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Effect of Slender Body Geometry on Flow Control at High Alpha

Vijaya Sirangu* and T. Terry Ng†

University of Toledo, Toledo, OH, 43606 *Research Assistant, Dept. of Mechanical, Industrial and Manufacturing Engineering.

†Professor, Dept. of Mechanical, Industrial and Manufacturing Engineering, Senior Member AIAA. Phone: (419) 530-8237

NOMENCLATURE

α = angle of attack, deg αSV = initial angle of attack for the onset of symmetric vortices, deg αAV = initial angle of attack for the onset of asymmetric vortices, deg αUV = initial angle of attack for the onset of unsteady vortices, deg β = sideslip angle, deg θ = strake location relative to windward meridian, pilot’s view, deg θA = forebody apex half angle, deg CM = pitching moment coefficient Cn = yawing moment coefficient CY = side force coefficient M = freestream Mach number e = ellipticity of forebody D = maximum diameter of body of revolution L = body length hstrake = deployment height of forebody strake Lstrake = length of forebody strake L = body length U = freestream velocity x = distance from the nose apex Re = Reynolds number based on model diameter and free-stream velocity

1.0 INTRODUCTION

Slender bodies of revolution advance through four distinct flow regimes when they are pitched from 0 to 90 deg, where each subsequent flow regime reflects the diminishing influence of the axial-flow component [1]. The axial flow component dominates at low angles of attack (0 ≤ α

≤ αSV) and the flow is attached. In this flow regime, crossflow effects will cause a thickening of the boundary layer on the leeside. It is important to mention that if the nose is blunt, the so-called nose-induced separation of the axial flow will take place as described by Ericsson and Reding [2]. This closed-type flow separation, which is often associated with standing, tornado-like vortices [3], creates reattaching flow on the aft body, which subsequently delays the development of open-type flow separation on the aft body with accompanying body vortices [4]. For intermediate angles of attack (αSV ≤ α ≤ αAV), the crossflow separates and rolls up into a symmetric vortex pair. At higher angles of attack (αAV ≤ α ≤ αUV), asymmetric flow separation occurs. In this flow regime, the axial-component is still large enough to produce steady-flow separation and vortices, but the separation becomes asymmetric and a side force and yawing

28th AIAA Applied Aerodynamics Conference28 June - 1 July 2010, Chicago, Illinois

AIAA 2010-4951

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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moment are generated at zero sideslip. The final flow regime occurs at very high angles of attack (αUV ≤ α ≤ 90 deg), where the axial component is greatly diminished. In this flow regime, flow separation and vortex shedding become unsteady starting on the aft body and advancing toward the nose with increasing angle of attack. At this very high angle of attack, the leeside flow resembles the wake of a two-dimensional cylinder normal to the flow.

Another fundamental phenomenon over slender bodies is that there are two different types of steady asymmetric vortex shedding. The first type occurs on pointed bodies where the vortex asymmetry, and thus the side force, tends to commence at the nose. With this type of vortex shedding, vortices are shed at a relatively fast rate to give alternating side-force cells on long, slender bodies [5,6]. The second type of vortex shedding occurs when a slight amount of nose bluntness, sometimes as little as 6%, is applied to the nose. In this vortex shedding regime asymmetric vortices develop initially at the rear of the body, and the alternating vortex shedding does not occur as readily. This implies that large side-force cells can cover the entire cylindrical aft body.

Some researchers have shown that asymmetric vortices generated by a slender forebody are not affected by the aft body vortices initially. Keener et al. [7] demonstrated this premise showing that the cylindrical aft body has no effect on the side force generated on the pointed ogive nose. In contrast, Montividas et al. [8] showed that the aspect ratio of a slender body has a significant effect on the flow regime developed at high angles of attack. They conducted experiments on a slender body with an aspect ratio, L/D = 10.3 and 32. The smaller aspect ratio, 10.3, showed a flow pattern with an asymmetric separation of a “steady longitudinal vortex.” On the other hand, a larger aspect ratio, 32, produced a flowfield that included asymmetric separation of tip vortices and an unsteady flow regime and vortex shedding on the aftbody.

1.1 General Background

In 1951, Allen and Perkins [16] were the first researchers to note the presence of asymmetric vortex flow behind an axis-symmetric body at high angles of attack. In 1953, Allen and Perkins [17] introduced a breakthrough paper discussing the use of an “impulsive cross-flow analogy” to allow for viscous effects on the force and moment characteristics of bodies that is still the basis for modern aerodynamic prediction tools for slender bodies. In 1972, Peake et al. [18] discussed that the asymmetry was initially influenced by conditions at the pointed nose and Mach number, and once it started it was influenced by the afterbody length. They also indicated that increasing the Reynolds number seemed to delay the onset of asymmetry.

Lamont and Hunt [19] were some of the early researchers to investigate the pressure and force distribution of bodies of revolution at high incidence and find large out-of-plane forces at large incidence. Rao [20] was one of the first researches to have success in suppressing side forces at high incidence by mounting a pair of helical trips on pointed forebodies. Ericsson and Reding [21,22] discussed the large influence that surface roughness has on the vortex-induced asymmetric loads, and added that small nose bluntness, nose booms, nose strakes, or body trips could be used effectively on a pointed slender body to reduce vortex-induced asymmetric loads. Later on, Ericsson and Reding [23] reviewed experimental results and found that for the high laminar Reynolds number at which the reviewed tests were performed, a likely source of the transient vortex behavior was the transition-promoting effects produced by the freestream turbulence. They also pointed out the detrimental and dangerous effects that a coupling of the

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vehicle motion and asymmetric vortex shedding could have on the rigid and elastic response of long slender bodies.

Brandon and Nguyen [24] conducted experiments on a generic airplane model and showed that forebody cross-sectional shape and fineness ratio, among other factors, can strongly affect both static and dynamic (roll) stability at high incidence. In the same year, Ericsson[ 25] presented a paper on moving wall effects that added to the understanding of high-alpha unsteady flows and the moving wall effects on boundary layer transition and separation. Ward and Katz [26]

conducted flow visualization experiments on an inclined ogive nose cone and demonstrated that the lee structure was asymmetric throughout the model, and was dominated by continuously generated, multiple, large-scale flow structures. Degani and Schiff [27] and Degani [28] were the first to successfully simulate the marked asymmetry that occurred experimentally on slender bodies of revolution at high angles of attack. Zilliac et al. [29] conducted a detailed investigation on the flowfield of an inclined ogive cylinder and concluded that microvariations in the tip geometry have a large influence on the downstream development of the flowfield. Luo et al. [30] conducted detailed investigations of the flowfiled around a sharp-nose ogive cylinder and an elliptic-tip ogive cylinder. Their experiments showed that the elliptic tip produced more predictable side forces with different roll angles than the sharp ogive tip. Lua et al. [31] used circular trips and helical grooves on a tangent ogive nose cylinder, and discovered that the circular trips were more effective in reducing side forces at high angles of attack.

Hsieh [3] conducted some early low supersonic investigations on the flow over a hemisphere-cylinder at incidence and showed that two separation regions, the nose separation bubble and the crossflow separation zone, could exist simultaneously at intermediate incidence. Hsieh also showed that the size of the nose separation bubble decreases as the freestream Mach number increases, and that the downstream side of the nose separation is first attached at low incidence and becomes detached as the incidence is increased. Later on, Hsieh and Wang [32] used thin-layer Navier-Stokes solutions to simulate incompressible laminar flow over a hemisphere-cylinder at incidence. Simulations were conducted by assuming a symmetrical flow with respect to the pitching plane. Results showed complex separated flow structures, particularly close to the nose, and a number of intricate structural characteristics unique to three-dimensional flows. Hoang et al. [33] investigated the flowfield around a hemisphere-cylinder at low Reynolds numbers and incidences up to α = 45 deg. They documented the appearance of nose vortex rings and “horn” vortices, and observed a symmetric flowfield. Further studies where conducted by Hoang et al. [34] on a hemisphere cylinder at incidences up to α = 30 deg for intermediate to high Reynolds numbers. They found that at low incidences the separation bubble takes the form of a ring, but as the incidence increases it becomes an isolated bubble. The authors documented the decrease of the separation bubble width with increasing Reynolds number, and that the nose structures are not connected with the separation lines that give rise to the vortical structures over the aft body region. Kumar et al. [35] recently conducted investigations on the effect of nose bluntness on the characteristics of vortex asymmetry and induced side forces on slender cones at high incidence. They showed that the onset of vortex asymmetry with nose-blunting correlates with geometrical parameters and is practically independent of Reynolds number.

Fidler [36] used active control of asymmetric vortices by rotating the nose, nose tip, and a band of the surface just aft of the nose on a pointed, slender body at high angle of attack. Malcom et al. [37] conducted detailed investigations on the manipulation of forebody vortices to produce

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controlled yawing moments at high incidence on a generic fighter model. They utilized individually controlled forebody tip strakes with controlled blowing ports on the forebody to generate controlled yawing moments. Ng [38] and Stahl [39] used a single strake to suppress the vortex asymmetry on bodies of revolution, but Ng showed that the small region close to the apex of the nose was the region of importance for control of vortex asymmetries and a small strake close to this region could be enough to suppress asymmetric vortex formation and presumably mitigate the resultant large yawing moments. Ng and Malcom [40,41] used a rotatable, miniature nose-tip strake and blowing and suction to produce controlled yawing moments on a F/A-18 model. Modi et al. [42] showed that delta strakes used as add-on tip devices could reduces side forces by over 95% for high incidences on a conical pointed forebody. Chen et al. [43] used nose-boom strakes on a F-16 model as an effective way of controlling forebody vortexes at high angles of attack. Viswanath [44] studied different elliptic cones and assessed their side forces and flowfield showing that higher maximum side forces were obtained for a horizontal ellipse than a vertical ellipse. Hodgkin and Wood [45] used tangential blowing on a generic fighter model to show increased yaw control above 60 deg. A recent study by Patel et al. [46] developed a closed-loop flow control system for missile yaw stabilization and enhanced maneuverability. Dynamic experiments successfully demonstrated the ability of their closed-loop system to generate and maintain a range of desired yawing moments during high-alpha pitch sweeps. Leu et al. [47] incorporated flexible micro balloon actuators in a slender cone cylinder and significantly reduced the side forces for some conditions.

1.2 Source of Vortex Asymmetry at High Angles of Attack

In the aeronautical field there have been several proposed source(s) of vortex asymmetry at high angles of attack. In 1971, Pick [48] was the first researcher to speculate that large side forces and dynamic out of plane forces occurred at high angles of attack due to micro-asymmetries and geometrical imperfections near the nose. This premise would hint towards a boundary-layer induced asymmetry in/near the location of flow separation which would in turn cause an asymmetry in the vortex flowfield. This view can be supported by several experimental results. Investigations by Dexter and Hunt [49], Lamont [50], and Yanta and Wardlaw [51] presented detailed experiments showing the effect of roll angle on the flowfield and measured side forces. These studies showed that small changes in the roll angle of the nose/tip produced drastic changes in the asymmetric vortex pattern and measured side forces. Later on, Zilliac et al. [29] assessed that the accumulation of dust on the tip region was enough to produce great changes in side force variations.

In 1977, Keener and Chapman [52] suggested that the cause of vortex asymmetry is a hydrodynamic (inviscid) instability in the vortex flowfield that results from ”the crowding together of the vortices as the apex angle is decreased.” They indicated that “vortex crowding” occurs until the vortex pairs become unstable. At this moment, one of the vortex will slide up over the other vortex, hence inducing an asymmetric vortex flowfield. This hypothesis is supported to a certain degree by some experimental results, such as Keener and Chapman [53]. They conducted a series of experiments to determine the onset of side forces at high angles of attack and found an estimation of the onset of vortex asymmetry on a pointed nose using the semi-apex angle and given by αAV = 2θA. On the other hand, this postulated source of asymmetry

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(hydrodynamic instability) cannot be used to satisfactorily explain the large and dramatic changes in the side force and flowfield that occur with small changes in the tip/nose roll angle.

More recently, Degani and Schiff [27] and Degani [28] conducted Navier-Stokes simulations and were the first to successfully simulate the marked asymmetry that occurred experimentally on slender bodies of revolution at high angles of attack. They suggested that the source of asymmetry was a convective instability of the symmetric vortices. This conjecture could help explain the effect of different tip/nose roll angles on the measured side forces and flowfield. It is possible that different asymmetric vortex patterns could be produced by micro-asymmetries and geometrical imperfections near the nose as it is rotated. However, the convective instability premise cannot explain why the onset angle of attack varies with the nose-tip semi-apex angle, and the reason for the existence of symmetric vortex pairs when the angle of attack is lower than the onset angle. A fault in this argument is also incurred if one assumes that the effect of micro-asymmetries and geometrical imperfections is to trigger a convectional instability, the result would be asymmetric vortices regardless of the magnitude of angle of attack.

An experimental study by Ng [38] concluded that the small region close to the apex of the nose was the region of importance for control of vortex asymmetries. Ng also proposed that nose blunting has the same effect of reducing the asymmetry as a strake, but with a different operating principle. The author indicated that blunting increased the distance between the two vortices.

1.3 High Angle of Attack Flow Control Methodology

Rao [14] suggested the possibility of manipulating the steady-state vortex system characteristics of slender bodies at high angles of attack to generate controlled side force by using jet blowing on a forebody shape characterized by a high fineness ratio. Yaw control up to 120° is demonstrated by Hodgkin and Wood [15] by using a slot optimized for the periodic vortex shedding region. For control in the regions of high vortex asymmetry, short slots near the forebody apex were most efficient, while for control at higher angles of attack, short slots further aft were acceptable. Another method is the use of helical trip first suggested by Scruton and Walsh [16], which has been used rather successfully in reducing vortex-induced instability of structures susceptible to wind-excited oscillations. With the helical trips the flow is forced to separate at varying peripheral locations along the length of body to result in vorticity flux variations along the length. This prevents the shed vorticity from concentrating into discrete two-dimensional cores, thereby suppressing the unsteady cross-force. Modi [4] showed a nose boom to be effective in the reduction of side forces. Tajfar [17], Stahl [18], Visawanath [19] and Brandon [20] are examples of using nose geometry modifications to control the vortices.

Strakes were designed with the intent of fixing the flow separation location along the length of the forebody [23]. In some flight regimes, the flow can be partially controlled by employing small strakes, which fix the boundary layer separation point and assist in making the leeward vortices symmetric or more deterministic [21]. Rao et al. [14] suggested two alternative modes of strake deployment. An asymmetric deployment (i.e., one strake deployed at a time) can force a strongly asymmetric vortex pattern and thus generates a side force that is, controllable via strake deflection. Another method is the simultaneous deployment (i.e., both strakes deployed), which will establish a symmetrical pair of augmented vortices, from which a controlled side force is generated via antisymmetric (or differential) strake deflection. They concluded that dual

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strakes were effective, but a single strake has approximately the same control if located in the correct position. Ng [24] performed surface oil flow visualizations which revealed that the presence of strake alters the position and the shape of the separation line. These findings suggest that the strake at the tip not only minimizes the interaction of the tip vortices, but also forces the origin of the separation line to move to the tip. The results also show that the effectiveness of the strake decreases when moved farther downstream from the nose. Lopera et al. [26] investigated effects of azimuthal and axial positions of the strake as well as the strake planform on the flow control of a relatively short missile body. He concluded that the most effective location for the yaw control was at 90° and 270° (left and the right meridians). Also, he concluded that the strake is effective in the position close to the nose seam where the forebody ends. Furthermore, out of the fourteen different strake planforms tested, the most effective strake in producing large yaw control is the rectangular strake planform

The present work is aimed at gaining insight into the effect of nose geometry on the baseline flowfield and control of vortices at high incidence on a projectile with a relatively low aspect-ratio nose attached to a long aft body. Flow visualizations will be presented in addition to force measurements. A vast amount of research in the field of high-alpha control, asymmetric flow control and side force alleviation can be found in the literature for high aspect-ratio pointed and ogive bodies, but a comparatively small field of research has been conducted on configurations with a relatively blunted nose. Static and dynamic effects of the nose geometry on the baseline flow and yaw control at high angles of attack are studied.

2.0 AERODYNAMIC MODELS AND TEST ARRANGEMENTS

Wind tunnel experiments were performed at The University of Toledo’s closed-loop circuit, single return subsonic wind tunnel with a test section 0.9 m x 0.9 m (3 ft. x 3 ft.). The tunnel is equipped with a C-strut model support and an automated turntable driven by an electric motor that allows for remote model positioning. Two-tempered glass sidewalls and a large Plexiglas window on the ceiling provided convenient access for flow visualization from different angles. The flow in the test section is uniform with a turbulence level of 0.2% outside of the wall boundary layers. The tunnel is equipped with a five-component internal sting mount (balance) that allows for measurements of rolling, pitching, and yawing moments and normal and side forces. Moment and force measurements were taken using a National Instruments SCXI unit, integrated with a 4 Hz low-pass filter for time-averaged measurements and a 1 kHz filter for unsteady measurements. A 0.5 W portable laser was used for laser sheet visualizations. The smoke supplied to the test section is produced by a Rosco Delta 3000 remote-controlled fog machine.

The model shown in Fig. 1 was tested. The overall length of the model is 22.16 inch and a base diameter of 2.63 resulting in an overall L/D of 8.4. The O-give nose has a length that is equal to the base diameter of 2.63 in., the hemisphere nose has a length that is equal to the base radius of 1.315 in., and the elliptical nose has an ellipticity of 3 resulting in a length of 0.867 in. Three different noses are tested: (1) hemispheric, (2) elliptic, and (3) o-give. The forebody length is dictated by the o-give nose, and cylindrical sections are added to the other two noses to maintain the same overall body length. The elliptical model has an elliptical forebody with 33% ellipticity. Additional to the baseline geometry, the missile body is tested with combinations of fairings, canards and tail fins. The components are shown in Figure 1. For comparison, results

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of two models with the same elliptical and hemispheric noses but a fineness ratio of 4 will also be presented.

The experiments were conducted at a free stream velocity of 18.5 m/s and Reynolds number of 78 x 103 based on the model maximum diameter. The Static tests were conducted for angles of attack ranging from -40° to 60° at 2° increments. Two thousand samples were taken at a sampling rate of 200 samples per second, corresponding to a sample-period of 10 sec. All experiments were repeated three times to verify the repeatability of the measurements, and the measurements were found to be repeatable.

Figure 1 Baseline model with O-give, elliptic and hemispheric forebodies: photo shown with O-give nose and fairings, and schematic shown with elliptical nose, body fairings, fins, and canards.

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3.0 RESULTS AND DISCUSSIONS

Experiments were conducted to determine the nose geometry that provides the desired baseline characteristics. Specifically, the baseline should (1) contain minimal natural asymmetry (or phantom yaw) and (2) be receptive to control. As oppose to most previous studies, both time-averaged and time dependent asymmetries will be considered.

3.1 – Effect of forebody geometry on mean asymmetry

An estimation on the onset of aft-body vortex asymmetry can be made using the correlation ααααAV ~ 4.2D/L [54]. This gives a value of approximately 29 deg for the three models. An estimation of the onset of vortex asymmetry on a pointed nose is given by ααααAV = 2θθθθA [53,55]. The hemispheric and elliptical noses are very blunt, and the O-give nose has a θθθθA of about 40o. As such, one would expect primarily a dominance of the aft-body asymmetry.

Figure 2 shows the baseline mean yawing moment coefficients for the three nose geometries. All three cases exhibit natural asymmetry starting at AoA of about 30o, which is in agreement with the aft-body asymmetry prediction. Based on the mean side force, the hemispheric nose produces the highest asymmetry and the elliptic nose the smallest.

Figure 2 Baseline Side Force Coefficient for O-give, elliptic and hemisphere forebodies.

Figure 3 shows the side force coefficients of the two models with the same elliptical and hemispheric noses but a L/D ratio of 4. The hemispheric (hemi-DEX) model shows significant

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asymmetric side forces from α = 34 to 54 deg. The side force switches from a rightward (positive) force at 42 deg to a leftward (negative) force at 48 deg. The elliptical (e0.33-DEX) shows a small side force to the left for α = 0 to 42 deg. For α = 44 to 54 deg, the elliptical-nose model showed a small rightward force with small oscillations. The side force increases rapidly in magnitude from α = 54 to 64 deg. The maximum side force measured for the elliptical nose was however 45 to 65% lower than the maximum side forces for the hemispheric nose.

Using the same correlation ααααAV ~ 4.2D/L, the onset of aft-body vortex asymmetry is estimated to be 60 deg for these two models. The observed side force behavior for the elliptical nose agrees well with this estimation. On the other hand, with the onset of asymmetry at α = 34 deg, the hemispheric nose exhibits a behavior that is more akin to a pointed-nose body. Based on the measured αAV of 34 deg, the effective θA is 17 deg. Also of interest is the diminishing of the asymmetric side force for the hemispheric nose at around 60 deg, which is exactly opposite from the expectation for a blunt-nose body. The disappearance of asymmetric side force at high angles of attack on pointed body is often a result of the advancement of vortex breakdown. In summary, the hemispheric nose behaves more like a pointed-nose body than a blunt-nose body. Also, the similarity of the hemispheric nose results in Figs. 2 and 3 indicates a dominance of the forebody vortex asymmetry that is mostly unaffected by the aft-body flow.

3.2 – Effect of forebody geometry on dynamic asymmetry

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60 70a

CY

e0.33-DEX-1 e0.33-DEX-2

Hemi-DEX-1 Hemi-DEX-2

Figure 3 Side force coefficient vs angle of attack for baseline L/D = 4.0 models at M = 0.1. (+) values indicate a rightward side-force and (-) values indicate a leftward side force.

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The effect of forebody geometry on the dynamic behaviors of the flow field was studied by recording time-resolved moment outputs. Since the dynamic response of the balance rendered the absolute values not meaningful without proper corrections, Fig. 5 serve mainly as a comparison of the fluctuation magnitudes. The results show that in all cases the rms fluctuations in pitching moment are relatively small, with the O-give nose showing also a relatively low fluctuation in the yawing moment. Both the hemispheric and elliptical noses, however, exhibit a significant level of fluctuation in the yawing moment. For the elliptical nose the fluctuation starts to increase at about 15o and rises to a peak at 40o, while for the hemispheric nose the fluctuation starts to increase at 20o and rises to a peak at 45o. The results indicate a significant dynamic flow asymmetry for the elliptic and hemispheric noses. In both cases, the peak fluctuation level is an order of magnitude larger than that of the O-give nose. Table 1 summarizes the observations from the mean and rms moment results. The results show that the hemispheric nose does not conform to predicted blunt nose behavior.

Figure 4 Rms of the pitch (P) and yaw (Y) balance outputs (arbitrary scale) for the baseline model with hemispheric, elliptical and O-give noses.

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Table 1 Summary of the mean and dynamic asymmetry results

Nose Overall L/D

Approx. αααα for onset of asymmetry

Approx. αααα for onset of large force fluctuation

Forebody asymmetry prediction: 2θθθθA

Aft-body asymmetry prediction: 4.2D/L

O-give 8.4 30o No ~80o 29o

Elliptical 8.4 30o 15o NA 29o

Elliptical 4.0 55o No NA 60o

Hemispheric 8.4 30o 20o NA 29o

Hemispheric 4.0 30o No NA 60o

3.3 - Flow Visualization Study of Effects of Forebody Geometry on the Baseline Flow

This section presents the laser-sheet-and-smoke flow visualizations conducted to investigate the effect of the forebody geometry on the flow field. Figure 5 shows approximately the sections where images were recorded. Location 1 was at 1" (0.045L) from the tip, location 2 at 2" (0.09L), location 3 at 4" (0.18L), location 4 at 5.5" (0.25L), location 5 at 7.5" (0.34L) and location 6 at 12.5" (0.56L). The flow at 50 degree angle-of-attack was examined.

1 2 3 4 5 6

Figure 5 - Sections where flow field images were recorded.

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Figure 6 shows the flows at location 1. A pair of symmetric vortices is observed over the O-give nose at section 1. The elliptic-nose flow shows a stagnant or recirculation region, while the hemispheric-nose flow appears to remain mostly attached.

Figure 7 shows the flows at section 2. Both the O-give nose and the hemisphere nose show two well defined symmetric vortices. The vortices formed over the O-give nose are closer to the body compared to the hemispheric nose. For the elliptical nose, the stagnant region remains but a single vortex forms over the right side and the flow is decidedly asymmetric.

Figure 8 shows the flows at section 3. Both the O-give nose and the hemispheric nose show a well defined vortex pair, with a slight asymmetry in the vortex pair over the O-give. For the elliptic nose a second vortex can now be observed, and the flow oscillates between the two patterns in (a) and (b).

Figure 9 shows the flows at section 5. Both the O-give nose and the hemispheric nose show a well defined vortex pair. Both vortex pairs are asymmetric but remain steady. For the elliptic nose, the flow oscillates between the two patterns in (a) and (b).

Figure 10 shows the flows at section 6. The O-give nose flow remains to be dominated by an asymmetric, steady vortex pair. The hemispheric nose, however, has become oscillatory in a manner similar to the elliptic nose.

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Figure 6 - Section1 for O-give (O), Elliptical (E) and Hemisphere (H) Nose Geometries

Figure 7 - Section 2 for O-give, Elliptical and Hemisphere Nose Geometries.

Vortex pair Stagnant flow

Vortex pair Vortex Stagnant flow Vortex pair

Section 1 - O Section 1 - E Section 1 - H

Section 2 - O Section 2 - E Section 2 - H

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Elliptical (a) Elliptical (b)

Figure 8 - Section 3 for O-give, Hemisphere and Elliptical Nose Geometries.

Section 3 - O Section 3 - H

Section 3 – E(a) Section 3 – E(b)

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Figure 9 - Section 5 for O-give, Hemisphere and Elliptical Nose Geometries.

Section 5 - O Section 5 - H

Section 5 – E(a) Section 5 – E(b)

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Figure 10 - Section 6 for O-give, Elliptical and Hemispheric Nose Geometries.

Figure 11 shows the sections on the L/D = 4.0 model where laser sheet visualizations were obtained. Representative results from off-surface visualization records for the hemispheric and elliptical models are shown in Figs. 12 and 13 respectively. Sections 2 and 5 in this case correspond approximately to sections 1 and 3 of the L/D = 8.4 model; the results can thus be compared to those in Figs. 6 and 8. The comparison indicates that for the hemispheric nose the aft-body length has very little impact on the flows at these locations. The opposite, however, is true for the elliptical nose. At cross-sectional station 5 (x/L = 0.42), Fig. 13b shows a pair of relatively weak and steay vortices over the leeward surface of the aftbody. At similar location for the L/D = 8.4 case in Fig. 8, the flow oscillates between two highly asymmetric vortex patterns.

Figure 14 visualization examples of the L/D = 4.0 hemispheric model. The smoke flow shows separation and reattachment of the flow and the formation of a “horse-shoe” vortex at the nose. The surface oil flow clearly shows the three-dimensional primary separation that occurs on the hemispheric nose. A second oil line, shortly downstream of the primary separation line but well upstream of the reattachment point can also be seen clearly. Furthermore, the left side

Section 6 - O Section 6 – H(a) Section 6 – H(b)

Section 6 – E(a) Section 6 – E(b)

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secondary separation line is observed to extend along the body in a fairly straight manner, whereas the right side secondary separation line is closer to the leeward meridian, and in the aft body shows a wavy pattern. The influence of the tail fins is also evident. From the flow visualizations, it can be deduced that the primary vortex starts forming just downstream of the hemispherical nose causing a distinct “kink” in the separations lines of the nose bubble. Of particular interest is the seemingly merging of the separated flow of the nose and the aftbody vortex, which provides a communication link between the left and right aftbody vortices.

Figure 15 shows visualization examples of the L/D = 4.0 elliptical model. The surface oil flow shows a large region of separated flow behind the elliptical nose, which is also observed with smoke stream visualization. In addition, the oil streakline patterns in the leeward surface appear to be nearly symmetric, and the primary separation line is well-defined with a distinct separation on the nose. The large separated flow region at the nose effectively separates the right and left aftbody vortices that appear to start forming just downstream of the nose.

Figure 11 Cross-sectional stations used for the L/D = 4.0 model for laser sheet visualizations.

1

2

3

4

5

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Figure 12 Laser sheet visualization of hemispheric model with L/D = 4.0 at α = 48o: a) station 2 (x/L = 0.13) and b) station 5 (x/L = 0.42).

Figure 13 Laser sheet visualization of elliptical model with L/D = 4.0 at α = 42o: a) station 2 (x/L = 0.13), b) station 5 (x/L = 0.42).

a

Left

b

a b

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Figure 14 Flow visualization of hemispheric L/D = 4 model at α = 48o.

Fin wake

Forebody secondary separation line

Leeward meridian

Primary forebody separation

Forebody flow reattachment

Kink in separation line

Primary separation

Imprint of secondary vortex

a

Secondary vortex

Primary vortex

Limiting streamline for separation bubble b

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Figure 15 Smoke stream visualization of elliptical L/D = 4 model at α = 48o.

Separated flow region

Primary side separation

Primary side separation

Primary nose separation

a

b

Limiting streamline of separated flow

Stalled flow region

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3.4 Summary of the Baseline Flows

The study reveals interesting static and dynamic effects of the nose geometry on the flow over the entire slender body, even though the nose is only a small portion of the total length. By taking into account both static and dynamic behaviors, the O-give nose appears to possess the most desirable baseline characteristics for high-α controls.

3.5 Moment Results with Aft-body Strake.

Experiments are conducted by placing the strake at body roll angles of 90o and 270o, with zero being the windward meridian and the angle increases in the clockwise direction from a pilot’s view. Effects of the strake height, length, axial position and the azimuthal angle have been studied. In the present discussion the emphasis is only on determining the effect of the forebody geometry.

The notations used in the graph with color code are given below:

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Figure 16 Effect of Strake on the yawing moment

Results of the yawing moment are shown in Figure 16. The strake is mounted on the cylindrical body just downstream of the nose. It is evident from the graphs that some yawing moment is generated with the aft-body strake regardless of the nose geometry. For all cases at angles up to α = 20o no significant yawing moment is observed. For α greater than 30o, the controlled yawing moment achieved by a single aft-body strake on the O-give nose is significantly larger and more predictable than the hemisphere and the elliptical nose geometries. For the O-give nose the right (90 deg) and the left (270 deg) yawing moments are similar in magnitude and opposite in direction.

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3.6 Flow Visualizations with Aft-body Strake

The flow at 50o angle-of-attack is examined at the sections shown in Figure 5. Only the O-give nose would be studied since it possesses the most desirable characteristics among the three. A strake 8-mm in height and 15-mm in length and mounted at azimuthal angle of 90o was used in the study.

Figure 17 Sections 1 to 6 for O-give nose geometry with control strake.

Figure 17 shows sections 1 through 6 along the length of the O-give nose model with control strake. There is no observable effect of strake at section 1, as the strake is mounted downstream of this location. A pair of symmetric vortices is observed at section 1 as in the no-control case. At section 2, which is downstream of the deployed strake, the left or strake-side vortex lifts off while the right vortex moves close to the surface. As the flow progresses along the length of the model, the asymmetry between the left and the right vortices increases. The flow pattern is expected to produce a yawing moment to the left, which is confirmed by measurements.

4.0 DISCUSSIONS AND CONCLUSIONS

The phenomenon of slender-body vortex asymmetry and its control have been studied. While some observations conform to commonly accepted notions on the subject, there are also important exceptions. For L/D = 8.4, aft-body stake control is effective only for the O-give nose. For L/D = 4.0, however, Ref. 15 shows that strake is effective for both the hemispheric

Section 1 Section 2 Section 3

Section 4 Section 5 Section 6

Strake

Strake

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and elliptical noses. The results show the importance of nose geometry and overall fineness ratio in determining the control effectiveness. All three noses tested can be considered as blunt, with the highest L/D ratio of 1 being the O-give. The O-give is also the only nose that is pointed. Nevertheless, the vortex asymmetry for all three cases is supposedly determined by the overall fineness ratio and the aft-body due to the short lengths and bluntness of the noses. The present results however show a less generalized behavior. Static vortex asymmetry for the O-give geometry occurs at the predicted angle of attack based on the overall fineness ratio. Contrary to the other two noses, the flow does not become unsteady for angles of attack up to 60o. This suggests a strong influence of the forebody where, with a short but pointed nose, the combined nose and aft-body behaves as a single pointed slender body. This flow behavior is confirmed by the off the surface flow visualization.

Static vortex asymmetry for the elliptical nose geometry occurs at the predicted angles of attack for the respective L/D ratios of 4.0 and 8.4. Overall, the elliptical nose flow has the smallest static asymmetry among the three noses tested but also becomes oscillatory the soonest when L/D is at 8.4. Flow visualizations reveal that the elliptical shape produces a large separation region that effectively isolates the left and right vortices downstream of the nose, thereby reducing the static asymmetry. The laser sheet visualization reveals a strong influence of the overall fineness ratio on the flow. The size and strength of the downstream vortices continues to grow along the body but the spacing between them remains largely unchanged due to the constant body diameter. For the L/D = 4.0 case, the vortices remain relatively weak along the entire body length and do not interact strongly. As such, no large asymmetry or oscillatory behavior is observed for most of the angle of attack range. When the L/D is increased to 8.4, however, the vortices eventually become sufficiently strong and interact to cause a dynamic asymmetry that is similar to the Karman vortex street. Also akin to the global instability associated with vortex street, this asymmetry feeds forward along the cylindrical portion of the body to cause most of the vortex flow to become oscillatory.

The hemispheric nose produces flow behaviors that are a combination of the other two noses. A significant static side force asymmetry is observed. The asymmetry is not affected by the aft-body length, which suggests a forebody dominated event. At moderate angles of attack and L/D = 8.4 the side force becomes oscillatory, which is typically caused by the aft-body flow. Flow visualizations reveal that the forebody flow merges with the aft-body vortices. In effect, the seemingly blunt nose does not prevent interactions between the vortices at the nose region but rather provides an effective communication path. As such, the hemispheric nose behaves like a pointed nose. As the flow progresses downstream, the interaction between the growing vortices eventually produces an oscillatory flow. The dynamic asymmetry however does not feed forward as far as in the elliptical case due to the stronger influence of the hemispheric nose flow.

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ACKNOWLEDGMENTS

This work was supported by Orbital Research, Inc. under a SBIR Phase II Contract No. N68936-07-C-0054 issued by the U.S. Navy. The authors would like to thank the Navy Program Monitors Howard McCauley and Tom Glover for their encouragement and support of this work.

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