1 BASIC STUDY FOR VENTILATED ...

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A water tunnel for the study of ventilated supercavitation must form a ... Engineering) constructed a new medium-sized high-speed cavitation tunnel (HCT) ...
BASIC STUDY FOR VENTILATED SUPERCAVITATION EXPERIMENTS IN HIGH-SPEED CAVITATION TUNNEL OF KRISO 8 Bu-Geun Paik, Kyoung-Youl Kim, Jong-Woo Ahn, Han-Shin Seol, Ki-Sup Kim, Korea Research Institute of Ships & Ocean Engineering, KIOST, Republic of Korea Seung-Jae Lee, Research Institute of Marine Systems Engineering, Seoul National University, Republic of Korea Young-Rae Jung, Min-Jae Kim, Kurnchul Lee, Agency for Defense Development, Republic of Korea 8 8 To design and manufacture the supercavitated underwater body it is necessary to evaluate the drag and kinematic/dynamic performances for a scale-downed model. The large amount of air ventilated behind a cavitator produces lots of tiny bubbles, which prevent clear observation of supercavitation at the test section. To enable the collection of small bubbles, a bubble collecting section of large volume is equipped upstream of the test section in the cavitation tunnel. In the present works, the High-speed Cavitation Tunnel (HCT) has been designed and manufactured to have the large test section to conduct various supercavitation experiments. HCT has the test section dimension of 0.3H x 0.3 W x 3.0L m3 and provides maximum flow speed of 20.4 m/s at the test section. The blockage and Froude effects on the ventilated supercavitation are investigated successfully at the test section. The basic studies such as the supercavitation evolution, drag measurements and cavity shape extraction with air flow rate are also carried out in HCT. 8 8 1. Introduction 8 If the cavitation formed by a cavitator which located at the head of the underwater body covers its surface, the moving speed of the body is dramatically increased because of the reduction of its skin friction. In the initial stage of a cavitator design in the supercavitating body, scale-downed model tests are necessary to investigate the drag performance and improve the design features since it is difficult to estimate the drag or kinematic performances directly in the full-scale model. At the tunnel of the Saint Anthony Falls Laboratory (SAFL) in the University of Minnesota Twin Cities, U.S.A., various supercavitation experiments have been conducted for the cavitator design, supercavitation physics, and control synthesis/experimental validation, giving remarkable results [1-2]. Basic studies on control synthesis and cavitator design for supercavitating body are going on in South Korea. In any study of supercavitation control synthesis for a rather large underwater body, investigations on basic features such as the shape variation of the ventilated supercavitation, blockage effects of supercavitation, and the Froude number effects on supercavitation shape are strongly required. Although elementary experiments on supercavitation have been conducted at the small high-speed cavitation tunnel in South Korea, various systematic and reliable studies on cavitator design and its performances for underwater body could not be performed because of the absence of a facility similar to SAFL’s cavitation tunnel. A water tunnel for the study of ventilated supercavitation must form a high-speed oncoming flow ahead of the cavitator, which is installed in the test section. Further, air or bubble collection is essential so as to ensure clear observations in the test section because so many bubbles are present in the test section as a result of the injection of large amounts of air downstream of the cavitator. Considering above experimental surroundings of supercavitation, KRISO (Korea Research Institute of Ships and Ocean 1

Engineering) constructed a new medium-sized high-speed cavitation tunnel (HCT) beside the existing medium-sized cavitation tunnel (MCT), and is ready to do supercavitation experiments with rather large underwater bodies. The new water tunnel was designed to have test section dimensions of 0.3 H x 0.3W x 3.0L m3 and a maximum speed of 20 m/s in the test section. The efficient collecting performance of non-condensable bubbles and the realization of a high-speed water flow are necessary for supercavitation experiments, then the design of a bubble collecting section and the validation of its performance are critical. In the present study, the validation of the bubble collecting performance was carried out with experimental method at HCT. In addition, the verification of the ventilated supercavitation was also conducted to confirm the normal operation performance of the manufactured HCT. After these procedures, the basic studies on the supercavitation cavitator and its performances were carried out in model scale. 2. Trial test for the operation of HCT The dimension of the test section in HCT (Fig. 1) is 0.3B x 0.3 H x 3.0L m3. To investigate the uniformity and turbulence intensity of the fluid flow formed at the test section 1-D LDV(laser Doppler velocimetry, FlowExplorer 300, Dantec Dynamics) was employed as in Fig. 2. The measurement positions were at the centres of each window in length and width direction. The X-directional(main flow direction) flow velocity component was measured in terms of the main motor RPM(revolution per minute) and was expressed at Table 1. The uniformity of main flow was within 1% and turbulence intensity of it was around 0.4% when the mean flow velocity was 15 m/s at the test section. The test for the one-tenth scale model of the real HCT was already performed by Froude number scaling[3] to ensure the designed maximum velocity of 20 m/s. The maximum flow velocity was 20.4 m/s at the center of the first window section in the HCT test section, which was found to satisfy the maximum design velocity. 8

Fig. 1 Manufactured high-speed cavitation tunnel (HCT)

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Fig. 2 Photo of tunnel test section and conventional 1-D LDV system Table 1 Flow velocity results in uniform flow region (200 ´ 200 cm2) Mean (m/s) Uniformity (%) Turbulence intensity (%)

1st window 15.01 99.6 0.38

2nd window 15.20 98.6 0.42

Fig. 3 Air flow-rate control system for air injection For the bubble collection experiments the air flow-rate control system was prepared to supply the desired air flow rate to the test section as shown in Fig. 3. The air flow-rate control system consists of pressure tank of 9 bars, regulator, flow control valves and on-off valves, and it can control the air flow rate up to 300 l/min within ±2% accuracy as the air compressor provides enough air to the pressure tank. To observe the small bubbles passing through the test section the shadowgraph technique was adopted as in Fig. 4. For the shadowgraph technique, one high speed camera(Photron, UX100), two LED lamps and light diffusion sheets were employed to make the field-of-view of 8.8 ´ 7.5 mm2 in the test section. The air-supply pipe system has 4 holes of 2 mm diameter and connected to the air flow-rate control system to inject air into the water flow as in Fig. 5. The water flow velocity at the test section was limited to 13 m/s, considering the structural instability of air supply pipe with 15 mm diameter. To visualize the air bubbles in high velocity water flow the frame rate of the high speed camera was set to 5000 frames/sec. as in Fig. 6. The number of air bubbles larger than 750 μm began to increase when air was injected into the tunnel water with the flow rate of 200 l/min. However, air bubbles smaller than 400 μm were observed 3 minutes after blocking air injection, and air bubbles smaller than 300 μm were just detected 10 minutes after the air injection was cut off, which proved the bubble collecting section was working well. 3

Fig. 4 Shadowgraph set-up for bubble visualization

Fig. 5 Air injection experiments

Fig. 6 Bubble observation results at the test section As the HCT provides high speed flow at the test section and large variation of pressure energy in the tunnel passage, its structural safety should be confirmed before its regular operation. To measure the structural vibration of HCT during its trial test four 1-D accelerometers were attached on the surface of the HCT as shown in Fig. 7. The first measuring position was on the test section, and the second and the third were on the elbows of the HCT, and the fourth one was on the impeller part. Especially, three 1-D accelerometers were combined and attached on the top surface of the test section because it would be very important location for supercavitation experiments. Figure 8 shows the time history of the acceleration values measured at the impeller RPM of 150. E1 is the first elbow which is located after the diffuser of the HCT’s upper part, and E4 is the fourth elbow located before the bubble collecting section. Small vibration appeared at the test section and the fourth elbow E4, and rather larger vibration occurred at the impeller and E1 parts. The impeller is a rotatory machine and main source of vibration in the HCT, 4

and E1 part provides additional vibration sources induced by lots of bubbles and flows rotating 90°, moving to the lower part of the HCT. The maximum acceleration value was found to be ±0.3 m/s2 in the flow range by 15 m/s, which confirmed the tunnel’s structural vibration was not large even if the bubble collecting section was working.

One-axis accelerometer

Fig. 7 One-axis accelerometer for vibration measurements

Fig. 8 Vibration measurement results at impeller rpm of 150 3. Verification experiments of ventilated supercavitation 8 After trial tests of the HCT itself, the additional verification experiments were conducted to confirm the feasibility of the ventilated supercavitation. The experimental set-up in the test section consists of strut, pipe (containing air injection and pressure cables) and cavitator as shown in Fig. 9. The cavitator of disk shape had 31.6 mm diameter and produced low pressure region just behind it to make cavitation. To form the ventilated supercavitation the air flow-rate control system should be used to supply air into the low pressure region behind the cavitator. The location of the air injection was decided to be 0.5dc(dc is the diameter of the cavitator) apart from the cavitator back side. The pressure Pc in the supercavitation has to be measured to obtain the ventilated cavitation number. This was measured at the position of 0.75dc apart from the cavitator back side. The experimental results of ventilated cavitation in the HCT were compared with those in the SAFL of Minnesota University. The verification tests were done at the blockage ratio of 10.7 (9% blockage effect by dc) when the blockage ratio D/dc is defined as the ratio of 5

the tunnel test section’s equivalent diameter to the cavitator diameter. The free stream velocity U¥ coming to the test section was 10 m/s (Froude number = U¥/(g×dc)0.5 = 18). Here, air entrainment coefficient Cq was determined according to the injected air flow rate as following.

=

(1)

=

(2)

Q means the air flow rate(unit : LPM, liter per min.). The ventilated cavitation number sc can be obtained from tunnel’s static pressure P¥, cavity pressure Pc and U¥.

Figure 10 shows the size of the foamy cavity increased with the air flow rate in the region of Cq < 0.2. Clear and transparent supercavitation formed and kept its shape when Cq > 0.2, as shown in Fig. 10(d). The supercavitation continues its shape though Cq decreased less than 0.2 if it formed once, which is called the hysteresis effect of ventilated supercavitation. When Cq became 0.06, the supercavitation collapsed and showed the cavity closure like re-entrant jet, and then returned to the foamy cavity as in Fig. 10(f). This sort of characteristics in the ventilated supercavitation were reported well by Kim et al.[4].

cavitator Strut

Pipe

Fig. 9 Pipe system set-up for ventilated supercavitation experiments Here, the reliability of the air flow meter need to be carefully checked in advance. In the case of wrong reading or wrong measuring of the air flow rate can cause serious errors or misunderstanding in the experimental results. In the present study, two air flow meters (one made by TSI Company and another made by LT Company) were selected as the candidate for the final air flow meter. Air entrainment coefficients were measured by each air flow meter and then the relation with the ventilated cavitation number was investigated. The detailed method to obtain minimum cavitation number from cavitation shape are described in Kim et al.[4]. Figure 11 shows that the ventilated cavitation number from two air flow meters and minimum cavitation number from cavitation shape are similar each other. However, the flow meter of LT company was finally chosen because results from it was more similar to the distribution extracted by Reichardt’s empirical formula [5] with the cavity shape information. After choosing the appropriate air flow meter, the feasibility in the supercavitation experiments was verified through additional ventilated supercavitation tests between KRISO and SAFL, which shows similar results each 6

other as in Fig. 12. This verification test confirmed that the supercavitation experimental results obtained at the newly manufactured HCT would be effective and reliable.

(a) Cq = 0.06

(b) Cq = 0.10

(c) Cq = 0.15

(d) Cq = 0.20

(e) Cq = 0.12

(f) Cq = 0.06

Fig. 10 Supercavitation evolution at dc = 31.6mm and Fn = 18 0.2

0.25

0.3

0.35

0.4

Empirical formula, 10m/s Exp.(LT) 10m/s Exp.(TSI) 10m/s

0.2

0.45 0.25

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0.15

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Exp.(KRISO) Fn=18.0 Exp.(SAFL) Fn=18.0

0.15

0 0.15

0.15 0.25

0 0.45

cavitation number, sc

Fig. 11 Experimental results for choosing air flow meter

Air entrainment coefficient, C q

Air entrainment coefficient, C q

0.15 0.25

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0 0.15

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0 0.6

cavitation number, sc

Fig. 12 Comparison of hysteresis curves between KRISO and SAFL

In the present study, Froude number effect on supercavitation shape was investigated at Fn = 10.8, 14.4, 21.6 as well as Fn = 18 as shown in Fig. 13. In the cases of Fn = 10.8 and 14.4, the cavity near the pipe strut shows upwardly inclined shape, affected by the buoyancy effect, and moves downstream. This sort of buoyancy effect was getting disappeared as Fn increased, and the tail of the cavity going downstream with the feature of straight as in Fig. 13(d). If the cavity tail moves upward by Froude number effect, the blockage ratio due to the cavity shape variation (in the point of cross-section) increases and makes the 7

minimum cavitation number increase, which is similar to the choking effect in the pipe system. The minimum cavitation number sm can be described as following. +1=

(3)

Here, D and Ds are the equivalent diameter of the tunnel test section and the maximum diameter of the cavity, respectively. Figure 14 shows that the sm decreased as the Froude number increased from 10.8 to 21.6. Thus, when Fn is getting large we need less air flow rate to obtain equivalent ventilated cavitation number, and the hysteresis effect is gradually reduced.

(a) Fn = 10.8

(b) Fn = 14.4

(c) Fn =18.0 (d ) Fn = 21.6 Fig. 13 Supercavitation shape with the variation of Froude number

Air entrainment coefficient, C q

0.15 0.25

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Exp. Fn=10.8 Exp. Fn=14.4 Exp. Fn=18.0 Exp. Fn=21.6

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0 0.15

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cavitation number, sc

Fig. 14 Variation of ventilated cavitation number in terms of air entrainment coefficient and Froude number

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4. Drag measurement of cavitator and extraction of cavity shape The cavitator, obstructing the oncoming flow ahead of the underwater body, produces supercavitation behind it and forms large drag on it. Many researchers such as Reichardt[6] and Garabedian[7] reported the drag on the cavitator is related with the cavity shape (Max. diameter and length). They proposed specific theoretical or empirical formulas to express the relation between cavitator drag and cavity shape. The formulas mainly mentioned that the drag on the cavitator would be a critical key to estimate the cavitation shape in the natural supercavitation formed at the unbounded flow. Thus, it is very important to measure precisely the drag on the cavitator because the estimation on the cavity shape is essential for the determination of the diameter and length of the underwater body in the design stage.

Drag sensor

Fig. 15 One-dimensional drag sensor and cavitator

1.1

CD

1.05

1

0.95 CD(Exp.) CD(Garabedian) 0.9

0.15

0.2

0.25

0.3

0.35

s

Fig. 16 Comparison of drag coefficients from the ventilated supercavitation experiments and Garabedian’s asymptotic formula Fig. 15 shows the one-dimensional drag sensor (Wonbang Forcetech, Max. 800N), which was diaphragm type and located just behind the cavitator. This sensor had good features of -0.14% linearity, -0.03% load history and 0.03% repeatability. In the present study, drag measurements were conducted in the cavitator-pipe system for the ventilated supercavitation as shown in Fig. 9, and the drag measurement results were compared with those calculated by Garabedian’s formula as following[7]. =

(1 + )

(4) 9

Here, CD and s are drag coefficient and cavitation number. The value of CD0 in infinity cavity of s = 0 is assumed to be 0.827. For the disk cavitator of 30 mm diameter, the drag coefficients were plotted with respect to the ventilated cavitation number as in Fig. 16. From the foamy cavity to re-entrant jet type cavity(just before the clear supercavitation begins) the drag coefficient follows the Garabedian’s line well, but after forming clear supercavitation at the minimum cavitation number of 0.185, it increased up to around 1.05 and was getting apart from the Garabedian’s line. As the location of the air ventilation was related to the pressure distribution just behind the cavitator, the study on the air ventilation location should be further investigated later. The shape of the supercavitation can be also estimated through Garabedian’s asymptotic formula as following.

=

=

/

log

(5) /

(6)

Here, Dmax, L and d c are maximum cavity diameter, maximum cavity length and cavitator diameter, respectively. CD and s¥ are the drag coefficient and the cavitation number in unbounded flow, respectively. The s¥ is can be converted from the tunnel cavitation number s as following when s is small,

σ =

(7)

where smin is the minimum cavitation number obtained from Brennen’s plot [8], decided fatefully by the blockage ratio (cavitator diameter/tunnel test section’s equivalent diameter) of the tunnel. window

Side View Flow Test Section

Cavitator Lights Light shaping diffuser Mounting strut

Flow Mounting shaft Top View

High Speed Camera

Fig. 17 Optical experimental setup

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Although the shape of the supercavitation can be estimated by the empirical or theoretical formula such as Garabedian’s, it can be also directly obtained by measuring it in experiments. In this study, the shape of the supercavitation was measured by shadowgraph technique. The high-speed camera operated with 1000 frames per sec. in back lighting (instead of front lighting) to obtain high-resolution edge contours of a supercavitation. As shown in Fig. 17, the back light and the high-speed camera were placed perpendicular to the measurement plane and a light-shaping diffuser was used to homogenize light sources with hotpots and uneven light distribution. In this study, the camera recorded 12-bit color images with a size of 1280×248 pixels and the resolution of the images was approximately 1.14 pixel/mm. Automatic extraction of supercavitation outlines from the shadow images needs to produce most effective and reliable results. The outlines were identified by applying the in-house code [9], which is based on an edge detection operator and a cubic spline algorithm. The outline extraction has three main steps: 1) Background subtraction (Background-subtracted images resulted from pixel-by-pixel subtraction of the background image from the images of the supercavitation.), 2) Edge detection (All parts of the image that were above a global threshold were segmented on the basis of the Sobel operator.), and 3) Outline smoothing (Cubic splines were fitted to discrete noisy data points provided by the Sobel operator.). Fig. 18 provides an overview of the image processing procedure for distinguishing supercavitation outlines from a shadow image.

(a) measured image

(b) background-subtracted image

(c) detected edges (d) extracted outlines Fig. 18 Sample output from the automatic outline extraction process Figure 19 shows the variation of shape parameters Dmax and XDmax normalized by dc according to the air entrainment coefficient Cq. Here, XDmax is the horizontal position of maximum diameter in supercavitation when the origin is located at the back side center of the cavitator. In general, the maximum length L of the supercavitation is defined by double XDmax. After the supercavitation occurred at around Cq = 0.1, its Dmax and L did not change though Cq increased. As mentioned before, the shape parameters of supercavitation would be also predicted by the drag coefficient CD by Eq. (5) and (6). In the case of maximum diameter XDmax, the value extracted from the experiments was similar to the value resulted from the estimation with CD as shown in Fig. 20(a). However, the cavity length L directly extracted from experiments was a little larger than the value from the estimation with CD as in Fig. 20(b). To tell the truth, Eq. (5) and (6) were based on the natural cavitation in an unbounded flow. The ventilation cavitation experiments were conducted at the cavitation tunnel with a closed circuit, and then the effect of bounded flow may have strong influence on the cavity shape, especially cavity length. As the model tests are generally carried out at the cavitation tunnel in the form of ventilated supercavitation, further study should be done regarding the cavity shape estimation method with the drag coefficient CD, which are inherently based on the natural cavitation and unbounded flow. 11

12

3

9

xDmax / dc

Dmax / dc

4

2

6

a = 180° (disk)

a = 180° (disk)

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1

0

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(a) maximum diameter (b) horizontal position of Dmax Fig. 19 The shape of supercavitation against air entrainment coefficient C q 6

50 Reichardt Garabedian disk 30mm

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(a) maximum cavity diameter (b) maximum cavity length Fig. 20 The prediction of cavity shape parameters with respect to s¥

5. Concluding remarks To conduct the ventilated supercavitation experiments in a cavitation tunnel, the performances of a bubble collecting and high-speed flow should be confirmed. In the present study, high-speed cavitation tunnel (HCT) with a bubble collecting section were successfully designed and constructed. A series of test in the full-scale water tunnel finally showed that the bubble collecting section was working well in terms of flow uniformity and bubble collection. The HCT was found to be very competent for conducting 12

ventilated supercavitation experiments, in terms of hysteresis effect in cavity formation and Froude number effect. In addition, the drag and cavity shape measurement techniques were properly employed in the HCT. In the point of cavity diameter, the direct measurements of it in experiments gave similar results to the values estimated with the drag coefficient. However, further study is necessary to estimate the cavity length from the drag coefficient because it was somewhat different from the value extracted by direct measurement of cavity length. 6. Acknowledgement This research was supported by grants from National R&D Projects “Study on the design and performance of supercavitation cavitator” funded by Civil Military Co-operation Center of Korea, UM14113RD1 (PNS2910) and “Study on ventilated super cavitation in the medium-sized cavitation tunnel” funded by National Re-search Foundation of Korea, NRF-2014M3C1A9060859 (PNS2810).

7. References 1. W. Zou, K. P. Yu, R.E.A. Arndt, E. Kawakami and G. Zhang, (2012), “On the stability of supercavity with angle of attack,” Proc. of the 8th International Symposium on Cavitation, CAV2012, Singapore. pp. 922-927 2. E. Kawakami and R.E.A. Arndt, (2011), “Investigation of the behav-ior of ventilated supercavities,” J. Fluids Engineering, 133 (9). 091305 3. B. G. Paik, I. R. Park, K. S. Kim, K. C. Lee, M. J. Kim and K. Y. Kim, (2017), “Design of a bubble collecting section in a high speed water tunnel for ventilated supercavitation experiments,” J. Mechanical Science and Technology, in press. 4. B. J. Kim, J. G. Choi, and H. T. Kim, (2015), “An Experimental Study on Ventilated Supercavitation of the Disk Cavitator,” J. of the Society of Naval Architects of Korea, 52 (3), pp. 236-247 5. R. T. Knapp, J. W. Daily and F. G. Hammit, (1970), “Cavitation,” University of Iowa, Iowa Institute of Hydraulic Research, IOWA : Institute of Hydraulic Research 6. H. Reichardt, (1946), “The laws of cavitation bubbles at axially symmetric bodies in a flow,” Ministry of Aircraft Production Volkenrode, MAP-VG, Reports and Translations 766, USA : Office of Naval Research. 7. P. R. Garabedian, (1956), “Calculation of axially symmetric cavities and jets,” Pacific J. Mathmatics, Vol. 6(4), pp.611-684. 8. Brennen, C., 1969. A Numerical Solution of Axisymmetric Cavity Flows. Journal of Fluid Mechanics, 37, pp.671-688. 9. S.J. Lee, E. Kawakami and R.E.A. Arndt, (2013), “Investigation of the behaviour of ventilated supercavities in a periodic gust flow”, J. Fluids Engineering, Vol 135, 081301-1.

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