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Numerical study of the effect of ship attitude on the perform of ship with air injection in bottom cavity
Ocean Engineering 186 (2019) 106119
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Numerical study of the effect of ship attitude on the perform of ship with air injection in bottom cavity Wu Hao a, b, * a b
Key Laboratory of High Performance Ship Technology, Wuhan University of Technology, Wuhan, 430063, China School of Transportation, Wuhan University of Technology, Wuhan, Hubei, 430063, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Air cavity ship Drag reduction Shape of air layer Heeling Trim
Air lubrication by means of a bottom cavity is a promising way for ship drag reduction. The characteristics of air layer under the bottom cavity and effect of drag reduction are sensitive to the attitude of ship model. To investigate the stability of air layer under different navigation condition of air cavity ship, a method with the combination of RANS equations and VOF model is proposed for the viscous-flow calculation of a large flat bottom ship, which is verified by the model-test result. The effect of heeling and trim on the formation and stability of air layer is investigated. Present numerical results show that there is a critical value of heeling arctanðh=Bc Þ with the definition the cavity depth and width of the h =Bc . The air layer would be stable if ship heeling is less than the critical value. The air layer broke when the heeling is greater than the critical value, and heeling increase, broken phenomenon aggravate. The trim angle of the ship is unfavorable to the stability of the air layer and it should be avoided as much as possible in the course of navigation.
1. Introduction Air layer drag reduction technology is an effective way to reduce ship friction. Some basic concepts of air layer drag reduction were proposed in the 19th century by Latorre (1997). Subsequently, researchers con ducted numerous experimental studies in the laboratory. In most air layer drag reduction experiments, the air is injected through continuous slots, which are either open or filled with porous material, to ensure a uniform air layer under the test surface (Kodama et al., 2000; Slyozkin, 2011). Ceccio (2010) presented different applications and a detailed explanation of the distribution of air under a ship’s hull during air in jection. Air layer drag reduction by means of a bottom cavity has been proven to be an effective method of ship drag reduction. Lay et al. €kiharju et al. (2012, 2013) conducted an experimental (2010) and Ma investigation about the drag reduction effects of a ventilated partial cavity at high Reynolds numbers for a large plate in the W. B. Morgan Large Cavitation Channel and established the basic energy economic calculation results for a hypothetical air lubricated ship. The stability of the air layer in the bottom cavity and the coverage area of air layer are the key factors that affect the effect of the air layer drag reduction for a ship. To obtain a uniform air layer under the bottom hull, Zverkhovskyi (2014) designed a device called a ‘cavitator’ to
impede the flow of water on the underside of the vessel, with a small slotted opening behind the cavitator delivering the air supply, This method was found to be particularly successful because it significantly reduces the air flow rate required to create the air layer. The effect of air layer thickness on drag reduction was verified experimentally by Shuji et al. (2010). The result shows that the energy consumed by the blower depends on the thickness of the bottom air layer. Following the funda mental experimental study on a flat plate with a cavity conducted in the Emerson Cavitation Tunnel of Newcastle University by Slyozkin et al. (2014), Butterworth et al. (2015) proposed an experimental test on an existing container ship model with a cavity of 0.0387 m2 at the bottom of the ship model. The model experiment results show that the effect of air layer drag reduction can reach 4–16%. The effect of air layer drag reduction and the air escape from the bottom hull were affected by the characteristics of the bottom cavity. According to conclusion of Slyozkin and Butterworth, the design of the bottom cavity plays an important role in the evaluation of the air €kiharju et al. (2010) conducted a series of tests layer drag reduction. Ma with a flat plate with a device called a ‘BFS’, which helps the air layer to form easily while reducing the air supply and pressure. Experimental test on a flat plate and a ship model with air lubrication system were successively conducted by Jang et al. (2014). From the tests, if there is
* School of Transportation, Wuhan University of Technology, Wuhan, Hubei, 430063, China. E-mail address: [email protected]. https://doi.org/10.1016/j.oceaneng.2019.106119 Received 14 October 2018; Received in revised form 23 March 2019; Accepted 16 June 2019 Available online 12 July 2019 0029-8018/© 2019 Elsevier Ltd. All rights reserved.
W. Hao
Ocean Engineering 186 (2019) 106119
no significant deterioration in the real sea condition, it is considered that the air lubrication at the bottom of the ship has great potential for en ergy saving. According to the experimental results, many scholars have carried out a mass of numerical research. Matveev (2003, 2007) solved an important problem with a simplified model, which is the interaction between the waves and the cavity. The result shows the main parameters that affect air layer in the ship bottom cavity is the shape of cavity and speed. The same author has developed a platform to test different types of Air Cavity Ships (ACS) using the necessary instrumentation to improve and optimize this technique (Matveev, 2015). The interaction between the cavity and the boundary of ship was analyzed by Amromin (2016). Choi et al. (2005, 2007, 2010) utilized an Unsteady Reynolds Aver aged Navier-Stokes (UnRANS) equation solver to study the viscous ef fects around the hull with an air plenum. The results of parametric studies over a range of hull form parameters are presented and the ef fects of air plenum parameters on the ship startup stability are investi gated. The developed numerical method is used to establish trends of the total resistance and its dependence on the Froude number. Kim and Moin (2010) performs direct numerical simulations in order to confirm the experimental results and examine the stability and mechanism of air layer drag reduction for different air injection rates. Besides, he also investigates the stability of air layer theoretically to find the stabilizing parameters and stability conditions for air layer drag reduction. An assessment of the streamlines and air distribution for a planing air cavity ship is proposed by Cucinotta et al. (2017, 2018) and an evaluation of the wetted and ventilated areas is conducted in order to understand the relation between the flow rate, the speed of the ship and the air distri bution. The results can be used for modifying the ship hull geometry in order to better accommodate the air layer. In this study, a method with the combination of RANS equations and VOF model is proposed for the viscous-flow calculation of a large flat bottom ship with bottom cavity. In Section 2 of the paper describes the materials and methods, which includes the model, the validation test and the CFD method. In Section 3 presents the validation of numerical method. Section 4 and Section 5 show the effect of ship heeling and trim on the shape of air layer and drag reduction. Finally, Section 6 presents the conclusions obtained from the study.
Table 1 Main parameters of the test model of bulk carrier. Definition
Symbol (unit)
Waterline length Length between perpendiculars Design speed
LWL (m) LPP (m) Vs (kn) Vm (m/s) BWL (m) T (m) SW (m2) Δ (t) CB CM CP
Waterline beam Draft Wet surface area Design displacement Block coefficient Midship section coefficient Prismatic coefficient
Value ship
model
235 231 14.5 – 38 12.5 12548 92000 0.838 0.997 0.840
6.184 6.079 – 1.21 1.000 0.329 8.690 1.67
bottom cavity. The ship model has a large flat structure, which is very suitable for setup of cavity. As the bottom of the ship is an arc-shaped flat structure, an arc-shaped cavity is used under the bottom of ship and a slope structure is set at the tail of the cavity. The length and width of the cavity is 4.32 � 0.82 m and the depth of the cavity is 25 mm. The area of the cavity is approximately 84% of the large flat structure. The principal particulars of the bottom cavity are shown in Table 2. Lc, Bc and h is the length, width, and depth of the ship bottom cavity, Sc presents the area of the bottom cavity. The cavity starts from the head of the flat bottom of the ship model. The head of the cavity is arc shape, and the tail is slope shape. 2.2. The CFD methods 2.2.1. Governing equations viscous flow In this study, the resistance of the ship model was simulated by the RANS codes of a commercial soft. RANS equation is the governing equation for the kinematical and hydrodynamic problem of viscous
2. Materials and methods 2.1. The model A low flat large ship was selected as a test hull form and a model ship was manufactured with a scale ratio of 38.0 to perform the tests. The bottom of the ship has a broad flat structure and a long parallel section of the body, which is very suitable for the application of air layer drag reduction technology. Fig. 1 shows the geometry model of the ship. The principal particulars of the ship are shown in Table 1. The flat bottom area, where reduction in the frictional resistance can be expected to occur, is about 40% of the total wetted surface area in the condition of design displacement. Fig. 2 shows the test model with
Fig. 2. The sketch map of bottom cavity design schemes.
Fig. 1. Geometry model of ship hull. 2
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Ocean Engineering 186 (2019) 106119
β ¼ 0:012, Cε1 ¼ 1:42, Cε2 ¼ 1:68, turbulent number for k and ε are σ k ¼ 1:39, σ ε ¼ 1:3.
Table 2 Main parameters of ship bottom cavity. Definition
Value
Lc/Lwl Bc/Bwl Sc/Sw h/T
69.83% 82.11% 37.37% 7.60%
2.2.3. Boundary conditions and meshes The accuracy of numerical computation is strongly dependent on the mesh quality. It is very important to choose a suitable size of domain firstly, which affects the solution accuracy and calculation cost. Too large domain will increase the computational time and cost. On the other hand, a small domain would adversely influence the solution. Figs. 3 and 4 show the regional division, numerical mesh and the boundary conditions for the ship model with air cavity. Based on the two-phase flow theory, the boundary conditions of present problem are set as follows. The inlet is 0.8 times plate length, which is corresponding to the velocity-inlet boundary condition. The distance is 2.0 times ship length from the model’s aft to the outlet, which is set as the outflow boundary condition. The top, bottom and side surface of the computa tional domain are all free slip wall boundary condition. The primary function for the grid is to capture the main features of the flow. Different block refinements are applied in the region. Fig. 5 shows the details of the mesh. The grids in bottom cavity of the ship model are refined to obtain the characteristics of air layer. The grid has been refined for the Kelvin wake solution near the free surface. Fig. 6 shows the grid of the ship hull surface. Fig. 7 shows the Wall yþ of the ship hull.
flow, which is mainly inclusive of the continuity equation and mo mentum equation. The specific formulas of the two equations can be written as following:
∂ ðρ Þ þ r⋅ðρm vm Þ ¼ 0 ∂t m
(1)
� � ∂ ∂ ∂p ∂ ρui uj ¼ þ ρu0 i u0 j þ ρfi ðρu Þ þ ∂t i ∂xj ∂xi ∂xj � � � � ∂ ∂ui ∂uj 2 ∂ul þ μ þ μ δij ∂xj 3 ∂xl i ∂xj ∂xi
(2)
Where ρ is the fluid density, μ is the fluid viscosity, p is the static pres 0 sure, fi is the mass force at unit, δij is the unit tensors, u i is the pulse of ui and ui is the velocity component of x direction respectively. Using the VOF model can effectively simulate the air-liquid stratified flow formed at the bottom cavity of the ship model and the free-surface. The VOF model description assumes that all immiscible fluid phases present in a control volume share velocity, pressure, and temperature fields. The VOF model relies on the fact that the two fluids, air and liquid do not interpenetrate each other in each control cell. The sum of the volume fractions of air and liquid is one. At this point, as long as the volume fraction of different components in the local cell is known, the parameter values of the flow field in the cell can be obtained. Specific related parameters can refer to user guide for STAR-CCMþ (2015).
2.3. The model tests The experiments were conducted in the towing tank of the Chinese Special Vehicle Research Institute, which is the longest towing tank in China. The towing tank is 550 m long, 6.5 m wide, 5.0 m deep, and equipped with a drive carriage facilitating shipped of 0–15 m/s for test. The model ship for the tests in the towing tank is shown in Fig. 8. An observation system has been installed at the bottom of the towing tank to obtain the shape of air layer in the bottom cavity. To avoid the interference between the pipe and the ship model, the air injection pipes is made of plastic hose and keep prevention contact between pipes and the ship model. Air was injected through array of holes on the base plate of each air injection devices according to the air supply chain. Compressed air by the air compressor was stored in the air cylinder on the tank trailer and the flow rate of air supplied to the air injection devices were adjusted by a personal computer and measure by several air flow meters. The air flow rate plays a key role in the formation of the air layer in the bottom cavity. The saturated air flow was selected as the research object of this paper, and the specific selection method and the value of the saturated air flow is provided by Wu (2017). Definition of non-dimensional air flow rate coefficient Cq as following:
2.2.2. Turbulence model Based on previous research by Wu et al. (2016a, 2016b), in present paper, the turbulence model is chosen as the RNG k-ε model. The tur bulent kinetic energy equation and the volume fraction equation for the air and water are expressed below. �� � �� ∂ ∂ ∂ μ ∂k μþ t (3) þ Pk ρε ðρkÞ þ ðρkui Þ ¼ ∂t ∂xi ∂xj σk ∂xj
∂ ∂ ∂ ðρεÞ þ ðρεui Þ ¼ ∂t ∂xi ∂xj
��
�
μþ
�
μt ∂ε ε þ C ε 1 Pk σε ∂xj k
Cε2 ρ
ε2 k
Rε
(4)
pffiffiffi Where μt ¼ ρCμ k2 =ε, Pk ¼ μt S2 , S ¼ 2Sij , Sij ¼ 0:5ð∂ui =∂xj þ ∂uj =∂xi Þ, Rε ¼ Cμ ρη3 ð1 η=η0 Þε2 =kð1 þ βη3 Þ, η ¼ Sk=ε, Cμ ¼ 0:0845, η0 ¼ 4:38,
Fig. 3. Regional division of the simulation. 3
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Ocean Engineering 186 (2019) 106119
Fig. 4. Mesh in all the regions of the simulation.
Fig. 8. Model ship for the tests in the towing tank. Fig. 5. Details of the region mesh.
Cq ¼
Q V⋅B⋅δ
(5)
where Q is the air flow rate, V is the inflow velocity, B is the transverse width of air inject entrance, δ is the thickness of boundary layer of the air inject entrance at no air injection, which is given by Eq. (6): δ ¼ 5:2Re
0:5
(6)
x
Here, Re is the Reynolds number of the air inject entrance, which is given by Eq. (7): Re ¼
V⋅x
(7)
ν
where x is the distance between the air injection and the bow of the ship model, ν is the water viscosity coefficient and ν ¼ 1.003 � 10 6 at normal temperature.
Fig. 6. Grid of the ship hull surface.
3. Validation of numerical method In order to evaluate the numerical results, a comparison with the results of experiment is carried out. In this paper, the shape of air layer and the resistance of ship model are verified. The absolute drag reduc tion of the resistance for the model ship is defined as follows:
ηA ¼
Rwithout cavity Rwithout
Rair cavity cavity
(8)
where Rcavity is the resistance of ship model with cavity but without air,
Fig. 7. Wall yþ of the ship hull.
Rair cavity is the resistance of ship model with cavity and air, Rwithout the resistance of ship model without cavity and air.
4
cavity
is
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Ocean Engineering 186 (2019) 106119
3.1. Verification of air layer shape
Table 3 Comparison of numerical calculations and experiment results.
Fig. 9 shows the calculated results and experiment results of the air layer at the bottom ship when Fr ¼ 0.155 and Cq ¼ 0.112. It can be seen that the shape of air layer was simulated effectively by the method of combining the RANS and VOF model. A continuous air layer was form at the bottom of ship when the ship model floating on even keel and the air bubble is evenly spilt from both sides of the stern. The coverage area of the air layer in the cavity decreases when the ship model heeling angle is two degree. The air layer moves to the heel side and most of it overflows on this side. However, when the ship model trim angle is one degree, the coverage of the air layer is greatly reduced and easily broken. It can only cover the area near the air injection, and then overflows outwards. In the calculation of the heel state, the shape of the air layer is difficult to simulate by numerical method because the shape of the air layer is relatively random when the air is difficult to cover the entire bottom cavity.
Conditions Fr
Cq
0.155
0 0.056 0.112 0.168 0.224
Experiment result (N)
Calculation result (N)
Error (%)
30.11 20.03 18.17 17.49 16.64
29.33 19.63 17.68 17.41 16.21
2.59 2.00 2.70 0.46 2.58
combination of RANS equations and VOF model is suitable for the nu merical simulation air layer drag reduction and the effect of ship attitude on perform of ship with bottom cavity. 4. Effect of heel 4.1. Effect on shape of air layer
3.2. Verification of ship resistance
Fig. 11 shows the shape of the air layer under different heeling for Fr ¼ 0.155 and Cq ¼ 0.056. It can be seen that the heeling has little effect on the coverage area of the bottom cavity when the heeling angle in crease 0–1.2� . However, the ship heeling affected the overflow of air from the tail of the bottom cavity. The air mainly overflows from the side of the heeling when the heeling angle is more than one degree. Fig. 12 shows the image of the air layer on the cross section of the ship model at different heel angles for Fr ¼ 0.155 and Cq ¼ 0.056. It is clearly shown that the thickness of the air layer changes along the width of the ship when the heeling angle increases. In order to show the thickness of the air layer along the width of the ship, Fig. 13 shows the variation of the boundary of the air layer with the heeling angle on the cross section of the middle of the ship model. In Fig. 13, the abscissa indicates the width of the ship. The direction is parallel to the bottom of the ship. The shaded part indicates the cavity. β represents the angle of heeling. θ represents the average angle of the air layer, which is the angle between the line connecting the two ends of the
Table 3 shows the comparison of calculation results and experiment results for the absolute drag reduction of the ship model under different air flow at Fr ¼ 0.155when ship model is floating on even keel. It can be seen that the total resistance error between the experimental value and the calculated value is within 3.0%. Fig. 10 shows the calculation results and test results of the absolute drag reduction of the ship model for an Fr range from 0.107 to 0.182 and Cq ¼ 0.056 in different navigational states. It can be seen that the total resistance error between the experimental value and the calculated value is also meet the requirement under different navigation state, all error values are within 3.5%. The result shows that the viscous flow field of the ship model with air layer by the combination of RANS and VOF model can accurately forecast the absolute drag reduction. Besides, the drag reduction is better when the ship model floating on even keel. The absolute drag reduction can reach more than 25% at the design speed. From the above analysis, it can find that the method with the
Fig. 9. Comparison of numerical results and experimental results of air layers. 5
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Ocean Engineering 186 (2019) 106119
(a) Floating on even keel
(b) Heeling 2°
(c) Trim 1°
Fig. 10. Comparison of numerical results and experimental results of the ship resistance.
when the heeling is more than arctanðh=Bc Þ ¼ 1:93� . It can be seen that the air layer begins to break when the heeling angle is greater than the critical value and the effective coverage area by air layer decreases. 4.2. Effect on ship resistance Fig. 15 shows the variation of drag reduction with the heeling angle of ship model when Fr ¼ 0.155 and Cq ¼ 0.056. It is obvious that the drag reduction is more than 20% when the heeling angle of ship model is less than 1.5� . The drag reduction decreases significantly when the heeling angle is more the critical angle arctanðh=Bc Þ ¼ 1:93� . 5. Effect of trim 5.1. Effect on shape of air layer Fig. 16 shows the shape of the air layer under different trim for Fr ¼ 0.155 and Cq ¼ 0.056. It can be seen that the air layer is relatively stable when the trim is small. However, the air layer starts to break when the trim angle is more than 0.5� . The air overflows from the head of the bottom cavity. In addition, the air layer at the end of the bottom cavity was disturbed by the trim angle seriously. Fig. 17 shows air layer image when the trim of ship model is 0.7� for Fr ¼ 0.155 and Cq ¼ 0.056. It can be seen that large tail angle has an adverse effect on the stability of the air layer and the air layer was broken in a larger area and the air overflow from the head of bottom cavity is very serious.
Fig. 11. Effect of heeling angle on bottom air cavity distribution.
5.2. Effect on ship resistance Fig. 18 shows the variation of drag reduction with the trim angle of ship model when Fr ¼ 0.155 and Cq ¼ 0.056. It can be seen that the drag reduction decreases with the trim angle increases. Moreover, the drag reduction is negative when the trim angle is greater than one degree. 6. Discussion and conclusion Fig. 12. The transverse section of air layer at different heeling angle.
Numerical simulations were conducted about the air layer on the lower surface of the flat ship model. It can be confirmed from the sim ulations that the air layer generated by air injection at the bottom of the hull can be used as an effective means to reduce the frictional resistance of the ship model. Accordingly, the following conclusions can be drawn from the numerical analysis:
cross-section of the air layer and the bottom plane of ship. It is shown that the average angle of the air layer increases with the heel angle increases. Table 4 shows the average angle of the air layer on the transverse section of the stern in different heeling angles when Fr ¼ 0.155 and Cq ¼ 0.056. From Table 4, it can be seen that the average angle of the air layer increases with the increase of the heeling angle, and is almost equal to the value of the heel angle. There is a critical angle arctanðh=Bc Þ ¼ 1:93� . Fig. 14 shows the shape of air layer for Fr ¼ 0.155 and Cq ¼ 0.056
(1) Air layer in the bottom cavity can be reasonably simulated based on the RANS equations and VOF two-phase flow model, and the absolute drag reduction of the ship model can be reasonably predicted. The coverage of the bottom air layer is closely related to the drag reduction of ship model. The absolute drag reduction 6
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Ocean Engineering 186 (2019) 106119
Fig. 13. Relative position of the air layer boundary. Table 4 Average angle of air layer section line with hull bottom at midship. β (� )
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.8
θ( )
0.0
0.205
0.392
0.604
0.814
0.999
1.194
1.397
1.901
�
Fig. 14. Air layer shapes at heeling angles larger than arctanðh=Bc Þ
rate can reach more than 25% for a bulk carrier model with bottom cavity in this study. (2) The attitude of the ship model has an important influence on the distribution of the bottom air layer. For a ship model with a bottom cavity, a stable air layer can be formed when the heeling is less than the critical value arctanðh=Bc Þ, the air layer broke when the heeling is greater than the critical value arctanðh=Bc Þ. The separation of air layer is intensified with the increase of heeling angle. (3) The trim angle of the ship is unfavorable to the stability of the air layer and it should be avoided as much as possible in the course of navigation.
cavity is shown in the above results and some related conclusions are listed. The conclusions show that the scheme of the bottom cavity in this paper is effective for the large vessels sailing in the calm water. Unfor tunately it also indicates that air cavity is inefficient for seagoing vessels in realistic operating conditions, especially in areas with poor sea con ditions. In order to make the air cavity ship to adapt to different sea conditions, the following discussion is given: (4) For different sea conditions, different depths of bottom cavity can be applied. Small bottom cavity can be used on the inland ships. In the large sea area, the depth of bottom cavity can be appro priately increased to improve the thickness of air layer and make the air layer in the bottom cavity more stable, which will improve the effect of drag reduction.
The numerical method for air layer drag reduction in the bottom 7
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Ocean Engineering 186 (2019) 106119
(6) In the future research, it is necessary to study the air layer shape in the bottom cavity and the drag reduction effect of the ship model in the wave. Acknowledgments This research is supported by the High Performance Marine Tech nology Key Laboratory of the Ministry of Education open funds (Grant No.2013033102). References Amromin, E.L., 2016. Analysis of interaction between ship bottom air cavity and boundary layer. Appl. Ocean Res. 59, 451–458. Butterworth, J., Atlar, M., Shi, W., 2015. Experimental analysis of an air cavity concept applied on a ship hull to improve the hull resistance. Ocean Eng. 110, 2–10. Ceccio, S.L., 2010. Friction drag reduction of external flows with bubble and gas injection. Annu. Rev. Fluid Mech. 42, 183–203. Choi, J.-K., Chahine, G.L., 2010. Numerical study on the behavior of air layers used for drag reduction. In: 28th Symposium on Naval Hydrodynamics Pasadena, California. Choi, J.-K., Hsiao, C.-T., Chahine, G.L., 2005. Design trade-off analysis for high performance ship hull with air plenums”. In: Proc. 2nd Int. Symposium on Seawater Drag Reduction, Busan, Korea. Choi, J.-K., Hsiao, C.-T., Chahine, G.L., 2007. Numerical studies on the hydrodynamic performance and the startup stability of high speed ship hulls with air plenums and air tunnels. In: Ninth International Conference on Fast Sea Transportation. Cucinotta, F., Nigrelli, V., Sfravara, F., 2018. Numerical prediction of ventilated planning flat plates for the design of air cavity ships. Int. J. Interact. Des. Manuf. 12, 537–548. Cucinotta, F., Guglielmino, E., Sfravara, F., 2018. Numerical and experimental investigation of a planing Air Cavity Ship and its air layer evolution. Ocean Eng. 152, 130–144. Jang, J., Choi, S.H., Ahn, S.M., Kim, B., Seo, J.S., 2014. Experimental investigation of frictional resistance reduction with air layer on the hull bottom of a ship. Int. J. Nav. Archit. Ocean Eng. 6, 363–379. Kim, D., Moin, P., 2010. Direct Numerical Study of Air Layer Drag Reduction Phenomenon over a Backward-Facing Step. Center for Turbulence Research Annual Research Briefs, pp. 351–363. Kodama, Y., Kakugawa, A., Takahashi, T., Kawashima, H., 2000. Experimental study on microbubbles and their applicability to ships for skin friction reduction. Int. J. Heat Fluid Flow 21 (5), 582–588. Latorre, R., 1997. Ship hull drag reduction using bottom air injection. Ocean Eng. 24 (2), 161–175. Lay, K.A., et al., 2010. Partial cavity drag reduction at high Reynolds numbers. J. Ship Res. 54 (2), 109–119. M€ akiharju, S., Elbing, B.R., Wiggins, A., Dowling, D.R., Perlin, M., Ceccio, S.L., 2010. Ventilated partial cavity flows at high Reynolds numbers. In: Proceedings of the International Conference on Multi-phase Flows. M€ akiharju, S.A., Perlin, Marc, Ceccio, Steven L., 2012. On the energy economics of air lubrication drag reduction. Int. J. Naval Archit. Ocean Eng. 4 (4), 412–422. M€ akiharju, S.A., et al., 2013. On the scaling of air entrainment from a ventilated partial cavity. J. Fluid Mech. 732, 47–76. Matveev, K.I., 2003. On the limiting parameters of artificial cavitation. Ocean Eng. 30, 1179–1190. Matveev, K.I., 2007. Three-dimensional wave patterns in long air cavities on a horizontal plane. Ocean Eng. 34, 1882–1891. Matveev, K.I., 2015. Hydrodynamic modeling of semi-planing hulls with air cavities. Int. J. Nav. Archit. Ocean Eng. 7, 500–508. Shuji, M., Chiharu, K., Youichiro, K., Shinichi, T., Seijiro, H., Ryosuke, S., 2010. Experimental study of air lubrication method and verification of effects on actual hull by means of sea trial. Mitsubishi Heavy Ind. Techn. Rev. 47 (3), 41–47. Slyozkin, A., 2011. Cavitating Streams in Uniform Flow or Investigations of Air-Fed Cavity for Hydrodynamic Drag Reduction. Department of Marine Technology, Newcastle University, Newcastle-upon-Tyne. Slyozkin, A., Atlar, M., Sampson, R., Seo, K.C., 2014. An experimental investigation into the hydrodynamic drag reduction of a flat plate using air-fed cavities. Ocean Eng. 76, 105–120. Wu, Hao, 2017. Experimental Study and Numerical Analysis of Air Layer Drag Reduction on Large Displacement Ships. Naval University of Engineering. Wu, Hao, Dong, Wencai, Ou, Yong-peng, 2016. Numerical method investigation of drag reduction with air layer at bottom of ship[J]. J. Nav. Univ. Eng. 28 (03), 70–75. Wu, Hao, Ou, Yong-peng, Dong, Wencai, 2016. Numerical study of method of flat plate viscous flow field with bubble. Ship Sci. Technol. 38 (15), 47–51. Zverkhovskyi, O., 2014. Ship Drag Reduction by Air Cavities. TU Delft, Delft University of Technology.
Fig. 15. Variation of drag reduction with the heeling angle of ship model.
Fig. 16. Effect of trim angle on shape of air layer.
Fig. 17. Air layer shape at trim angle is 0.7� .
(5) It is thought that set vertical partitions in the bottom cavity may be a good idea to improve the coverage of air layer when ship heeling. In addition, the coverage of air layer would be better by setting multiple air injection holes in the bottom cavity and in jection simultaneously when ship trim.
8
Contents lists available at ScienceDirect
Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Numerical study of the effect of ship attitude on the perform of ship with air injection in bottom cavity Wu Hao a, b, * a b
Key Laboratory of High Performance Ship Technology, Wuhan University of Technology, Wuhan, 430063, China School of Transportation, Wuhan University of Technology, Wuhan, Hubei, 430063, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Air cavity ship Drag reduction Shape of air layer Heeling Trim
Air lubrication by means of a bottom cavity is a promising way for ship drag reduction. The characteristics of air layer under the bottom cavity and effect of drag reduction are sensitive to the attitude of ship model. To investigate the stability of air layer under different navigation condition of air cavity ship, a method with the combination of RANS equations and VOF model is proposed for the viscous-flow calculation of a large flat bottom ship, which is verified by the model-test result. The effect of heeling and trim on the formation and stability of air layer is investigated. Present numerical results show that there is a critical value of heeling arctanðh=Bc Þ with the definition the cavity depth and width of the h =Bc . The air layer would be stable if ship heeling is less than the critical value. The air layer broke when the heeling is greater than the critical value, and heeling increase, broken phenomenon aggravate. The trim angle of the ship is unfavorable to the stability of the air layer and it should be avoided as much as possible in the course of navigation.
1. Introduction Air layer drag reduction technology is an effective way to reduce ship friction. Some basic concepts of air layer drag reduction were proposed in the 19th century by Latorre (1997). Subsequently, researchers con ducted numerous experimental studies in the laboratory. In most air layer drag reduction experiments, the air is injected through continuous slots, which are either open or filled with porous material, to ensure a uniform air layer under the test surface (Kodama et al., 2000; Slyozkin, 2011). Ceccio (2010) presented different applications and a detailed explanation of the distribution of air under a ship’s hull during air in jection. Air layer drag reduction by means of a bottom cavity has been proven to be an effective method of ship drag reduction. Lay et al. €kiharju et al. (2012, 2013) conducted an experimental (2010) and Ma investigation about the drag reduction effects of a ventilated partial cavity at high Reynolds numbers for a large plate in the W. B. Morgan Large Cavitation Channel and established the basic energy economic calculation results for a hypothetical air lubricated ship. The stability of the air layer in the bottom cavity and the coverage area of air layer are the key factors that affect the effect of the air layer drag reduction for a ship. To obtain a uniform air layer under the bottom hull, Zverkhovskyi (2014) designed a device called a ‘cavitator’ to
impede the flow of water on the underside of the vessel, with a small slotted opening behind the cavitator delivering the air supply, This method was found to be particularly successful because it significantly reduces the air flow rate required to create the air layer. The effect of air layer thickness on drag reduction was verified experimentally by Shuji et al. (2010). The result shows that the energy consumed by the blower depends on the thickness of the bottom air layer. Following the funda mental experimental study on a flat plate with a cavity conducted in the Emerson Cavitation Tunnel of Newcastle University by Slyozkin et al. (2014), Butterworth et al. (2015) proposed an experimental test on an existing container ship model with a cavity of 0.0387 m2 at the bottom of the ship model. The model experiment results show that the effect of air layer drag reduction can reach 4–16%. The effect of air layer drag reduction and the air escape from the bottom hull were affected by the characteristics of the bottom cavity. According to conclusion of Slyozkin and Butterworth, the design of the bottom cavity plays an important role in the evaluation of the air €kiharju et al. (2010) conducted a series of tests layer drag reduction. Ma with a flat plate with a device called a ‘BFS’, which helps the air layer to form easily while reducing the air supply and pressure. Experimental test on a flat plate and a ship model with air lubrication system were successively conducted by Jang et al. (2014). From the tests, if there is
* School of Transportation, Wuhan University of Technology, Wuhan, Hubei, 430063, China. E-mail address: [email protected]. https://doi.org/10.1016/j.oceaneng.2019.106119 Received 14 October 2018; Received in revised form 23 March 2019; Accepted 16 June 2019 Available online 12 July 2019 0029-8018/© 2019 Elsevier Ltd. All rights reserved.
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Ocean Engineering 186 (2019) 106119
no significant deterioration in the real sea condition, it is considered that the air lubrication at the bottom of the ship has great potential for en ergy saving. According to the experimental results, many scholars have carried out a mass of numerical research. Matveev (2003, 2007) solved an important problem with a simplified model, which is the interaction between the waves and the cavity. The result shows the main parameters that affect air layer in the ship bottom cavity is the shape of cavity and speed. The same author has developed a platform to test different types of Air Cavity Ships (ACS) using the necessary instrumentation to improve and optimize this technique (Matveev, 2015). The interaction between the cavity and the boundary of ship was analyzed by Amromin (2016). Choi et al. (2005, 2007, 2010) utilized an Unsteady Reynolds Aver aged Navier-Stokes (UnRANS) equation solver to study the viscous ef fects around the hull with an air plenum. The results of parametric studies over a range of hull form parameters are presented and the ef fects of air plenum parameters on the ship startup stability are investi gated. The developed numerical method is used to establish trends of the total resistance and its dependence on the Froude number. Kim and Moin (2010) performs direct numerical simulations in order to confirm the experimental results and examine the stability and mechanism of air layer drag reduction for different air injection rates. Besides, he also investigates the stability of air layer theoretically to find the stabilizing parameters and stability conditions for air layer drag reduction. An assessment of the streamlines and air distribution for a planing air cavity ship is proposed by Cucinotta et al. (2017, 2018) and an evaluation of the wetted and ventilated areas is conducted in order to understand the relation between the flow rate, the speed of the ship and the air distri bution. The results can be used for modifying the ship hull geometry in order to better accommodate the air layer. In this study, a method with the combination of RANS equations and VOF model is proposed for the viscous-flow calculation of a large flat bottom ship with bottom cavity. In Section 2 of the paper describes the materials and methods, which includes the model, the validation test and the CFD method. In Section 3 presents the validation of numerical method. Section 4 and Section 5 show the effect of ship heeling and trim on the shape of air layer and drag reduction. Finally, Section 6 presents the conclusions obtained from the study.
Table 1 Main parameters of the test model of bulk carrier. Definition
Symbol (unit)
Waterline length Length between perpendiculars Design speed
LWL (m) LPP (m) Vs (kn) Vm (m/s) BWL (m) T (m) SW (m2) Δ (t) CB CM CP
Waterline beam Draft Wet surface area Design displacement Block coefficient Midship section coefficient Prismatic coefficient
Value ship
model
235 231 14.5 – 38 12.5 12548 92000 0.838 0.997 0.840
6.184 6.079 – 1.21 1.000 0.329 8.690 1.67
bottom cavity. The ship model has a large flat structure, which is very suitable for setup of cavity. As the bottom of the ship is an arc-shaped flat structure, an arc-shaped cavity is used under the bottom of ship and a slope structure is set at the tail of the cavity. The length and width of the cavity is 4.32 � 0.82 m and the depth of the cavity is 25 mm. The area of the cavity is approximately 84% of the large flat structure. The principal particulars of the bottom cavity are shown in Table 2. Lc, Bc and h is the length, width, and depth of the ship bottom cavity, Sc presents the area of the bottom cavity. The cavity starts from the head of the flat bottom of the ship model. The head of the cavity is arc shape, and the tail is slope shape. 2.2. The CFD methods 2.2.1. Governing equations viscous flow In this study, the resistance of the ship model was simulated by the RANS codes of a commercial soft. RANS equation is the governing equation for the kinematical and hydrodynamic problem of viscous
2. Materials and methods 2.1. The model A low flat large ship was selected as a test hull form and a model ship was manufactured with a scale ratio of 38.0 to perform the tests. The bottom of the ship has a broad flat structure and a long parallel section of the body, which is very suitable for the application of air layer drag reduction technology. Fig. 1 shows the geometry model of the ship. The principal particulars of the ship are shown in Table 1. The flat bottom area, where reduction in the frictional resistance can be expected to occur, is about 40% of the total wetted surface area in the condition of design displacement. Fig. 2 shows the test model with
Fig. 2. The sketch map of bottom cavity design schemes.
Fig. 1. Geometry model of ship hull. 2
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Ocean Engineering 186 (2019) 106119
β ¼ 0:012, Cε1 ¼ 1:42, Cε2 ¼ 1:68, turbulent number for k and ε are σ k ¼ 1:39, σ ε ¼ 1:3.
Table 2 Main parameters of ship bottom cavity. Definition
Value
Lc/Lwl Bc/Bwl Sc/Sw h/T
69.83% 82.11% 37.37% 7.60%
2.2.3. Boundary conditions and meshes The accuracy of numerical computation is strongly dependent on the mesh quality. It is very important to choose a suitable size of domain firstly, which affects the solution accuracy and calculation cost. Too large domain will increase the computational time and cost. On the other hand, a small domain would adversely influence the solution. Figs. 3 and 4 show the regional division, numerical mesh and the boundary conditions for the ship model with air cavity. Based on the two-phase flow theory, the boundary conditions of present problem are set as follows. The inlet is 0.8 times plate length, which is corresponding to the velocity-inlet boundary condition. The distance is 2.0 times ship length from the model’s aft to the outlet, which is set as the outflow boundary condition. The top, bottom and side surface of the computa tional domain are all free slip wall boundary condition. The primary function for the grid is to capture the main features of the flow. Different block refinements are applied in the region. Fig. 5 shows the details of the mesh. The grids in bottom cavity of the ship model are refined to obtain the characteristics of air layer. The grid has been refined for the Kelvin wake solution near the free surface. Fig. 6 shows the grid of the ship hull surface. Fig. 7 shows the Wall yþ of the ship hull.
flow, which is mainly inclusive of the continuity equation and mo mentum equation. The specific formulas of the two equations can be written as following:
∂ ðρ Þ þ r⋅ðρm vm Þ ¼ 0 ∂t m
(1)
� � ∂ ∂ ∂p ∂ ρui uj ¼ þ ρu0 i u0 j þ ρfi ðρu Þ þ ∂t i ∂xj ∂xi ∂xj � � � � ∂ ∂ui ∂uj 2 ∂ul þ μ þ μ δij ∂xj 3 ∂xl i ∂xj ∂xi
(2)
Where ρ is the fluid density, μ is the fluid viscosity, p is the static pres 0 sure, fi is the mass force at unit, δij is the unit tensors, u i is the pulse of ui and ui is the velocity component of x direction respectively. Using the VOF model can effectively simulate the air-liquid stratified flow formed at the bottom cavity of the ship model and the free-surface. The VOF model description assumes that all immiscible fluid phases present in a control volume share velocity, pressure, and temperature fields. The VOF model relies on the fact that the two fluids, air and liquid do not interpenetrate each other in each control cell. The sum of the volume fractions of air and liquid is one. At this point, as long as the volume fraction of different components in the local cell is known, the parameter values of the flow field in the cell can be obtained. Specific related parameters can refer to user guide for STAR-CCMþ (2015).
2.3. The model tests The experiments were conducted in the towing tank of the Chinese Special Vehicle Research Institute, which is the longest towing tank in China. The towing tank is 550 m long, 6.5 m wide, 5.0 m deep, and equipped with a drive carriage facilitating shipped of 0–15 m/s for test. The model ship for the tests in the towing tank is shown in Fig. 8. An observation system has been installed at the bottom of the towing tank to obtain the shape of air layer in the bottom cavity. To avoid the interference between the pipe and the ship model, the air injection pipes is made of plastic hose and keep prevention contact between pipes and the ship model. Air was injected through array of holes on the base plate of each air injection devices according to the air supply chain. Compressed air by the air compressor was stored in the air cylinder on the tank trailer and the flow rate of air supplied to the air injection devices were adjusted by a personal computer and measure by several air flow meters. The air flow rate plays a key role in the formation of the air layer in the bottom cavity. The saturated air flow was selected as the research object of this paper, and the specific selection method and the value of the saturated air flow is provided by Wu (2017). Definition of non-dimensional air flow rate coefficient Cq as following:
2.2.2. Turbulence model Based on previous research by Wu et al. (2016a, 2016b), in present paper, the turbulence model is chosen as the RNG k-ε model. The tur bulent kinetic energy equation and the volume fraction equation for the air and water are expressed below. �� � �� ∂ ∂ ∂ μ ∂k μþ t (3) þ Pk ρε ðρkÞ þ ðρkui Þ ¼ ∂t ∂xi ∂xj σk ∂xj
∂ ∂ ∂ ðρεÞ þ ðρεui Þ ¼ ∂t ∂xi ∂xj
��
�
μþ
�
μt ∂ε ε þ C ε 1 Pk σε ∂xj k
Cε2 ρ
ε2 k
Rε
(4)
pffiffiffi Where μt ¼ ρCμ k2 =ε, Pk ¼ μt S2 , S ¼ 2Sij , Sij ¼ 0:5ð∂ui =∂xj þ ∂uj =∂xi Þ, Rε ¼ Cμ ρη3 ð1 η=η0 Þε2 =kð1 þ βη3 Þ, η ¼ Sk=ε, Cμ ¼ 0:0845, η0 ¼ 4:38,
Fig. 3. Regional division of the simulation. 3
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Ocean Engineering 186 (2019) 106119
Fig. 4. Mesh in all the regions of the simulation.
Fig. 8. Model ship for the tests in the towing tank. Fig. 5. Details of the region mesh.
Cq ¼
Q V⋅B⋅δ
(5)
where Q is the air flow rate, V is the inflow velocity, B is the transverse width of air inject entrance, δ is the thickness of boundary layer of the air inject entrance at no air injection, which is given by Eq. (6): δ ¼ 5:2Re
0:5
(6)
x
Here, Re is the Reynolds number of the air inject entrance, which is given by Eq. (7): Re ¼
V⋅x
(7)
ν
where x is the distance between the air injection and the bow of the ship model, ν is the water viscosity coefficient and ν ¼ 1.003 � 10 6 at normal temperature.
Fig. 6. Grid of the ship hull surface.
3. Validation of numerical method In order to evaluate the numerical results, a comparison with the results of experiment is carried out. In this paper, the shape of air layer and the resistance of ship model are verified. The absolute drag reduc tion of the resistance for the model ship is defined as follows:
ηA ¼
Rwithout cavity Rwithout
Rair cavity cavity
(8)
where Rcavity is the resistance of ship model with cavity but without air,
Fig. 7. Wall yþ of the ship hull.
Rair cavity is the resistance of ship model with cavity and air, Rwithout the resistance of ship model without cavity and air.
4
cavity
is
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Ocean Engineering 186 (2019) 106119
3.1. Verification of air layer shape
Table 3 Comparison of numerical calculations and experiment results.
Fig. 9 shows the calculated results and experiment results of the air layer at the bottom ship when Fr ¼ 0.155 and Cq ¼ 0.112. It can be seen that the shape of air layer was simulated effectively by the method of combining the RANS and VOF model. A continuous air layer was form at the bottom of ship when the ship model floating on even keel and the air bubble is evenly spilt from both sides of the stern. The coverage area of the air layer in the cavity decreases when the ship model heeling angle is two degree. The air layer moves to the heel side and most of it overflows on this side. However, when the ship model trim angle is one degree, the coverage of the air layer is greatly reduced and easily broken. It can only cover the area near the air injection, and then overflows outwards. In the calculation of the heel state, the shape of the air layer is difficult to simulate by numerical method because the shape of the air layer is relatively random when the air is difficult to cover the entire bottom cavity.
Conditions Fr
Cq
0.155
0 0.056 0.112 0.168 0.224
Experiment result (N)
Calculation result (N)
Error (%)
30.11 20.03 18.17 17.49 16.64
29.33 19.63 17.68 17.41 16.21
2.59 2.00 2.70 0.46 2.58
combination of RANS equations and VOF model is suitable for the nu merical simulation air layer drag reduction and the effect of ship attitude on perform of ship with bottom cavity. 4. Effect of heel 4.1. Effect on shape of air layer
3.2. Verification of ship resistance
Fig. 11 shows the shape of the air layer under different heeling for Fr ¼ 0.155 and Cq ¼ 0.056. It can be seen that the heeling has little effect on the coverage area of the bottom cavity when the heeling angle in crease 0–1.2� . However, the ship heeling affected the overflow of air from the tail of the bottom cavity. The air mainly overflows from the side of the heeling when the heeling angle is more than one degree. Fig. 12 shows the image of the air layer on the cross section of the ship model at different heel angles for Fr ¼ 0.155 and Cq ¼ 0.056. It is clearly shown that the thickness of the air layer changes along the width of the ship when the heeling angle increases. In order to show the thickness of the air layer along the width of the ship, Fig. 13 shows the variation of the boundary of the air layer with the heeling angle on the cross section of the middle of the ship model. In Fig. 13, the abscissa indicates the width of the ship. The direction is parallel to the bottom of the ship. The shaded part indicates the cavity. β represents the angle of heeling. θ represents the average angle of the air layer, which is the angle between the line connecting the two ends of the
Table 3 shows the comparison of calculation results and experiment results for the absolute drag reduction of the ship model under different air flow at Fr ¼ 0.155when ship model is floating on even keel. It can be seen that the total resistance error between the experimental value and the calculated value is within 3.0%. Fig. 10 shows the calculation results and test results of the absolute drag reduction of the ship model for an Fr range from 0.107 to 0.182 and Cq ¼ 0.056 in different navigational states. It can be seen that the total resistance error between the experimental value and the calculated value is also meet the requirement under different navigation state, all error values are within 3.5%. The result shows that the viscous flow field of the ship model with air layer by the combination of RANS and VOF model can accurately forecast the absolute drag reduction. Besides, the drag reduction is better when the ship model floating on even keel. The absolute drag reduction can reach more than 25% at the design speed. From the above analysis, it can find that the method with the
Fig. 9. Comparison of numerical results and experimental results of air layers. 5
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Ocean Engineering 186 (2019) 106119
(a) Floating on even keel
(b) Heeling 2°
(c) Trim 1°
Fig. 10. Comparison of numerical results and experimental results of the ship resistance.
when the heeling is more than arctanðh=Bc Þ ¼ 1:93� . It can be seen that the air layer begins to break when the heeling angle is greater than the critical value and the effective coverage area by air layer decreases. 4.2. Effect on ship resistance Fig. 15 shows the variation of drag reduction with the heeling angle of ship model when Fr ¼ 0.155 and Cq ¼ 0.056. It is obvious that the drag reduction is more than 20% when the heeling angle of ship model is less than 1.5� . The drag reduction decreases significantly when the heeling angle is more the critical angle arctanðh=Bc Þ ¼ 1:93� . 5. Effect of trim 5.1. Effect on shape of air layer Fig. 16 shows the shape of the air layer under different trim for Fr ¼ 0.155 and Cq ¼ 0.056. It can be seen that the air layer is relatively stable when the trim is small. However, the air layer starts to break when the trim angle is more than 0.5� . The air overflows from the head of the bottom cavity. In addition, the air layer at the end of the bottom cavity was disturbed by the trim angle seriously. Fig. 17 shows air layer image when the trim of ship model is 0.7� for Fr ¼ 0.155 and Cq ¼ 0.056. It can be seen that large tail angle has an adverse effect on the stability of the air layer and the air layer was broken in a larger area and the air overflow from the head of bottom cavity is very serious.
Fig. 11. Effect of heeling angle on bottom air cavity distribution.
5.2. Effect on ship resistance Fig. 18 shows the variation of drag reduction with the trim angle of ship model when Fr ¼ 0.155 and Cq ¼ 0.056. It can be seen that the drag reduction decreases with the trim angle increases. Moreover, the drag reduction is negative when the trim angle is greater than one degree. 6. Discussion and conclusion Fig. 12. The transverse section of air layer at different heeling angle.
Numerical simulations were conducted about the air layer on the lower surface of the flat ship model. It can be confirmed from the sim ulations that the air layer generated by air injection at the bottom of the hull can be used as an effective means to reduce the frictional resistance of the ship model. Accordingly, the following conclusions can be drawn from the numerical analysis:
cross-section of the air layer and the bottom plane of ship. It is shown that the average angle of the air layer increases with the heel angle increases. Table 4 shows the average angle of the air layer on the transverse section of the stern in different heeling angles when Fr ¼ 0.155 and Cq ¼ 0.056. From Table 4, it can be seen that the average angle of the air layer increases with the increase of the heeling angle, and is almost equal to the value of the heel angle. There is a critical angle arctanðh=Bc Þ ¼ 1:93� . Fig. 14 shows the shape of air layer for Fr ¼ 0.155 and Cq ¼ 0.056
(1) Air layer in the bottom cavity can be reasonably simulated based on the RANS equations and VOF two-phase flow model, and the absolute drag reduction of the ship model can be reasonably predicted. The coverage of the bottom air layer is closely related to the drag reduction of ship model. The absolute drag reduction 6
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Ocean Engineering 186 (2019) 106119
Fig. 13. Relative position of the air layer boundary. Table 4 Average angle of air layer section line with hull bottom at midship. β (� )
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.8
θ( )
0.0
0.205
0.392
0.604
0.814
0.999
1.194
1.397
1.901
�
Fig. 14. Air layer shapes at heeling angles larger than arctanðh=Bc Þ
rate can reach more than 25% for a bulk carrier model with bottom cavity in this study. (2) The attitude of the ship model has an important influence on the distribution of the bottom air layer. For a ship model with a bottom cavity, a stable air layer can be formed when the heeling is less than the critical value arctanðh=Bc Þ, the air layer broke when the heeling is greater than the critical value arctanðh=Bc Þ. The separation of air layer is intensified with the increase of heeling angle. (3) The trim angle of the ship is unfavorable to the stability of the air layer and it should be avoided as much as possible in the course of navigation.
cavity is shown in the above results and some related conclusions are listed. The conclusions show that the scheme of the bottom cavity in this paper is effective for the large vessels sailing in the calm water. Unfor tunately it also indicates that air cavity is inefficient for seagoing vessels in realistic operating conditions, especially in areas with poor sea con ditions. In order to make the air cavity ship to adapt to different sea conditions, the following discussion is given: (4) For different sea conditions, different depths of bottom cavity can be applied. Small bottom cavity can be used on the inland ships. In the large sea area, the depth of bottom cavity can be appro priately increased to improve the thickness of air layer and make the air layer in the bottom cavity more stable, which will improve the effect of drag reduction.
The numerical method for air layer drag reduction in the bottom 7
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Ocean Engineering 186 (2019) 106119
(6) In the future research, it is necessary to study the air layer shape in the bottom cavity and the drag reduction effect of the ship model in the wave. Acknowledgments This research is supported by the High Performance Marine Tech nology Key Laboratory of the Ministry of Education open funds (Grant No.2013033102). References Amromin, E.L., 2016. Analysis of interaction between ship bottom air cavity and boundary layer. Appl. Ocean Res. 59, 451–458. Butterworth, J., Atlar, M., Shi, W., 2015. Experimental analysis of an air cavity concept applied on a ship hull to improve the hull resistance. Ocean Eng. 110, 2–10. Ceccio, S.L., 2010. Friction drag reduction of external flows with bubble and gas injection. Annu. Rev. Fluid Mech. 42, 183–203. Choi, J.-K., Chahine, G.L., 2010. Numerical study on the behavior of air layers used for drag reduction. In: 28th Symposium on Naval Hydrodynamics Pasadena, California. Choi, J.-K., Hsiao, C.-T., Chahine, G.L., 2005. Design trade-off analysis for high performance ship hull with air plenums”. In: Proc. 2nd Int. Symposium on Seawater Drag Reduction, Busan, Korea. Choi, J.-K., Hsiao, C.-T., Chahine, G.L., 2007. Numerical studies on the hydrodynamic performance and the startup stability of high speed ship hulls with air plenums and air tunnels. In: Ninth International Conference on Fast Sea Transportation. Cucinotta, F., Nigrelli, V., Sfravara, F., 2018. Numerical prediction of ventilated planning flat plates for the design of air cavity ships. Int. J. Interact. Des. Manuf. 12, 537–548. Cucinotta, F., Guglielmino, E., Sfravara, F., 2018. Numerical and experimental investigation of a planing Air Cavity Ship and its air layer evolution. Ocean Eng. 152, 130–144. Jang, J., Choi, S.H., Ahn, S.M., Kim, B., Seo, J.S., 2014. Experimental investigation of frictional resistance reduction with air layer on the hull bottom of a ship. Int. J. Nav. Archit. Ocean Eng. 6, 363–379. Kim, D., Moin, P., 2010. Direct Numerical Study of Air Layer Drag Reduction Phenomenon over a Backward-Facing Step. Center for Turbulence Research Annual Research Briefs, pp. 351–363. Kodama, Y., Kakugawa, A., Takahashi, T., Kawashima, H., 2000. Experimental study on microbubbles and their applicability to ships for skin friction reduction. Int. J. Heat Fluid Flow 21 (5), 582–588. Latorre, R., 1997. Ship hull drag reduction using bottom air injection. Ocean Eng. 24 (2), 161–175. Lay, K.A., et al., 2010. Partial cavity drag reduction at high Reynolds numbers. J. Ship Res. 54 (2), 109–119. M€ akiharju, S., Elbing, B.R., Wiggins, A., Dowling, D.R., Perlin, M., Ceccio, S.L., 2010. Ventilated partial cavity flows at high Reynolds numbers. In: Proceedings of the International Conference on Multi-phase Flows. M€ akiharju, S.A., Perlin, Marc, Ceccio, Steven L., 2012. On the energy economics of air lubrication drag reduction. Int. J. Naval Archit. Ocean Eng. 4 (4), 412–422. M€ akiharju, S.A., et al., 2013. On the scaling of air entrainment from a ventilated partial cavity. J. Fluid Mech. 732, 47–76. Matveev, K.I., 2003. On the limiting parameters of artificial cavitation. Ocean Eng. 30, 1179–1190. Matveev, K.I., 2007. Three-dimensional wave patterns in long air cavities on a horizontal plane. Ocean Eng. 34, 1882–1891. Matveev, K.I., 2015. Hydrodynamic modeling of semi-planing hulls with air cavities. Int. J. Nav. Archit. Ocean Eng. 7, 500–508. Shuji, M., Chiharu, K., Youichiro, K., Shinichi, T., Seijiro, H., Ryosuke, S., 2010. Experimental study of air lubrication method and verification of effects on actual hull by means of sea trial. Mitsubishi Heavy Ind. Techn. Rev. 47 (3), 41–47. Slyozkin, A., 2011. Cavitating Streams in Uniform Flow or Investigations of Air-Fed Cavity for Hydrodynamic Drag Reduction. Department of Marine Technology, Newcastle University, Newcastle-upon-Tyne. Slyozkin, A., Atlar, M., Sampson, R., Seo, K.C., 2014. An experimental investigation into the hydrodynamic drag reduction of a flat plate using air-fed cavities. Ocean Eng. 76, 105–120. Wu, Hao, 2017. Experimental Study and Numerical Analysis of Air Layer Drag Reduction on Large Displacement Ships. Naval University of Engineering. Wu, Hao, Dong, Wencai, Ou, Yong-peng, 2016. Numerical method investigation of drag reduction with air layer at bottom of ship[J]. J. Nav. Univ. Eng. 28 (03), 70–75. Wu, Hao, Ou, Yong-peng, Dong, Wencai, 2016. Numerical study of method of flat plate viscous flow field with bubble. Ship Sci. Technol. 38 (15), 47–51. Zverkhovskyi, O., 2014. Ship Drag Reduction by Air Cavities. TU Delft, Delft University of Technology.
Fig. 15. Variation of drag reduction with the heeling angle of ship model.
Fig. 16. Effect of trim angle on shape of air layer.
Fig. 17. Air layer shape at trim angle is 0.7� .
(5) It is thought that set vertical partitions in the bottom cavity may be a good idea to improve the coverage of air layer when ship heeling. In addition, the coverage of air layer would be better by setting multiple air injection holes in the bottom cavity and in jection simultaneously when ship trim.
8