Acta Mech Sin (2010) 26:787–791 DOI 10.1007/s10409-010-0358-z
TECHNICAL NOTE
Effects of tip perturbation and wing locations on rolling oscillation induced by forebody vortices Bing Wang · Xue-Ying Deng · Bao-Feng Ma · Zhen Rong
Received: 8 January 2010 / Revised: 19 March 2010 / Accepted: 19 March 2010 / Published online: 8 July 2010 © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH 2010
Abstract The wing rock motion is frequently suffered by a wing-body configuration with low swept wing at high angle of attack. It is found from our experimental study that the tip perturbation and wing longitudinal locations affect significantly the wing rock motion of a wing-body. The natural tip perturbation would make the wing rock motion of a nondeterministic nature and an artificial mini-tip perturbation would make the wing rock motion deterministic. The artificial tip perturbation would, as its circumferential location is varied, generate three different types of motion patterns: (1) limit cycle oscillation, (2) irregular oscillation, (3) equilibrium state with tiny oscillation. The amplitude of rolling oscillation corresponding to the limit cycle oscillatory motion pattern is decreased with the wing location shifting downstream along the body axis. Keywords Wing rock motion · Asymmetric vortices flow · High angle of attack aerodynamics · Nose tip perturbation
1 Introduction A wing rock phenomenon is liable to occur on aircrafts flying at high angles of attack [1,2]. The wing rock is characterized by a self-induced limit cycle oscillatory motion, primarily a roll motion, and the occurrence of wing rock would impact the flight safety of aircrafts. In order to reveal the aero-dynamic mechanism underlying the wing rock and The project was supported by the National Natural Science Foundation of China (10432020, 10872019 and 10702004). B. Wang · X.-Y. Deng (B) · B.-F. Ma · Z. Rong Key Laboratory of Fluid Mechanics, (Beihang University), Ministry of Education, Beihang University, Beijing 100191, China e-mail:
[email protected]
effectively avoid its harm to aircrafts, lots of research efforts have been made, as summarized in the review papers [1,2]. The wing rock could be induced by the leading edge vortex from a slender delta wing alone and has been studied intensively. And these research results have revealed that no wing rock would occur if the sweep angle of a delta wing is less than 75◦ [3]. Brandon and Nguyen [4], however, found in their experiments that a wing-body model could exhibit wing rock even for a very low swept wing (∧ = 26◦ ). Ericsson [5] attributed the mechanism driving the wing-body rock to the induction of forebody vortices with moving wall effects. In order to reveal the flow physics of wing rock experienced by a wing-body configuration with forebody vortices at a high angle of attack, one should first study and analyze what are the respective functions of slender body and wing in the wing rock motion. It has been known that the forebody vortices will become asymmetric over a slender body at high angles of attack [6–8]. The asymmetric vortices are extremely sensitive to tip perturbations, and even the natural tip perturbation arising from machining tolerance could dramatically change the forebody vortex orientation, which is an inherent and unique feature of the forebody asymmetric vortices. And there is non-determinacy in the asymmetric vortices flow induced from the natural tip perturbation. If an artificial perturbation is added on the nose tip, the asymmetric vortices flow would become deterministic and its orientation would regularly change in two cycles with varied perturbation circumferential location around the tip [7,8]. To our knowledge, however, the previous studies of this kind of wing rock have not dealt with tip perturbations imposed on the forebody nose. Therefore, in this note, we try to study how the artificial tip perturbation with different circumferential location influences the wing rock motion patterns on a wing-body model.
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Fig. 1 Model for free-to-roll experiments. a A wing-body model; b artificial tip perturbation, d = 0.2 mm; and c various locations of a wing along a body
Fig. 2 Variation of average amplitudes with circumferential location of nose, wing location x/D = 4, Re = 1.93 × 105 . a Natural tip perturbation and b artificial tip perturbation
In addition to the effect of tip perturbation, the wing locations in the model configuration also affect the wing rock motion significantly, as suggested in previous researches, but the experimental evidence seems to be not conclusive, even contradictive. The experimental results by Brandon and Nguyen [4] showed that the amplitude of the rolling oscillation would increase with the wing shifting downstream along a body axis. In contrast, Williams and Nelson’s result [9] indicated that the amplitude would decrease with the wing shifting downstream. There was no deep research and physically sound explanation about these phenomena. Therefore, our experiments also plan to study and analyze the effect of wing location on the amplitude of rolling oscillation.
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2 Experiments and results The experiments were carried out in the D-4 wind tunnel of Beihang University, which was a low turbulence low speed wind tunnel with a test section of 1.5 m × 1.5 m. The free-toroll model was a wing-body configuration with a low swept wing as shown in Fig. 1a. We chose low swept wing to avoid the effect of high swept wing leading edge vortex on wing rock motion and make the rolling oscillation arise mainly from the effect of forebody asymmetric vortices. In order to find out whether there are effects of the non-determinacy of asymmetric vortices flow with natural tip perturbation on the wing rock motion, there are two exchangeable
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Fig. 3 Time history for three types of motion, wing location x/D = 4, Re = 1.61 × 105 . a γ = 0◦ , b γ = 45◦ , c γ = 135◦ , and d γ = 90◦
model noses n1 and n2 with the same shape and the same machining tolerance. Figure 1b shows the artificial nose tip perturbation of mini-ball with 0.2 mm diameter used in the experiments, and the circumferential locations of tip perturbation can be changed through a small rotatable nose driven by a small stepping motor inside the model. The wing could shift longitudinally to four locations along the body axis as shown in Fig. 1c, and the wing location is defined by the distance of the most forward point of the wing to the body tip. The experiments were carried out on a freeto-roll rig, and the motion history was recorded using a digital optical encoder. Instantaneous roll angles were measured with a resolution of 0.088◦ . The experiments were conducted at Re = 1.61 × 105 and Re = 1.93 × 105 based on the diameter of the cylinder of the model, and the boundary layer on the forebody would exhibit a laminar separation without reattachment at these Reynolds numbers. The angle of attack was fixed at 50◦ where the asymmetric vortices were sufficiently developed and exhibited a bi-stable state with circumferential variation of tip perturbation. It is indicated from the experiment results shown in Fig. 2a, where amplitude is average value of sample data and γ denotes circumferential angles of noses, that the wing rock motions with noses n1 and n2 can not be repeatable, which should be attributed to the non-determinacy of asymmetric vortices flows in response to natural tip perturbations. However, if a mini-ball as an artificial perturbation is added on the nose tip of n1 and n2, the experiment results of wing
Fig. 4 Variation of average amplitudes with circumferential location of tip perturbation, wing location x/D = 4, Re = 1.61 × 105
rock motions of models n1 and n2 become repeatable and deterministic as shown in Fig. 2b. Based on the determinacy of wing rock motion with artificial tip perturbation of model, the effect of the circumferential locations of the artificial tip perturbation on the wing rock motion of wing-body model is shown in Figs. 3 and 4, where the longitudinal position of the wing is set at x/D = 4. The 0◦ circumferential angle of tip perturbation is defined as the symmetry plane of the windward side. The results show that there exist three types of motion when the circumferential
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Fig. 5 Time history of free-to-roll motion with different wing positions, α = 50◦ , Re = 1.61 × 105 . a x/D = 3, b x/D = 4, c x/D = 5 and d x/D = 6
angles of tip perturbation are changed from 0◦ to 360◦ , i.e. a limit cycle oscillation as shown in Fig. 3a, an equilibrium state with a tiny oscillation as shown in Fig. 3b and c, and an irregular oscillation as shown in Fig. 3d. Figure 4 shows the variation of average amplitudes of motion with the circumferential angles of the tip perturbation. It is also indicated in the figure that the limit cycle oscillation occurs when the perturbation is located near 0◦ or 180◦ , the irregular oscillation occurs when the perturbation is located near 90◦ and 270◦ , and the motion exhibits an equilibrium state with tiny oscillation when the perturbation is located at other positions. Based on the determinacy of wing rock motion with an artificial tip perturbation, the effect of the wing position on the wing rock motion has also been studied experimentally. The mini-ball tip perturbation was set at 0◦ of circumferential angle where the model exhibits a limit cycle oscillation. Figure 5 shows the time history of wing rock motion of the model for various wing locations, in which it is indicated that the amplitude of rolling oscillation would decrease as the wing shifts downstream, and this phenomenon is more clearly shown in Fig. 6. However, what is the flow physics for such wing rock motion behavior or rolling moment on the wing, which drives the wing rock motion? In fact, in the flow field over the wing-body model especially over the wing at high angles of attack, the forebody asymmetric vortices flow will become a dominant flow phenomenon, as proved by the above part of study. The rolling moment on the wing, which drives the free-to-roll motion, should be mainly dependent on
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Fig. 6 Average amplitude varied with wing positions, α = 50◦ , Re = 1.61 × 105
both the strength of forebody asymmetric vortices and their specific positions in this vortices flow field. It is well known that the asymmetric vortices system over a slender body is a multi-vortices structure with vortices shedding alternately [7]. And the distribution of sectional side forces on a body could be denoted as the distribution of strength of forebody asymmetric vortices. It has been known that the distribution of sectional side forces on a slender body alone decrease gradually along the body axis as shown in Fig. 7, refer to Ref. [7] for detail. So the rolling moment on the wing or the
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References
Fig. 7 The wing positions and the distribution of sectional side force on slender body alone, α = 50◦ , Re = 1.29 × 105
amplitude of rolling motion induced by the forebody asymmetric vortices should also decrease with wing shifting downstream since the strength of forebody vortices decreases as clearly shown in Fig. 7.
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