 

nonlinear behavior of poststall is still present for the actuated cases. The results 

indicate that the amplitude of the oscillation is a more-sensitive parameter for lift 

enhancement than the effect of reduced frequency of the oscillation. The 

augmentation of lift is more noticeable for the larger amplitude. The results suggest 
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that the higher reduced frequency, k2 = 1.0, for A = 1.5°, is more effective in 

enhancing lift than the lower reduced frequency (Fig. 5d). Moreover, the effect of 

reduced frequency is less noticeable for the higher amplitude, A = 5°. The results 

suggest that unsteady lift enhancement is possible for canard-controlled projectiles. 

However, achieving high-amplitude (e.g., >1.5°) oscillations at the given reduced 

frequency could prove to be impractical.

Fig. 5 Lift coefficient of dynamic canard as a function of equivalent mean angle of attack, 

unfiltered (a, c) and filtered (b, d), for reduced frequency of oscillation of k2 = 0.5 (a–b) and 

1.0 (c–d), M∞ = 0.5

The lift coefficient as a function of equivalent mean angle of attack for all parameter 

combinations at M∞ = 0.2 is presented in Fig. 6. Compared with that of the higherspeed case, M∞ = 0.5, the baseline lift distribution for the M∞ = 0.2 case increases 

linearly until α = 14° then nonlinearly until reaching a peak at approximately α = 

19° (Fig. 6). The lower-speed case stalls at a larger angle than the higher-speed case 

at the same reduced frequency, k1 = 0.005, while undergoing linear ramp motion. 

For the actuated cases, similar behavior to that of the higher-speed case is exhibited; 

the unfiltered data show large oscillation in lift for the canard that is magnified 

while undergoing prescribed large amplitude oscillation (i.e., A = 5°). The lift 

coefficient distribution increases proportionally to the prescribed dynamic motion 

at lower angles of attack. However, it seems to exhibit nonlinear behavior poststall. 
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Furthermore, the lower reduced frequency causes the canard to achieve larger lift 

values poststall than the higher reduced frequency at the same amplitude (Fig. 6a). 

As described previously, the lift coefficient data were filtered to remove the 

frequency associated with the prescribed oscillation and are presented in Figs. 6b 

and 6d. As was observed for the higher-speed case, the dynamic motion is 

ineffective in increasing lift at small angles of attack. However, it is able to delay 

the onset of stall. For all cases, the larger amplitude, A = 5°, is more effective in 

augmenting lift at higher angles of attack.

Fig. 6 Lift coefficient of dynamic canard as a function of equivalent mean angle of attack, 

unfiltered (a, c) and filtered (b, d), for reduced frequency of oscillation of k2 = 0.5 (a–b) and 

1.0 (c–d), M∞ = 0.2

The influence of the tip vortex is evident through the reduction in peak lift 

coefficient of the 3-D case compared with the peak achieved for the 2-D case. The 

vortex strength increases with angle of attack, creating downwash that effectively 

reduces lift while increasing drag of the canard. In addition to the lift detriment, the 

tip vortex trails downstream, affecting the performance of control surfaces in the 

wake of the canard. Therefore, it is of high interest to investigate the effect of 

dynamic motion on the tip vortex.
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3.2.2 Tip Vortex Mitigation

The effect of pitch oscillation on the development of the tip vortex was simulated 

using a modified ramp-oscillation motion. Similar to the previous prescribed 

motion, this motion superimposes a high-frequency oscillation on a linear ramp. 

However, unlike the previous prescribed motion, the modified motion performs the 

high-frequency oscillation when the canard reaches α = 10°. Furthermore, when the 

oscillation begins, the motion is held at a mean value of α = 10°, which results in a 

motion in which pitch oscillates about α = 10°. The prescribed dynamic ramp 

schedule for the baseline (A = 0°) and actuated cases (A = 1.5° and 5°) at a reduced 

frequency of k2 = 1.0, at M∞ = 0.5, is presented in Fig. 7. This modified dynamic 

motion is mathematically expressed in Eq. 5.

αα(tt) = � ωω1tt if α ≤ 10°

AA (ωω2tt) + 10° if α > 10° . (5)

Fig. 7 Prescribed dynamic motion of 3-D canard for tip vortex mitigation at k2 = 1.0, 

M∞ = 0.5

The tip vortex was qualitatively assessed using contour slices of the domain near 

the canard tip. A plane of nondimensional vorticity magnitude for all combinations 

near the canard tip (y/c = 0.1, or 2 mm, inboard from the tip) at M∞ = 0.5 undergoing 

pitch oscillation about α = 10° at k2 = 0.5 and 1.0 is presented in the following 

videos, Figs. 8–11.
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CONTOU~4.MP4

Fig. 8 Contour of time-accurate nondimensional vorticity magnitude near canard tip 

(y/c = 0.1 inboard from tip) undergoing pitch-oscillation about α = 10° at an amplitude of 

A = 1.5° and reduced frequency k2 = 0.5 at M∞ = 0.5

CONTOU~3.MP4

Fig. 9 Contour of time-accurate nondimensional vorticity magnitude near canard tip 

(y/c = 0.1 inboard from tip) undergoing pitch-oscillation about α = 10° at an amplitude of 

A = 1.5° and reduced frequency k2 = 1.0 at M∞ = 0.5
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CONTOU~1.MP4

Fig. 10 Contour of time-accurate nondimensional vorticity magnitude near canard tip 

(y/c = 0.1 inboard from tip) undergoing pitch-oscillation about α = 10° at an amplitude of 

A = 5.0° and reduced frequency k2 = 0.5 at M∞ = 0.5

CONTOU~2.MP4

Fig. 11 Contour of time-accurate nondimensional vorticity magnitude near canard tip 

(y/c = 0.1 inboard from tip) undergoing pitch-oscillation about α = 10° at an amplitude of 

A = 5.0° and reduced frequency k2 = 1.0 at M∞ = 0.5

Clearly, the development of the tip vortex is affected due to actuation. The pitchoscillation causes an oscillation in vorticity concentration downstream. To fully 

analyze and compare the development of the tip vortex, the flow solution was timeaveraged over the last cycle of oscillation for all parameter combinations. A plane 

of nondimensional vorticity magnitude for all combinations near the canard tip 

(y/c = 0.1, or 2 mm, inboard from the tip) at M∞ = 0.5 and 0.2 is presented in 
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15

Figs. 12 and 13, respectively. The qualitative results indicate that the development 

of the tip vortex downstream for both speeds, M∞ = 0.5 and 0.2, are almost identical. 

Fig. 12 Contour of time-averaged (over the last oscillation cycle) nondimensional vorticity 

magnitude near canard tip (y/c = 0.1 inboard from tip) for baseline (a), a = 1.5° (b, d) and 

A = 5° (c, e) at reduced frequencies k2 = 0.5 (b–c) and 1.0 (d–e), M∞ = 0.5
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Fig. 13 Contour of time-averaged (over the last oscillation cycle) nondimensional vorticity 

magnitude near canard tip (y/c = 0.1 inboard from tip) for baseline (a), a = 1.5° (b, d) and 

A = 5° (c, e) at reduced frequencies k2 = 0.5 (b–c) and 1.0 (d–e), M∞ = 0.2

The time-averaged vorticity magnitude for the baseline case at both speeds show 

the development of a vortex that trails far downstream (Figs 12a and 13a). The 

vortex is characterized by a concentration of increased vorticity magnitude, which 

remains coherent downstream. Farther downstream, the vorticity concentration 

diffuses due to viscosity. For all combinations, there is a clear reduction in vorticity 

magnitude when the canard undergoes dynamic motion. Because of the pitch 

oscillating motion, the vorticity magnitude is less, and the vortex is less coherent 

(Figs. 12b–e and 13b–e). The radial vorticity influence increases in size farther 

downstream most likely due to increased viscous diffusion. The larger amplitude 

of oscillation is more effective in reducing the magnitude but causes the vortex 
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17

influence to increase radially (Figs. 12c and 12e, and 13c and 13e). The effect of 

reduced frequency is evident in the shape of the wake flow from the canard. The 

vorticity magnitude concentration appears as a standing wave in which the nodes 

of the wave are associated with high concentrations of vorticity. Moreover, since 

the higher reduced frequency is twice the lower reduced frequency value, the wave 

length of the vorticity concentration wave of the higher reduced frequency is half 

the length of the lower reduced frequency actuated case.

In addition to vorticity magnitude, the turbulent kinetic energy (TKE) was 

investigated downstream of the canard tip. The development of a tip vortex is 

associated with an increase of the TKE due to 2 mechanisms: 1) the introduction of 

an unsteady coherent flow structure and 2) the random velocity fluctuations present 

in the mean shear flow of the tip vortex core. The normalized TKE (TKE*) is 

defined as

TTTTTT∗ = 1

2

�uu′uu′+vv′vv′+ww′ww′�

UU∞

2 , (6)

where u’, v’, and w’ are the fluctuating components of velocity obtained from 

Reynolds decomposition of the velocity field. The time-averaged, nondimensional 

TKE* for all parameter combinations near the canard tip at M∞ = 0.5 and 0.2 is 

presented in Figs. 14 and 15, respectively. As previously observed for vorticity 

magnitude, the TKE field for all combinations at both speeds, M∞ = 0.5 and 0.2, 

are qualitative similar. The baseline case shows high concentration of TKE 

downstream of the canard tip due to the formation of the vortex. There is a higher 

concentration of TKE closer to the trailing edge for the higher speed; however, the 

region is larger radially for the lower speed. At the lower speed, the tip vortex 

exhibits more unsteadiness, evident by large regions of TKE farther downstream 

compared with the higher-speed case. Farther downstream, for both speeds, the 

TKE diffuses due to viscosity. The effect of actuation is shown through the 

distribution of the TKE concentration downstream. Similar to the vorticity field, 

the shape of the TKE region of the tip vortex is dependent on the actuation 

frequency. The results show that actuation causes TKE to diffuse sooner 

downstream compared with the baseline. Moreover, increasing the amplitude of 

actuation augments diffusion, which is shown to be more effective than increasing 

actuation frequency. 
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Fig. 14 Contour of time-averaged (over the last oscillation cycle) nondimensional TKE, near 

canard tip (y/c = 0.1 inboard from tip) for baseline (a), A = 1.5° (b, d) and A = 5° (c, e) at 

reduced frequencies k2 = 0.5 (b–c) and 1.0 (d–e), M∞ = 0.5
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Fig. 15 Contour of time-averaged (over the last oscillation cycle) nondimensional TKE, near 

canard tip (y/c = 0.1 inboard from tip) for baseline (a), A = 1.5° (b, d) and A = 5° (c, e) at 

reduced frequencies k2 = 0.5 (b–c) and 1.0 (d–e), M∞ = 0.2

The time-averaged slices provide a qualitative assessment of the tip vortex; 

however, a more quantitative approach is necessary to fully understand the effect 

of the dynamic motion on the tip vortex wake flow. Since there was no observed 

qualitative difference between M∞ = 0.5 and 0.2 cases in the development of the tip 

vortex, only the M∞ = 0.5 case was further explored. 

To quantify the tip vortex, contour slices were obtained downstream of the trailing 

edge tip of the canard. From the time-averaged flow solution, a total of 11 contour 

slices, ranging from x/c = 0 to x/c = 10, spaced evenly every x/c = 1, were studied. 

The effectiveness of pitch oscillation on mitigating the tip vortex was studied by 
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20

identifying and detecting vortices in the selected contour slices. Many techniques 

are available to characterize vortices in flows.

43–47 In the present case, 5 parameters 

were investigated: 1) peak vorticity magnitude, 2) Q-criterion, 3) circulation, 

4) tangential velocity, and 5) vortex core radius. Vortices are often identified in 

flows by regions of high vorticity. However, high-vorticity regions are also present 

in parallel shear flows where no vortices are present. Therefore, the Q-criterion was 

developed to help define vortices in flows as spatial regions where the vorticity 

tensor dominates the rate of strain. The Q-criterion, Q, is mathematically expressed 

in Eq. 6.

QQ = 1

2 (‖ΩΩ2‖ − ‖SS2‖) > 0, (6)

where Ω and S are the vorticity tensor and rate of strain tensor, respectively. The 

peak value of Q was used to identify the center of the vortex and set as the origin 

for the contour slices. In addition to the Q-criterion, the tangential velocity 

distribution downstream of the canard was computed to quantify the induced 

velocity due to the tip vortex. The tangential velocity was computed by converting 

the cross-stream velocity components into polar coordinates. The tangential 

velocity, Vθ, is expressed in Eq. 7.

VVθθ = VV VV (θθ) − WW (θθ), (7)

where V and W are the cross-stream and normal velocity components, respectively, 

and θ is the rotation angle about the center of the vortex. 

Figure 16 presents the nondimensional vorticity, Q-criterion, and tangential 

velocity for all oscillation amplitudes at x/c = 2 downstream of the canard tip at a 

reduced frequency of k2 = 1 and at M∞ = 0.5. As was found in Fig. 12, the tip vortex 

from the baseline case results in a coherent structure indicated by a high 

concentration of vorticity near the center of the vortex (Fig. 16a). The Q-criterion 

value shows the isolated regions of rotation similar to the vorticity field (Fig. 16d). 

The tangential velocity contour shows a typical vortex-structure concentration of 

high velocity symmetric about the center of the vortex, which defines the vortex 

core radius and low velocity within the core. Outside the core, the velocity reduces 

asymptotically in the radial direction (Fig. 16g). The effect of actuation is 

noticeable for both A = 1.5° and A = 5° oscillations (Figs. 16b, 16e, 16h, and 

16c, 16f, and 16i, respectively). The vorticity field shows a reduction in magnitude 

stretched in the normal direction compared with the baseline case (Fig. 16b and c). 

Moreover, the larger amplitude case shows 2 concentrations of vorticity 

approximately symmetric about the cross-stream direction. The Q-criterion shows 

a considerable reduction in magnitude and is skewed in the normal direction 

(Figs. 16e and 16f). The tangential velocity show that actuation causes the vortex 
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to become distorted, depicted by the asymmetric concentrations of velocity about 

the vortex core (Fig. 16h). The results indicate an increase in the radius of the vortex 

core. Furthermore, the wake flow structure for the larger amplitude case is no longer 

a coherent vortex (Fig. 16i). Interestingly, although the vorticity and tangential 

velocity magnitude are considerably less than the baseline for both actuated 

combinations, there is greater influence of tangential velocity in the radial direction 

(Figs. 16h and 16i). The results prove that the tip vortex obeys conservation of 

angular momentum. 

Fig. 16 Contours of time-averaged nondimensional vorticity (a–c), q-criterion (d–f), and 

tangential velocity (g–i) at x/c = 2 downstream of canard tip for baseline (a, d, and g), a = 1.5° 

(b, e, and h), and a = 5° (c, f, and i) case at reduced frequency, k2 = 1.0, M∞ = 0.5

Expanding the analysis to all downstream locations, distributions of vorticity 

magnitude and tangential velocity for all parameter combinations are presented in 

Figs. 17 and 18, respectively. The distributions are presented at each downstream 

location along the centerline in both spanwise (z*, represented by solid lines) and 

cross-stream (y*, represented by dashed lines) directions of the cut plane between 

z* and y* = –1 to 1. The vorticity distribution defines the profile of vorticity 

concentration normal to the cut plane, typically exhibiting a peak at the center of 

the vortex while decreasing asymptotically in the radial direction. Furthermore, the 
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tangential velocity distributions show a linear region near the center, radially 

increasing until achieving a maximum at the edge of the vortex, defining the core 

radius, and then asymptotically decreases. 

Fig. 17 Distributions of time-averaged nondimensional vorticity magnitude along centerline 

in both spanwise (z*, solid) and cross-stream (y*, dashed) directions at x/c = 1 to 10 

downstream of canard tip for baseline (a), a = 1.5° (b, d) and 5.0° (c, e), at reduced frequencies, 

k2 = 0.5 (b–c) and 1.0 (d–e), at M∞ = 0.5
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Fig. 18 Distributions of time-averaged nondimensional tangential velocity along centerline 

in both spanwise (z*, solid) and cross-stream (y*, dashed) directions at x/c = 1 to 10 

downstream of canard tip for baseline (a), a = 1.5° (b, d) and 5.0° (c, e), at reduced frequencies, 

k2 = 0.5 (b–c) and 1.0 (d–e), at M∞ = 0.5

The baseline distributions of both the vorticity magnitude and tangential velocity 

show symmetry in both cross and spanwise directions (Figs. 17a and 18a). As 

expected, the peak vorticity values are within the vortex core, whereas the 

tangential vorticity reaches a maximum at the edges of the vortex core. 

Furthermore, the magnitude of vorticity and tangential velocity is inversely 

proportional to downstream distance, x/c. Compared with the baseline, all actuated 

combinations show significant decreases in magnitude for both vorticity and 

tangential velocity at each given downstream location (Fig. 17b–d). Moreover, as 

the vorticity peak drops, the radial influence increases, obeying conservation of 
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24

angular momentum. In actuated cases, both vorticity magnitude and tangential 

velocity distributions show asymmetry along each cross-stream direction as well as 

along the streamwise direction at different downstream locations, suggesting that 

the vortex core moves as the vortex advects downstream (Figs. 17b–d and 

Figs. 18b–d). 

Increasing the amplitude of pitch-oscillation causes a greater reduction in 

magnitude and increase in radial influence for both vorticity and tangential velocity 

(Figs. 17c and 17e, and Figs. 18c and 18e). The distributions of tangential velocity 

show that the larger amplitude oscillation case significantly disrupted the 

development of the tip vortex, resulting in negligible values of tangential velocity 

past x/c = 7 downstream of the canard tip (Figs. 18c and 18e). The effect-reduced 

frequency is not as noticeable as amplitude; however, the peak values of vorticity 

magnitude and tangential velocity downstream are dependent on the wave length 

of the standing wave wake flow, as similarly shown in Fig. 12. To clearly quantify 

the effect of the multiple actuation combinations on the development of the tip 

vortex, the peak values of the parameters to characterize a vortex, as identified 

previously, was explored. 

Figure 19 presents the time-averaged nondimensional peak values of vorticity 

magnitude, Q-criterion, circulation, tangential velocity, and vortex core radius at 

10 downstream locations from the canard tip. Figure 19 identifies the peak values 

and circulation within the area y* = –1 to 1, z* = –1 to 1 about the vortex center at 

each downstream location. The strength of a vortex can be characterized through 

circulation, or the flux of vorticity. The maximum vortex core radius is defined as 

the distance from the center of the vortex to the radial location of peak tangential 

velocity.
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Fig. 19 Line plots of time-averaged nondimensional peak vorticity (a), tangential velocity 

(b), circulation (c), Q-criterion (d), and vortex core radius (e) at x/c = 1 to 10 downstream of 

canard tip for baseline, A = 1.5° , and A = 5° cases at reduced frequencies, k2 = 0.5 and 1.0, at 

M∞ = 0.5

For all cases, the peak vorticity value is inversely proportional to downstream 

location (Fig. 19a). The vorticity decays due to viscosity. Compared with the 

baseline, pitch oscillating the canard causes the peak vorticity value to significantly 

decrease at all downstream locations. The increase in amplitude of the oscillation 

is more effective in reducing the peak vorticity than actuation frequency. The effect 

of frequency can be seen through the shape of the vorticity distribution: the vorticity 

peaks define the nodes of the standing wave as similarly observed in 

Fig. 12. Similar behavior is observed for Q-criterion (Fig. 19d). The effect of 

actuation significantly reduces the peak Q-criterion values when compared with the 
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26

baseline case. The results suggest that the development of the tip vortex has been 

altered due to actuation and that the rotational components of the vortex have been 

significantly reduced. Furthermore, the peak tangential velocity distribution shows 

a decrease in magnitude with actuation (Fig. 19b). The tip vortex follows the 

conservation of angular momentum, and therefore the decrease in vorticity results 

in an increase of the vortex core radius (Fig. 19e). The decrease in vorticity 

magnitude results in a greater radial influence of tangential velocity. The circulation 

distribution supports these findings, as the flux of vorticity is conserved for all 

combinations (Fig. 19c). 

Further research is required to understand which parameter (tangential velocity, 

vorticity, etc.) produces detrimental performance during vortex–fin interactions. 

Although the pitch oscillation motion was able to reduce the vorticity of the tip 

vortex, the result led to a radial increase of tangential velocity. It is possible that 

the increased area of influence will cause further performance detriment in vortex–

fin interactions. Future work is planned to investigate the performance of a 

downstream control surface in the wake of a pitch-oscillating canard.

4. Conclusion

Lift enhancement was observed for a 2-D airfoil and a 3-D canard undergoing ramp 

pitch oscillation at high frequency and amplitude. The actuated cases were able to 

generate higher lift coefficients at higher angles of attack, demonstrating successful 

implementation of dynamic stall. Although lift augmentation was observed, 

achieving the necessary amplitude of oscillation for such an effect could prove to 

be impractical. Furthermore, the dynamic effect was negligible at low angles of 

attack. In addition to lift enhancement, the effect of pitch oscillation was studied as 

a possible way to mitigate the tip vortex. The time-averaged flow solution of the 

actuated cases demonstrated a decrease in vorticity magnitude, TKE, Q-criteria,

and tangential velocity. However, the radial influence of the vortex was increased 

due conservation of angular momentum. Additional work investigating the effect 

of the altered vortex on the performance of a control surface farther downstream is 

required and will be pursued.
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List of Symbols, Abbreviations, and Acronyms

2-D 2-dimensional

3-D 3-dimensional

ARL US Army Research Laboratory

CFD computational fluid dynamics

CFL Courant-Friedrichs-Lewy

DSRC Department of Defense Supercomputing Resource Center

NACA National Advisory Committee for Aeronautics (NACA)

RANS Reynolds-averaged Navier-Stokes

TKE turbulent kinetic energy
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1 DEFENSE TECHNICAL

(PDF) INFORMATION CTR

DTIC OCA

2 DIRECTOR

(PDF) US ARMY RESEARCH LAB

RDRL CIO L

IMAL HRA MAIL & RECORDS

MGMT

1 GOVT PRINTG OFC

(PDF) A MALHOTRA

5 AMRDEC

(PDF) L AUMAN

J DOYLE

K KENNEDY

M MCDANIEL

C ROSEMA

6 ARDEC

(PDF) M STOLK

YIN CHEN

T RECCHIA

D HOSIER

M DUCA

G RODEBAUGH

1 NWSCDD G33

(PDF) S KOSKI

1 USMA

(PDF) DEPT OF MECHANICAL

ENGINEERING

C VERHULST

30 DIR USARL

(PDF) RDRL VTA

C KRONINGER

RDRL VTV

R SINGH

RDRL WM

B FORCH

S KARNA

A RAWLETT

S SCHOENFELD

J ZABINSKI

RDRL WML

P PEREGINO

N TRIVEDI

RDRL WML A

W OBERLE

RDRL WML B

E BYRD

RDRL WML C

S AUBERT

RDRL WML D

R BEYER

RDRL WML E

V BHAGWANDIN

I CELMINS

J DESPIRITO

S SILTON

F FRESCONI

J VASILE

P WEINACHT

RDRL WML F

T BROWN

M ILG

B KLINE

J MALEY

B NELSON

RDRL WML G

M MINNICINO

J SOUTH

RDRL WML H

J NEWILL

RDRL WMP

D LYON

RDRL WMM

M VANLANDINGHAM
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