# Ice-Water-Gas Interaction during Icebreaking by an Airgun Bubble

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Set-Up and Principles

#### 2.1. The Laboratory-Scale Airgun

_{0}is the working pressure of the airgun, V

_{0}is the volume of the airgun, m

_{g}is the amount of gas, P

_{b}is the pressure inside the bubble and $\tau $ is a coefficient based on the airgun design. However, it is hard to determine the coefficient $\tau $ by using experimental data directly, because it is hard to observe when the gas has been released completely from gas chamber into water or bubble. This parameter will be studied specially in future work.

#### 2.2. Experimental Set-Up

^{3}. The distances between the bubble surface and the tank walls were large enough compared with the bubble diameter, so the boundary effect of the tank wall can be ignored. The water depth was 580 mm and the distance of the exhaust port of the airgun below the free surface could be adjusted according to working conditions. An air-free ice plate was prepared by degassed water and located on the free surface of the water. Then, the experiment could start and the dynamic change of ice-water-gas interaction was recorded and analyzed. The ice sample used in this paper was a circular ice plate with a diameter of 380 mm, and the thickness depended on the requirements of the test. The detailed preparation process, as well as the mechanical properties of the ice plate, can refer to Yuan et al. [10] and Ni et al. [29]. The bending strength was 2.39 MPa by the three-point bending test. The Young’s modulus was 6.25 GPa and compressive strength was 9.41 MPa by the uniaxial compression test. Other physical properties are suggested to refer to those of freshwater at the same temperature (−5 °C) for reference. For example, Poisson’s ratio can be taken as 0.33 from recommendation of Hobbs [33]. The water temperature during the test was about 10 °C and the pressure of the surrounding liquid was hydrostatic pressure, which was about 1.96 kPa for the exhaust port with a submergence depth of 0.2 m.

#### 2.3. Bubble Shape and Nondimensionalization

_{p}, conserved in the bubble [34,35,36] as

_{0}is the volume of the air gun, P

_{0}is working pressure, and c

_{1}is a coefficient for the design of the gun. When the bubble achieves the maximum, the moving velocity of the bubble at that moment is zero, so the kinetic energy is zero and the potential energy [34,35,36] can be written as

_{max}is the maximum volume of the bubble, ${P}_{h}$ is the hydrostatic pressure, and c

_{2}and c

_{3}are coefficients related to bubble shape, and so on. Considering energy conservation between Equations (2) and (3), one can obtain the link between ${d}_{\mathrm{max}}^{}$ and P

_{0}as

_{4}and C are coefficients.

_{max}gets slow when P

_{0}gets large.

## 3. Results and Discussions

#### 3.1. Pressure Measurement

_{0}was 1.52 MPa and the explosion distance h was 52 mm. The shooting frequency was 20,000 frames/s, and the typical photos of the case were shown in Figure 6 at different moments. The time-history curve of measured pressure P

_{m}in the center of the plate was presented in Figure 7, in which P

_{m}was relative pressure with an initial value of 0 kPa.

#### 3.2. Typical Case Study

#### 3.3. The Damage Patterns of Ice under Airgun Bubble Loads

- (1)
- Radial slits pattern

- (2)
- Radial and circumferential slits pattern

- (3)
- Radial cracks pattern

- (4)
- No crack pattern

#### 3.4. Influence of Parameters

#### 3.5. Repeatability and Randomness of the Results

_{0}= 2.44 MPa, h = 70 mm, t

_{ice}= 20 mm with dimensionless parameters H = 0.75, T = 0.30. The case was done twice and adopted to investigate the repeatability and randomness of the results. It can be seen that the evolution of the bubble was almost consistent, which denoted the bubble was relatively stable with parameters. On the other hand, the damage pattern of the ice was also the same, which were both ‘radial slits (shock wave)’ pattern, although the specific cracks were different. Just as mentioned in a previous study [5], for ice breaking, it was concerned with damage pattern rather than specific crack because of the randomness of crack generation. All these phenomena illustrated the complexity of the ice mechanics [46]. That was also the reason why we were concerned with the damage patterns, but not the specific cracks in Section 3.3.

## 4. Conclusions

- 1.
- Influenced by the airgun structure, the shape of the bubble was not spherical in the expansion stage but presented a unique ‘pear-like’ shape, which was quite different from the spherical shape of the spark bubble. An initial shock wave was accompanied by the generation of the airgun bubble, followed by oscillatory pressure peaks caused by the directional fast air injection, then cycles of shock waves with damping amplitudes along with the minimum volumes of the bubble. At the same time, a bubble jet and its induced high-pressure peak (even higher than that induced by shock wave) were also observed and measured. The initial shockwave and secondary shockwave together with the jet impact were expected to contribute to the icebreaking mainly.
- 2.
- High-pressure airgun bubbles had more cycles underwater than spark bubbles did. As a result, the retarded flow formed by bubble pulsation and collapse played an important role in the process of icebreaking. It aggravated the cracks extending into slits and pushed the ice plate breaking up along the slits. Moreover, once the ice plate separated, a free surface appeared and a spike may have also been generated, which enhanced the effect of icebreaking significantly.
- 3.
- There were three typical patterns of icebreaking under the airgun bubble: ‘radial slits’ pattern, ‘radial and circumferential slits’ pattern, and ‘radial cracks’ pattern, under different parameters. For the former two, both initial shock waves and secondary shock wave together with bubble jet can induce these patterns. According to different reasons, the first pattern was further classified as ‘radial slits (shock wave)’ and ‘radial slits (jet)’, whereas the second pattern was further classified as ‘radial and circumferential (shock wave) slits’ and ‘radial (shock wave) and circumferential (jet) slits’. The third one was most scarce, as it had very strict conditions for both ice thickness parameters $T$ and distance parameters $H$ simultaneously.
- 4.
- The selection of an optimal distance of the bubble is an important problem for practical icebreaking application. It involves many factors, such as ice properties, bubble properties, boundary conditions, etc. As far as the parameters (H and T) concerned in this paper, the smaller the H was, the better the icebreaking effect was. This may be because shockwaves could contribute more at a nearer distance to the ice. Further study on this problem will be continued involving more parameters.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. The Detailed Development of the Bubble Jet and Volume

**Figure A1.**Images of the jet evolution of the bubble in Figure 6. (

**a**) t = 7.95 ms, (

**b**) t = 8.15 ms, (

**c**) t = 8.35 ms, (

**d**) t = 8.50 ms, (

**e**) t = 8.65 ms, (

**f**) t = 8.75 ms, (

**g**) t = 8.85 ms, (

**h**) t = 8.95 ms.

**Figure A2.**Volume variation of the bubble in Figure 6.

## References

- Sazonov, K.; Dobrodeev, A. Ice Resistance Assessment for a Large Size Vessel Running in a Narrow Ice Channel Behind an Icebreaker. J. Mar. Sci. Appl.
**2021**, 20, 446–455. [Google Scholar] [CrossRef] - Ni, B.Y.; Chen, Z.W.; Zhong, K.; Ll, X.A.; Xue, Y.Z. Numerical simulation of a polar ship moving in level ice based on a one-way coupling method. J. Mar. Sci. Eng.
**2020**, 8, 692. [Google Scholar] [CrossRef] - Du, Y.; Sun, L.; Pang, F.; Li, H.; Gao, C. Experimental Research of Hull Vibration of a Full-Scale River Icebreaker. J. Mar. Sci. Appl.
**2020**, 19, 182–194. [Google Scholar] [CrossRef] - Zhai, M.X.; Li, X.Q.; Hui, F.M.; Cheng, X.; Heil, P.; Zhao, T.C.; Jiang, T.Y.; Cheng, C.; Ci, T.Y.; Liu, Y.; et al. Sea-ice conditions in the Adélie Depression, Antarctica, during besetment of the icebreaker RV Xuelong. Ann. Glaciol.
**2015**, 56, 160–166. [Google Scholar] [CrossRef] - Wang, Z.; Turner, J.; Sun, B.; Li, B.; Liu, C. Cyclone-induced rapid creation of extreme Antarctic sea ice conditions. Sci. Rep.
**2014**, 4, 5317. [Google Scholar] [CrossRef] - Ni, B.Y.; Wang, Q.; Xue, Y.Z.; Wang, Y.; Wu, Q.G. Numerical Simulation on the Damage of Ice Floe by High-Pressure Bubble Jet Loads, 3rd ed.; Workshop and Symposium on Safety and Integrity Management of Operations in Harsh Environments: St. John’s, NL, Canada, 2017. [Google Scholar]
- Ni, B.Y.; Pan, Y.T.; Yuan, G.Y.; Xue, Y.Z. An experimental study on the interaction between a bubble and an ice floe with a hole. Cold Reg. Sci. Technol.
**2021**, 187, 103281. [Google Scholar] [CrossRef] - Cui, P.; Zhang, A.M.; Wang, S.; Khoo, B.C. Ice breaking by a collapsing bubble. J. Fluid Mech.
**2018**, 841, 287–309. [Google Scholar] [CrossRef] - Kan, X.Y.; Zhang, A.M.; Yan, J.L.; Wu, W.B.; Liu, Y.L. Numerical investigation of ice breaking by a high-pressure bubble based on a coupled BEM-PD model. J. Fluids Struct.
**2020**, 96, 103016. [Google Scholar] [CrossRef] - Yuan, G.Y.; Ni, B.Y.; Wu, Q.G.; Xue, Y.Z.; Zhang, A.M. An experimental study on the dynamics and damage capabilities of a bubble collapsing in the neighborhood of a floating ice cake. J. Fluids Struct.
**2020**, 92, 102833. [Google Scholar] [CrossRef] - Jorgensen, J.K.; Gyselman, E.C. Hydroacoustic measurements of the behavioural response of arctic riverine fishes to seismic airguns. J. Acoust. Soc. Am.
**2009**, 126, 1598–1606. [Google Scholar] [CrossRef] - Hermannsen, L.; Tougaard, J.; Beedholm, K.; Nabe-Nielsen, J.; Madsen, P.T. Characteristics and propagation of airgun pulses in shallow water with implications for effects on small marine mammals. PLoS ONE
**2015**, 10, e0133436. [Google Scholar] [CrossRef] [PubMed] - Chahine, G.L.; Kalumuck, K.M.; Hsiao, C.T. Simulation of surface piercing body coupled response to underwater bubble dynamics utilizing 3DYNAFS, a three-dimensional BEM code. Comput. Mech.
**2003**, 32, 319–326. [Google Scholar] [CrossRef] - Goh, B.H.T.; Gong, S.W.; Ohl, S.W.; Khoo, B.C. Spark-generated bubble near an elastic sphere. Int. J. Multiph. Flow
**2017**, 90, 156–166. [Google Scholar] [CrossRef] - Chen, H.L.; Ni, B.Y.; Hu, W.J.; Xue, Y.Z. Model experimental study of damage effects of Ship structures under the contact jet loads of bubble in a water tank. Shock Vib.
**2018**, 2018, 8456925. [Google Scholar] [CrossRef] - Tatlisuluoglu, A.; Beji, S. Blast Pressure Measurements of an Underwater Detonation in the Sea. J. Mar. Sci. Appl.
**2021**, 20, 706–713. [Google Scholar] [CrossRef] - Duan, Y.S.; Wang, X.H.; Liu, S.B. Application of blasting technique to against ice jam. J. Glaciol. Geocryol.
**2003**, 25, 220–226. [Google Scholar] - Barash, R.M. Ice-Breaking by Explosives; Naval Ordnance Laboratory Technical Report NOLTR 66–29; Naval Ordnance Laboratory: White Oak, MD, USA, 1966. [Google Scholar]
- Mellor, M. Breaking Ice with Explosives; USA Cold Regions Research and Engineering Laboratory: Hanover, NH, USA, CRREL Report 82-40; 1982. [Google Scholar]
- Mellor, M. Derivation of guidelines for blasting floating ice. Cold Reg. Sci. Technol.
**1987**, 13, 193–206. [Google Scholar] [CrossRef] - Wang, Y.; Qin, Y.; Yao, X. A combined experimental and numerical investigation on damage characteristics of ice sheet subjected to underwater explosion load. Appl. Ocean. Res.
**2020**, 103, 102347. [Google Scholar] [CrossRef] - Wang, Y.; Qin, Y.Z.; Wang, Z.K.; Yao, X.L. Numerical study on ice damage characteristics under single explosive and combination explosives. Ocean. Eng.
**2021**, 223, 108688. [Google Scholar] [CrossRef] - Asuelimen, G.; Blanco-Davis, E.; Wang, J.; Yang, Z.L.; Matellini, D.B. Formal Safety Assessment of a Marine Seismic Survey Vessel Operation, Incorporating Risk Matrix and Fault Tree Analysis. J. Mar. Sci. Appl.
**2020**, 19, 155–172. [Google Scholar] [CrossRef] - Giles, B.F. Pneumatic acoustic energy source. Geophys. Prospect.
**1968**, 16, 21–53. [Google Scholar] [CrossRef] - Chen, Y.; Zhang, X.K.; Qiu, X.L.; Ge, H.K.; Liu, B.J.; Wang, B.S. A new method to generate seismic wave on the land. Chin. Sci. Bull.
**2007**, 11, 1317–1321. (In Chinese) [Google Scholar] - Chelminski, S.; Watson, L.M.; Ronen, S. Research Note: Low-frequency pneumatic seismic sources. Geophys. Prospect.
**2019**, 67, 1547–1556. [Google Scholar] [CrossRef] - Mellor, M.; Kovacs, A. Breakage of Floating Ice by Compressed Gas Blasting; Cold Regions Research and Engineering Laboratory (CRREL): Hanover, New Hampshire, USA, 1972; pp. 1–9, Special Report 184. [Google Scholar]
- Coburn, J.L., Jr.; Ehrlich, N.A. Advanced icebreaking concepts. Nav. Eng. J.
**1973**, 85, 11–19. [Google Scholar] [CrossRef] - Ni, B.Y.; Wu, Q.G.; Yuan, G.Y. Air Gun Device for Underwater High Pressure Gas Ice-Breaking Experiment. Chinese Patent 109900177, 20 April 2021. (In Chinese). [Google Scholar]
- De Graaf, K.L.; Brandner, P.A.; Penesis, I. Bubble dynamics of a seismic airgun. Exp. Therm. Fluid Sci.
**2014**, 55, 228–238. [Google Scholar] [CrossRef] - Cheremisinoff, N.P. Applied Fluid Flow Measurement Fundamentals & Technology; Marcel Dekker Inc: New York, NY, USA, 1979. [Google Scholar]
- Ni, B.Y.; Zhang, A.M.; Wang, Q.X.; Wang, B. Experimental and numerical study on the growth and collapse of a bubble in a narrow tube. Acta Mech. Sin.
**2012**, 28, 1248–1261. [Google Scholar] [CrossRef] - Hobbs, P.V. Ice Physics; Oxford University Press: Oxford, UK, 1974. [Google Scholar]
- Rayleigh, J.W. On the pressure developed in a liquid during the collapse of a spherical cavity. Philos. Mag.
**1917**, 34, 94–98. [Google Scholar] [CrossRef] - Willis, H. Underwater Explosions, Time Interval between Successive Explosions: Report, British Report; The National Archives: Kew, Richmond, 1941.
- Wehner, D.; Landr, M.; Amundsen, L. On Low Frequencies emitted by Air Guns at Very Shallow Depths—An Experimental Study. Geophysics
**2019**, 84, 61–71. [Google Scholar] [CrossRef] - de Graaf, K.L.; Penesis, I.; Brandner, P.A. Modelling of seismic airgun bubble dynamics and pressure field using the Gilmore equation with additional damping factors. Ocean Eng.
**2014**, 76, 32–39. [Google Scholar] [CrossRef] - Yu, Q.; Xu, Z.; Zhao, J.; Zhang, M.; Ma, X. PIV-Based Acoustic Pressure Measurements of a Single Bubble near the Elastic Boundary. Micromachines
**2020**, 11, 637. [Google Scholar] [CrossRef] - Carlomagno, G.M.; Ianiro, A. Thermo-fluid-dynamics of submerged jets impinging at short nozzle-to-plate distance: A review. Exp. Therm. Fluid Sci.
**2014**, 58, 15–35. [Google Scholar] [CrossRef] - Kitagawa, K.; Nagahiro, D.; Ohtani, K.; Abe, A. Collision of Underwater Explosion with Compressible Porous Wall; Springer: Cham, Switzerland, 2019. [Google Scholar]
- Cui, X. Experimental Study of Hopkinson Bar Based Measurement Methodology to Wall Pressure Generated by Near-Field Underwater Explosion. Ph.D. Thesis, Harbin Engineering University, Harbin, China, 2019. (In Chinese). [Google Scholar]
- Lauterborn, W.; Ohl, C.D. Cavitation bubble dynamics. Ultrason. Sonochemistry
**1997**, 4, 65–75. [Google Scholar] [CrossRef] - Lauterborn, W.; Bolle, H. Experimental investigations of cavitation-bubble in the neighbourhood of a solid boundary. J. Fluid Mech.
**1975**, 72, 391–399. [Google Scholar] [CrossRef] - Geers, T.L.; Hunter, K.S. An integrated wave-effects model for an underwater explosion bubble. J. Acoust. Soc. Am.
**2002**, 111, 1584–1601. [Google Scholar] [CrossRef] - Bazant, Z.P.; Kim JJ, H.; Li, Y.N. Part-through bending cracks in sea ice plates: Mathematical modeling. Am. Soc. Mech. Eng. Appl. Mech. Div. AMD
**1995**, 207, 97–105. [Google Scholar] - Bai, X.; Zemlyak, V.; Vasilyev, A.; Kozin, V. Stressed-Deformed State of Ice Crossings at the Surface Reinforcement of Composite Materials. J. Mar. Sci. Appl.
**2020**, 19, 430–435. [Google Scholar] [CrossRef]

**Figure 1.**Equipment of the airgun: (1) air storage chamber, (2) solenoid valve, (3) exhaust port, (4) cylinder body, (5) capacity control rod, (6) piston seal, (7) intake port, (8) solenoid valve outer shell, (9) sealing element, (10) movable bar, (11) reset spring, (12) electromagnetic coil, (13) cast iron, (14) wire interface. (

**a**) real objects, (

**b**) schematic view.

**Figure 6.**Image of underwater airgun bubble near a rigid wall. (

**a**) t = 0 ms, (

**b**) t = 1.95 ms, (

**c**) t = 5.00 ms, (

**d**) t = 8.35 ms, (

**e**) t = 8.85 ms, (

**f**) t = 10.80 ms, (

**g**) t = 13.35 ms, (

**h**) t = 16.00 ms, (

**i**) t = 18.90 ms, (

**j**) t = 23.65 ms, (

**k**) t = 27.35 ms, (

**l**) t = 31.05 ms.

**Figure 8.**Images of icebreaking by an airgun bubble with $T$ = 0.28 and $H$ = 1.02. (

**a**) t = 0 ms, (

**b**) t = 0.60 ms, (

**c**) t = 4.80 ms, (

**d**) t = 8.65 ms, (

**e**) t = 9.20 ms, (

**f**) t = 9.90 ms, (

**g**) t = 16.35 ms, (

**h**) t = 69.10 ms, (

**i**) t = 215.05 ms, (

**j**) t = 423.95 ms.

**Figure 13.**The damage patterns of ice under airgun bubble loads with the same condition H = 0.75, T = 0.30 (P

_{0}= 2.44 MPa, h = 70 mm, t

_{ice}= 20 mm). (

**a1**) t = 0.00 ms, (

**a2**) t = 0.90 ms, (

**a3**) t = 4.50 ms, (

**a4**) t = 25.00 ms, (

**b1**) t = 0.00 ms, (

**b2**) t = 0.90 ms, (

**b3**) t = 4.50 ms, (

**b4**) t = 25.00 ms.

**Table 1.**Different damage patterns of the ice along with distance parameter $H$ and thickness parameter $T$.

T | 0.00–0.17 | 0.18–0.20 | 0.21–0.24 | 0.25–0.26 | 0.27–0.28 | 0.29–0.31 | ||||
---|---|---|---|---|---|---|---|---|---|---|

H | No. | |||||||||

Smalldistance | 0.00–0.69 | 3 | 5 | 8 | 4 | 1 | ||||

0.70–0.76 | 1 | 7 | 4 | |||||||

Mediumdistance | 0.77–0.84 | 2 | 1 | 7 | 4 | 3 | ||||

0.85–1.10 | 4 | 3 | 1 | 0 | 0 | |||||

Largedistance | 1.11–1.40 | 2 | 3 | 2 | 0 | 0 | ||||

1.41–2.30 | 3 | 2 | 1 | 0 | 0 | 0 | ||||

Radial and circumferential slits | Radial slits(Shock wave) | Radial slits(Jet) | Radial cracks | No crack |

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## Share and Cite

**MDPI and ACS Style**

Wu, Q.-G.; Wang, Z.-C.; Ni, B.-Y.; Yuan, G.-Y.; Semenov, Y.A.; Li, Z.-Y.; Xue, Y.-Z.
Ice-Water-Gas Interaction during Icebreaking by an Airgun Bubble. *J. Mar. Sci. Eng.* **2022**, *10*, 1302.
https://doi.org/10.3390/jmse10091302

**AMA Style**

Wu Q-G, Wang Z-C, Ni B-Y, Yuan G-Y, Semenov YA, Li Z-Y, Xue Y-Z.
Ice-Water-Gas Interaction during Icebreaking by an Airgun Bubble. *Journal of Marine Science and Engineering*. 2022; 10(9):1302.
https://doi.org/10.3390/jmse10091302

**Chicago/Turabian Style**

Wu, Qi-Gang, Zuo-Cheng Wang, Bao-Yu Ni, Guang-Yu Yuan, Yuriy A. Semenov, Zhi-Yuan Li, and Yan-Zhuo Xue.
2022. "Ice-Water-Gas Interaction during Icebreaking by an Airgun Bubble" *Journal of Marine Science and Engineering* 10, no. 9: 1302.
https://doi.org/10.3390/jmse10091302