Mechanisms for Conical Forebody Flow Control Using Plasma Actuators

Transcription

1 39th AIAA Fluid Dynamics Conference June 29, San Antonio, Texas AIAA th AIAA Fluid Dynamics Conference and Exhibit, June 29, Grand Hyatt Hotel, San Antonio, TX Mechanisms for Conical Forebody Flow Control Using Plasma Actuators Feng Liu, Shijun Luo University of California, Irvine, CA Chao Gao, Jianlei Wang, Zijie Zhao Yinzhe Li, and Jiangnan Hao, Northwestern Polytechnical University, Xi an 772, China Duty cycle modulation of the alternating blowing from two opposite facing plasma actuators on the leeward surface near the apex of a cone of semi-apex angle to control the mean lateral force and moment and the flow control mechanisms are presented. The pressure distributions over the cone forebody are measured using steady and unsteady pressure-tappings. The flowfields are visualized by a two-dimensional particle image velocimetry. The experiments were perfomed in a 3. m.6 m open-circuit wind tunnel at 45 angle of attack and Reynolds number of 5 4 based on the cone base diameter. The opposite bi-stable vortex patterns appear when the port or starboard actuator is activated while the other is kept off during the test. The phase-locked (locked to the plasma duty cycle) averaged flow induced by the duty-cycled plasma actuation is periodic and varies smoothly between two opposite states like the bi-stable states but much smaller in amplitude. The ensemble-averaged pressure from sampling times as low as one second becomes a constant no matter the plasma actuation is steady or unsteady. However, the phasedlocked average of plasma duty cycle requires much more sampling time to reach a limit. Nomenclature C n = yawing moment coefficient about cone base, yawing moment/q SD = pressure coefficient C Y = overall side-force coefficient, overall side force/q S C Y d = ensemble-averaged local side-force coefficient, local side force/q d c Y d = phase-locked averaged local side-force coefficient D = base diameter of circular cone forebody d = local diameter of circular cone forebody F = frequency of a.c. voltage source f = frequency of duty cycle L = length of circular cone forebody q = free-stream dynamic pressure Re = free-stream Reynolds number based on D T = period of duty cycle t = time of duty cycle U = free-stream velocity V p p = peak-to-peak voltage of a.c. voltage source w = input power of a.c. voltage source Professor, Department of Mechanical and Aerospace Engineering. Associate Fellow AIAA. Researcher, Department of Mechanical and Aerospace Engineering. Professor and Associate Director, Aerodynamic Design and Research National Laboratory. Graduate Student, Department of Fluid Mechanics of 9 American Institute of Aeronautics and Astronautics Paper Copyright 29 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

2 α = angle of attack θ = meridian angle measured from windward generator, positive when clockwise τ = fraction of time when starboard actuator is on over a duty-cycle period ψ = phase angle of duty cycle Ω = reduced angular frequency of duty-cycle, 2πfD/U I. Introduction Proportional lateral control on slender forebodies at high angles of attack is highly needed in aerodynamic design of air vehicles. The fact that the separation vortices over pointed forebodies generate large airloads and are very sensitive to small perturbations near the body apex offers an exceptional opportunity for manipulating them with little energy input to achieve active lateral control of the verhicle in place of conventional control surfaces. It has been found experimentally that unsteady dynamic control techniques are needed to achieve this goal. 3 Recently, Liu et al. 4 reported wind-tunnel experiments that demonstrate nearly linear proportional control of lateral forces and moments over a slender conical forebody at high angles of attack by employing a novel design of a pair of single dielectric barrier discharge (SDBD) plasma actuators near the cone apex combined with a duty cycle technique. Various methods have been used to study vortex flowfield over bodies. Hall 5 found the location of boundary layer searation observed by Keener s oil flow 6 coincides well with the end of the pressure recovery in Lamont s pressure data 7 for 3.5 ogive nose tested under nearly same conditions. The primary flow features can be inferred from pressure data with orifices every around the circumference of the body. Bernhardt and Williams used smoke-strobe light to show the side views of forebody vortices and smoke-laser sheet to present an axial view of the forebody wake in proportional control of asymmetric forebody vortices. Lamont 7 used miniature pressure tappings for measuring unsteady pressures in addition to the time-averaged pressure tappings to demonstrate that his experimental setup had produced the hoped-for absence of serious flow unsteadiness. Thomas, Kozlov and Corke 8 used ensemble averaged and phase-locked averaged particle image velocity and vorticity field to reveal detailed flow mechanisms for cylinder flow control under steady and unsteady plasma actuations. In this work, we investigate the flow mechanisms under the plasma actuations of Ref.4. Three modes of operations of the actuators are considered. The plasma-off mode corresponds to the case when neither of the two actuators is activated. The port-on or starboard-on mode refers to the conditions when either the port or starboard actuator is activated while the other is kept off during the test, respectively. The third mode is the duty-cycled plasma actuation in which the two actuators on the cone is activated alternately with a specified duty cycle. For the first two modes, the flow can be considered as steady. For the mode of plasma duty cycle the flow is unsteady. For steady flow only ensemble averages are studied, For unsteady flow, in addition to ensemble averages, the phase-locked to duty cycle averages are examined. We employ steady and unsteady pressure tappings and particle image velocimetry (PIV) technique to study the flows over the cone forebody. 4 In the following sections, the experimental setup is described. The experinental results on the flows of plasma-off, port-on, starboard-on and the plasma duty cycle are presented and discussed. Finally conclusions are drawn. II. Experimental Setup The model is that used in Ref. 4 except the pressure instrumetations. The model consists two separate pieces. The frontal portion of the cone is made of plastic and has a length of 5 mm. The rest of the model is made of metal. The total length of the cone is mm with a base diameter of 63.6 mm. Two long strips of SDBD plasma-actuators are installed symmetrically on the plastic frontal cone near the apex as shown in Fig. (a). The plasma actuator consists of two asymmetric copper electrodes each of.3 mm thickness. A thin Kapton dielectric film wraps around the cone surface and separates the encapsulated electrode from the exposed electrode as shown in Fig. (b). The right edge of the exposed electrode shown in Fig. (b) is aligned with the cone at the azimuth angle θ = ±2, where θ is measured from the windward meridian of the cone and positive is clockwise when looking upstream (Fig. (a)). The length of the electrodes is 2 of 9 American Institute of Aeronautics and Astronautics Paper

3 2 mm along the cone meridian with the leading edge located at 9 mm from the cone apex. The width of the exposed and encapsulated electrode is mm and 2 mm, respectively. The two electrodes are separated by a gap of.5 mm, where the plasma is created and emits a blue glow in darkness. (a) arrangement (b) SDBD Figure. Sketches of the plasma actuators. Each of the two actuators on the cone model is separately driven by an a.c. voltage source (model CTP- 2K by Nanjing Suman Co.). The waveform of the a.c. source is sine wave. The peak-to-peak voltage and frequency are set at V p p 4 kv and F 8.9 khz, respectively. The duty cycles are achieved by modulating the carrier a.c. voltage sources by a digital pulse wave generator, PC-7 made by the Nanjing Suman Co, at a frequency of Hz which yields a reduced angular frequency, Ω 2. The input power for the plasma on is w = 9.3 W. The input power for the plasma duty cycle has a minimum, w min.5 W at τ = 5%, and a maximum, w max 23. W at τ = % and 9%. The tests are conducted in an open-circuit low-speed wind tunnel at Northwestern Polytechnical University. The test section has a 3. m.6 m cross section. The model is rigidly mounted on a support from the port side of the model aft-cylinder as shown in Fig. 2. The support is fixed onto the turning plate of angle of attack inbedded in the bottom wall of the wind-tunnel test-section. The model support is not symmetric with respect to the incidence plane of the model and, thus, would have an asymmetric interference on the flow around the cone forebody. The cone-cylinder model is tested at α = 45. The free-stream velocity U = 5 m/s. The Reynolds number based on the cone base diameter is 5 4. Local side force, overall side force and yawiing moment acting on a station of the cone forebody is calculated from the measured pressures. The local side-force coefficient C Y d is normalized with the local diameter of the cone and is positive when pointing to the starboard side of the cone. The yawing moment coefficient C n is normalized with the base diameter of the cone and is positive when yawing to the starboard side of the cone. The model is carefully cleaned prior to each run of the wind tunnel. Surface pressure measurements are chosen for the model-load instrumentation to maximize the information provided about the complex flow and to allow rigid mounting of the model required for the high-angleof-attack tests. The 252 time-averaged pressure tappings are arranged in rings of 36, every around the circumference of the cone, at Stations to 7 as shown in Ref.4. In addition to the time-averaged tappings, unsteady pressure tappings are mounted around the circumference of Station 8 shown Fig. 3, 7 tappings are distributed every 3 from θ = 9 to 27 and the rest 3 at θ = and ±5. The time-averaged pressure tappings are Models 986 and 84 by the PSI Company, which sample at frequency of Hz and 27 Hz, respectively. The unsteady pressure tappings are Model XCQ 93 by the Kulite Semiconductor Products Inc. with sampling frequency of 5 Hz. Input pressure range is.35 BAR and perpendicular acceleration sensitivity % FS/g is.5 3. Consecutive 5 seconds samplings of both steady and unsteady pressure tappings are recorded for analyses. Particle image velocimetry (PIV) is chosen for the flowfield measurement because the method is to a large degree noninstrusive. The cross-flow field over Station 2 are measured by a two-dimensional PIV system as shown in Figs. 5 and 4. Station 2 is located about 7 mm behind the trailing edges of the plasma actuators. At this distance the possible adverse effects of the electrostatic force of the plasma actuator on the the PIV measurement might be negligible. The PIV system is manufactured by the Dantec Dynamic Company. The Nd:YAG Laser, a product of the Beamtech Optronics Co., emits single pulse of energy 2 mj and produces double pulses with a time interval of 6 µs. The repeat rate of the laser double-pulse is set at 9 Hz and consecutive seconds of sampling are performed for each case. The laser sheet coincides with the cross section of Station 2 and has height and width 3 mm mm and thickness mm. A CCD camera of 3 of 9 American Institute of Aeronautics and Astronautics Paper

4 Figure 2. Model in the wind tunnel, leeward view Figure 3. The model 4 of 9 American Institute of Aeronautics and Astronautics Paper

5 Figure 4. PIV test layout. Figure 5. PIV system and plasma genertors. 5 of 9 American Institute of Aeronautics and Astronautics Paper

6 6 2 pixels is used to record the cross-flow image. A software of version is used to calculate the cross-flow velocity vector field from the double-pulse images. The camera is located downstream of the laser plane in the incidence plane of the model and supported by a tripod fixed on the angle-of-attack turning plate (Fig. 2). The flow seeds are smoke particles of approximately µm in diameter commonly used in cinema industry, mixed with atmosphere air and sucked into the test section of the open-circuit wind tunnel through the entrance. It was found that seed distribution is not uniform in regions remote from the model. In the remote regions on the PIV image, irregular velocity vectors occur and they are replaced by the freestream crossflow velocity vector, i.e., v = and w = U sinα. III. Base Plasma-Off Flow at Zero Angle of Attack Station - Station 2 Station 3 - Station 4 Station Station 6 Station Figure 6. Ensemble-averaged pressure distributions over various stations for plasma off at α = and U infty = 5 m/s. In order to check the accurary of the model setup in the wind tunnel, a test is run at zero angle of attack and with plasma off. Fig. 6 presents the ensemble-averaged pressure distributions over the circumference of Stations 8 at α =. Aside from some slight irregularities, the measured pressure distributions indicate essentially an axisymmetric flow around the cone. In the present study, the model support is not symmetric to the incidence plane and the plasma actuators are made by hands and then attached to the cone tip surface with glue. The dielectric film wraps around the entire circumference. No allowance is made on the cone surface for the attachment, which could have been the cause for the mentioned irregularities of the pressure distributions. Nevertheless, the disturbances were tolerably small. IV. Flow of Plasma-Off, Port-on and Starboard-On, Ensemble-Averaged Results The flows for plasma-off, port-on and starboard-on are all steady flows. Only ensemble-averaged pressures measured from steady and unsteady tappings are considered in this section. 6 of 9 American Institute of Aeronautics and Astronautics Paper

7 s 5s.5 s.5 5s (a) Station 2 s.5 5s.5 s 5s (b) Station 8 Figure 7. Comparison of pressures ensemble-averaged over s 5 s for starboard-on, α = s.5s.5.75s.5.s (a) Station 2.25s.5.5s.5.75s.s (b) Station 8 Figure 8. Comparison of pressures ensemble-averaged over.25 s s for starboard-on, α = of 9 American Institute of Aeronautics and Astronautics Paper

8 A. Variation of Ensemble Averaged Pressures with Sampling Time The variation of the ensemble-averaged results with the sampling time is studied. Consider the pressure distributions around the circumference of Stations 2 and 8 where the PSI-986 and Kulite transducers are mounted with sampling frequency of Hz and 5 Hz, respectively. Figures 7 and 8 compare the ensembleaveraged pressure distributions obtained with sampling times of s 5 s and.25 s s, respectively, for starboard-on. The comparisons reveal that there are no differences in the averaged pressures for the sampling times greater than.5 s. The same is true for plasma-off and port-on (not shown here for brevity). We will present the 5 s averaged data next. It is seen that the suction peaks of pressure distribution seem well captured by the only pressure tappings on Station 8. B. Ensemble-Averaged Pressure Distribution and Boundary-Layer Separation Plasma Off Port on Starboard on Figure 9. Comparison of ensemble-averaged pressure distributions for plasma-off, port-on and starboard-on at Station 2, α = 45, U = 5 m/s. Table. Comparison of ensemble-averaged separation locations and local side force coefficient at Station 2 for plasma-off, port-on and starboard-on at α = 45, U = 5 m/s over Station 2. 8 of 9 American Institute of Aeronautics and Astronautics Paper

9 Mode Port side Starboard side C Y d Plasma-off.5 Port-on 9.88 Starboard-on.22 Figure 9 compares the ensemble-averaged pressure distributions for plasma-off, port-on and starboard-on at α = 45, U = 5 m/s over Station 2. The pressure distributions for plasma-off and starboard-on are incidentally coincided. They are nearly anti-symmetric to that for port-on with respect to the line θ = 8. It is noted that in the tests of Ref. 4 the present model for plasma-off experienced a side force closed to that for port-on. In fact, the force asymmetry for a slender body of revolution at high angle of attack depends on the small asymmetric disturbances in the flow, including the micro surface imperfections on the tip on the body. 9 The location of the boundary layer separation point can be inferred as the end point of the pressure recovery as demonstrated by Hall. 5 Table compares the mean meridian angle of the boundarylayer separation point on the cross-flow plane of Station 2 and local side force coefficient calculated from the measured pressures for the modes of plasma-off, port-on and starboard-on. The plasma blowing edge is located at θ = ±2. The plasma blowing direction is tangent to the circular circumference and windward. The plasma jet tends to stay attached to the adjacent circular circumference due to Coanda effects. In comparison with the plasma-off, when plasma is port-on the port-side boundary-layer separation point is moved windward from θ = to θ = 9 while the starboard-side boundary-layer separation point is moved leeward from θ = to θ =. The plasma blowing edge is located in the boundary-layer separation region and the plasma jet blows toward the separation point. The effect of the plasma actuation is to push the separation point of the same side boundary layer wndward and to pull the separation point of the opposite side boundary layer leeward. The change of the local side force follows immediately that of the boundary-layer separation locations. It is noted that the changes produced by port-on and starboard-on are opposite in direction but not equal in magnitude. Among other factors, the asymmetric model support and the imperfections of the model, particularly those due to the installment of the plasma actuators mentioned earlier, are believed to have prevented the results from exact bi-stable. It is known that for plasma-off the flow asymmetry depends on the body roll angle or the micro surface imperfections of the model. 9 In case that the plasma-off pressure distribution would coincide with that of port-on, it is expected that the starboard-on will become effective to induce the anti-symmetric one. C. Ensemble-Averaged Vortex Pattern by PIV Technique PIV investigations are performed at Station 2 which is remote from the plasma actuators to avoid the possible adverse effects of plasma actuation but still close to the plasma actuator to reveal the effect of the plasma actuation. Ensemble averaged data of the 89 instantaneous images at α = 45 are presented in Figure for plasma-off, plasma port-on and plasma starboard-on. The cross-flow velocity field is displayed as vectors superposed upon the contour plot of the calculated axial vorticity ω x, and the vectors subsampled by a factor of two in each direction for visual clarity. The free-stream velocity U is drawn in scale on the right side directly above the label of ω x. The magnitude of maximum crossflow velocity is seen of the same order of U for all cases. ω x is positive when the vorticity is counter-clockwise and negative when clockwise. The part of the body circumference covered by the PIV photo has a circular angle of 28 from θ = 6 to 244. When plasma is off, as shown in Fig. (a) the port-side shear layer is curved around the body circumference and rolled into a vortex core located close to the body surface and near the incidence plane, and the starboard-side shear layer is outboard and rolled into a vortex core located away from the body. The pressure suction peak on the port side is higher than that on the starboard side, and the local side force is negative. The same is true for starboard-on as shown in Fig. (c). For port on, a portward and windward wash flow appears over the lee portion of the body circumference as shown in Fig. (b). The portward and windward wash flow is correlated to the boundary-layer separation point movements as noted in the last subsection and the vortex-pattern change: the port-side shear layer and vortex core move outboard and the starboard-side shear layer and vortex core move inboard and closer to the body surface than those of the port side. Therefore, the local side force becomes positive. In the PIV figures, besides the vortex core (primary vortex), there are multiple substructures in the shear layer, rotating in the same direction as the vortex core, regions of opposite vorticity along the body surface, 9 of 9 American Institute of Aeronautics and Astronautics Paper

10 U z/d y/d (a) plasma-off ω x (/sec) U z/d y/d (b) port-on ω x (/sec) U z/d y/d (c) starboard-on ω x (/sec) Figure. Ensemble-averaged cross-flow velocity vectors and axial vorticity contours for plasma-off, port-on and starboard-on at Station 2, α = 45, Vectors are subsampled by a factor of two in each direction. of 9 American Institute of Aeronautics and Astronautics Paper

11 which represent the secondary vortex and patches of turbulence. All the vortices are strongly interacted with each other. Table 2 presents the ensemble-averaged maximum axial vorticity and its location with the local side force coefficient for plasma-off, port-on and starboard-on at α = 45, U = 5 m/s over Station 2. It is found that the location of the maximum axial vorticity nearly coincides with the vortex core center where the crossflow velocity v=w=. Table 2. Ensemble-averaged maximum axial vorticity and its location with C Y d at α = 45, U = 5 m/s over Station 2. Port side Starboard side Mode C Y d ω x (s ) y/d z/d ω x (s ) y/d z/d Plasma-off Port-on Starboard-on V. Flow of Plasma Duty Cycle, Ensemble-Averaged Results Flow of plasma duty cycle is unsteady and has reduced frequency Ω 2. The frequency range of typical aircraft aerodynamic maneuvers based on the delta-wing root chord c is fc/u =..3 from Menke, al et. The plasma duty-cycled frequency is much higher than that of the aircraft maneuvers. Therefore, the aircraft motion can not respond the phase-locked-averaged pressures but the ensemble-averaged pressures. A. Variation of Ensemble-Averaged Pressures with Sampling Time s 5s.5 s.5 5s (a) Station 2 s.5 5s.5 s 5s (b) Station 8 Figure. Comparison of pressures ensemble-averaged over s 5 s for plasma duty cycle, τ =.2, α = 45. To investigate the ensemble averages Stations 2 and 8 are selected as typical examples. Figures and 2 compare the ensemble-averaged pressure distributions obtained with sampling times of s 5 s and.25 s s, respectively, for duty cycle τ =.2. The comparisons reveal that there are almost no differences in the averaged pressures for the sampling times greater than s. The same is true for other duty cycles (not shown here for brevity). We will present the 5 s averaged data next. The required averaging time for convergent pressures for plasma duty cycle pressures is greater than that for plasma-off and plasma-on. B. Ensemble-Averaged Pressure Distribution, Side Force and Yawing Moment The plasma duty cycle frequency is f = Hz. The period of the duty cycle is T =.s. For τ =.2, the time for port and starboard plasma actuation in the period of. s is.8 s and.2 s, respectively. The of 9 American Institute of Aeronautics and Astronautics Paper

12 s.5s.5.75s.5.s (a) Station 2.25s.5.5s.5.75s.s (b) Station 8 Figure 2. Comparison of pressures ensemble-averaged over.25 s s for plasma duty cycle, τ =.2, α = 45. convergent pressure distribution shown in Fig. (a) looks similar to that for port-on, but the strong suction peak on the starboard side are lower and, thus, the positive local side force is decreased. The boundary-layer separation positions are same as those of port-on. It is expected that the ensemble-averaged vortex pattern would be similar to that of port-on C Yd C Yd port on τ=.2 τ=.7 starboard on station 2 station τ (a) variation with τ x/l (b) variation with x/l Figure 3. Variations of ensemble-averaged local side force produced at α = 45. Figure 3(a) presents the ensemble-averaged local side force coefficient C Y d versus τ at Stations 2 and 8, α = 45, U = 5 m/s, where the values C Y d at τ = and τ =. are taken from those of the port-on and starboard-on, respectively. It is seen that the variation of C Y d with τ is almost linear and C Y d seems well captured by the only tappings on Station 8. Fig. 3(b) presents ensemble-averaged local side force C Y d versus x/l for port-on, starboard-on and τ =.2 and.7 over the cone forebody. This is true for all pressure stations and all τ. Figure 4 presents the ensemble-averaged overall side force coefficient C Y and yawing moment coefficient C n on the cone forebody versus τ at α = 45. The values of C Y for τ = and τ = are the two extremes and C Y for other τ are intermediates inbetween. Therefore, the highly needed lateral proportional control on slender forebodies at high angles of attack is achieved. To understand how the ensemble-averaged pressures are produced by the unsteady plasma actuations, the phase-locked averages 2 of 9 American Institute of Aeronautics and Astronautics Paper

13 C Y C n τ (a) overall side force τ (b) yawing moment Figure 4. Ensemble-averaged overall side force and yawing moment on cone produced by duty-cycled plasma control at α = 45. are investigated at Station 8. VI. Flow of Plasma Duty Cycle, Phase-Locked-Averaged Results The phase-locked-averaged pressures are investigated to reveal the plasma-duty-cycled flow mechanisms over the conical forebody at high angles of attack. For this purpose the Kulite pressure-transducers are implemented because they can operate quick, enabling them to detect very brief, small fluctuations in pressure. The Kulite sampling has a rate of 5 Hz and is taken consecutively for 5 s in the tests. The frequency of duty cycle is Hz. In one period of the duty cycle there are 5 readings evenly distributed at phase-angle increment of 7.2. At a given phase angle there are 5 samples to be averaged in 5 s. The PSI transducer could not resolve the flow of plasma duty cycle due to its pressure acquisition technique. A. Variation of Phase-Locked Averages with Sampling Time To study how the phase-locked averged pressures vary with the sampling time, Figures 5 and 6 compare the phase-locked-averaged pressure distributions (θ) over averaing times of s 5 s at various phase angle ψ for duty cycle τ =.2 and.7, respectively, at Station 8. The local side force are calculated from the measured pressures. Figure 7 compares the phase-locked-averaged local side force coefficient distributions c Y d (t/t) over the sampling times of s 5 s for τ =.2 and.7 at Station 8 where the time t = s is set at the beginning of the port plasma actuation. Large fluctuations are observed at small averaging times, because at a given phase angle of the duty cycle there are only samples per second (from the pressure transduer) to be averaged. However, by comparing the results of various averaging times, those of the 5 s are approaching a limit and, thus, is presented next. B. Phase-Locked-Averaged Local Side Force and Pressure Distributions Figure 8 presents the variation of the phase-locked-averaged local side force coefficient c Y d (over 5 s) with t/t at τ =.2 and.7, and compared with the ensemble-averaged local side force coefficient C Y d which is read from Fig. 3(b) and plotted in dotted line. The value of the ensemble-averaged local side force C Y d is, in fact, the average of the phase-locked c Y d over a period of the duty cycle. For τ =.2, c Y d is greater than C Y d when t/t <.65, and less than C Y d when t/t >.65. For τ =.7, c Y d is greater than C Y d when t/t <.35, and less than C Y d when t/t >.35. The variation of phase-locked side force with time follows closely the plasma duty cycle activation. The curve of c Y d (t/t) is a smooth curve rather than a sharp square-wave curve and the maximum and minimum value is less than the C Y d given by port-on and 3 of 9 American Institute of Aeronautics and Astronautics Paper

14 s 5s - s - 5s (a) ψ = s.5 5s.5 s 5s (b) ψ = π/ s.5 5s s.5 5s s.5 5s s.5 5s (c) ψ = π (d) ψ = 3π/2 Figure 5. Comparison of pressures phase-locked-averaged over s 5 s at various ψ for τ =.2 at Station 8, α = of 9 American Institute of Aeronautics and Astronautics Paper

15 s 5s - s - 5s s 5s - s - 5s (a) ψ = (b) ψ = π/ s 5s - s - 5s s 5s - s - 5s (c) ψ = π (d) ψ = 3π/2 Figure 6. Comparison of pressures phase-locked-averaged over s 5 s at various ψ for τ =.7 at Station 8, α = 45 5 of 9 American Institute of Aeronautics and Astronautics Paper

16 s 5s s 5s.8.8 s.2 5s.2 s 5s c Yd.6.6 c Yd t/t (a) τ = t/t (b) τ =.7 Figure 7. Comparison of local side forces phase-locked-averaged over s 5 s at Station 8, α = c Yd τ=.2 τ= t/t Figure 8. Phase-locked-averaged local side force c Y d compared with the ensemble-averaged side force C Y d (dotted line) for τ =.2 and.7 at Station 8, α = of 9 American Institute of Aeronautics and Astronautics Paper

17 starboard-on, respectively. The behavior of c Y d (t/t) is different from that predicted by Hanff et al. 2 in their Figure 2(a). The reason for this deviation is that the flow under plasma duty cycle is unsteady rather than steady. It is believed that the aerodynamic features found here for the Station 8 would be true over the entire conical forebody. Figures 9 and 2 present the phase-locked-averaged pressure distributions (over 5 s) compared with the ensemble-averaged pressure distributions at various phase angles ψ for τ =.2 and.7, respectively, at Station 8. At τ =.2, as ψ is increased from the beginning the stronger suction peak on the starboard side of the cone for the phase-locked average starts to rise from that for the ensemble average. When ψ = 3π/2 the weaker suction peak on the port side of the cone for the phase-locked average begins to rise from that for the ensemble average. At τ =.7, the most significant changes of the phased-locked-averaged pressures from the ensemble-averaged pressures are: at ψ = and π the pressures on the starboard side of the cone of the phase-locked average are lowered and at ψ = π and 3π/2 the pressures on the starboard side of the cone of the phase-locked average are increased. The pressure changes match with the duty-cycle actuations phase-locked average ensemble average (a) ψ =.5.5 phase-locked average ensemble average (b) ψ = π/ phase-locked average ensemble average (c) ψ = π.5.5 phase-locked average ensemble average (d) ψ = 3π/2 Figure 9. Phase-locked-averaged pressure distribution (θ) compared with ensemble-averaged pressure distribution for various ψ for τ =.2 at Station 8, α = of 9 American Institute of Aeronautics and Astronautics Paper

18 phase-locked average ensemble average (a) ψ =.5.5 phase-locked average ensemble average (b) ψ = π/ phase-locked average ensemble average (c) ψ = π.5.5 phase-locked average ensemble average (d) ψ = 3π/2 Figure 2. Phase-locked-averaged pressure distribution (θ) compared with ensemble-averaged pressure distribition for various ψ for τ =.7 at Station 8, α = of 9 American Institute of Aeronautics and Astronautics Paper

19 VII. Conclusions A novel design and placement of a pair of plasma actuators on the forebody tip combined with the duty cycle technique provide proportional lateral control of a slender conical forebody at 45 angles of attack and low speed. The flow mechanisms are studied by steady and unsteady pressure tappings and a two-dimensional particle image velocimetry. Crossflow velocity-vectors and vorticity-contours over the forebody clearly reveal that a portward-/starboardwindward wash flow over the forebody lee surface appears when port-/starboard-actuator is activated, respectively. The sideward-windward wash flow is correlated to the leeward shift of the other-side boundary-layer separation point, the closing-in of the other-side vortex core and the moving-out of the same-side vortex core, the higher suction peak on the other side, and the side force pointing to the other side of the body. Under duty cycle of frequency Hz, the ensemble-averaged pressures, no matter measured by steady or unsteady pressure tappings, reach stationary values as sampling time is over s. It is found that the ensemble-averaged overall side force and yawing moment vary linearly with duty cycle between those produced by port and starboard actuator alone. The phase-locked averaged pressures can only be obtained by unsteady pressure tappings. It is found for the first time, that the magnitudes of the phase-locked-averaged local side force are much less than those produced by port and starboard actuator alone and the variation of the phase-locked-averaged side force with time is smooth rather than abrupt as predicted by some other authors. The reason for the deviations is that the flow under duty cycle is unsteady. Acknowledgments The present work is supported by the Foundation for Fundamental Research of the Northwestern Polytechnical University, NPU-FFR-W8 and the PhD Programs Foundation We are grateful to Dr. Xuanshi Meng of Department of Fluid Mechanics, NPU for many important discussions. References Bernhardt, J. E. and Williams, D. R., Proportional control of asymmetric forebody vortices, AIAA Journal, Vol. 36, No., Nov. 998, pp Hanff, E., Lee, R., and Kind, R. J., Investigations on a dynamic forebodey flo w control system, Proceedings of the 8th International Congress on Instrumentation in Aerospace Simulation Facilities, Inst. of Electrical and Electronics Ehgineers, Piscataway, NJ, 999,pp. 28/-28/9. 3 Ming, X. and Gu, Y., An innovative control technique for slender bodies at high angle of attack, AIAA Paper , June Liu, F., Luo, S.J.,Gao, C., Meng, X.S., Hao, J.N., Wang, J.L. and Zhao, Z.J., Flow control over a conical forebody using duty-cycled plasma actuators, AIAA Journal, Vol. 46, No., Nov. 28, pp Hall, R.M., Influence of Reynolds number on forebody side forces for 3.5-diameter tangent-ogive bodies, AIAA , Jun Keener, E.R., Flow-separation patterns on symmetric forebodies NASA TM 866, Lamont, P.J., Pressure around an inclined ogive cylinder with laminar, transitional, or turbulent separation, AIAA Journal, Vol. 2, No., Nov. 982, pp Thomas, F.O., Kozlov, A. and Corke, T.C., Plasma actuators for cylinder flow control and noise reduction, AIAA Journal, Vol. 45, No. 8, Aug. 28, pp Zilliac, G.G., Degani, D. and Tobak, M., Asymmetric vortices on a slender body of revolution, AIAA Journal, Vol. 29, No. 5, May. 99, pp Menke, M., Yang, H. and Gursul, I., Experiments on the unsteady nature of vortex breakdown over delta wings, Experiments in Fluids, Vol. 27, No. 3, 999, pp of 9 American Institute of Aeronautics and Astronautics Paper