INFLUENCE OF NOSE PERTURBATIONS ON BEHAVIORS OF ASYMMETRIC VORTICES OVER SLENDER BODY*

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1 ACTA MECHANICA SINICA (English Series), Vo1.18, No.6, December 2002 The Chinese Society of Theoretical and Applied Mechanics Chinese Journal of Mechanics Press, Beijing, China Allerton Press, INC., New York, U.S.A. ISSN INFLUENCE OF NOSE PERTURBATIONS ON BEHAVIORS OF ASYMMETRIC VORTICES OVER SLENDER BODY* Chen Xuerui (N~)I Deng Xueying (Xll~) 1 Wang Yankui (tt.~) 1 Liu Peiqing (~]N~)~ Gu Zhifu (NNN) 2 l( Institute of Fluid Mechanics, Beijing University of Aeronautics & Astronautics, Beijing , China) 2(Department of Mechanics & Engineering Science, Peking University, Beijing , China) ABSTRACT: The influence of nose perturbations on the behaviors of asymmetric vortices over a slender body with a three-caliber ogive nose is studied in this paper. The tests of a nose-disturbed slender body with surface pressure measurement were conducted at a low speed wind tunnel with subcritical Reynolds number of I 105 at angle of attack (~ = 50 ~ The experiment results show that the behaviors and structure of asymmetric vortices over the slender body are mainly controlled by manual perturbation on the nose of body as compared with geometrical minute irregularities on the test model from the machining tolerances. The effect of the perturbation axial location on asymmetric vortices is the strongest if its location is near the model apex. There are four sensitive circumferential locations of manual perturbation at which bistable vortices over the slender body are switched by the perturbation. The flowfleld near the reattachment line of lee side is more sensitive to the perturbation, because the saddle point to saddle point topological structure in this reattachment flowfield is unstable. Various types of perturbation do not change the perturbation effect on the behaviors of bistable asymmetric vortices. KEY WORDS: asymmetric vortex, slender body of revolution, bistable flow, high angle of attack aerodynamics 1 INTRODUCTION The flow over a nonsliding slender body of revolution at high angles of attack has been studied extensively over past several decades [1~1~ It was found that the flowfield with angles of attack appears in turn as an attached flowpattern, a steady symmetric vortices flowpattern, a steady asymmetric vortices flowpattern and an unsteady vortices shedding flowpattern. Among them the steady asymmetric vortices flow is the most important re- search area in which there is a fascinating flow phenomena: the magnitude and sign of the side force on the axisymmetric slender body model will be changed with roll angle [4'11~14]. From our present knowledge, the asymmetric vortices flowfield over the slender body is very sensitive to the disturbance from the minute irregularities on or near the nose tip. These Received 17" December 2001, revised 28 April 2002 * The project supported by the National Natural Science Foundation of China ( ) and the Foundation of National Key Laboratory of Aerodynamic Design and Research (00JS HK01)

2 582 ACTA MECHANICA SINICA (English Series) 2002 small irregularities on the model are produced from model machining tolerances. However, their size and distribution on the model surface are unknown. This is one of the reasons for large discrepancies, which exist between test results obtained by different investigators [4,12]. It is the uncertainty of the distribution and size of perturbations from model machining micro-irregularities that causes the uncertainty of the asymmetric vortices flow when the model at a high angle of attack is rolled to different orientations. This kind of uncertainty makes it impossible to get the relation between the disturbance and the response of asymmetric vortices flowfield. Therefore, it is difficult to study the bistable behaviors of asymmetric vortices under uncertain disturbance. In order to study the influence of nose perturbation on asymmetric vortices some modification of cross section shape on model nose was made or various kinds of perturbation on the nose region were applied by many investigators [15~21]. Moskovitz et al. [16], Bridge and Hurnung [17], Luo et al.[ls] and Lee et al. [m] have investigated the side force behaviors of slender bodies with elliptic nose. It is found in Refs.[16~19] that a smooth two cycles of sinusoidal variation in the local side force per 360 ~ of roll is generated at moderate angles of attack. However, at high angles of attack the bistable state in the side force is formed, in which the side force exhibits a square-wave-like behavior and changes its direction abruptly over approximately 90 ~ of roll angle. It appears that the variation of the local side force with roll angle from an elliptic nose model is more regular than one from a sharp ogive nose model. In fact, the elliptic nose of the slender body should not be considered as a nose perturbation. Their boundary condition appears non-symmetric when the slender body is rolled. Degani and Tobak [2~ have studied the disturbance effect on side forces by means of retractable wire located near the tip and have found the variation of the side force with the extension size of wire protuberance at certain roll angles of model. Recently, Berhardt and Williams [9,21] have studied the influence of bleed or suction at two small holes drilled into each side of model tip and located at ~ from the forward stagnation line on the local side force. Their experimental results show that the local side force and forebody vortex position change continuously with bleed or suctional momentum coefficient C~ at c~ ~ And if the angle of attack is large enough (c~ = 55~ the side force and forebody vortex position have characteristics similar to the bistable behavior, and the side force appears two stable states with an equal magnitude but an opposite direction. The states corresponding to both stable states are called the regular states of asymmetric vortices flowfield around slender body [12]. In order to get the relation between the perturbation and response of asymmetric vortices flow, an experimental model with manual perturbation on the body nose is used in the present study. However, there are some fundamental problems about the asymmetric vortices flows with manual perturbation on the body nose, which should be made clear. First, when the various types of manual perturbation are added to the model nose in the wind tunnel testing there are also some geometric minute irregularities on the testing model due to machining tolerances. Therefore, the experimental results should include both effects of manual perturbation and machining imperfections. How to find what is an effect of manual perturbation? Second, the manual perturbation was usually fixed on a certain location of the model nose in the previous studies [9,15,2~ to find the perturbation response. What is the perturbation location effect where both axial and circumferential locations are included on the asymmetric vortices flow? Third, is there any effect on the asymmetric vortices flow with different types of manual perturbation? The present study will deal with above

3 Voi.18, No.6 Chen Xuerui et al.: Influence of Perturbations on Asymmetric Vortices 583 problems. And the answer of these questions not only can improve the understanding of the effect of disturbance on asymmetric vortices behaviors, but also lay a foundation for asymmetric vortices control. 2 DESCRIPTION OF EXPERIMENTS 2.1 Experimental Model The testing model is a steel slender body consists of a 3.0 caliber ogive nose and a 914mm-long cylindrical afterbody. The diameter of afterbody is 100mm. The pressure tappings are located at 18 stations of equal D distance along the model axis. The first pressure measuring station is 3.35D from the model tip. There are 24 pressure tappings (15 ~ apart) at each measuring station. The sketch of the model is shown in Fig I ~ I 1 ~ b I I I I I I I I ~ ~ " I q T ]-- I- V --I-- ~ ] --I-- T'--I I ~ I I I I I, I ~ I, I ' x L'/a Fig.1 Sketch of model geometry and pressure tapping locations (in millimeter) 2.2 Experimental Apparatus and Conditions The present experiments were carried out in the Peking University Low Speed Openreturn Wind Tunnel with 2.25 m in diameter of the test section. The freestream turbulence level in the test section is less than 0.2%, and the maximum speed in the test section is 50 m/s. The model was connected to a stepping motor through tail sting for making model roll to the specific roll angle. All pressure measurements were carried out using nine sets of 48-port Scanivalve equipped with nine +l-psi pressure transducers with an accuracy of +5% of the full scale. An AST 586 computer controlled the stepping motor to rotate the model to a proper roll angle and then the computer controlled the Scanivalve to acquire pressures step by step. Each tapping was sampled 512 times and averaged as a time-averaged pressure and the accuracy of the measuring pressure coefficient for each measuring station ranges from 0.9% to 3.5%. The accuracy here is equal to a/cpmax where a and Cpmax are the mean square root of the measuring pressure coefficient and maximum value of Cp for each pressure measuring station, respectively. To ensure the experiment performed at a suhcritical Reynolds number, the freestream velocity was fixed as 15 m/s, corresponding to a Reynolds number of ReD = p~v~d/# = x Data Processing The body coordinate system used in data processing is the one illustrated in Fig.2. The origin of the coordinate system is located at the center of the first pressure measuring station. Note that the dimensionless coordinates of pressure measuring stations x/d should be negative values, but they were given as positive values just for convenience in this paper. The cross sectional azimuthal angle 0 = 0 ~ is fixed at the windward symmetric plane of the model. The roll position corresponding to 7 = 0~ is determined with a special mark made on the model at the windward symmetric plane and this mark will not be changed in experiments. The positive direction of the azimuthal angle 0 and roll angle 7 is defined

4 584 ACTA MECHANICA SINICA (English Series) 2002 Z measuring station "-,~.'~ "-Z/ \, Fig.2 Definition of coordinate system as clockwise when looking downstream. The sectional side force is obtained from the integration of the circumferential pressure distribution. 3 MANUAL PERTURBATIONS IN EXPERIMENT There are two different types of manual perturbation used in experiments. The grit type perturbation on tip of nose is shown in Fig.3(a). Perturbation A consists of two grains of grit that are connected together on the nose. It is attached to the nose generator of 7 = 0~ and 0 = 0 ~ The distance LO/D between the nose apex and the forefront of grits is equal to 02. Other characteristic scale parameters of perturbation A are shown in Table 1. Another grain of grit is attached to the same generator at a distance of L1 to construct a tri-grain type perturbation with perturbation A as the baseline configuration. In order to study the effect of the perturbation axial location on asymmetric vortices, L1 takes different values to form perturbation C, D and E as shown in Table i. (a) Grit type perturbation Fig.3 (b) Top view of perturbation G Sketch of various types of perturbation Table 1 Parameters for grit type perturbations Type of perturbation L1/D Parameters A LO/D = 02 C 7 ho/d = 04 D 4 hl/d = 07 E 32 h2/d = 1 (c) Side view of perturbation G To study the effect of the circumferential location of perturbation on asymmetric vortices behaviors, a small triangle metal block is attached to the nose apex at ~ and O = 0% It is defined as perturbation G as shown in Fig.3(b) and Fig.3(c). The mini-block

5 Vol.18, No.6 Chen Xuerui et al.: Influence of Perturbations on Asymmetric Vortices 585 is an isosceles triangle, bid = 1, hid = 2, t/d = 05. The mini-block is moved from ~/-- 0 ~ and 0 = 0 ~ to ~/= 0 ~ and 0 = 90 ~ with axial position fixed, which is defined as perturbation I as shown in Fig.4. r k "%y,~ erturbatlon ~. J Fig.4 Sketch of manual perturbations and natural geometrical irregularities on the cross-section of model nose (Sawtooth represents the unknown distribution of geometrical irregularities on model surface) 4 RESULTS AND ANALYSIS 4.1 Dominant Effect of Manual Perturbation on Bistable Vortices In the previous experimental studies [9'15'17,21], manual perturbation attached to the nose was used to investigate the effect of nose disturbance on asymmetric vortices flow. However, some unknown minute geometrical irregularities already exist on the test model due to machining imperfections, which are shown in an enlarged sketch of the model section in Fig.4. These machining imperfections will also influence the behaviors of asymmetric vortices flow when being rolled with the model. The "natural" curve in Fig.5 represents the variation of sectional side force coefficient Cz with roll angle ff on the first pressure measuring station, when there is no any manual perturbation added to the nose. This curve is irregular because the size and distribution of these machining imperfections on the model are random and irregular too. If any manual perturbation, whose size and location are known, is attached on the model, the machining imperfections and the manual perturbation will influence the asymmetric vortices flow jointly. In fact, the results achieved by previous 1.5 : perturbation - -' U(~ Fig.5 Sectional side force Cz vs. roll angle ~f for miniblock type perturbations (x/d -- 0, a = 50 ~

6 586 ACTA MECHANICA SINICA (English Series) 2002 researchers are the joint effect of these two types of disturbance. In order to study the effect of nose disturbance on asymmetric vortices flow, the effect of the manual perturbation must be identified. The following experiments were designed to solve this problem. First, the test of perturbation G with roll-angle was conducted, and then the test was repeated after removing the mini-block G from the nose and reattaching it to its original position. The variations of Cz vs. V corresponding to perturbation G and its repeated test at different x/d measuring stations are given in Fig.6 and Fig.7, respectively. Comparison of both figures shows that they are almost the same, which means that the influence of the manual perturbation on asymmetric vortices flow is repeatable. It should be noted that, as shown in Fig.5, the square-wave-like Cz vs. 7 curves marked by "G" and "reapt. G" from manual perturbation G and its repeated test at the measuring station x/d = 0 are almost the same but they are quite different from one without manual perturbation marked by "natural" ~/(o).v /d i ~/(~ i ~/d Fig.6 Sectional side force Cz vs. roll angle ~/ (Perturbation G, a = 50 ~ Fig.7 Cz vs. V for repeated test of perturbation G (a = 50 ~ Second, the mini-block G was moved circumferentially only from "y = 0 ~ and 0 = 0 ~ to V = 0~ and 0 = 90 ~ which is defined as perturbation I, as shown in Fig.4. The test results of Cz vs. 7 at different stations with perturbation I are given in Fig.8. Because the circumferential location of perturbation I is 90 ~ ahead of perturbation G at a same roll angle of the model, the phase of curves Cz-'y in Fig.8 should be adjusted by shifting backward 90 ~ along the "y coordinate, and the results were plotted in Fig.9. Comparison of curves in Fig.6 and Fig.9 shows clearly that they are consistent with each other. But one fact must be emphasized here is that the location relationship between perturbation G and natural geometrical irregularities of model from machining is obviously different from that between perturbation I and natural geometrical irregularities as illustrated in Fig.4. The consistence of curves in Fig.6 and Fig.9 and the repeatable effect of perturbation G imply that the side force on the model mainly depends on the manual perturbation and that the influence of geometrical irregularities is neglectable. Furthermore, it can be seen from Fig.5 that the curve with phase adjustment for the perturbation I and the curves corresponding to perturbation G and its repeated test are in agreement with each other, but they are quite different from that at the natural state. The results of the comparison in Fig.5 clearly suggest that manual perturbation has a dominant effect on asymmetric vortices flow behaviors and side force on the model when manual perturbation and geometrical minute irregularities exist on the model together. And the influence of geometrical minute irregularities is quite weaker, even can be ignored if compared with that of the manual perturbation.

7 Vol.18, No.6 Chen Xuerui et al.: Influence of Perturbations on Asymmetric Vortices o o~ - o- i x/d x/d ~/(~ ~/(~ Fig.8 Sectional side force Cz vs. roll angle 7 (Perturbation I, a = 50 ~ Fig. 9 Cz-7 curve after phase shift backward 90 ~ from Fig.8 (Perturbation I, a = 50 ~ 4.2 Influence of Perturbation Location on Bistable Vortices In the last section, it has been seen that the geometrical minute irregularities from machining tolerance do influence the behaviors of asymmetric vortices flow. The variation of side force in the natural state is shown in Fig.5. However, when manual perturbation G or I was attached to the tip of the nose, it is shown that the manual perturbation will control the behavior of bistable vortices and that the geometrical irregularities can be ignored. It should be noted that this conclusion comes from condition that the manual perturbation added to the nose tip is much larger in size than the natural geometrical irregularities. However, if there is a manual perturbation somewhere from the tip, what will be the effect of manual perturbation on bistable vortices? That is the location effect of perturbation on bistable vortices, which will be investigated as follows. Based on perturbation A case, another grain of grit was attached to the nose away from the tip on the same generator of the model to form a tri-grit type perturbation defined as perturbation C, as shown in Fig.3(a). Then the third grain of grit was moved toward the nose tip to form perturbations D and E (shown in Table 1). The comparison of Cz vs. ~ curves on station x/d = 0 in case of perturbations A, C, D and E at angle of attack a = 50 ~ was shown in Fig.10. The curve for case of perturbation A is atypical squarewave-like curve as that of perturbations G and I. The other three curves corresponding to tri-grain type perturbations C, D and E are almost the same as the curve of perturbation i ~/(~ perturbation Fig.10 Sectional side force Cz vs. roll angle ~/for grit type perturbations (x/d = 0, a = 50 ~

8 588 ACTA MECHANICA SINICA (English Series) 2002 A except at ~ and ~ (the difference of curves at this two roll angles will be discussed in detail later). The consistence of the four curves in Fig.10 implies that the manual perturbation on the nose tip location has a dominant effect on the behaviors of bistable vortices. And those perturbations, which are far from the tip, has a secondary effect, even can be ignored as compared with the tip perturbation. The influence of the circumferential location of perturbation on asymmetric vortices flow can be analyzed with the test results of roll angle variation. It must be emphasized that all grit type perturbations were located on 0 = 0 ~ of the model when ~/ -- 0 ~ so the azimuthal orientation 0 of the manual perturbation is equal to the roll angle 7 of the model during the model rotation. As shown in Fig.10, when the circumferential location of perturbation A is rotated with the rotation of the model, the asymmetric vortices flowfield over the model exhibit two alternative switched regular states named as Left Vortex Pattern (LVP) and Right Vortex Pattern (RVP). LVP represents a pattern where the left vortex (look downstream) of the asymmetric vortices is near the model surface, while the right vortex is far from the model surface, which results in a positive side force. In contrast, RVP represents a pattern where the right vortex is near the surface, while the left vortex is far from model surface, which results in a negative side force. The sectional flow patterns of the asymmetric vortices fiowfield for LVP and RVP are visualized by dye flow visualization technique with laser sheet in the water tunnel as shown in Fig.ll. When the model is rotated about its body axis, as shown in Fig.10, first appears LVP at V = 0~ then it abrupt switches to RVP when perturbation A is rotated to 0 = 60 ~ Then, LVP and RVP switch over alternatively when the azimuthal orientation of perturbation A is at 0 = 165 ~ 270 ~, and 345 ~. In order to analyze the local flow behaviors where the manual perturbation makes the bistable vortices flow switch over, a circumferential pressure distributions at station x/d = 0 over the entire roll angle are given in Fig.12(a), which corresponds to Fig.10. Obviously, there are two types of symmetric pressure distribution corresponding to LVP and RVP in Fig.12(a). The switchover positions of perturbation A are marked by a verticm line and the switchover directions are marked by an arrow as shown in Fig.12(a). During the model rotation, it can be seen in Fig.12(a) that LVP first switches to RVP when the grit is rotated to an upstream position of the left separation point of LVP (0 = 60~ Then RVP switches back to LVP when the grit is rotated to the reattachment point of RVP (0 = 165~ (a) LVP flow pattern (b) RVP flow pattern Fig.ll Sectional vortices flow patterns (x/d = 0, c~ = 50 ~

9 Voi.18, No Chen Xuerui et al.: Influence of Perturbations on Asymmetric Vortices -.. RVP i reattacl~ment pointi LVP,e~ / i A': A \N,,,i//,A separation point ~(~separat[on point C -y go ~ (} ~165 ~180 ~ ~285 3O0 ~ q~ ~/(~ ~/(~ (a) Perturbation A (7 = 0~ '~ 360~ (b) Perturbation D (7 = 165 ~ ~" 210 ~ Fig.12 Pressure distribution on x/d ~- 0 section with azimuthal angle at different roll angles 589 j+lg~ I After that, LVP switches again to RVP when the grit is rotated to the downstream position of LVP's right separation point (0 = 270~ Finally, when the grit is rotated back near the windward stagnation point (0 = 345~ RVP switches back to the original LVP again. What is the mechanism of switchover of LVP and RVP to each other in bistable vortices fiowfield? It can be found in Fig.10 that, the structure of asymmetric vortices is switched from RVP to LVP when the perturbation is at azimuthal orientation of 0 = 165 ~ And some oscillations of side force appear when the perturbations are rotated to 0 = 195 ~ which indicates that the asymmetric vortices structure has the potential to switch from LVP to RVP at 0 = 195 ~ In fact, in some of our experimental results, there really exists the phenomenon that the side force switched from positive to negative values at 0 = 195 ~ It means that the structure of asymmetric vortices switches from LVP to RVP. But with the increase of roll angle, the RVP switches back again. In Fig.12(a), it can be seen that the azimuthal orientations of 0 = 165 ~ and ~ are the reattachment points of RVP and LVP in lee side fiowfield, respectively. In Ericcson's studies [22] on the origination of asymmetry from symmetric vortices over slender bodies at high angle of attack, he has found that there is some instability around the reattachment flowfield. Recently, Li and Deng[ 23] have studied the topological structure of flowfield over slender body at high angle of attack, and have pointed out that there is a topological structure of the saddle point to saddle point in the reattachment flowfield which is of unstable topological structure. In the present study, the reattachment flowfield around 0 = 165 ~ has exhibited its instability. The structure of asymmetric vortices is switched from RVP to LVP by the perturbation and the reattachment point is also moved from 0 = 165 ~ to 0 = 195 ~ in the LVP state. For the same reason, the flowfield around 0 = 195 ~ is unstable too. Therefore, when the perturbation is rotated to 0 = 195 ~ the side force oscillation and even vortices switchover can be seen. For clarity, the variations of pressure distributions from ~/= 165 ~ to ~, = 210 ~ in case of perturbation D are illustrated in Fig.12(b). Obviously the pressure distribution at ~ = 195 ~ is different from that of LVP and RVP. As described above, the oscillation of side force at ~/ -= 195 ~ corresponding to different perturbations are all because of the instabihty in the reattachment flowfield. In Fig.12(a), the azimuthal positions of 0 = 165 ~ and 0 = 195 ~ are all reattachment points corresponding to RVP and LVP, respectively, and the flowfields around them are all unstable too. However, when the perturbation is at 0 = 165 ~ the flowfield structure switches from RVP to LVP, and when the perturbation is at 0 = 195 ~ the flowfield structure only oscillates. The different responses for both unstable

10 590 ACTA MECHANICA SINICA (English Series) 2002 reattachment fields need further study. Moreover, the switchover mechanism at the other three circumferential positions is still unknown and need more investigations in the future. 4.3 Effect of Various Types of Perturbation on Bistable Vortices Two types of manual perturbation have been used in the present study to find the effect of disturbance on the bistable vortices over slender body. They are the grit type perturbation represented by perturbation A and the mini-block type perturbation represented by perturbation G. Are the effects of these two types of perturbation on the bistable vortices the same or not? Perturbations A and G are both perturbations attached to the nose tip, and their sizes are roughly the same. The curves of Cz vs. 7 corresponding to the two types of perturbation at x/d = 0 station are shown in Fig.13. It is found from Fig.13(a) that the curves are in agreement with each other, except that they are out of phase. If the phase of the curve corresponding to perturbation G is adjusted by shifting forward 15 ~ along the 7 coordinate, the two curves almost coincide as shown in Fig.13(b). The phase-shift between bistable vortices flowfield corresponding to perturbations A and G come from the difficulty of accurately locating the grit and mini-block on the same position of the nose tip of model. 1.5 "~ ~/(~ 360 Jerturbation o ,~i(o) 360,erturbatlon (a) Without phase shift (b) With phase shift Fig.13 Comparison of Cz vs. 7 for various types of perturbation (x/d = 0, a = 50 ~ The asymmetric vortices in a bistable state contain two asymmetric regular states, LVP and RVP, which are mirror images with each other. They control the behaviors of the whole flowfield and aerodynamic characters of the slender body. In order to verify whether the structure of bistable vortices excited by the two types of perturbations A and G are the same or not, the comparison of the distribution of side force with the axial location and the pressure distributions at the measuring stations in a regular state for both perturbations A and G are made. A positive regular state and a negative regular state are selected in Fig.13(b) which correspond to roll angles ~ and 7 = 120~ The distributions of side force coefficient Cz with axial location x/d in the two regular states induced by perturbations A and G are plotted in Fig.14. During a recent study of the structure of asymmetric vortices over slender body, Deng [24] has pointed out that the curve of Cz vs. x/d reaches a maximum where one vortex on one side is lifted off the body surface and a new vortex on the same side forms immediately and it is close to the body surface. Then the vortex on the other side will become a vortex far from the body surface and is lifted off again at a certain x/d. Therefore, a multi-vortice flowfield around the slender body is formed. The perfect consistence of the curves in Fig.14(a) and Fig.14(b) shows that the bistable vortices flowfield induced by

11 Voi.18, No.6 Chen Xuerui et al.: Influence of Perturbations on Asymmetric Vortices perturbation l perturbation x/d x/d (a) 7=30 ~,a=50 ~ (b) 3,=105 ~,(~=50 ~ Fig.14 Comparison of Cz vs. x/d for various types of perturbation perturbations A and G have the same lifted off locations and the same spatial vortices development state over the slender body. In order to further verify whether the structure of asymmetric vortices is identical or not, comparison of pressure distribution on the measuring stations was made. The results show that the pressure distributions at all measuring stations are identical for both perturbations A and G. For clarity, comparison of pressure distributions at only three stations at ~/= 30 ~ was shown in Fig.15. A good consistence of the pressure distributions at all stations along the body suggests that the structure of bistable vortices is identical for both perturbations A and G. f ' )erturbation o1( ~ y., ~ o i ~ -2.o, = i i -2.5 i i -3,0! i el( ~ ) :~erturbation (a) :c/d = 0 (b) x/d = o1(~ i 360 *erturbation (c) x/d= 4.5 Fig.15 Variation of Cp vs. O for various types of perturbation (7 = 30 ~ a = 50 ~

12 592 ACTA MECHANICA SINICA (English Series) 2002 From above detailed discussions, it was found that, the behaviors of bistable vortices, the circumferential switchover locations, vortices lifted off locations in the regular state and the spatial vortices development state are all identical for different types of perturbations. Therefore, it can be concluded that, the manual perturbation added to the nose tip plays only a trigger function for switchover of the asymmetric bistable vortices. Different types of manual perturbation will never affect the trigger function and will never influence the structure and development of asymmetric vortices flowfield. 5 CONCLUSIONS The experiments with nose perturbation have been conducted on an ogive nose cylinder model by rolling the model at angle of attack c~ = 50 ~ The influence of manual perturbations on bistable vortices at high angle of attack has been investigated. The experiments are performed in low speed wind tunnel with subcritical Reynolds number ReD = Following conclusions can be obtained from discussion of experimental results: (1) The effect of manual perturbation added to the nose tip on asymmetric vortices is repeatable. The behaviors and structure of asymmetric vortices over a slender body are mainly controlled by the manual perturbation on the nose tip as compared with geometrical minute irregularities on the test model from the machining tolerances. The effect of the latter even can be ignored. (2) For the effect of axial location of perturbation, the experimental results show that the manual perturbations on the nose tip have a dominant effect on bistable vortices as compared with those perturbations away from the nose apex. The effect of the latter can even be ignored. (3) There are four sensitive circumferential locations of manual perturbation, at which bistable vortices over the slender body are switched over between LVP and RVP. The flowfield over the switchover location at the reattachment point of lee side is an unstable flow structure topologically. (4) Various types of perturbation do not change the effect of perturbation on the behaviors of bistable asymmetric vortices and the flowfield structure of a regular state. However, there are some questions that need further study in the future: (1) What is the flow mechanisms to trigger the switchover of the bistable asymmetric vortices flowfleld for the perturbation located at ~ = 60 ~ ~ and t? ~ respectively? (2) What is the effect of perturbation size or strength on bistable asymmetric vortices? Acknowledgement The authors are very grateful to Mr. Wang Gang for his work in experiments of flow visualization in water tunnel. REFERENCES 1 Allen H J, Perkins EW. Characteristics of flow over inclined bodies of revolution. NACA RMA50L07, 1951? Chapman GT, Keener ER. The aerodynamics of bodies of revolution at angles of attack to 90 ~ AIAA , Ericsson LE, Reding JP. Vortex-induced asymmetric loads in 2-D and 3-D flows. AIAA , Hunt BL. Asymmetric vortex forces and wakes on slender bodies. AIAA , 1982

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