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Oscillation Pattern of Parachute and Concave Body

Norio Arai1, Hiroyuki Houzu2, Yoko Takakura3 Tokyo Noko University, Koganei, Tokyo, 184-8588, JAPAN

In this study, the experiment for the oscillation of a parachute after inflation process is done at low Reynolds number. Especially, effects of the payload motion to the canopy (parachute) motion are focused. A solid concave body is set in a vertical water tunnel which is driven by siphon’s low. Here, the uniform flow direction is opposed to the gravity direction in order to simulate the real parachute vertical drop. Four types of supporting system are applied to investigate the effects of the payload motion. There are differences about degree of freedom of payload between four type tests. The displacement of the object is measured by using CCD camera motion analyzer, and experimental data is processed by a short-time Fourier transform(STFT). Results are summarized as follows. The degree of freedom of payload affects on the concave body motion significantly. The oscillation pattern of the concave body changes by time, those are linear, arc, and circular motion.

I. Introduction ecently the parachute is widely used as one of aerodynamic decelerator system. However its aerodynamic characteristics are not understood well because of the complicated interaction between the parachute and the

ambient flow. As before, the experimental and numerical approaches are done to clarify the phenomenon. Desabrais1 executed water tunnel test focused on parachute’s canopy inflation and canopy’s cyclic breathing in the steady flow. Cruz2 executed wind tunnel test focused on canopy’s opening load for various disk gap band parachutes. But, there are only few experimental results for after canopy inflation phenomenon because of the difficulty. On the other hands, numerical simulations are executed by many researchers. Stein3 calculated about the cross parachute with the attention to the fluid structure interaction. Tezduyar3 calculated the phenomenon of a traveling of parachute in the far wake of an aircraft. However, it is hard to catch the phenomenon (deformation, oscillation etc.) by numerical simulation because of its lightness, flexibility and strong nonlinear fluid-structure interaction. Additionally, computational resources restriction makes difficult to do the large simulation of 3-dimensional case, which is the realistic requirement. In many experiments and numerical simulations, the supporting point of the canopy is fixed at a stationary point, which does not move in the ambient flow, while the canopy may move in it. However, considering the realistic canopy drop, both the payload (supporting point) and the canopy may move, in which we can observe the relative motion of the payload and the canopy. Therefore, strictly speaking, these investigations could not simulate the realistic motion of the parachute. In this article, with emphasis on the relative motion of the supporting point and the canopy, the experimental test about after inflation of canopy is done. The objective of this study is to research the 3-dimentional behavior of concave body and how degree of freedom for payload effect on canopy’s behavior.

II. Experimental Setup

A. Water Tunnel

In this study, the water tunnel shown in Fig. 1 is used. This water tunnel can create uniform flow which direction is opposed to the direction of gravity vector to simulate the relationship between flow direction and gravity vector

1 Professor, Dept .of Mechanical Engineering, Associate Fellow. 2 Graduate student, Dept. of Mechanical Engineering. 3 Research associate, Dept. of Mechanical Engineering, Associate Fellow.

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19th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar21 - 24 May 2007, Williamsburg, VA

AIAA 2007-2531

Copyright © 2007 by Norio ARAI. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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direction. The water flow is driven by siphon’s low. Flow velocity is controlled by water head gap between tank A and B shown in Fig. 1. Velocity range of this water tunnel is 0.091 – 0.128 m/sec. The test section is 190mm inner diameter cylindrical geometry and made of acrylic board. The upstream tank A and down stream tank B are overflowed to keep the water head height constant.

tank Btank A

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Fig. 1 Schematic of water tunnel.

B. Rigid and Deformable (permeable and/or impermeable) Canopy with Fixed Supporting System

First of all, we investigate the three kinds of canopy motion, in which the supporting point is fixed. Three models are rigid, permeable deformable, and impermeable deformable canopy, respectively. The rigid canopy is hemisphere and made of polyethylene resin. The deformable canopy is made of nylon fabric and is similar to the realistic one. (See Fig.2.)

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Rigid canopy Deformable canopy

Fig. 2 Rigid and deformable canopy.

C. Rigid Canopy with Moving Supporting System

Next in order to investigate the effects of the degree of freedom for the supporting point on the oscillation pattern of canopy, we have taken a video movie of the rigid canopy, in which that is made by polyethylene resin, thickness is 0.8 mm and radius is 25mm. The object is solid and impermeable. In this study, only one type object is applied. In order to clarify the differences among supporting systems, we have applied four types as shown below. Four type tests are named as follows and schematic diagrams are shown in Fig.3. Test A

Two threads which length is equal to the channel width cross the flow channel. Distance between the object and the supporting point is 50 mm. The supporting point does not move. Test B

A thread crosses the flow channel to support the object. The thread length is 40 mm longer than the width of channel. Supporting point can move. The movement in x-direction is little while that in y-direction may be observed. Test C

Two threads cross the channel to support the object. Both thread length are 40 mm longer than width of channel. Supporting point can move up and down in a vertical line. Test D

Two threads cross the channel to support the object. Both thread length are 40 mm longer than width of channel. And weight is fixed on supporting point, which looks like a payload. This weight is adjusted to balance the fluid force. The weight is 5.6 g.

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X

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test A test B test C test D

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Fig.3 Schematics of test models.

D. Experimental Condition

Experiment is done at flow velocity, 0.1278 m/s. Reynolds number based on characteristic length L=0.078mm is 8700. The object displacement in X-Y section is measured by imaging sensor. By using mirror, x-component displacement and y-component displacement are measured simultaneously. The coordinate origin is set on the object supporting point at rest state. Displacement of the object is measured during about 20 minutes at sampling frequency 6.06 Hz. Gabor transform (Short-Time Fourier Transform(STFT) is done by using displacement results. Those are reduced to clarify the oscillation pattern (Lissajous figure), and then are classified.

III. Results and Discussion

A. Rigid and Deformable (permeable and/or impermeable) Canopy with Fixed Supporting System Clarified oscillation patterns are shown in Fig.4. Oscillation patterns are classified into three kinds of oscillation

pattern, those are linear motion, circular arc motion, and circular motion. The appearance frequency is different from each other and depends on the Re number and the body characteristic (rigid, deformable, permeable). linear motion, circular arc motion, circular motion

Results are summarized in Fig.4 ranging Reynolds number 9,600 to 14,400. Generally we can see both the arc and the circular motion. However, in case of the rigid canopy, we can see the linear motion too. In this experiment, the supporting point is fixed. Differences between the linear (in-line) motion and the are/circular motion are from the difference between the rigid body and the deformable body. The shape of the deformable body may be changed by the structure of the wake, while the body is affected directly by the wake because the shape of the rigid body does not changed. The deformable body seems to dodge the effect of strong vortices.

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Re=9600 Re=11600 Re=14400 Rigid Deformable Deformable Permeable Impermeable

Fig.4 Oscillation pattern.

B. Rigid Canopy with Moving Supporting System

(1) Test A Figs.5 and 6 show Lissajous diagram during 1-80 sec, 1040-1120 sec respectively. Figs.7 and 8 show STFT

results of x-component frequency and y-component frequency. Fig.5 shows the Lissajous pattern with a circler and an arc motion while we can observe the linear (in-line) motion little. Hence Fig.6 shows the in-line type motion. From STFT results, we can observe both 0.4 Hz and 0.08 Hz frequency components. The lower (0.08 Hz) component seems to come from a small displacement distance arc type motion and/or an in-line motion, that is shown in Fig.5 given in the early stage, while the higher (0.4 Hz) component seems to come from a large displacement linear (in-line) motion shown in Fig.6 given in the late stage. The feature of type A is that the oscillation mode of the concave body changes in time.

(2) Test B Lissajous diagrams are shown in Figs.9 and 10 during 400-480 sec and 960-1040 sec respectively. Time

histories of frequencies are shown in Figs,11 and 12. In this test, the object can move longer range to y-direction than x-direction. It means that the length of the thread of pendulum is longer in y-direction than that in x-direction. Therefore Lissajous diagram becomes longer in y-direction, and hence, spectrum power of y-direction is stronger than x-component. (The amplitude of displacement in y-direction is larger than that in x-direction.). We can see only low frequency. The reason seems that the arc and/or circular motion governs the motion and that the displacement becomes large to require much time in motion. Also we can see the staying of body a little.

(3) Test C Lissajous diagrams at type C are shown Figs.13, 14 and 15 during 180-260 sec, 960-1040 sec and 1360-1440 sec

respectively. Figs.16 and 17 show time history of frequency. Fig.13 shows the circular and arc type Lissajous. In this stage, both 0.05 Hz and 0.4 Hz frequency components are distinguished. It seems like to type A. Fig.14 shows the in-line motion sometimes in x-direction and sometimes in y-direction. However, the strange thing is that the linear (in-line) motion mainly in y-direction can be observed as shown in Fig.15. The object moves with a circler type oscillation mode until 550 sec. Then the mode changes in the linear (in-line) motion mode gradually. This

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feature is similar to type A, in which the lower component comes from the arc type motion while the higher one comes from the in-line motion.

(4)Test D Lsissajous diagrams are shown Fig. 18 and 19 about 1-80 sec and 480-560 sec. The time history of frequency is

shown Figs.20 and 21. In this case, the object can move freely. The supporting threads across the channel exist only reason for avoid the crash to the channel side wall. The object balances out fluid force and weight gravity. The object moves mainly in arc pattern. The probability of the development of arc and/or circular motion is increased compared with test A and C. Consequently, the probability of the development of lower frequency becomes higher and the power becomes stronger too. We can see the differences between type D and types A and C as shown in Figs.20 and 21. This difference is caused by the difference of the degree of freedom each other.

Fig.5 Lissajous Diagram Type A (1-80 sec). Fig.6 Lissajous Diagram Type A (1040-1120 sec).

Fig.7 Time History of X-Frequency(Type A). Fig.8 Time History of Y-Frequency(Type A).

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Fig.9 Lissajous Diagram Type B (400-480 sec). Fig.10 Lissajous Diagram Type B (960-1040 sec).

Fig.11 Time History of X-Frequency(Type B). Fig.12 Time History of Y-Frequency(Type B).

Fig.13 Lissajous Diagram Type C (180-260 sec). Fig.14 Lissajous Diagram Type C (960-1040 sec).

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Fig.15 Lissajous Diagram Type C (1360-1440 sec).

Fig.16 Time History of X-Frequency(Type C). Fig.17 Time History of Y-Frequency(Type C).

Fig.18 Lissajous Diagram Type D (1-80 sec). Fig.19 Lissajous Diagram Type D (480-560 sec).

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Fig.20 Time History of X-Frequency(Type D). Fig.21 Time History of Y-Frequency(Type D).

IV. Conclusions

The experiment to clarify the oscillation pattern of the concave body in the uniform flow is carried out. And the effect of four different types to support the body on the oscillation mode is also examined. As a result, following conclusions are obtained. (1) Oscillation patterns are classified in three types (linear (in-line), arc, and circular mode). Mainly the higher

oscillation frequency comes from the in-line mode while the lower one comes from the arc/circular mode. (2) When the degree of freedom of the body becomes larger, the arc type governs the oscillation pattern.

Acknowledgments Authors would like to thank the considerable assistance of Mr. Yuji Suzuki in experiment, who is an

undergraduate student of Tokyo Noko University.

References

1 Desabrais, K. J., “Velocity Field Measurements in the near wake of the canopy,” PhD Thesis, Worcester Polytechnic Institute, 2002.

2 Stein, W., et al., “Parachute Fluid-structure interactions: 3-D computation,” Comput.Methods Appl.Mech.Engrg., Vol. 190, No. 27, 3-4 Oct. 2000, pp., 373, 386.

3 Tezduyar, W., Osawa, Y., “Fluid-structure interactions of a parachute crossing the far wake of an aircraft,” Comput.Methods Appl.Mech.Engrg., Vol. 191, No. 7, 6-7 Dec. 2001, pp., 705, 716.